curriculum advice for generalist teachers in very small schools (2nd edition)

Curriculum advice for generalist teachers in very small schools (2nd Edition) Peter Farrell, EdD

Peter Farrell: Sunday, 2 Nov 14

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Chapter 1 – Introduction .......................................... 9 Why I wrote this book ....................................................... 9 Who should read this book .......................................... 11 How this book is organised ......................................... 12 The 2nd Edition .................................................................. 15

SECTION ONE – THINKING SCIENTIFICALLY (USING SCIENTIFIC METHOD) ............................. 16 Chapter 2 – Biology Teacher ................................ 19 What is biology? ............................................................... 19 Where can it lead? ........................................................... 19 Where am I taking the students? .............................. 20 What’s my approach? .................................................... 21 What does success, look like, feel like, or sound like? ........................................................................................ 23 From real life 1 ................................................................. 24 From real life 2 ................................................................. 26

Chapter 3 – Chemistry Teacher .......................... 28 What is chemistry? .......................................................... 28 Where can it lead? ........................................................... 28 Where am I taking the students? .............................. 30 What’s my approach? .................................................... 31 What does success, look like, feel like, or sound like? ........................................................................................ 34 From real life 1 ................................................................. 35 From real life 2 ................................................................. 38

Chapter 4 -‐ Physics Teacher ................................. 39 What is physics? ............................................................... 39 Where can it lead? ........................................................... 39 Where am I taking the students? .............................. 40 What’s my approach? .................................................... 41 What does success, look like, feel like, or sound like? ........................................................................................ 43 From real life ..................................................................... 44


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CONCLUSION TO THINKING SCIENTIFICALLY 46 SECTION TWO – THINKING SYSTEMATICALLY ....................................................................................... 49 Chapter 5 – Civics and Citizenship Teacher .... 51 What is civics and citizenship? .................................. 51 Where can it lead? ........................................................... 51 Where am I taking the students? .............................. 52 What’s my approach? .................................................... 53 What does success, look like, feel like, or sound like? ........................................................................................ 56 From real life 1 ................................................................. 56 From real life 2 ................................................................. 64

Chapter 6 – Economics Teacher .......................... 71 What is an economic study? ........................................ 71 Where can it lead? ........................................................... 71 Where am I taking the students? .............................. 74 What’s my approach? .................................................... 74 What does success, look like, feel like, or sound like? ........................................................................................ 75 From real life ..................................................................... 76

Chapter 7 – Environmental Education Teacher ....................................................................................... 78 What is environmental education? .......................... 78 Where can it lead? ........................................................... 78 Where am I taking the students? .............................. 80 What’s my approach? .................................................... 81 What does success, look like, feel like, or sound like? ........................................................................................ 83 From real life ..................................................................... 84

Chapter 8 – Geography Teacher ......................... 85 What is geography? ........................................................ 85 Where can it lead? ........................................................... 85


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Where am I taking the students? .............................. 86 What’s my approach? .................................................... 87 What does success, look like, feel like, or sound like? ........................................................................................ 87 From real life ..................................................................... 87

CONCLUSION TO THINKING SYSTEMATICALLY ....................................................................................... 90 SECTION THREE – SITUATED THINKING ......... 92 Chapter 9 – Financial Literacy Teacher ........... 94 What is financial literacy? ........................................... 94 Where can it lead? ........................................................... 94 Where am I taking the students? .............................. 95 What’s my approach? .................................................... 96 What does success, look like, feel like, or sound like? ........................................................................................ 98 From real life ..................................................................... 98

Chapter 10 – Health and Physical Education Teacher ..................................................................... 100 What is health and physical education (H&PE)? ............................................................................................... 100 Where can it lead? ......................................................... 100 Where am I taking the students? ............................ 101 What’s my approach? .................................................. 101 What does success, look like, feel like, or sound like? ...................................................................................... 102 From real life ................................................................... 103

Chapter 11 – Home Economics Teacher ........ 105 What are home economics? ...................................... 105 Where can it lead? ......................................................... 105 Where am I taking the students? ............................ 105 What’s my approach? .................................................. 106


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What does success, look like, feel like, or sound like? ...................................................................................... 106 From real life ................................................................... 107

CONCLUSION TO SITUATED THINKING .......... 108 SECTION FOUR – THINKING AESTHETICALLY ..................................................................................... 109 Chapter 12 – Dramatic Art Teacher ................ 110 What is dramatic art? ................................................. 110 Where can it lead? ......................................................... 110 Where am I taking the students? ............................ 110 What’s my approach? .................................................. 111 What does success, look like, feel like, or sound like? ...................................................................................... 111 From real life ................................................................... 112

Chapter 13 – Technology Teacher ................... 113 What is technology? ..................................................... 113 Where can it lead? ......................................................... 113 Where am I taking the students? ............................ 113 What’s my approach? .................................................. 114 What does success, look like, feel like, or sound like? ...................................................................................... 114 From real life ................................................................... 114

Chapter 14 – Information and Technology Teacher ..................................................................... 117 What is information and technology (IT)? ......... 117 Where can it lead? ......................................................... 118 Where am I taking the students? ............................ 118 What’s my approach? .................................................. 119 What does success, look like, feel like, or sound like? ...................................................................................... 120 From real life ................................................................... 120

Chapter 15 – Visual Art Teacher ....................... 122


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What is visual art? ........................................................ 122 Where can it lead? ......................................................... 122 Where am I taking the students? ............................ 124 What’s my approach? .................................................. 126 What does success, look like, feel like, or sound like? ...................................................................................... 126 From real life ................................................................... 127

CONCLUSION TO THINKING AESTHETICALLY ..................................................................................... 128 SECTION FOUR – THINKING WITH LANGUAGE ..................................................................................... 129 Chapter 16 – English Teacher ............................ 131 What is English? ............................................................. 131 Where can it lead? ......................................................... 131 Where am I taking the students? ............................ 131 What’s my approach? .................................................. 132 What does success, look like, feel like, or sound like? ...................................................................................... 133 From real life ................................................................... 134

Chapter 17 – English as a Second Language Teacher ..................................................................... 136 What is English as a second language? ............... 136 Where can it lead? ......................................................... 137 Where am I taking the students? ............................ 137 What’s my approach? .................................................. 138 What does success, look like, feel like, or sound like? ...................................................................................... 140 From real life ................................................................... 141

Chapter 18 – Foreign Language Teacher ....... 143 What is foreign language? ........................................ 143 Where can it lead? ......................................................... 143 Where am I taking the students? ............................ 143


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What’s my approach? .................................................. 144 What does success, look like, feel like, or sound like? ...................................................................................... 145 From real life ................................................................... 145

Chapter 19 – History Teacher ........................... 147 What is history? .............................................................. 147 Where can it lead? ......................................................... 147 Where am I taking the students? ............................ 148 What’s my approach? .................................................. 149 What does success, look like, feel like, or sound like? ...................................................................................... 151 From real life ................................................................... 151

CONCLUSION TO THINKING WITH LANGUAGE ..................................................................................... 153 SECTION FIVE – THINKING MATHEMATICALLY ..................................................................................... 154 Chapter 20 – Mathematics Teacher ................. 155 What is mathematics? ................................................. 155 Where can it lead? ......................................................... 155 Where am I taking the students? ............................ 157 What’s my approach? .................................................. 160 What does success, look like, feel like, or sound like? ...................................................................................... 162 From real life ................................................................... 162

Chapter 21 -‐ Common misconceptions in learning mathematics .......................................... 165 Introduction ..................................................................... 165 Level 1 – Trusting the count ..................................... 166 Level 2 – Place value .................................................... 168 Level 3 – Multiplicative thinking ............................ 169 Level 4 -‐ Partitioning ................................................... 171 Level 5 – Proportional reasoning ........................... 173


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Level 6 – Generalising, equivalence, number properties and patterns, and the use of algebraic text ....................................................................................... 175 Conclusion ......................................................................... 177 Bibliography for chapter 21 ..................................... 178

CONCLUSION TO THINKING MATHEMATICALLY ..................................................................................... 180 SECTION SIX – SIX WAYS OF THINKING .......... 181 Thinking with language ............................................. 183 Thinking mathematically .......................................... 185 Situated thinking ........................................................... 187 Thinking aesthetically ................................................. 189 Thinking systematically .............................................. 190 Thinking scientifically ................................................. 191 Curriculum outlines ...................................................... 192 In closing ........................................................................... 196 About the author ........................................................... 198


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Chapter 1 – Introduction

Why I wrote this book I am trained as a generalist teacher and I work in a very small school where I teach a multi-‐level classroom that includes middle-‐years kids. I teach a wide-‐range of subjects for which I am ill-‐prepared at times; yes, I have a teaching diploma, and more recently a post graduate certificate in primary mathematics teaching, but prior to teacher training I undertook undergraduate and post graduate studies in biological science. So, quite simply, many of the things I teach my students are outside of my comfort zone. To survive and thrive as a generalist I first developed the Six Rs approach to pedagogy. These were reading, writing, ‘rithmatic, researching, retelling and reasoning. It is about delivering these, especially without content background that this book is about. Researching is about using a subject discipline to frame your enquiry. Different subjects use different frameworks leading to different perspectives and ways of understanding our world. For example the scientists and historians both value evidence but weigh what it means to them quite differently.


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Retelling is about using the framework for the discipline to communicate what I know in an orthodox way. Retelling using a different disciplinary framework, can lead to novel ways of sharing understanding. For me, reasoning is about having opinions, being able to defend them, being able to ask clarifying questions and identify the big ideas in a topic. It is also about being able to think in a disciplined way. By this I mean thinking about an object, the way an artist would. Thinking about an event the way an economist would. Thinking about a problem the way an environmentalist would. This book is for generalist teachers and those colleagues teaching out of method and my aim is not to describe how a chemist thinks, but how a teacher of chemistry needs to think, I think this is important because what teachers do, what you do – in you classroom, counts. And, depending who you read, it can account for 50-‐70% of what happens to student outcomes. What teachers can do is a function of their knowledge of the students in their classroom, the pedagogical approaches adopted and finally, their knowledge of, and enthusiasm for, the subject. Just your enthusiasm accounts for about 10% of the student outcomes. I believe, if you have some idea where you are going and what it will look


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like when you get there, then you will do a much better job for your students. It’s mostly about setting up and nurturing a positive learning environment.

Who should read this book In the Australian context all primary school teachers are generalists and, as part of their pre-‐service education, are shown pedagogy for a wide range of methods suited to the primary school teaching and learning environment. This is done without due consideration of their content knowledge. Some secondary school teachers may have undertaken generalist teacher training after their degree too, but this time focussed upon middle years pedagogy. Some teachers, qualified with a Bachelor of Education degree, may find the education component of their degree was given greater emphasis than the academic component and so struggle to teach in some disciplines because of a lack of subject knowledge. At senior secondary level teachers are expected to have completed a relevant major in their undergraduate degree followed by specific training in the pedagogical methods matching that major.


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This book is aimed at: . Generalist teachers delivering an integrated curriculum to a multilevel classroom . Generalist teachers delivering subject specific curriculum in the primary and middle years setting . Specialist teachers teaching outside their method in the primary and middle years . Substitute teachers in the primary and middle years . School leaders and department heads allocating teachers to subjects and classes

How this book is organised For my research I looked at curriculum documents, the web-‐pages of professional organisations, peer-‐reviewed papers, and op-‐ed pieces written by academics and teachers, and I drew on my own experience, and the experience of colleagues, to discover how specialist teachers think, what their predispositions are, and how they implement rigor in their teaching. “The education superpowers [believe] in rigor. People in these countries [agree] on the purpose of school: School [exists] to help students’


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master complex material. Other things mattered too, but nothing mattered as much.” (Amanda Ripley – The smartest kids in the world – Simon & Schuster) This book is organised around the different kinds of complex material in school. I have organised that complex material into six ways of thinking: . Section one – thinking scientifically . Section two – thinking systematically . Section three – situated thinking . Section four – thinking aesthetically . Section five – thinking with language, and . Section six – thinking mathematically These six ways of thinking are useful to you as you attempt to deal with an overcrowded curriculum. I think teachers might find my arrangement especially useful for integrated studies. I think school leaders may find it useful for matching up teachers with subjects. Teachers used to thinking in a particular way will find working in those subjects that also think in the same way much easier. The


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sections are not presented in order of importance. There is an introduction at the beginning of each section explaining the big idea in the way of thinking to follow. Each chapter exemplifies a subject within that way of thinking. All of the subject chapters are structured in the same way. It begins with a chapter number and chapter title indicating which specialist teacher we are dealing with. The first heading in the chapter describes the subject area in very broad terms while the next heading suggests where study of the subject might lead after school. Where am I taking the students describes the overall learning intention for the subject and the next section, called what’s my approach, describes the learning methodology for that discipline. The next two sections might seem odd at first, but understanding how this kind of class looks and feels and sounds, will give the generalist teacher or specialist not teaching in their method, confidence that what they are and the class are doing is on track. From real life is an example of teaching and learning in the discipline. Finally, I have included links to the more significant and useful and interesting websites and documents I have found along the way. The final chapter attempts to pull it all together.


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Returning now to the first chapter, this chapter, this is the introduction and talks about my motivation for writing the book and who should read it and how it is organised.

The 2nd Edition The second edition has been made to address some typographical and grammatical errors in the first book, which highlights the dangers of not having a proof-‐reader. While it is not a full-‐blown re-‐write, there are some additional examples from real life and I have also moved the useful links at the end of each chapter to a separate document for ease of updating. This new version also reflects upon the fact that I have more consistently applied the Six Ways of Thinking to my own teaching practice. Let’s get on.


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SECTION ONE – THINKING SCIENTIFICALLY (USING SCIENTIFIC METHOD) The major idea you have to get across to your students is that scientists can change their mind, and are expected to, in the face of new evidence. And this is the strength of science, not the weakness. The reason scientists think like this is because of the scientific method. This is a formal process where problems are tackled in a particular way: 1. The scientist asks a question. 2. The scientist does background research. 3. The scientist constructs a hypothesis (this is an assumption about what is going on). 4. The scientist tests their hypothesis by doing an experiment (or making a model). 5. The scientist analyses their results and draws a conclusion that may include further experiments. 6. The scientist communicates the results in a transparent way.


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a. Experiments should be replicable – that is if other scientist do them then similar results will be seen. b. Peer-‐review is a process by which scientists working in the same field critically analyse the work of the author. c. Science is built upon the work of others. Remember steps 1 and 2 above. In fact much of science teaching is predicated on using scientific method whereby the experiment clears up student misunderstanding. Many science disciplines tackle ‘systems’ and some topics could be tackled with systematic thinking as described in Section Two, however it is the method described above, the way of thinking, that makes science different. I would argue that if your students are not conducting experiments or observing and modelling natural phenomena then they are not really thinking like a scientist. It is for this reason I have placed environmental education in the thinking systematically section. Over the next three chapters making up the section, thinking scientifically, I present teaching like biology, chemistry and physics teachers. While each chapter does stand alone


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I recommend that you read the entire section. Let’s begin with my university major, biology.


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Chapter 2 – Biology Teacher

What is biology? Biology is a science discipline concerned with the study of living things. Biologists accept that: . Life has evolved over hundreds of millions of years . Living things interact with each other and their environment, and . That form and function are related in living things

Where can it lead? There are eight sub-‐disciplines within biology. They include: . (Biology) The study of life cycles . (Botany) The study of plants . (Cellular biology) The study of cellular biology . (Ecology) The study of ecosystems . (Genetics) The examination of genetic inheritance


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. (Microbiology) The study of microorganisms . (Physiology) The study of body systems, and . (Zoology) The study of animals Biology can be conducted at your desk, in the field, or in the laboratory.

Where am I taking the students? There is a huge array of biology-‐related careers. Some are utterly specialised, like endocrine biology whereas others, like plant nurseryman, apply more generalised biological knowledge. Some of your students may be intending to become biologists and some may use aspects of biology in other work but the vast majority of your students will only access biology through infotainment, news media and/or social media. Consider the following issues: . Alternative medicine and therapies . Extinction of species . Genetically modified crops . Habitat destruction . Human population growth


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. Reproductive technologies, and . Vaccination These topics relate to biology and without doubt the discussion of these issues are skewed by ideology. Your students need to understand what people mean when they hear a phrase from a scientist like, “The science suggests.” This is not an opinion like an ordinary person would have, it is an opinion based on the evidence uncovered so far. It’s not an off-‐the-‐cuff remark and the reason it’s not definitive, is that science is a discipline subject to revision.

What’s my approach? For this subject you might undertake a classic ‘project’, a desktop study, or run an experimental approach, which I prefer. Your classic biology ‘project’ is about researching and retelling, finding out information about a plant or animal or living system, and informing others of what you know. This needn’t be in essay, poster or power-‐point form, other ways of retelling, like the visual and performing arts may serve equally well or better. What you are doing has a scientific theme but it isn’t being done scientifically.


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A desktop study is carried out without any actual experiment. It’s about posing a question then accessing the available data and information, and drawing conclusions from that. It is a way by which your students can address some of the really big issues in biology facing humankind. It is arguably more scientific than the project approach above because while no physical experiment is conducted a ‘thought experiment’ is. An experimental approach follows the scientific method described earlier. It’s about posing a question, doing some research, setting up an experiment, getting results, coming to an understanding of what they mean, and telling others about it. In your experimental biology class your students will be very concerned with factual evidence and real data. That is, what they can accurately observe with one or more of the five senses. These are smell, touch, taste, sight and sound. Your students may be using instruments and technology to make their observations, and they should be recording their observations in a very disciplined manner. Their observations may be numerical, written or drawn. Keeping an up to date laboratory notebook is an important task.


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Your students will be coming up with reasons to explain a particular observation. These interpretations may not be correct, or only partly correct, at this point. Your students will be thinking out loud about how they might go about confirming or rejecting these initial thoughts. This may be through further research or through testing. Where an experiment or a model is warranted then your students will be concerned with either controlling variables or allowing for them. Experiments generally try to test single variables where just one aspect is altered. Models are more complicated as they are generally used to explain systems and where they don’t then the model is altered not the variable. For those of you fortunate enough to be connected to the Internet, there are an amazing number of sites which provide ideas for experiments and explain scientific phenomena. UTube deserves a particular mention in this regard.

What does success, look like, feel like, or sound like? Your students will be making predictions about the outcome of their experiments. This is called a hypothesis. They will observe their experiment (see above).


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Your students will be classifying living organisms based on particular criteria. Like size, form, colour, complexity, place in the ecosystem, life cycle, interaction with the physical environment. Your students will use tables and graphs. Your students will be making models to represent living creatures and systems. Models may be drawn or constructed in physical, digital or mathematical forms. Your students will be researching and retelling what they know. They will be reading or experimenting, and making presentations, using email and social media, writing science reports.

From real life 1 As a biology teacher you have to be prepared to do experiments where observations can be made of living things with the equipment and resources at hand. My grade 3-‐6 students wondered about what made earthworms lay eggs. They came up with two explanations: One, that the earthworms needed good food and two, that earthworms needed lots of room. We set up an experiment to test that hypothesis.


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We set up four big tubs two with high densities of worms and two tubs with low densities. One each of these tubs was then given good quality food like vegetable scraps in equal amounts and the other two were given shredded photocopy paper. More replication of each set up would have been better but we used what we had. While we were waiting for the worms to settle in and get used to the feeding regime and population density, the children began recording what was done in laboratory notebooks. They also made scientific drawings of earthworms and generally increased their knowledge of these creatures, their biology, ecology, and physiology. They were also taught how to write a science report during literacy time. At the end of the experiment, about three weeks, we counted worms and worm eggs and tabulated the data. We found that the densities used made little difference to egg production while food quality was very important – the animals getting shredded paper produced many more eggs than the worms on a better diet. The children then had to explain that finding which was probably the worm’s response to a stressful situation. The experiment was written up as a science report.


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This experiment could have easily followed up with an examination of what else might stress worms into laying eggs.

From real life 2 In 2014 my class and I examined the effect of coloured light on the growth of snow peas. The aim of the experiment was to understand the function of photosynthesis. We grew the plants inside clear soft-‐drink bottles covered, or not, with green, red or blue cellophane. We hypothesised that the filtered light would effect the growth of plants. Use two litre bottles as one litres are too small. We kept the plants outside, where they received natural sunlight and we regularly watered them. After about a month, the plants were removed from the ground and compared in groups. We had to stop because the plants were outgrowing the bottles they were in. The students used Excel (a spreadsheet) to work out average growth and relative root sizes, and then to make graphs. This was a lesson all by itself. We also grew seeds in wet tissue and looked at these under a dissection microscope we had. A magnifying glass works equally well but without the novelty impact.


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The experiment was written up as a scientific report using a mix of modelled, shared, guided and independent writing. I showed the students how to put the introduction together. We shared the writing of the method section and I guided them in how to write the story being told by each graph they made. Using a single website (ehow.com) the students wrote their own conclusion for the experiment. That is, how did our experiment compare and contrast with other similar experiments. This complex writing task proved challenging but at the same time, gave the more able writers in the class, an opportunity to use writing as a way of thinking. While we were waiting for our plants to grow the children engaged in scientific drawing of Snow Pea seedlings. This proved to be a very beneficial activity and the children came to a greater understanding of the plant’s structure. All in all, this was a really great piece of learning.


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Chapter 3 – Chemistry Teacher

What is chemistry? Chemistry is a physical science. It is the study of substances and the interactions between them. These interactions are between electrons whereas physics studies interactions at the sub-‐atomic level. Chemistry can be divided into the three broad fields of organic (mainly carbon-‐based), inorganic (carbon is mostly excluded), and physical chemistry (systems, processes, and dynamics).

Where can it lead? There are a number of sub-‐disciplines in chemistry: . (Analytical chemistry) The science of recognizing different substances and determining their constituents . (Biochemistry) The study of the chemicals, chemical reactions and chemical interactions that take place in living organisms . (Computational chemistry) The development of computers and software for solving chemical problems


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. (Inorganic chemistry) The study of the properties and reactions of inorganic compounds . (Materials chemistry) The study of fundamental issues that are unique to materials . (Neurochemistry) The study of neurochemicals; including transmitters, peptides, proteins, lipids, sugars, and nucleic acids; their interactions, and the roles they play in forming, maintaining, and modifying the nervous system . (Nuclear chemistry) The study of how subatomic particles come together and make nuclei . (Organic chemistry) The study of the structure, properties, composition, mechanisms, and reactions of organic compounds . (Physical chemistry) The study of chemical systems and processes and the energetics and dynamics of such systems and processes . (Theoretical chemistry) The study of chemistry via fundamental theoretical reasoning usually within mathematics or physics


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. (Quantum chemistry) The application of quantum mechanics to chemistry

Where am I taking the students? Chemistry is a study of the abstract and the difficulty for your students is reconciling their tacit knowledge, which may be wrong, with the scientific principles contained within chemistry. Some ideas in chemistry are counter-‐intuitive and thus challenging, which is why experiments are used to prove an idea. And, at the macro level it is possible to see the results of some chemical experiments, like the production of a new compound, but a lot of time chemistry is invisible and relies upon models, formulas and equations to explain itself. Unlike some other subjects, where opinion counts as much as knowledge, in chemistry (and science) it is necessary to know things. Facts are the building blocks of science and the way the facts fit together builds coherent knowledge. A poor understanding of an initial idea will lead to subsequent difficulties with later concepts. One metaphor I read while researching this topic that may be helpful to you is that chemistry is like chess. Each piece can act in particular ways, but each piece reacts with the


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other pieces around it depending on their type, position and proximity. The clever chemist uses his/her knowledge to arrive at a desired outcome just like a chess master can see more than one way to achieve and/or prevent a checkmate. You should be aware that there is an identifiable chemical industry making a range of products. Other major industries employing chemists are the petroleum, pharmaceutical and food industries. Few of your students will become ‘chemists’, but they may work in fields where their knowledge of chemistry, and the principles of studying chemistry, will more than useful to them. Chemistry links with other disciplines to create areas of study like biochemistry, geochemistry, and chemical engineering.

What’s my approach? I want you to acknowledge at the outset that chemistry is a difficult subject to teach ‘off the cuff’, so irrespective of whether the learning and teaching is taking place in a primary or secondary setting, you need to prepare in advance. Your approach is to encourage investigation. You want your students to be curious, questioning, and communicative. You need to begin with identifying the big conceptual idea and link this with their


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current understanding. You will be applying scientific method. There are three themes taught in school chemistry. These are: . Composition and structure of substances . Properties of substances, and . Reactions between substances (this topic is further subdivided) a. Energetics – the distribution of energy and equilibrium in a reaction b. Dynamics – the mechanism of, and rates of, a reaction A lot of chemistry can take place in a lab but it is possible for students to perform chemistry experiments in a normal classroom or outside. Irrespective of the location you need to be aware of the need to keep yourself and your students safe. You may prefer to use video demonstrations, or demonstrate the experiment yourself, or if the materials and equipment are benign then have the students carry out the experiments. If the children are working through the experiment then maintain control by breaking the process down into small steps, and having the class


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complete each step before going onto the next one. Encourage recording of the process. In your experimental chemistry class your students will be very concerned with factual evidence and real data. That is, what they can accurately observe with one or more of the five senses. These are smell, touch, taste, sight and sound. Your students may be using instruments and technology to make their observations, and they should be recording their observations in a laboratory notebook in a very disciplined manner. Their observations may be numerical, written or drawn. Your students will be coming up with reasons to explain a particular observation. These interpretations may not be correct, or only partly correct, at this point. Your students will be thinking out loud about how they might go about confirming or rejecting these initial thoughts. This may be through further research or through testing. Where an experiment or a model is warranted then your students will be concerned with either controlling variables or allowing for them. Experiments generally try to test single variables where just one aspect is altered. Models are more complicated as they are generally used to explain systems and where


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they don’t then the model is altered not the variable.

What does success, look like, feel like, or sound like? Completely unqualified teachers with no understanding of laboratory safety will need to be very selective about their experiments and take advice from more qualified teachers if unsure. Your students may be wearing protective clothing like lab coats or art smocks and safety glasses may be issued. Your students will be making predictions about the outcome of their experiments; this is called a hypothesis. They will observe their experiment (see above). The kids will be working in small groups following written or verbal instructions. They should be sharing the tasks around, and recording what they are doing In some settings, like a laboratory, specialist equipment like glassware, Bunsen burners, models, and other apparatus will be used. In other settings more general equipment will be used like clean glass jars, kitchenware The language of chemistry is populated with jargon and your students have to master the


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jargon, and there will be a buzz in the room as the children interact with one another.

From real life 1 I am not a science teacher but I do have a scientific background and I know and understand ‘scientific method’ I want to describe a recent chemistry experiment my class performed in an ordinary classroom. For our first session, we used an enquiry-‐based learning approach to determine that the class wanted to study chemistry, as opposed to physics or biology this time round. A further polling of the room identified the children were very interested in studying reactions, especially explosions, that was never going to happen. So the follow-‐up research in the same session required the children to find out on-‐line what a reaction was and what caused them. And then they had to search the WWW for reaction experiments that might be suitable for our class to carry out. They had to think about safety, availability of equipment, and potential difficulties in obtaining materials. The children came up with about five experiments and one, about rust, looked doable in our context. We had measuring cups; glass jars, scissors, little blackboards, and water and vinegar and soap-‐free steel wool


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were easily obtained from the local supermarket. Metals containing iron can rust and rust can be a pretty big deal. But what is rust and what is going on? The students decided that some kind of reaction was happening to cause rust and it might have something to do with water or acid. I put the kids in groups of three so that everyone would be able to share tasks. I set myself up out the front. First I made sure the children had a notebook and a pencil to record what they had done, handed out the jars, then cut up the steel wool pads into fourths and passed these around, two to a group (we were going to do replicates). At the front I kept about a dozen old kid-‐sized blackboards. The first job was to decide on the ratio of acid to water we were going to try. The students came up with 0:1, 1:1, and 1:0. I suggested we have a 1:2 and it was proposed that we should have a 1:3 as well. Groups of children were given responsibility for an acid: water ratio. As I was distributing the vinegar by the half-‐cup the groups had to calculate how much water they needed to achieve their ratio. For example 1:1 was equal measures while 1:3 meant one half cup of vinegar and three half cups of water. There were four parts in the


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whole thing and three quarters of the mix was water. While the others were waiting I directed them to record what we had been doing so far. I made a start on writing a table on the board out the front and most of the kids copied this. Once the jars were made up with the acid: water mix and labelled appropriately the children fully dunked their steel wool quarters but not before we decided on a time limit for this process (controlling a variable). We decided on 1:30s. We repeated this process with the second piece of steel wool. On retrieval the steel wool was allowed to drip dry and then were placed on my old blackboards. I used chalk to mark out where each piece was to go. By the time we completed treating the second piece of steel wool the first pieces were already showing signs of rusting (going brown). The children were quite excited about this and I had to encourage them to record their observations immediately, maybe in a table. In about 15 minutes we were seeing a result that suggested to us that the more dilute acid: water treatments were causing the steel wool to rust. What’s going on?


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Back to the research, whereupon the class hypothesised that the little bit of acid in the vinegar removed the outer ‘skin’ of the steel in steel wool thereby allowing it to react with water. The more water the better? There was even a chemical equation for what was happening. We conducted a second set of experiments in our next session to investigate this hypothesis.

From real life 2 A classic little trial that is simple to do is the salt in water experiment. This is where the students predict how much, and then dissolve salt in a known amount of water, and keep going until they reach saturation point. This is when no more salt will dissolve and then try and explain what has happened? The web is full of little ideas like this.


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Chapter 4 -‐ Physics Teacher

What is physics? Physics is a physical science. It is concerned with the explanation of natural phenomena through the use of models, theories, and laws. Like all sciences it is evidence-‐based and subject to revision.

Where can it lead? There are many sub-‐disciplines: . (Atomic and molecular physics) The study of the structures of the atom and molecules . (Acoustics) The study of sound that are the mechanical waves in gases, liquids, and solids . (Applied physics) The science of using physics to help human beings, and solve their problems in unique and novel ways, often leading to new technology . (Elementary particle physics) The study of particle motions (spinning) and particle types (fermions, leptons, quarks, hadrons, bosons) and the forces that act on them like gravity, electromagnetism and nuclear . (Fluids) The study of the movement, flow and behaviour of liquids and gases


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. (Mechanics or classical physics) The study of Newton’s Laws . (Nuclear physics) The study of the constituents of the nucleus, and different types of radiation . (Optics) The study of the generation of electromagnetic radiation, the properties of that radiation, and the interaction of that radiation with matter, especially its manipulation and control . (Plasma physics) The study of the collection of charged particles and electromagnetic fields . (Solid-‐state physics) The study of particles moving inside crystals or other solids (physics of condensed matter) . (Thermodynamics) The study of the way heat moves from one object to another or acts in gas at the atomic level

Where am I taking the students? Like mathematics and other sciences, physics is a conceptual subject, and as such challenges misconceptions. Your approach is to surface the misconceptions held by your students and use models and experimentation that illustrate the right way to think about physical


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phenomena. It won’t be an easy task because some students will have held their construct of the natural world for some time but unless they can alter their concept they will not progress in physics. Simply being able to recall laws and apply formulas is not enough. Your students have to believe the evidence presented by direct and indirect observation of experiments. Physics can be the basis of a career as a pure researcher, as an applied scientist, engineer, educator and technician. It can lead into areas not thought of as technical or scientific too. It all depends upon how far one goes with their physics education. The reality for most physics graduates is that very few will become physicists (a PhD is necessary for that). The majority of graduates will become engineers, computer programmers/IT workers, or will end up doing something non-‐technical and non-‐scientific.

What’s my approach? There are two big themes in school-‐based physics and these are: . Thermal, nuclear and electrical physics, and . Linear motion and waves


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Physics works hand in glove with mathematics. If physics is about physical phenomena and experimentation then mathematics is abstract representation and modelling. You will be facilitating experiments and the use of scientific method in your physics class. In your experimental physics class your students will be very concerned with factual evidence and real data. That is, what they can accurately observe with one or more of the five senses. These are smell, touch, taste, sight and sound. Your students may be using instruments and technology to make their observations, and they should be recording their observations in a laboratory notebook in a very disciplined manner. Their observations may be numerical, written or drawn. Your students will be coming up with reasons to explain a particular observation. These interpretations may not be correct, or only partly correct, at this point. Your students will be thinking out loud about how they might go about confirming or rejecting these initial thoughts. This may be through further research or through testing. Where an experiment or a model is warranted then your students will be concerned with


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either controlling variables or allowing for them. Experiments generally try to test single variables where just one aspect is altered. Models are more complicated as they are generally used to explain systems and where they don’t then the model is altered not the variable.

What does success, look like, feel like, or sound like? Your students will be making predictions about the outcome of their experiments. This is called a hypothesis. They will observe their experiment (see above). . The kids will be working in small groups and following written or verbal instructions. They should be sharing the tasks around, and recording what they are doing . Your students may be wearing protective clothing like lab coats or art smocks and safety glasses may be issued . In some settings, like a laboratory, specialist equipment, models, and other apparatus will be used. In some settings the apparatus will be created as part of developing the experiment . The language of physics is populated with jargon and your students have to master the


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jargon, and there will be a buzz in the room as the children interact with one another.

From real life At my school we studied Newton’s three laws of motion. This is a great topic to start the study of physics. There are these three relatively simple laws that children can test by experimentation. Newton’s Three Laws of Motion are: First Law (the law of inertia): An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Second Law (F=ma): The acceleration (a) of an object as produced by a net force (F) is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass (m) of the object. Third Law: For every action, there is an equal and opposite reaction. In class I introduced each law to the students but without a lot of explanation. We were going to experiment, but not before we played with the materials, outside. To carry out our


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study we used spheres of different sizes and masses like Ping-‐Pong balls, tennis balls and 1 and 2kg shot puts. We made ramps from materials found around the school and, for about 10 minutes, the students rolled the different spheres and bounced them off each other. Then I set the question, how could the children use these materials to demonstrate each of the laws. I placed them into three groups to work it out. After about 15 minutes the students believed they had created a demonstration or set of demonstrations for their law. We visited each group in turn. Some demonstrations were clear while others needed some tweaking and the class discussed this and created a better demonstration of the law.


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CONCLUSION TO THINKING SCIENTIFICALLY I anticipate that wherever you work there will exist a national or state curriculum for science and it will lay down step by step all the content that should be covered at each grade level. International tests have begun to appear which attempt to test the recall of that knowledge. The TIMSS (Trends in International Mathematics and Science Study) intends to investigate three levels: the intended curriculum, the implemented curriculum and the achieved curriculum. The intended curriculum is defined as the mathematics and science that societies intend for students to learn and how education systems are organised to meet this demand; the implemented curriculum is what is actually taught in classrooms, who teaches it, and how it is taught; the achieved curriculum is what students have learned. In my work environment, a very small 1.5 teacher school, it is impossible for quite practical reasons to cover the content concerned with science in the national curriculum and so, rather than worrying myself about that, I concern myself with the


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processes of experimental science that lead students to thinking scientifically. Thinking scientifically is about making observations from the evidence they themselves gather. Thinking scientifically is about trying to control the variables, thus seeing the impact of just one or two factors. For example, the worm experiment set up a test of two factors, population density and food quality. In the snow pea experiment we investigated the impact of coloured light filtration on plant growth. The chemistry experiment examined just one factor, the ratio of water to acid, and its effect on steel wool. Results from the first experiment led to revised, more finessed designs for the subsequent experiments. The physics study was somewhat different because in this instance we applied existing laws (Newton’s Three Laws of Motion) against observed phenomena. Now it is possible to place thinking scientifically in a wider context as some science is controversial and bumps up hard against morality, ethics, and ideology. For example, in our worm experiment we never once posed the question about if it was right to ‘force’ our worms into responding to the artificial conditions we created for them. We did not examine the idea that by manipulating


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the environment we were actually domesticating the worms and improving their chances of survival as a species. These are worthwhile discussions to have with your students, but by themselves these discussions, under my criteria, are not thinking scientifically. Your students should be able make observations from the evidence arising from experimentation. One final point before we move on. You may have noticed that I have not included any reference to ‘space’ in this section about thinking scientifically and I will explain why now. Your students will not be able to engage in any meaningful experimentation about space in an ordinary classroom during daylight hours. At best, the topic of space might best be dealt with as systematic thinking, albeit with scientific undertones, where the students create models to explore relative size and distances between stars and planets and moons. Thinking systematically is the subject of the next section.


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SECTION TWO – THINKING SYSTEMATICALLY The subjects discussed in this book that are about systems understanding are civics & citizenship, economics, environmental education and geography. These systems can be either manmade or natural. Systems are self-‐regulating and work via complex feedback mechanisms, attempt to maintain their equilibrium. Too much or too little feedback sees the system break down. Introducing systems thinking in your teaching means that your students are not exposed to discrete pieces of information in a piecemeal fashion rather they approach issues in a holistic way. They will: . Appreciate the big picture . Learn that systems change over time . Know that systems look different with a change of perspective . Consider the issue fully . Appreciate the interdependencies in a system . Where, what and how leverage can impact on the system


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. Develop mental models and physical models to represent the system . Anticipate short and long-‐term consequences . Be able to identify waypoints and indicators of change (successive approximation) . Be able to surface and test their assumptions . Appreciate the system’s structure . Understand the impact of time delays, and . Expect unintended consequences


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Chapter 5 – Civics and Citizenship Teacher

What is civics and citizenship? Civics and citizenship is the study of democracy, equity and justice. Civics is about understanding how our society works and is governed, politically, judicially, and socially. Citizenship is about understanding the nature of the relationship between the individual and the state legally, politically and socially. Under the new national curriculum, the subject of legal studies now falls under the civics and citizenship umbrella, but it does not have the same ‘punch’ as it once did. This is a shame because legal systems and the work of courts, particularly criminal courts, are considered worthy of being made into entertainment and this is a topic that students find very engaging.

Where can it lead? There are a few possibilities: . (Citizen) A person protected by rights and having civic responsibilities . (Governor) A person at the national and state levels with specific powers to appoint


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governments, ministers, and dissolve parliament . (Judicial officer) A person with the authority to make judgements under the law . (Lawyer/solicitor) A person trained to deal with legal matters . (Political science) The study of politics . (Politician) A person elected to public office, and . (Public servant) A person employed by government to implement its policies

Where am I taking the students? In my opinion, civics and citizenship is a contested learning space with political ideologies biasing the curriculum, first one way, and then the other, with every change of government. Topics to be covered should include: . The nature of citizenship . Diversity and identity . Equity and justice, and . Political and legal systems


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It is very likely the prior knowledge of your students is shallow and poorly reasoned because they are not really interested in civics, or may have adopted, without much critical thought, ways of thinking that align with their friends, family, and social and news medias. It is your job to overcome their inertia and to challenge their rationale for being of a particular persuasion, or none. To do this you and your students need to deal with ‘thick’ issues as opposed to ‘thin’ issues. “Thin democracy is exemplified in activities such as students contributing to a food drive. Thick democracy would explore why people are hungry in the first place and attempt to solve the problem.” (Dr. David Zynger – Monash University) Scarcely any students will get jobs as political scientists, and few will go onto to become politicians, judges or lawyers, although more might join the public service, all students have the opportunity to become citizens. So your main purpose is to ensure they are informed.

What’s my approach? Civics and citizenship is best discovered through a systemic thinking process as outlined in the introduction to this section. Raising awareness of different perspectives is


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a part of thinking systematically and the following frameworks may help you: . An ideological framework – an ideological framework influences how political parties, lobby groups, special interest groups, and individuals make decisions based on what is important to them . A pragmatist framework – is about finding the first option that settles the matter that can be put into operation . A participatory framework – includes a variety of approaches including consensus, consultative and/or or democratic. It’s about getting agreement . A political framework – this is about satisfying the most powerful players affected by the problem, and . A rational framework – this is about optimising the outcome for all the stakeholders – finding the best solution, for everyone. It is values-‐based Other frameworks are available – I suggest you Google it. Other opportunities for teaching this subject may be addressed in passing, for example:


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. Weekly singing of the national anthem . The celebration of culturally and religiously significant days . The creation of class rules . The election of school captain using preferential voting . The activities of a junior school council . The raising of funds for charity . An excursion to parliament house, and . The undertaking of projects for school and local community improvement An apolitical approach to civics and citizenship does, in my experience, lead to a ‘thin’ learning event for students. All they have to do is learn enough content to pass the test, and then promptly forget about it, it’s boring for them and boring for you. If you want your students to engage in a ‘thick’ learning experience then engage in the big issues and openly wear your political colours in the classroom and play devil’s advocate and deal with the big issues.


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What does success, look like, feel like, or sound like? If you are tackling ‘thick issues’ your class will be solving the unsolvable and passions will be high, especially when you play devil’s advocate or, even better you have those students, representing different approaches, challenge the suppositions underpinning a particular solution. Your class could get loud. You will find yourself defending your own point of view and challenging your students to defend theirs. It’s not important who is right just who can make the best case. The groups, depending on their personal point of view, may be engaged in vigorous debate amongst themselves as they grapple with the issues and the constraints of working within a particular framework. Especially, one they are uncomfortable with. Some kids will want to jump ship. Your students will be engaged in ‘quick and dirty’ research, bookmarking useful websites, and printing off useful information.

From real life 1 During Term 2, 2014 I challenged my students to ‘solve unemployment’. The subject was


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deliberately chosen because I knew that in Australia, youth unemployment, was a particular concern, and perhaps with studying this topic my students would form a view that remaining at school and working hard was in their best interests. With respect to civics and citizenship the topic touched on issues of understanding how Australian society works and the relationship between some individuals and the rest of society. Students would be exposed to issues of diversity, equity and identity. From an economics perspective the topic of solving unemployment related to where work was and was not, what skills were valued and what skills were no longer in demand, and the impact of government decisions and economic conditions. From the outset I determined that this piece of work would be organic and that we would see where it would take us. It is for this reason that at first we did not determine prior knowledge, or identify what questions we wanted to answer, as per enquiry-‐based learning methodology. You see I did not want them to just answer a question I wanted them to solve a problem; a big, sticky, complex problem. Another decision taken was that I did not want a ‘product for assessment’, I wanted to facilitate their questioning, researching and


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pondering, and so I decided I would be the scribe for the class. However, I am getting ahead of myself. For our first session I introduced thinking systematically and thereafter the children were given responsibility for answering who, what, where, when, why and how people became unemployed. They researched on line and I put their information onto a plain-‐looking power-‐point. This took a couple of sessions and some questions were easier to answer than others and some students were more effective than others in finding things out. One student, a grade six, became very interested in the whole issue and began to conduct research at home. In the end, with some students helping other kids we had a rough and ready understanding of the issue. The main points were: LD and CB With regard to who is unemployed the children learnt that non-‐graduates do less well than graduates, and that some people just stop looking for work altogether, and not always because they have reached retirement. However, a little unemployment is a good thing otherwise workers become too expensive to hire and keep. GW


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Unemployment was defined as a person who is looking for work but cannot find a job. It was also discovered that a person can be under-‐employed due to over-‐qualification or, education or, not having ‘enough’ paid work or, not using their personal skills and knowledge. It was also noted that work had become more casual. LM The main times when unemployment might occur were when a person finishes school, when businesses close, when economic activity slows down (GFC), and when someone is between jobs. ES It was learnt that unemployment was not universal although some states did better than others and in the states, some areas did better or worse than other places. In Newcastle it was found that youth unemployment was particularly bad (18.2%). Even some countries (Greece) were badly affected by the GFC with a quarter of that nation unemployed. JM and JL The students looking at ‘how?’ people became unemployed re-‐interpreted their question to how do you get and keep your job. They said you need to have the right skills, experience, and qualifications to get the job, and to keep it


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you had to be responsible, interested, punctual, present, flexible and polite to others. ENGAGING WITH JOURNALISM With this background knowledge now in place we read our first serious article together as a class. It was a blog piece and, as it turned out, so poorly written it was impossible to read aloud and we had to abandon it; we had much better luck with the second article. Creighton (2014) the economics correspondent for the Australian Newspaper had written an article looking at the issue of unemployment and he identified four hurdles that were in the way of solving the issue. Creighton had not written this article with primary school children in mind and so on the first read I read the piece to the class, explaining and clarifying as I went. As it turned out, with their pre-‐existing knowledge the children were able to stay the course and were engaged by what the journalist wrote. What I observed myself was just how important our understanding of fractions, percentages, and proportions were in order to get a proper appreciation of the big picture. As I read long, the children did identify gaps, conundrums and affirmations in/of their pre-‐existing understanding of the issue. One of the most interesting facts provided by Creighton was who was considered to be employed in government figures which turned out to be anyone who


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was working one hour a week. This immediately raised the profile of under-‐employment, discovered by GW earlier, to much greater importance. After reading the piece I challenged the children to find and paraphrase the four hurdles described by Creighton which included a too much regulation and taxation around employment, excessive minimum employment conditions, the evolution of technology and, the excessive and unnecessary hours being worked by people in employment. A follow up challenge was to identify whose perspective was being represented by each of the hurdles. USING AN IDEOLOGICAL LENS In the next session I introduced the children to the thinking frameworks and focussed on just one. The ideological framework and, using very simple criteria, I indicated the different principles that had been adopted by the Liberal, Labor and the Greens. This related to issues of individual rights, the economy and the environment, the role of government (big versus small), and whose interests are represented (workers versus employers). The children were randomly allocated into a party and asked to overcome the four hurdles identified by Creighton with those ideological principles in mind. It was a surprise to the


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children how little agreement there was between the three parties and that the issue of unemployment might actually be unsolvable. LINKING WITH LITERACY The next article read by the class was chosen quite by chance. ‘Dole Jackpot’ was on the front page of the ? edition of the Herald Sun (newspaper) and because it was so topical I knew we had to read it. And so we did, during the morning literacy block. After making some predictions about what it was about I read the article to the children and then clarified the meaning of words and phrases throughout the article. Over the next couple of sessions the students read the article aloud and engaged with the piece via the literacy circle methodology. What was interesting about this piece of work was that the children became more critical and noted that the title of the article did not match up with the reality of what was described in the text. They also noted that one stakeholder, the long-‐term unemployed person, was not represented in the article. They also made the link to other learning happening at school, about financial literacy, that the Newstart Allowance was far from being a jackpot amount. At this point the class appears to have a pretty good understanding of unemployment and under-‐employment and the consequences of


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that. They realise it is very hard to solve unemployment unless we change our minds, as a society, about addressing over-‐employment. Something Creighton (2014) made reference to in his article was how the famous British economist, John Maynard Keynes, anticipated, with some glee back in the thirties, that we should all be enjoying more leisure time due to the positive impact of technology and education. Nowdays, it would appear that too much leisure time is frowned upon. THE THOUGHT BUBBLE: A LEARNING ARTEFACT Leisure is frowned upon in my classroom and in spite of my earlier intention to not require a learning product from my students I had so much time left in the term that I felt we had to do something more. I decided to choose a learning artefact that would not necessarily take a lot of time to prepare but would facilitate further thinking in a systematic way about this topic. I chose the thought bubble. Communication is an inter-‐disciplinary curriculum area that involves presenting and responding to complex ideas. It is graded and reported upon from grade five upwards. It is the perfect way for the students to share what they have understood and are still puzzled about in another subject. The approach to


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presenting can be iterative, with personal laptops used to film ‘selfies’ of the student as they rehearse their thought bubble. For those who prefer to write, a word processor is a great way to think and edit simultaneously. A thought bubble can be an observation, a query, and idea. It should lead the listeners to asking clarifying questions and the speakers providing thoughtful responses. It should be thinking and speaking in paragraphs.

From real life 2 One way I deal with the ‘thin’ components of civics and citizenship is to have my students undertake the Australian Citizenship Test. It’s easy enough to find on-‐line. Marking a practice test indicates the areas of weakness of the class and those areas you may need to teach. Subsequent testing will indicate the student’s learning success. After completing a practice citizenship test one year it became apparent that the children did not really understand the mechanism of preferential voting. Let’s look at what we did about this shortfall in terms of thinking systematically: . Appreciate the big picture Governments in Australia are elected democratically and the party with the most seats in parliament forms government. The leader of this group becomes the prime


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minister. Councils don’t run on party lines, the mayor is chosen by a majority of councillors. . Learn that systems change over time It wasn’t always this way as initially Australia, not yet a country but a colony, was ruled by a governor appointed by the English monarch. Aboriginal people lived as loose affiliations of extended family groups connected to a particular place and, for very long time, organised their own affairs. Now Australian citizens can vote at local, state and federal elections, and we still have governors but their job is different, they are the head of state. We have a constitutional monarchy running on the Westminster parliamentary system. . Know that systems look different with a change of perspective Where a citizen is unable to find common cause with a mainstream political party then they may feel dis-‐enfranchised. . Consider the issue fully Is preferential voting and leadership of the parliamentary wing of the party the best method for electing a prime minister and a


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government? Our head of state is appointed not elected. Would that make a difference? . Appreciate the interdependencies in a system The governor is appointed by the monarch in England who takes the advice of the prime minister when doing so however, the governor is empowered to ‘sack’ the PM. The prime minister/premier is the leader of the parliamentary party with the most seats in the lower house and s/he needs the votes of his or her elected colleagues to stay in position. The leader of the opposition parliamentary party also needs the support of his/her elected colleagues. To be elected a local member has to get more than 50% of the votes in a preferential system. With a few exceptions most local members rely on a political party to support their [re] election. Donations to political parties above certain amounts are a matter of public record. Each electorate has a local branch of the party. In some parties the local members pre-‐select candidates but it is not unheard of for the state and federal party machines to select candidates especially to safe seats.


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Citizens vote for their candidates. . Where, what and how leverage can impact on the system We, the people, don’t elect the prime minister his or her parliamentary colleagues do. We elect our local member and if that person happens to be the sitting PM or leader of the opposition then that electorate has more leverage. As citizens our impact and leverage on the system comes around at election time where we are required by law to vote. Even though most of us do not directly vote for the prime minister the prime minister can influence how many people choose to cast their vote. We have not mentioned them before but there is an upper house called the senate and it has, in the past, effected what the lower house can do. . Develop mental models and physical models to represent the system This was actually done during the election of our school captains and the junior school council.


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First of all we decided who was eligible to vote and it was decided all students except new students could participate. Students could self-‐nominate for any position and were expected to deliver a prepared speech to the ‘electorate’. Voting slips were prepared with the list of nominees and an empty box by each name. The students were asked to rank their preferences 1, 2, 3 and so on. Four people nominated and, after counting the votes for first place, no student had over 50% of the vote. The person with the least amount of votes was removed from the contest and their votes were redistributed based upon who had been marked as the second preference. Once again, no one had more than 50% of the vote and so the person with the least votes remaining was removed from the contest and their votes redistributed based on who was marked second. This resulted in one person getting over 50% of the vote with preferences. This student was elected school captain for the following year. The vice captain was elected in the same way. Only two students nominated for the two junior school council positions so no ballot was held


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Our own election for captain served as a model for what happens as far as selecting a local member. . Anticipate short and long-‐term consequences Once elected governments can stop previous policies and introduce their own. With a change of government senior public servants can find themselves out of favour and removed from their posts. Previous PMs often quit shortly after the election and a by-‐election is necessary. . Be able to identify waypoints and indicators of change (successive approximation) In Australia it is said by some commentators that Australians don’t vote in new governments, they vote out old ones . Be able to surface and test their assumptions The students assumed that the person getting the most votes was elected. The idea of preferential voting had not occurred to them. Some students assumed that the prime minister was selected in much the same way as the American president. . Appreciate the system’s structure


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Some electorates are considered ‘safe seats’ while others are considered marginal because they often change hands with the change of government. . Understand the impact of time delays This particular element was not a factor in our thinking. . Expect unintended consequences Incomplete or incorrectly filled in voting slips can influence the vote. People who do not register in time to vote cannot vote. People who choose not to vote do not get counted.


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Chapter 6 – Economics Teacher

What is an economic study? Economics is a subject concerned with the study of production, consumption and the transfer of wealth and resources and how decisions are made about these. Economics is about resource allocation and making choices, and balancing the wants and the needs of consumers, producers and governments. Macroeconomics examines the subject at a larger societal scale and microeconomics focuses upon the individual or family unit.

Where can it lead? There are many places the study of economics can take you: . (Agricultural economist) The study of agricultural environments and resources and the supply of product into the marketplace . (Building economist) The collection, analysis and presentation of facts, figures and forecasts relevant to housing and renovation industries . (Econometrician) A speciality that integrates statistics and mathematics into economic analysis


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. (Economic natural resources manager) This is a study of primary and natural resources and how to manage these . (Finance manager) This is a person who plans, organises, directs, controls and coordinates the financial and accounting activities within an organisation . (Graduate quantitative traders assistant) The primary role of a GQTA is to support the Traders in the execution of trading strategies and the maintenance of trading operations . (Health economics associate) This is the study of healthy behaviours, health care choices and general wellbeing of the community. It studies the structure and funding of health care delivery as well as the impact of medical procedures and pharmaceutical interventions . (International trade analyst) Trade analysts focus on fundamental and technical analysis to assess the future price movement of securities . (Market analyst/researcher) This is about collecting and analysing data on customer demographics, preferences, needs, satisfaction, and buying habits to identify potential markets and factors affecting product demand


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. (Marketing consultant) A marketing consultant will be skilled and knowledgeable in consumer behaviour and marketing process. This includes having the ability to identify the companies target market and position their product or service offering in a way that will interest consumers and make them want to buy . (Merchant banker) A merchant banker is responsible for offering consultation services for mergers and acquisition, giving advice to businesses that plan to enter the international market and helping small businesses expand for a bigger target market. They also provide capital to businesses or make investment transactions with traders and sellers . (Public servant) Trained economists may join the state and federal public service as graduate recruits and serve in a variety of departments using their knowledge of economics, and . (Stockbroker) A stockbroker is a regulated professional individual, usually associated with a brokerage firm or broker-‐dealer, who buys and sells stocks and other securities for both retail and institutional clients, through a stock exchange or over the counter, in return for a fee or commission


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Other opportunities could include journalism, teaching, foreign affairs and international consulting

Where am I taking the students? The underpinning idea you have to demonstrate to your students is how economics operate in local, national, regional and/or global contexts. To think like an economist you are, to some extent, thinking like a physical scientist. You are trying to make models of large-‐scale events in order to predict long-‐term trends with respect to prosperity, sustainability, and terms of trade. Based upon your knowledge, and framed by your ideological lens, you will make predictions on the outcomes of geographic events, new government policies, or changes to current legislation. The employment outlook for economics graduates looks enormously positive. A very high proportion of graduates are attracted into the public service while others enter the banking and finance sectors.

What’s my approach? You can start with determining what the students think they know. One way I do this is to make them do a benchmark test before and


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after the unit. The benchmark is in the form of a diagram or list or drawing. A benchmark at the end provides a great before and after measure of learning. I like identifying the ‘big questions’ that the class might have about a particular subject and a little time spent identifying these (I use an enquiry-‐based learning approach) can, with a little guidance from you, often send the class in a particular learning direction. Solving problems is a very good way to approach this topic. You may have to adjust your expectations based upon the make up of your class but applying systematic thinking as described in the introduction to this section to economic enquiry is well worth it.

What does success, look like, feel like, or sound like? . Busy because they will be reading and interpreting graphical information and making decisions . Your students will be solving problems and making decisions, and . Interacting with each other as they collaborate, cooperate and compete. Earning and losing money or credit is how the world, keeps score


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From real life My class and I imagined we were off to colonise another planet and at first we just had the exploratory crew. I think there was about six, and the kids had to decide what job each of the six had. There was a captain, an engineer, a medical doctor, and a scientist who knew biology and geology. I think we had a cook too and a second in charge who was in charge of security and defence. Consensus was easily achieved about who should be on that trip. Before I began the next step I introduced the students to Maslow’s, ‘Hierarchy of Needs’ and we used this model as a framework for working on the next step. Colonisation began with 25 people flying in, in addition to the original six. And with some toing and froing the students worked out the trades, professions and occupations needed to ensure the survival of our imaginary community. They even started to consider the issue of gender balance. You have probably guessed already what happened next. The numbers increased again and again, and each time, the students had to decide what types of people they needed working in the colony. Over time, new workers were needed because as the colony increased


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in size more systematic responses were required to solve problems. Then at some point the students decided they needed to achieve self-‐sufficiency, as it was not realistic to expect to be supplied from Earth all the time. At this point, the children looked to private enterprise, including farming and mining and a variety of other businesses. They wondered what they should be and how they would be paid. Next, with so many people, the students expected that children would be born and that needed to be allowed for in the community in terms of specialists and family accommodation. We used Excel to keep track of numbers. But the conversation was rich, it was passionate, and children thought hard about short term and long term needs. The children discussed what the ‘government’ should do, what ‘private enterprise could do and how much ‘help’ the government should provide. Everyone had to be employed; even the children of the colony were expected to make a contribution as soon as that was possible. It was a great little unit of work.


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Chapter 7 – Environmental Education Teacher

What is environmental education? There are two schools of thought around environmental education. ‘Environmental science’ is about earth, water, air and living creatures and the interaction between them. It draws upon aspects of geology, physics, chemistry and biology. ‘Environmental studies’ are a closely related teaching area very concerned with sustainability but not at all troubled by scientific rigor.

Where can it lead? There is a wide range of careers, including: . (Agricultural engineer) Agricultural engineers study and advise on the use of engineering science and technology in agricultural production and management of natural resources . (Conservationist) This is someone who works to protect animals, plants, and natural resources or to prevent the loss or waste of natural resources . (Environmental engineering) Environmental engineering is the integration of science and engineering principles to improve the natural


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environment, to provide healthy water, air, and land for human habitation and for other organisms, and to remediate pollution sites . (Environmental scientist) Environmental scientists measure and record features of the environment and, study, assess and develop methods of controlling or minimising the harmful effects of human activity on the environment . (Environmental technician) Are people who work for environmental scientists . (Landscape architect) Through their understanding of natural landscapes and built environments, landscape architects seek to improve our quality of life by providing balanced, innovative planning and design solutions for the outdoor environments

. (Park ranger) Working, as a Park Ranger is as varied as the environment they manage. Park rangers have a conservation role, an interpretive role, a sustainability role and a law enforcement role too, and . (Urban planner) This is a professional who works in the field of urban planning/land use planning for the purpose of optimizing the effectiveness of a community's land use and infrastructure?


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Where am I taking the students? This subject is very much about system thinking over various timescales. Our planet for example, was formed over billions of years, and is part of a solar system, which in turn, is part of the galaxy, and then the universe. Going in the other direction, Earth is comprised of many systems like the water cycle, carbon cycle, hydrogen and nitrogen cycle, and oceanic forces. The Earth’s crust is still unstable in some places and warming of the planet is expected to have an impact on sea level and ocean currents. This will affect both the climate generally and the weather specifically. Systems can be studied at still smaller scales at the level of the ecosystem and habitat. The themes you want to engage your students in are: . Biodiversity . Biological responses to change . Habitat . Human induced change . Natural processes, and . Sustainability


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What you want your students to understand is that simple cause and effect does not explain what happens within a complex system like the planet or large parts of it. Causes and effects cascade through systems because they are dynamic and, upon reaching certain threshold measures, can result in abrupt changes.

What’s my approach? As part of my research for this chapter I found myself reading a special edition of the, ‘Australian Journal of Environmental Education’ It was entitled, ‘the “ness” of environmental education’. What is clear from the one of the papers by Professor Annette Gough is that there is no consensus around this subject and that tensions abound. For example: . Matching national aspirations with the (Australian) national curriculum . Delivery via school values or through the curriculum, and . Delivery as a stand-‐alone subject or in passing across the curriculum Since its introduction in 1975 this subject has struggled to find its place in national and state curriculums. In more recent times two offshoots


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have established themselves. Environmental Science, which comes at the topic from a scientific perspective (i.e. facts and concepts) and is likely to be acceptable to teachers with training in a science method who will make the topic about the environment, rather than for it. Environmental studies have been coupled with outdoor-‐education, and have a more holistic approach (i.e. values, cognitive learning, and social skills) acceptable to teachers without a science methodology. (A paraphrasing of Professor Annette Gough – RMIT University – see link) The aim of this book is to suggest your predisposition to teaching in the different curriculum areas and I anticipate, as was suggested by Prof. Gough, that you will follow an environmental science perspective if you know and are comfortable with a scientific method, and a more values-‐driven strategy if your background is not in the sciences. As a non-‐scientist you can still carry out ‘experiments’ but you won’t be afraid to change the variables as you go along in order to achieve the results you want. If you are following scientific method then any experiment you do will proceed through to completion without interruption. In either case I recommend you embed your approach in a local context.


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What does success, look like, feel like, or sound like? If this subject is taught as a science then success will have a similar look, feel and sound to biology, chemistry and physics. With respect to teaching environmental studies and sustainability, students can carry out small but meaningful projects like reducing their energy-‐use and litter production, increasing biodiversity, and improving habitat through tree planting and nest box making. Successful lesson sequences are more likely to follow an action-‐research approach: . Observe – what is happening? . Reflect – what does it mean? . Plan – what do we want to change? . Act – what are we doing? . Observe – what is happening? The level of proof will be much less rigorous and the methodology followed by the group may be much more contested. There may be an inclination to twist the facts to suit the theory.


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From real life Thinking systematically our class examined the problem of salinity in Australia. This is about the only time I draw anything more complex than a stick figure as my blackboard begins to reveal the interaction between the water table, deep rooted trees and transpiration and how an unintended consequence of clearing the land for farming has led to rising salinity. From this drawing the students were directed to look at the Great Artesian Basin and thus began to appreciate the big picture. This learning was ‘about’ the environment. Coming at the topic holistically we then planted about 100 native trees around our school. We hoped to replace damaged tress and improve the environment for native fauna. This event was ‘for’ the environment. At the same time we held back about 12 seedlings of the same species and subjected them to different levels of saline stress. In this way the students could observe for themselves the adverse impact of rising salinity. This learning was ‘about’ the environment.


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Chapter 8 – Geography Teacher

What is geography? According to the Royal Geographic Society (RGS) geography is about the understanding of social and physical processes in terms of place. It is concerned with location, distribution, spatial interaction and scale. The RGS says some 80% of business decisions, are influenced by geographical factors.

Where can it lead? There are two types of geography, physical and human: 1. Physical geography – the study of processes and patterns in the natural environment. It covers a wide-‐range of topics including: . (Geomorphology) The study of landforms . (Hydrology) The study of water movement . (Glaciology) The movement of glaciers and ice . (Biogeography) The distribution and movement of life . (Climatology) The study of climate


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. (Meteorology) The study of the atmosphere and weather . (Paedology) The study of surface soil . (Paleogeography) The study of fossils distribution . (Coastal geography) The study of coasts . (Oceanography) The study of oceans, and . (Geometrics) This is the gathering, studying and storing of geographical information There are clear links to environmental education and some aspects of geology. 2. Human geography – is the study of built environments and the impact of human activity on the environment. It includes topics covering culture, development, economics, health, politics and others. It links with environmental studies.

Where am I taking the students? Straddling both the sciences and social studies paradigms, professional geographers make use of quantitative and qualitative research methodologies and rely upon enquiry-‐based approaches to discovery. Geography’s most fundamental instruments are the map and the


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plan, although other mediums, notably satellite imaging, are becoming more significant. Geographers make observations, carry out surveys, take photographs and draw sketches. They analyse, graph and tabulate data, and make reports.

What’s my approach? In your classroom your approach has to be spatial. You need to use maps and models as storytelling media.

What does success, look like, feel like, or sound like? . Geography is about creating objects of learning . Your students will be engaged in discussion, and telling each other ‘stories’ as they interpret the map and the model, and . Geography is a subject that can be embedded in IT both for learning and for creating products

From real life Describing and naming physical landforms is a standard lesson in the primary syllabus and could be done quite simply as a PowerPoint with captioned images showing examples of crests, escarpments, valleys, plains etc. It relates to geomorphology. However it is


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possible to do this is a far more interesting way. First of all, this work probably should be done outside. You need a large table, some plastic sheeting and sand, quite a lot of sand. Oh and wooden paddle-‐pop sticks and sticky labels. Next, protect the table top with the plastic sheet and pile on the sand (we took this from our long-‐jump pit). Divide the table into areas and allow your students to play. Tell them they are making a landscape. Then get them to clean up and go and Google landforms (images are good) and when they see a landform image that matches what they have created on the sand table then they are to label that place using the sticky labels and paddle pop sticks. As you can imagine there is a lot of toing and froing between computer and model unless you have Wi-‐Fi and laptops. If working with younger students it might be worthwhile if useful websites could be identified in advance. After this, as a group, affirm the labelling of each ‘feature’ and identify unlabelled features. At some point, some students may notice a particular feature is not represented and want to create it on the sand-‐board.


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In subsequent sessions students can ‘make’ particular features. A nice tweak to the particular features lesson, although a bit messy, is to introduce ‘rain’ and see where the water goes (you may want to induce a tilt in the table top). How in some places it disappears quickly off the edge of the table whereas in others the water tends to pool and only slowly find its way off the table. Like I said, it’s messy. The test of knowledge involves you creating a landscape on the sand table and then inviting each child to individually label the features they know and tell you a story about them.


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CONCLUSION TO THINKING SYSTEMATICALLY Thinking systematically is all about the big picture. Yes, events can and do happen which may affect us personally but more often than not we are but a small part of a much larger context. The four subjects making up this way of thinking, civics & citizenship, economics, environmental education, and geography really hang together and complement each other. They could be easily integrated into thick question topics requiring an interdisciplinary response. It’s so not surprising really as in some educational jurisdictions these topics would be called social studies. What might be surprising to you is that History has not been included in this section and for a time, in the draft, it was. Then, because it is not about thinking systematically, I moved it. Historical methodologies have much in common with learning English and I placed it in the ‘thinking with language’ section. Looking at the examples I provided we could have situated our space colony onto the sand table and over time tried to develop sustainable approaches to self-‐sufficiency. As the colony developed the expectations of the


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citizenry could have been established as well as a legal code. Different forms of governance could have been examined and compared to our current, Australian government. Finally, we could have made decisions about how our economy would work.


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SECTION THREE – SITUATED THINKING I have taken the term, situated thinking, to mean learning aimed at lifting the capacity for individuals to survive and thrive in the real world without outside assistance. It’s about getting your students ready for their life as a citizen. Subjects like financial literacy, health and PE, and home economics, find their way into this way of thinking. Situated thinking requires children to be active rather than passive. Situated thinking environments will: . Provide an authentic context that reflects the way the knowledge will be used in real-‐life . Provide authentic activities . Provide access to expert performances and the modelling of processes . Provide multiple roles and perspectives . Support collaborative construction of knowledge . Provide coaching and scaffolding at critical times . Promote reflection to enable abstractions to be formed


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. Promote articulation to enable tacit knowledge to be made explicit, and . Provide for integrated assessment of learning within the tasks


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Chapter 9 – Financial Literacy Teacher

What is financial literacy? To be financially literate is to be able to take charge of your own monetary affairs. To be able to manage your income and spending on a week to week basis and plan for the future, including retirement. To make informed decisions about accessing credit and repaying the same. To be financially literate is to understand the effects of different kinds of interest on savings and loan repayments, and the risks attributed to different forms of investment.

Where can it lead? Unlike the other subjects this does not lead to identifiable jobs per se’ rather, it is about the student becoming an informed and financially savvy citizen. Notwithstanding the previous statement, some students may develop an interest in business, consumer affairs, financial counselling, or planning, marketing, or managing their own investment portfolio. It is expected that every student will be, if s/he is not already, a customer or consumer: . (A customer) A purchaser of goods


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. (A consumer) An ultimate user of goods . (A loyal customer) a returning customer . (A discount customer) a customer who makes decisions based on the size of the markdown . (An impulse customer) a customer who buys on a whim, and . (A needs-‐based customer) a customer with a specific intention to buy a particular type of item

Where am I taking the students? There is an imperative behind financial literacy that if young people have a better understanding of this kind of thinking then their own quality of life and that of the community will be enhanced. It would be a unique individual who was not impacted by economics and business-‐related issues. Many of your students will work for businesses, will make purchases from businesses, and possibly be a seller of products and services to businesses or individuals. In fact, your students are already consumers and later, as adults, they will vote, pay taxes and function in an economic environment. In some respects this teaching area is as big as literacy and numeracy.


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Business-‐people are thinking about the market, the relationship with the customers, the workforce, and the suppliers. They are concerned about production, distribution and consumption. They have an eye on the bottom line managing costs and maximising profits. They research the market, set targets, make plans and take risks. Business is about enterprises making and losing money. For the consumer it’s about perceived value and quality of life, it’s about doing research and making decisions, then planning for the future, and living in the here and now. It’s about predicting the future with a change of government or government policy. For consumers it’s about earning enough income and paying your bills.

What’s my approach? Financial literacy are divided into three main categories: . Increasing consumer and financial literacy – this is about individual responsibility for personal assets and purchases, and how these can affect quality of life . The nature of work and its future – this topic introduces students to work skills and attitudes required to thrive in today’s


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workplace, and examines the nature of work and the rights and responsibilities of employers and employees, and . The business environment – this is about how businesses are structured, operate and solve their problems In all cases you can start with determining what the students think they know. One way I do this is to make them do a benchmark test before and after the unit. The benchmark is in the form of a diagram or list or drawing. A benchmark at the end provides a great before and after measure of learning. I like identifying the ‘big questions’ that the class might have about a particular subject and a little time spent identifying these (I use an enquiry-‐based learning approach) can, with a little guidance from you, often send the class in a particular learning direction. Solving problems is a very good way to approach this topic. You may have to adjust your expectations based upon the make up of your class. Business teachers tell me that pop quizzes can be a useful way to reinforce key ideas and knowledge.


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What does success, look like, feel like, or sound like? In your financial literacy class your students will be noisy because they are each consumers already, and there are plenty of ‘light-‐bulb’ moments in this subject. The students will argue with you and each other about what’s going on and why. Busy because they will be reading and interpreting graphical information and making decisions. Your students will be solving problems and making decisions. Interacting with each other as they collaborate, cooperate and compete. Earning and losing money or credit is how the world, keeps score.

From real life If you are a substitute teacher and your school allows you some flexibility about what you might teach then Bob Voerghertz’s, ‘Earn and Learn’, is worthwhile doing. In fact it’s worth doing with your regular class. At our school we have basically just one person we use as our substitute teacher. In fact we could expect her to attend our school at least four times a term at different times. In light of this I asked her if she would take on


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the senior class (about 13 kids at the time) for an, ‘Earn and Learn’ unit lasting the entire year. She agreed and from then on, the first two hours of her day in my school was this organised chaos where my students invented businesses, sold products, banked money, paid bills, and eventually taxes. The children brought artefacts representing their business to school and it was a challenge to store it some times. Needless to say, the children were happy to know I was going to be away from school and two hours seemed barely enough. It was very successful and very situated.


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Chapter 10 – Health and Physical Education Teacher

What is health and physical education (H&PE)? H&PE is concerned with learning skills, knowledge and behaviours to maintain a healthy lifestyle. A healthy lifestyle is one where physical, mental, emotional and social wellbeing is maintained.

Where can it lead? . (Active recreation) This is about being active without being part of an organised sport . (Amateur sport) This is about continuing to play organised sport either as an individual or as part of a team throughout your adult life . (Healthy choices) This is your student using situated thinking to assess risk around activity and diet . (Professional sport) This is about being paid for your skill, talent and dedication in a, and to a, particular sport, game, or exercise or activity . (Health professional) The health professional includes nursing and other ancillary health workers, and


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. (Sports professional) include coaches, psychologists, teachers, therapist, trainers and scientists being paid for their knowledge, skill and training

Where am I taking the students? You want the students to develop their gross motor skills, physical fitness and tactical awareness to a point where they are able to safely participate in games, sports, and outdoor recreation. You want your students to develop the knowledge and pre-‐disposition for engaging in a healthy lifestyle for themself, their family, their peers and the wider community. Your students will understand the significant phases of the human lifecycle particularly puberty and sexuality, and those factors that shape their personal identity.

What’s my approach? With respect to physical education you can teach in a variety of ways: . Skill and drill . Game sense


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If teaching via a skill and drill approach you will break down the activity into its component parts, teach each skill, have the students' practise the skill, and then put the parts back together to engage in the whole activity. Game sense approaches the activity in a more holistic manner. Your students engage in the whole activity, possibly with modified rules, with stops along the way to identify problems and solutions. Guided questioning helps the students to improve the quality of play while specific skills are taught when required. As skills improve modified rules are adjusted to reflect the standard rules of the game. Healthy living and human lifespan components should be situated in the children’s own lives and the actions they take now and those they anticipate for the future.

What does success, look like, feel like, or sound like? . With regard to activity all children are involved and feel the game is fair, and . Situated thinking about is about having the children relating what is taught to the child’s own life.


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From real life At my school we have developed a handball game played by two teams, on a court with a goal at either end. One team wears a sash while the other does not. There are at least six players in reserve on the sideline. These players may substitute players on the field after they make a mistake or score a goal. In the course of the game a student may play for both teams. A partially deflated beach ball works very well as it may be caught and thrown one-‐handed (obviously bounce passing is not an option). I do all throw-‐ins, including starting the game, backwards, over my head. The rules are adjustable and include the number of steps allowed with the ball (three is good), where you cannot shoot from, what is out of bounds, what players must touch the ball before scoring (younger students), what happens if the ball is intercepted. Any rule transgression means a substitution. The game may be stopped for a rule change. Rules may be made for individual students. For example the very sporty kid who hogs the ball may have to wait for the ball to be touched by two other players before s/he gets it again.


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The game can be stopped for skill transference. Skills taught can be passing, catching, marking, intercepting, shooting, and moving into space.


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Chapter 11 – Home Economics Teacher

What are home economics? Home economics are about teaching students life skills in food, nutrition, family, health and human development. Home economics is an action-‐based subject that encourages behaviours that lead to enhanced wellbeing for the individual, their families, and the wider community. It is a subject that encourages situated thinking, independence and interdependence. At the time of writing, home economics is a contested curriculum subject in Australia where, in some jurisdictions, it comes under health and physical education while in others, design and technology. The professional body, Home Economics Institute Australia argues that it deserves to be a stand-‐alone subject area in its own right.

Where can it lead? It leads into the daily lives of your students.

Where am I taking the students? Home economics are clearly trans-‐disciplinary in its pedagogy and firmly rooted in the real-‐world life of students. With this subject you will empower your students to take charge of


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their own social future and the well being of themselves and others.

What’s my approach? . Identify healthy and unhealthy foods . Investigate eating speed . What makes a good mealtime? . Let’s go shopping . Good snacks are? . Investigate the advantage of water with meals . The best lunch box has? . Watch out, fast food, and . How much is enough?

What does success, look like, feel like, or sound like? . Home economics is integrated into other subject areas like science, mathematics, financial literacy, interpersonal learning. . It is flexibly delivered catering to student needs and the needs of your school


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. Your teaching should be heavily biased towards hands-‐on practical experiences . There are volunteers to help you and the students, and . It should be fun

From real life In order to show the link between what is purchased at the supermarket and to encourage the students to try different foods. The infant class embarked on a vegetable garden project where, using raised beds, and permaculture methods, the children grew a variety of vegetables with the aim of using these to prepare meals. As the vegetables were harvested at different times this allowed for the opportunity to make meals featuring that particular vegetable. Situated in real life the unit enabled the students to think about food and what was served at their place. It also encouraged students to explore different foods and introduced them to the idea of fresh and processed foods.


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CONCLUSION TO SITUATED THINKING In Victoria, Australia, where I teach there is a mandated amount of time for children to be involved in physical activity and that has to be delivered separately. Frankly, any ‘competent adult’ could take on situated thinking; in fact, many parents might be worthwhile taking on as guest speakers or as workshop facilitator. If you don’t want to go quite that far then the para-‐professionals at your school might serve.


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SECTION FOUR – THINKING AESTHETICALLY Aesthetic awareness can be easily confused with just fine arts. Everyday aesthetic awareness is about appreciating an object, person, place, experience or way of thinking. But this appreciation does not always extend to the finer qualities. For the purposes of this book only dramatic and visual arts, and information technology and technology are included in this section, but other subjects can also generate aesthetic moments like a work of literature, a mathematical proof, an experiment in science, or a natural phenomenon.


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Chapter 12 – Dramatic Art Teacher

What is dramatic art? Drama can be used to explore and explain many other subjects in the national curriculum, and it can also be studied and experienced in its own right. It is an ancient form of expressions that is still used today. Drama becomes theatre when it is performed in front of an audience.

Where can it lead? Very few of your students will end up as professional actors but working in an amateur theatre company may be an outlet for some. All of your students will probably become consumers of drama as paying members of a theatre audience or a purchaser or renter of DVDs. Some careers require an individual to act out a role either all the time or part of the time. It’s a way to keep one’s life in balance. The way I act around my friends is different to how I act around school stakeholders, and my staff sees a different person to what a parent sees. I am acting out a role.

Where am I taking the students? Drama is a subject that leads students to interact with one another like almost no other subject. Unless they are performing a one-‐


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person show then they have to work together and solve problems, lots of problems. The process of choosing a script or writing a script and then editing it is based in aesthetic thinking, rehearsal is an aesthetic process, the performance is about providing an audience with an aesthetic moment.

What’s my approach? There are two sides to art forms: . Creating and making art, and . Exploring and responding to art Your approach has to be hands-‐on, interactive, and develop the aesthetic capacity and capability of your students.

What does success, look like, feel like, or sound like? . Make sure you identify the boundaries and provide a little structure as far how you are going to get them back . Stand back because it will probably be noisy, and . You’ll be roving


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From real life I have had kids act out a play we wrote together in English – It was called, “The Dumb Ray Gun.” Sometimes the script led the acting and other times the acting led the script. It was fun and we performed it at the school concert. I have used commercial scripts of variable quality that means different levels of problem solving are required. Long rehearsals can be difficult. Short skits are good especially when the children can alter them to make them work. Last year my whole school, all 18 kids, ended up in one skit called, “Pebbles.” It was meant to be for about five children – one played a teacher and one child was Pebbles. The other kids arrived; one-‐by-‐one, late for class with the excuse they were throwing pebbles in the pond. When the last kid arrived the child playing the teacher was ballistic screaming I suppose you were throwing pebbles in the pond. “No Miss,” the boy replied. “I am Pebbles!” In the end, all 18 kids in the school wanted into this skit and worked it out so that is precisely what happened. And Pebbles, when he arrived on stage, he was drenched.


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Chapter 13 – Technology Teacher

What is technology? A technology teacher may have a background in woodwork, metalwork, textiles, and/or food. Technology is an experiential and practical subject whereby students translate ideas into meaningful products and systems of work.

Where can it lead? It can lead into a trade or occupation that requires the use of the hands and the brain. Tradespeople bring a known suite of solutions to a well-‐understood range of problems. This is why evaluating both the process and the product is important. Processes have to be effective and safe, and products need to be fit for purpose.

Where am I taking the students? There are many occasions in a student’s life where they make things but it is mostly an iterative or instinctive thing. An object made in the technology subject is intentional. There is a design brief, a description of the object in text and non-‐text forms, and then there is the production process itself where the steps to be followed are identified and then followed. Next is a rigorous analysis of the object and


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evaluation of the process and identifying where improvements could be made.

What’s my approach? Objects must be intentionally designed and then deliberately produced so that the end product matches the initial design. Unlike art there is an expectation that the production process will be mapped out ahead of time and that this process will be evaluated, along with the made object, at the end of the production phase.

What does success, look like, feel like, or sound like? . It’s noisy, bustling and extremely engaging . There is head scratching as problems are encountered and mini conferences as the solutions are shared, and . The work environment is a safe one and the processes taught and followed are safe

From real life My class entered the Engquest challenge a couple of years ago and designed, built, and analysed lifting machines constructed from pvc pipe, pipe fittings, line, pulley blocks and other miscellaneous materials. The machines had to raise 2kg 0.5m in the air. PVC pipe was


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selected because the class had experience using drinking straws and pins in the past. The first step was to design their machine and then, based on the design, the components would be ordered, but not before they were costed. Designs deemed too expensive by the class were revised and designs unlikely to make the transformation into products at all were rejected while others needing work were given time for this to happen. The components were purchased through hardware and irrigation piping suppliers. The children were given exactly what they had ordered no more no less and then production began. It was expected that the machine would meet the criteria of lifting 2kg, 0.5m into the air, and that the product would closely resemble the design. In the course of making the machines the students solved many problems and dealt with a variety of unintended consequences. Evaluating the products was straightforward and many students would revise their approach if given the opportunity. The best design was simple and elegant and performed to specifications. It looked just like the drawing and was slightly less than average in cost. The most expensive design was over-‐


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built and could have lifted 5x the weight it needed to.


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Chapter 14 – Information and Technology Teacher

What is information and technology (IT)? IT has inveigled its way into all aspects of our society, at work, at home and at school. It frames how we think, how we socialise, and how we learn and demonstrate what we know. Your students need to be able to function effectively and efficiently in this environment. IT is an inter-‐disciplinary subject concerned with using digital tools, to find, manage and create information and digital artefacts. The concept, process and products around IT can be judged on aesthetic grounds. This book was first created on a word processor, information was sought on-‐line, and when finished it was uploaded to a website to create an eBook. My approach to the book has encompassed both forward planning and iterative processes where the book has been continually reviewed and revised until I feel good about what I have to share with others. IT can create a wide range of products and support various kinds of learning environments. Some IT is quite generic like those applications found in a Microsoft-‐based


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computer while others are quite specialised, but even the most generic of programs are attaining extremely high levels of sophistication. IT can be taught as a stand-‐alone topic or as a part of other authentic learning.

Where can it lead? IT can lead to specialised employment but the reason we have placed this topic in with situated thinking is that to learn IT you have to do IT yourself. IT can: . Visualise your thinking . Make products, and . Communicate with others

Where am I taking the students? I would like to share what an IT savvy principal once said to me about the difference between iPads and laptops. He said iPads are for practise and laptops are for creating. If this is true then the technology you have will affect where you are taking your students. In fact, unless you have specialised knowledge it might be more appropriate to ask where are the students taking you?


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What’s my approach? It depends on whether IT is being taught as a stand-‐alone. That is, here is an application, learning environment, or digital product, let me show you how it works step-‐by-‐step. Obviously for this approach you will need to be quite knowledgeable. If IT is being taught ‘en passant’ then it may be a matter of going far enough that the students can then explore alone or in groups. Your knowledge needs to be better than that of a naive user but not necessarily expert. Sometimes the fall back position for novice IT teachers is like a coach approach where the students, ‘play with the application’, and you note where the skill or knowledge shortfalls are and teach accordingly. Rather than filling in these deficits yourself, you will make use of the expertise of the students themselves. I have never yet failed to find students who ‘get IT’. Access can be an issue and while 1:1 student to computer ratios might be considered ideal, pairing kids up with a single machine can encourage lots of interaction with each other and the IT.


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What does success, look like, feel like, or sound like? . Sometimes it’s noisy, the kids will share information and ideas out loud . Sometimes it’s quiet – they’re concentrating . Because it’s so easy the steps of drafting, editing, publishing become blurred. Making IT products is an iterative process . IT learning environments offer students the opportunity of marching to the beat of their own drum rather than being in lock-‐step with everyone else . The students will probably learn more from each other than from you. Allow time and space for that to happen, and . Students can be caught up in the how and forget about the what, and the when. Time limits are important.

From real life In a DC&T (design, construction and technology) lesson the kids were designing a lifting machine and one asked if they could do it on computer rather than on paper. “What do you mean?” I asked.


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“Can we use Google Sketchup?” he asked. “What’s that?” “It’s a program on our computers. It’s part of the school stuff. It’s really good,” he replied. I had no idea but a couple of other kids made encouraging noises. “OK, give me a look. You other guys keep going with your drawing.” A couple of minutes passed. All the kids had their own laptops. “Here you go,” said the boy. Who then demonstrated what it could do. “That’s amazing.” I said. I quickly decided that all the kids should have a look and the pencils, paper and erasers were abandoned. I used the fallback approach described above and let the kids just play with it. In our next session I asked them to get serious about designing our project. It wasn’t easy and many students returned to pencil and paper.


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Chapter 15 – Visual Art Teacher

What is visual art? Visual arts are an umbrella term encompassing a range of sub-‐disciplines each with their own particular conventions, processes, skills, techniques, knowledge and understandings. Art has a history and art works have been used in many cultures to represent a moment in history, in human thought, or a value.

Where can it lead? At one time painting and to a lesser extent sculpture were the only disciplines in visual-‐arts, collectively called fine arts, and everything else was considered a craft. Taken together, there are many visual art genre including: . (Ceramics) includes pottery but also extends to glass, bricks, tiles, porcelain and heat resistant materials. Ceramics are inorganic and made by heating and cooling . (Crafts) a craft is literally any artistic object that is made with skill by hand . (Design) to design is to plan and make decisions about (something that is being built or created) usually in a non-‐text format


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. (Digital media) digital media is the creative convergence of digital arts, science, technology and business for human expression, communication, social interaction and education . (Drawing) is one of the simplest and most efficient means of communicating visual ideas. The wide availability of drawing instruments and appropriate surfaces makes drawing more common than other media . (Film-‐making) this is an art form highly reliant on technology. Filmmaking as an art is different to ‘regular’ film making in respect to the intent. Film as art is by the artist for the artist whereas regular filmmaking has a commercial intent. Nonetheless both intents use similar techniques. . (Graphics) these are visual presentations on a surface, such as a wall, canvas, computer screen, paper or stone. They are usually made to brand, inform, for commercial design or to illustrate . (Painting) is the practice of applying paint, pigment, colour or other medium to a surface (support base) using a variety of implements


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. (Photography) is the act of composing and capturing a still image either on film or digital media, and processing that picture . (Print-‐making) is a term applied to a very broad range of techniques which have in common that ink is applied to a surface, usually paper via, and . (Sculpting) to make or represent (a form) by carving, casting, or other shaping techniques

Where am I taking the students? Visual art is experiential and experimental and is a deliberate communication of thoughts, feelings and concepts to an audience using a range of media, materials, equipment and technologies. You want your students to develop efficacy as producers and to develop their appreciation of visual art forms. You want the students to develop the language of art and to think like an artist. According to an Australia Council study there are between 8,500-‐10,000 individuals in Australia who describe themselves as professional visual artists (note this survey did not include designers). The same study indicated that for the majority of artists (of any kind) their art does not provide enough income to support them and so many are part time. The report went on to say that most


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professional artists are older than the rest of the workforce, reflecting that commercial success takes time, and that professional artists keep working longer. So the chances of a student having a sustainable career as a professional visual artist are vanishingly small. However, the opportunities for individuals to see and appreciate art, especially in metropolitan areas, are much more likely. All is not lost however, there are careers for which the visual arts has a place, like these: . In media and commercial arts . In arts management . In art-‐based trades (there are many) . In design, and . In art teaching and therapies In these careers individuals start out with some natural talent and ability but have augmented these with further education and training. One final point before moving on is that we should not overlook the potential benefits of an individual maintaining an


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amateur’s interests in creating and appreciating art throughout their lifetime.

What’s my approach? Some sub-‐disciplines can only be tackled in a studio type environment whereas others could be a reasonable proposition for a general use classroom. Art can be taught and learnt as a stand-‐alone topic or in combination with other subject areas. Distinct sub-‐disciplines are more likely to be taught in middle to upper secondary school. National curriculum writers suggest some art forms will need brief but frequent visits whereas others will require more intense immersion albeit less frequently. It is interesting that the same writers do not suggest how the visual arts should be taught only what. Realistically, as a non-‐specialist teacher, your time as a visual arts teacher might be better spent developing your student’s appreciation for the arts and the practical work undertaken by your students might be better focussed on the commercial aspects of visual art.

What does success, look like, feel like, or sound like? With regard to making visual art objects the work is more instinctive than the process followed in technology and the steps are not always mapped out.


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. You should encourage your student to keep a portfolio of their work and digital images are good for this . The students should maintain a studio diary showing planning, reflections, and future intentions

From real life I’m going to let you into a little secret, one of the reasons I wrote this book is that I don’t get art. I can follow a technology process but the iterative, instinctive art approach is simply too loose for me. Having said that I do like the communication possibilities of cartooning which can encompass a broad range of skills in the students. I think learning to draw can teach perspective and proportion and I have organised a series of lessons to practice this. In both cases I did not set myself up as an expert but rather as a fellow student.


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CONCLUSION TO THINKING AESTHETICALLY Thinking aesthetically is about appreciation. Appreciation of the final product, the process of making that final product, and the thinking that went into the idea for that product. Of course this appreciation may be positive or negative and there is nothing amiss about that but what is important is being able to verbalise this appreciation. The arts make products, as does technology, the difference between the two is the planning that goes into the process. Art is considered a more iterative process while technology relies upon forward planning. However, it is not difficult to comprehend that complex art installations and productions need some elements of forward thinking to be brought to a successful conclusion. At the same time more skilled and knowledgeable technicians create products and processes while thinking on their feet or through some trial and error process; an iterative process. IT fits between these two approaches. I think art, IT and technology have a lot in common especially from an aesthetic point of view.


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SECTION FOUR – THINKING WITH LANGUAGE The acquisition of language is arguably the most critical skill a student can take on. Reading is a fundamental part of primary school teaching and reading ability explains 40% of test score variability. High achieving students read three times as much as low achieving students. Here’s something to think about. To finish in the top 2, 10 and 30% of readers, individual students need to read for 67, 33, and 17 minutes a day respectively. The other side of the coin to reading is writing. Long complex texts require organisation and structure and with skill, knowledge and technique we can inform and entertain others and, more importantly, frame our own thinking. In this section thinking with language I have combined English with LOTE (languages other than English), ESL (English as a second language), and history. That’s right, history. I feel I should justify my decision. First of all, I am trying to simplify the delivery of an overcrowded curriculum and combining history with English helps to do that. It is a relatively simple combination given that historical approaches to thinking can be so easily applied to English and so many skills


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and conventions in English can be used to express one’s understanding of history. LOTE and ESL are in some ways two sides of the same coin. For LOTE, English speakers are learning a foreign language and in ESL foreign language speakers are learning English. In LOTE the learning will usually be taught as a stand-‐alone whereas for the ESL student the learning of English happens, hopefully, all the time. Learning a foreign language has very real cognitive benefits for the students.


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Chapter 16 – English Teacher

What is English? Australian Standard English is the language by which Australian society regulates its activity, communicates within and without itself, and how individuals formulate ideas and intentions and explain feelings and emotions.

Where can it lead? There are professions where mastery of English is paramount like advertising copywriter, author, editor, journalist, playwright, poet, proofreader, public relations, speechwriter, teacher, and technical writer, but for most of us we just need to be functionally literate enough for our work and our lifestyle.

Where am I taking the students? You want your students to: “Learn to listen to, read, view, speak, write, create and reflect on increasingly complex and sophisticated spoken, written and multimodal texts across a growing range of contexts with accuracy, fluency, purpose, [appreciation and enjoyment]. (Victorian Curriculum and Assessment Authority)


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What’s my approach? Unlike many other subjects taught in schools, there are no light bulb concepts to understand in English, but there are plenty of conventions, rules and skills to master. In my opinion relentless practice is the only way to learn English. You must teach skills and knowledge in different ways. Don’t just rely on a single teaching approach. Work very hard to integrate what you do with the wider curriculum. Don’t forget that English is subject to high-‐stakes testing – of teachers. Don’t make national test preparation separate; integrate it into your on-‐going curriculum. Look for the links between your own lessons, units of work, other subjects, other classes, different grades, and the wider community. Make these obvious to your students and encourage them to look for these links too. Show your students those strategies for thinking about, and doing their work, so they can adopt these to more novel learning situations.


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Maintain high expectations of your students. Don’t just stop when a ‘desired’ response is given. More successful English students can tease out all the issues, appreciate different points of view, and extend their understanding of text beyond the superficial. Set up learning situations where your students can collaborate and work together creating problems and solving them. Encourage the kids to learn from and be challenged by each other. Demonstrate how to do this. You should have a single learning intention for the class but the success criteria for your students will be adjusted. Stretching and shrinking a learning task is one way to deliver teaching to a diverse range of learners. Busy work, like crosswords and spelling, can be used to allow for different finishing times.

What does success, look like, feel like, or sound like? There will be times when you are modelling a reading, writing, speaking & listening skill to your students. This is when you do all the work and they watch. Don’t go too long with this – the kids can get bored. A step after modelling is guiding and sometimes I morph the two. Guiding means you do all the work and the class helps. Make


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sure everyone is getting an opportunity to help. Sometimes having the kids discuss their ideas in groups before having a spokesperson share the consensus view (or not) with the rest of the class can ensure all voices get heard. Next comes sharing. This is arguably my favourite part because the kids do the work while I coach from the sidelines so to speak. I like the kids to work in very small collaborative groups which are either randomly chosen, or I have been more tactical in my choices. Coaching can be for the individual, group or class. Independent practice is where the class tackles the task without your support. This is the rare occasion where the class is relatively quiet. It’s not a test but it can provide the evidence on what needs to be taught next.

From real life Your students have different capacities for learning different material. The students who learn fastest, are learning from whole class and group teaching, are learning from overhearing and observing what you are teaching others, and when you teach them specifically. The worst learners learn from none of these scenarios but the majority of learners fall somewhere in the middle.


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I prefer random groups where different students have opportunities to be a leader or a follower depending on the make-‐up of the group.


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Chapter 17 – English as a Second Language Teacher

What is English as a second language? This is a subject area populated with acronyms: . EAL – English as an additional language is applied to students . ESL – English as a second language. This is applied to qualified teachers . LBOTE -‐ language background other than English. This is terms is applied to students and families, and . MEA -‐ multicultural educational assistants. This is applied to classroom aides ESL teachers are specially trained to work with LBOTE students and funding is available to schools with a significant population of EAL students. Some 25% of students in Victorian government schools are LBOTE and for the majority, an ESL teacher is a specialist with whom they have a relatively small amount of contact. By far the majority of the student’s time will be spent in a mainstream classroom. It is those non-‐specialists teachers that this chapter is about.


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Where can it lead? . Teaching spoken English . Teaching reading and writing in English . Teaching other subjects in English, and . Multicultural perspectives and cross-‐cultural understanding

Where am I taking the students? Your EAL students will be learning English at the same time as learning your subject. They are working significantly harder than the English-‐speaking natives in your class. Where you are taking them depends, to a large extent, on where they start from, EAL students: · May begin school at any year level · May have been born in Australia or overseas · May have little, some or no exposure to English prior to their arrival in this country · May have been to school in another country for the same time as their chronological peers · May have had little or no previous formal schooling in any country, or


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. May have had severely interrupted education in their first language. I read, while researching this chapter, that it can take students up to seven year to acquire enough English to be proficient in social and academic situations. You will be in for the long haul.

What’s my approach? Your approach will be predicted, to a large extent, by your own exposure to multicultural diversity. The greater it is the more positive you will be about EAL students in your own classroom. Notwithstanding your own point of view it is very likely that the government school you work for will expect you to teach EAL kids. Any teacher working for schools in receipt of government funding can anticipate a whole-‐school approach with documented curriculum, policy and targeted plans. Those teachers need to make themselves aware of their school’s approach and documentation. In a funded school it is expected that [a] member[s] of staff will be ESL qualified and will coordinate EAL student learning and support mainstream teachers with planning and curriculum delivery. Subject teachers need to allow extra-‐time to work with the ESL specialist.


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It is probable that MEA staff will be deployed in classrooms or with students. MEA’s will communicate with students in the student’s first language and will need time to do that during class time. They act as a conduit between the school, the family and the wider community. MEAs are a source of information about the cultural aspects of the life of EAL students. Most MEAs are employed part-‐time. Due to the dynamic nature of the EAL student cohort changes to individual and group learning programs will happen. Because of the special funding it is likely that data about student outcomes will be collected and analysed. So how do your EAL students acquire proficiency in English from you? . You will present them with integrated and meaningful reading, writing, listening, speaking, and thinking opportunities . You will provide opportunities for your students to think out loud and listen to others in group situations . You will model and scaffold language acquisition opportunities for your EAL students, and


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. You will encourage your students to use the skills and strategies they have learnt in their first language

What does success, look like, feel like, or sound like? My research of this area suggests schools have an eclectic response to ESL delivery. It is very much contingency based. There will be greater emphasis on talking than usual and you will need to model appropriate ways of having a discussion in your subject area, and to police these. You should expect your EAL students to listen more than they talk at first. You should expect the introduction of unanticipated cultural perspectives. Seek these out and embrace them. You will focus on content rather than spelling and grammar when looking at EAL student writing. Bi-‐lingual glossaries will become a feature of your teaching. You should permit the first language to be used when initially engaging EAL students in new concepts, ideas and skills, will assist the learning of the ideas. While being more insistent on revision and testing to be done as


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much as possible in English, this will make the learning of English more authentic. Your EAL students will need more time to complete work but you won’t ‘dumb’ the work down. Your expectations will be adjusted to suit individual students.

From real life I have never had an EAL student but my daughter, Kate; a secondary school teacher has had plenty. This is her advice: We have MEAa at our school but I have never had them in my class and so I make sure I use the kids themselves to help. We do have an EAL coordinator but I have not had a lot to do with her; She is a leading teacher. I mainly teach business and humanities to the middle years, although I have had a VCE business class too. To be effective I rely on dialogue and discussion and make sure I come at the topic in a variety of ways. Afterwards you have to get one-‐on-‐one with the ESL kids to make sure they understand things. They come from such a variety of backgrounds that you can’t stereotype and assume one way will be good enough.


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ESL kids need more time to get stuff done and I cut them some slack with respect to spelling, punctuation and grammar.


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Chapter 18 – Foreign Language Teacher

What is foreign language? For native English speakers it’s any other language including sign language (AusLan). It is reasonable to say that, at the time of writing, 2014, LOTE (languages other than English) is a politically popular subject and Australian schools are under pressure to deliver LOTE to their students. At the same time finding appropriately qualified teachers can be problematic, a situation exacerbated by the extremely high language proficiency required by some states. I think it is quite probable non-‐specialists will teach this subject.

Where can it lead? There are two places it can take you: . A facility with another language, and . An understanding of another culture

Where am I taking the students? You are looking to challenge and enrich the overall learning experience of your students. The acquisition of two or more languages strengthens will lift the overall literacy of your students and interestingly, prove beneficial to learning mathematics. You are empowering


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your students as active agents in an increasingly globalised world, and let’s not forget the culturally diverse nature of school populations.

What’s my approach? Your approach will depend on your level of affinity with the language you’re teaching. Your approach as a non-‐speaker may be to focus only on the cultural aspects of the language and the society it is based in. In other words handling it like civics and citizenship or history but of another place or people. The smallest amount risk for the non-‐speaker as far as facilitating language acquisition might be for you to approach the language as a fellow-‐learner, learning alongside your students as you, and they, engage with on-‐line content. An alternative to this, or a way of augmenting it, might be to work with an unqualified native speaker, like an MEA (multicultural education aide), or a member of the wider community. You would drive the teaching and they would provide the practice. As a person with some affinity for the language you may literally have to stay one step ahead of the class with respect to language acquisition and deliver on a culturally rich learning experience.


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If you speak the language at a high level, or at least, much higher than your students, then, as a generalist, you could combine subject areas like health with the language.

What does success, look like, feel like, or sound like? . If the classroom you are working in is your own, or allocated primarily to LOTE teaching, then it may be populated with various resources and culturally-‐appropriate images, objects and icons. . Students will be working with each other and learning technology . At times the class will represent a drama class as students act out scenarios . On occasion the class may look like an art class as students create representations of cultural objects . Bi-‐lingual lists may be used, and . The class will be noisy because you and your students will be conversing

From real life I have never attempted or been asked to teach a foreign language, however I have asked one of my staff to do it. Melissa learnt French at


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high school and passed it as a VCE subject. She had more than enough French to work with primary school children approaching the language for the first time. For a little bit of novelty Melissa combined the learning of French with an integrated health and civics project about, ‘My body, my family and my community, and the food we eat.’ It was a similar approach to what we suggested for LBOTE students in the previous chapter. Melissa has been teaching the unit to the whole school (15 students) and it has been extraordinarily successful, to the point where French language signage can be found around the school, reminding children of things like flushing the toilet and washing hands.


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Chapter 19 – History Teacher

What is history? History is the study of the past based upon evidence and any interpretation is to be supported by the evidence. History, like science, is subject to revision. As well as the facts of history, it is also a way of knowing, like science. History in Australia is a subject that politicians like to manipulate. However, the new curriculum was written and re-‐written by many contributors and the idea that it is skewed one way, or another, isn’t supported (see links).

Where can it lead? . (Archivist) Archivists work in a wide variety of places managing documents and records. They can be found in governments, manuscripts libraries, corporations, religious bodies, universities, schools, museums, professional and trade associations, and community organisations. Some may work as private consultants . (Museum historian (curating)) Museum historians collect objects relating to historical themes, which throw light on historical


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questions and help to interpret the past. As objects are collected, information about their provenance (history) and context (the set of assumptions, feelings and expectations surrounding their manufacture and use) is also collected. This information is used in the interpretation of the objects. In this research, a wide range of evidence, including documentary research, oral history interviews and photographic research, is used, and . (Professional historian) A professional historian is usually highly qualified and focussed on a particular person, time, period and place. Many professional historians work as lecturers in universities

Where am I taking the students? History is a way of understanding past events. You want your students to know: . That life in the past was different from the present . That people in the past may have had values, beliefs and customs different from their own . That there may have been several causes for a particular event . That there can be short and long term consequences from an event


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. How an individual, group or event can have varying significance to the history of a place . How to synthesise information from a range of sources to support an explanation or argument, and . How to recognise that there can be different interpretations of the same historical event. Under the new Australian curriculum history has two areas of study: . Historical content, and . Historical enquiry skills

What’s my approach? History is about making sense of the past and there are some key concepts to be mastered in order to do this: . Sources – these may be primary or secondary. Primary sources of evidence are eyewitness interviews, personal accounts written at the time, images, tools and artefacts. Secondary sources include film, books and documentaries made well after the fact . Evidence – is information gathered from a relevant source


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. Continuity and change – some aspects of human activity have changed over time whilst others have stayed pretty much the same . Cause and effect – it is a unique situation in history that a single cause results in a single effect. Usually the causes of an event are many and the effects of the event cascade through the pages of history. Some of these are intended while others are not . Perspectives – whose story are we telling and who is telling the story affects how a historical event is seen. Gender, politics, socio-‐economic factors, and life experience influence personal perspectives . Empathy – in a historical sense is about seeing a situation from another point of view while taking into account the context and values of the times . Contestability – was the arrival of the first fleet in Sydney in 1788 an invasion or a settlement? Historians using the same sources and evidence could arrive at quite different conclusions about that question, and . Significance – attributing significance is about making a judgement. Were the impacts widespread and/or long reaching? Are the


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affects more significant now than they were at the time?

What does success, look like, feel like, or sound like? . The class will be using the jargon of history. Words like artefact, chronology, evidence and source . The students will be sequencing events into their chronological order . Your students will generate thick/fat questions . Your students will make judgements about the evidence and the source of that evidence . Your students will flexibly look at their questions from a variety of perspectives, and . Your students will be able to communicating and explain their understanding through a variety of means (written, digital, and artistic)

From real life This was not a lesson but a historical enquiry by an advanced grade 1 student. At our little rural school we run affinity projects for one term a year. This is where the students decide on a project to pursue for


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themselves. One particular year a student, Nadia (not her real name), decided to make a scrapbook of the history of the school (we are 85 years old). It was fascinating to watch her ‘go back’ in time. For evidence she had access to digital images, colour photos, black and white photos, a couple of history books about the school, one written in the 70’s. We had old handwritten meeting books from 1928 and people still around, who had been involved with the school for decades. The things this little girl found most interesting was the differences in the school revealed by different photographs. Over time the school changed from open fields to a built environment. As a very young student, Nadia was not in a position to judge cause and effect, but she was able to empathise with the student stories and images from the past and appreciate that while there were differences, there were similarities too. The history of your school is not a bad place to begin to learn how to conduct historical enquiry.


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CONCLUSION TO THINKING WITH LANGUAGE In the introduction to this book I did not put one way of thinking ahead of the others but it must be acknowledged that language frames our thinking. Our proficiency as readers, writers, speakers and listeners, is either a limiting or empowering factor in our ability to communicate in society. Illiteracy is correlated with: . Unemployment . Poverty . Ill-‐health . Superstition . Criminality, and . Inadequate parenting skills Seems to me that right there is a really good case for getting this right.


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SECTION FIVE – THINKING MATHEMATICALLY This section is divided into two chapters. The first is written and presented like the other chapters in the book. The second chapter in the section is about the common misconceptions in mathematics and it was written at an earlier time than the rest of the book. I have provided this additional information because many maths teachers in the primary and middle years of school do not have a major in mathematics. It can be skipped.


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Chapter 20 – Mathematics Teacher

What is mathematics? Mathematics along with English is one of the largest subjects in the Australian curriculum. Mathematics as a discipline is undergoing a bit of a crisis in Australia as too many senior students in secondary school and undergraduate students in university are either, not taking on mathematics, or taking on general maths rather than advanced courses, and as a consequence there are fewer specialist teachers to go around.

Where can it lead? Many professions, trades and occupation make use of mathematics. The list that follows requires at least a major in mathematics and often a whole lot more: . (Actuary) The application of mathematical techniques to the insurance industry . (Applied mathematics) is about using mathematics to solve problems in government, science and engineering . (Biomathematician) combines mathematics and biology and health sciences . (Biostatistics) combines biology and statistics


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. (Cryptologist) this is a field concerned with security, telecommunications, banking and satellite technology . (Financial mathematics) is a speciality concerned with the stock market, derivatives and mortgages. Many traders have mathematical qualifications . (Operations research) This is about using mathematics to optimise complex throughputs and support decision-‐making . (Research mathematician) This is mathematical research for its own sake . (Statistician) this is an area of mathematics with a broad range of application to a number of fields like medicine, economics, industry, marketing, and government. Statisticians produce trustworthy data, analyse it for its meaning, and make practical conclusions about it . (Physicist) mathematics and physics go together so often that it is unlikely that anyone could be a physicist without a significant background in mathematics


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I read on one of the links that the word ‘analyst’ tacked onto a job title is strongly suggestive of a career requiring mathematics.

Where am I taking the students? Like art, mathematics has conventions, processes, skills, techniques, knowledge and understandings, but all too often mathematics is presented to students without history, simply as a tool. Like art, mathematics has a beauty, and like art, where only a few professionals use more than the most elementary of skills to successfully pass through life (like balancing a cheque-‐book, counting change, measuring a room for carpet, understanding a newspaper article, determining a good buy or planning a home improvement project). Notwithstanding the reality of where most students go with mathematics, we force more and more complexity on our students making the claim that what they are learning is practical. For those students, not intending to be analysts, engineers or scientists, this is an absurd proposition. So we have what might be characterised as practical instrumental mathematics. This is mathematics that is adequate for general use in employment and for functionality as a citizen. And then there is specialised


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mathematics suited to analysis, science, technology and engineering, and the further study of mathematics itself. Apparently only 0.5% of Australian university graduates are mathematics majors, and only 40% of university graduates use mathematics professionally. Everyone uses practical instrumental mathematics. A further complication for practical instrumental mathematics is that it is based in real life and as such has a social element. Problems are not necessarily presented in a neat textbook fashion but rather more messily. There can be more than one answer. As a non-‐specialist I recommend you approach mathematics in an aesthetic way. Yes there are conventions, tools and formulas and processes to learn but mathematics is a form of art. The lives of its major thinkers can be examined and the significance of what they gave us acknowledged in your maths class. The solutions to a problem can be judged on its elegance, the process of arriving at the solution can be weighed, and finally the student can feel satisfaction from what they do. Areas of mathematics study in Australian schools include:


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. Number and algebra . Geometry and measurement, and . Statistics and probability One final point I would make about pre-‐disposition is this. When children are ‘doing’ art quite often the resilience and persistence to do a better job is there. If you are teaching maths in an absolutist sense then these qualities can go missing because there is only one way to do it and only the right answer is acceptable. As a generalist teaching mathematics I think you are best served by knowing where kids commonly get stuck at each level. They are: . Level 1 -‐ Trusting the count . Level 2 – Place-‐value . Level 3 – Multiplicative thinking . Level 4 – Partitioning . Level 5 – Proportional reasoning, and . Level 6 -‐ Generalising, equivalence, number properties and patterns, and the use of algebraic text.


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I discuss, in some detail, the common misconceptions in learning mathematics in the next chapter. A piece of advice I got from John, a middle school mathematics teacher, is making sure that the kids know their times tables. With rote-‐recall there is a huge reduction of the cognitive load. But rote recall does not imply rote learning.

What’s my approach? . Building conceptual understanding . Improving procedural fluency . Developing strategies for solving problems . Improving mathematical reasoning, and . Fostering a productive disposition In larger schools it is very likely you will have to follow a school-‐based scope and sequence document. Just how comfortable you are with this depends on your background in mathematics. The only time I like workbooks is when the student's share one and work on it together.


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But, and it’s a big but, I shuffle the pairs around so everyone gets more chances to lead. I also match workbooks to ability. There is no point in a grade 7 doing grade work if they are not up to it or, are far beyond it. I really like on-‐line mathematics courses, Mathletics for example. Students can work at their own pace, and in their own interests, although it is possible and necessary to set work for them. I like deficit teaching. Find out where the shortfalls are in the class and back-‐teach them in. Before and after tests can indicate progress. Effect Size (ES) is calculated as follows: 1. Calculate the average of the post-‐test scores 2. Calculate the average of the pre-‐test scores 3. Calculate the standard deviation of both sets of scores 4. Subtract the pre-‐test score from the post-‐test score and divide this result by the standard deviation 5. A score of 0.4 indicates you have made a competent effort and the students have learnt something from you. Scores of more than 0.4


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show your teaching has been more than competent and scores like 0.6 show you have added some real value to your students’ learning. Scores less than 0.4 indicate you have not added value and negative scores indicate you have caused harm to their learning.

What does success, look like, feel like, or sound like? . If there was ever a subject capable of generating ah ha moments then mathematics is that subject. It’s the conceptual understanding. Things are hard until ‘you get it’ and then it ‘it’s easy’. . Give the kids plenty of chances to look at strategies . Start easy and ramp it up . Task and problem selection are very important

From real life Long division is an arithmetic computation that has long relied on learning a procedure that is beyond many. Let’s examine a different strategy that combines place value understanding, and repeated subtraction. So imagine 5030 divided by 47


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Let’s begin. First, I don’t know all my 47 times tables but I do know some. If I multiply 47 by 100 it will get 100 times bigger. Let’s try that: 47 x 100 = 4700 – mmm, that’s pretty close to 5030. About 330 off I need some more. 47 x 10 = 470 -‐ is going to be too big Let’s try something smaller. 47 x 5 = half of 470 which is 235 4700 (100 x) + 235 (5 x) = 4935 -‐ I’m a bit under a 100 shy of the answer and two more 47s should get me close. That’s 2 x 47. Let’s make it 50 + 50 – 6 = 94 4935 (105 x) + 94 (2 x) = 5029 So 5030 divided by 47 goes 107 times with a remainder of 1. This was calculated using place value, halving and doubling and mostly easy mental arithmetic.


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Once the students understand this approach the classic long-‐division approach of 47 into 5 won’t go, 47 into 50 and so on, actually makes more sense. The point here is you teach strategies based upon concepts where you can, rather than rote-‐learned procedures.


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Chapter 21 -‐ Common misconceptions in learning mathematics This chapter is based upon an unpublished thesis I wrote about how I tutored Mathletics in my multi-‐level classroom. Tutoring is about providing point of need assistance to your student. The trick is to provide conceptual assistance not just procedural.

Introduction In 2009 I undertook a post-‐graduate certificate in primary mathematics teaching. This course was for DEECD employees (Dept. of Education and Early Childhood Development, Victoria, Australia), and was led by Professor Dianne Seimon of RMIT University (Royal Melbourne Institute). The theme of that course was around the common misunderstandings in learning mathematics. As well as providing RMIT course material, I had access to a departmental website authored by Professor Seimon, and the work of other researchers who are cited in the text. There is a bibliography at the end of this chapter. There are six levels of common misconceptions in learning mathematics and they are:


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. Level 1 -‐ Trusting the count . Level 2 – Place-‐value . Level 3 – Multiplicative thinking . Level 4 – Partitioning . Level 5 – Proportional reasoning, and . Level 6 -‐ Generalising, equivalence, number properties and patterns, and the use of algebraic text Each level of common misconception is discussed in turn.

Level 1 – Trusting the count ‘A key indicator of the extent to which students have developed mental objects for the numbers 0 to 10 is the extent to which they can recognise collections of these numbers without counting, that is, they can subitise (Seimon 2006)’. Subitising is the ability to make sense of how many without counting for example, to instantly recognise () as three (Chapin & Johnson, 2000, p. 11). Willis (2002) notes that some children can chant out the numbers but cannot count (p.118) whilst others can subitise very small collections say () but cannot do


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() because they cannot count (p.120). Willis goes on to state that larger collections usually have to be organised in a recognisable pattern before being subitised correctly. Students who are unable to count may not realise that counting is an accepted strategy to work out how many, or may not have made the connection between the numbers spoken and the objects counted (cardinality). Rectifying these deficiencies are the first task of formal instruction (Booker, Bond, Briggs & Davey 1998, p. 59). Another issue for the student might be an inability to recognise, read or write number names and numerals. Booker et al. (1998, p. 60) makes a strong argument that children learning to count must have opportunities to see and use numbers as names (four), objects () and symbols (4). It is also possible that poor organisation of the objects might also lead to some items not being counted at all or counted more than once. Chapin & Johnson (2000, p. 11) suggest that students need to count a great many things early in their learning, and that strategies for coordinating counting need to be demonstrated to students. Chapin & Johnson (2000, p. 47) identify six common counting strategies and these include: counting all, counting down from,


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counting down to, counting up from, counting on from first, and counting on from larger. Chapin & Johnson (2000, p. 47) suggest that while students are capable of creating novel counting techniques do not assume that students are able to simply memorise these techniques. Counting strategies are conceptually based and each strategy makes different demands on the user. In all instances there are varying degrees of the student ‘trusting the count’ (Seimon 2006).

Level 2 – Place value ‘A key indicator of the extent to which students have developed a sound basis for place-‐value is the extent to which they can efficiently count large collections and confidently make, name, record, compare, order, sequence, count forwards and backwards in place-‐value parts, and rename 2 and 3 digit numbers in terms of their parts (Seimon 2006).’ Booker et al. (1998) devote a whole chapter (chapter 3) to numeration opening with a quote that, ‘beyond simple counting, all calculations with whole numbers and decimal fractions make use of place value (p.53)’ and later state, ‘naming [and renaming] numbers is the most fundamental concept needed in numeration (p.54)’. Booker et al. (1998) say that numeration is a crucial topic in its own


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right as well as being a ‘foundation for many other procedures (p.55)’. Indeed an inability to understand place value is a very common cause of misunderstanding in mathematics. Students with weak place-‐value knowledge may have an inability to trust the count or even count efficiently using two, five or ten as units of the count. They may have inadequate part-‐part-‐whole knowledge for the numbers 0 to 10, in fact they not be able to make much sense of numbers beyond 10 for example, 14 is 10 and four more, or that the number six in sixty four represents six 10s (Seimon 2006). Willis (2002, p. 123) notes that some children have a sense of twoness or fiveness etc. but this may or may not translate to an understanding of skip counting. Some children may not realise that skip counting is simply a more efficient way of counting large collections than by ones.

Level 3 – Multiplicative thinking ‘A key indicator of the extent to which students have developed a broader range of ideas to support multiplicative thinking is the extent to which they manipulate both the size of the group and the number of groups to meet specific needs (e.g., instead of committing 6 eights to memory in a meaningless or rote way, recognise that this can be thought of as 5


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eights and 1 more eight, or 3 eights doubled) (Seimon 2006)’. Chapin & Johnson (2000, p. 53) indicate that in earlier times multiplication and division focussed on the step-‐by-‐step process of the calculation to an eventual correct answer. Little focus was given to conceptual understanding but Chapin & Johnson (2000, p. 60) argue that both procedural understanding and conceptual understanding are equally important and go further to say that multiplication and division are the, ‘visible parts of an enormous conceptual iceberg that also includes ratio, rational numbers, linear function, dimensional analysis and vector space’. Chapin & Johnson (2000, p. 60) put the view that moving from counting to additive to multiplicative thinking occurs slowly. Students experiencing difficulties with multiplicative thinking may not trust the count or see different countable units in their own right (e.g. view 6 items as 1 six (“a six”) rather than 6 ones). They may have poorly developed or non-‐existent mental strategies for addition and subtraction and demonstrate an over-‐reliance on physical models to solve simple multiplication problems. The student may have had limited exposure to alternative models of multiplication (Seimon 2006).


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Level 4 -‐ Partitioning ‘Key indicators of the extent to which students have developed an understanding of fractions and decimals is the extent to which they can construct their own fraction models and diagrams, and name, record, compare, order, sequence, and rename, common and decimal fractions (Seimon 2006)’. Chapin & Johnson (2000) devote one chapter each to the subjects of fractions and decimals, chapter five and six respectively. In their introduction to fractions Chapin & Johnson (2000, p. 73) state that, ‘this topic has caused more trouble for elementary and middle school students than any other area of mathematics’. Fractions are rational numbers but can have multiple meanings and interpretations for example, fractions can be parts of wholes or parts of sets, fractions can be calculated from the division of two numbers, a fraction can represent a ratio between two quantities and, fractions can also indicate scale (Chapin & Johnson 2000, p. 74). In chapter six, Chapin & Johnson (2000, p. 98) introduce decimals as an extension of place value knowledge and suggest teachers experience little trouble with respect to the performance of computations however, they claim conceptual teacher understanding of


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decimals is such that, ‘many of us find it hard to articulate even the most fundamental ideas’. It should be noted that unlike the Booker text, which is Australian, the Chapin & Johnson text is American. The initial problem starts with the fact that decimal numbers are real numbers and while it is possible to write some decimals as fractions it is not universal (Chapin & Johnson 2000, p. 98). Next is the misunderstanding about the purpose of the decimal point which is to indicate the positions of the ones place and subsequently all other places. The base 10 numeration system relies upon the face and place value of a digit. Seimon (2006) stated students might experience difficulties with fractions because they view the denominator in the same way as the numerator (i.e., as a count or ‘how many’ number, rather than an indication of ‘how much’). The student may have had a limited exposure to practical experiences that show what happens as the number of parts is increased, and how fractional parts are named. The student may have had the groups of only idea for multiplication and division or little or no access to strategies that support the construction of appropriate fraction representations. Booker et al. (1998, p. 96) makes a strong case for the teaching of


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language and the use of physical models to represent fractional ideas.

Level 5 – Proportional reasoning At level 5 we move from common misunderstanding in primary mathematics into the realm of misconception occurring in secondary school mathematics. However, I believe it is always useful to know where students are headed even if it is not our responsibility or task to teach at that level. ‘A key indicator of the extent to which students have developed a broader range of ideas to support proportional reasoning is the extent to which they use multiplicative strategies such as partitioning to solve problems involving simple proportion (e.g., find for 1 or a common composite unit such as 3 in a comparison involving 6 and 9, then multiply as appropriate). Another indicator is the extent to which students can work meaningfully with multiple representations of proportional relationships (Seimon 2006)’. Howe et al. (2010, p. 391) state that by the end of elementary schooling in the USA and the UK the emphasis on rational number in mathematics teaching increases by an order of magnitude. Misunderstandings about rational numbers resonate in the USA whilst ratios and percentages are of particular concern to UK


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policymakers and so it is not very surprising that the factors adversely affecting Australian students around proportional thinking are many. Seimon (2006) created a long list that included: . Students with a limited range of ideas for multiplication and division . Students with a limited experience of manipulating real and rational numbers . A reliance on rule-‐based procedures to rename fractions . A limited understanding of what it means to multiply or divide a quantity by a rational number, and . A limited understanding of ratio ‘The chain that runs from rational number through proportional reasoning to achievement in science carries implications for practice. For one thing it suggests that rational number should be introduced in a fashion that anticipates other parts of the chain (Howe et al., 2010, p. 393)’. Howe et al. (2010, p. 393) suggest that, ‘many key science notions in science revolve around intensive quantities which combine direct and


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indirect proportions’. ‘In fact, all intensive quantities can be represented using ratios, whilst a subset can be represented using fractions, decimals and percentages (p.393).

Level 6 – Generalising, equivalence, number properties and patterns, and the use of algebraic text ‘A key indicator of the extent to which students are ready to engage with these curricula expectations is their capacity to deal with equivalent forms of expressions, recognise and describe number properties and patterns, and work with the complexities of algebraic text (Seimon 2006) Warren & Cooper (2009, p. 90) conclude that a student’s understanding of mathematics in this domain is directly impacted by the effectiveness of the teaching the student has experienced. They say (p.91) there is no one model to bring students to abstract thinking but an effective model does clearly show the underlying mathematical idea and allows for some extending of that idea. An effective teaching sequence allows the student to work from the static to the dynamic to the abstract model while at the same time the models become less overt and more mentally embedded in the student’s mind but the basis for the model is in the real world (p.91).


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Seimon (2006) notes that the difficulties experienced by students in making the transition from arithmetic to algebra may be due to: . Their poor understanding of the meaning of symbols or the conventions used in algebraic expressions . Their limited understanding of arithmetic, numeration and computation . Their slavish reliance on procedural rules rather than conceptual understanding . Their lack of experience in communicating mathematical relationships in words and/or translating relationships described in words into symbolic expressions . Their limited access to multiplicative thinking and proportional reasoning Seimon’s list suggests that the misunderstandings around generalised mathematics are set in place long before the student enters the grade 9 mathematics classroom.


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Conclusion The common misunderstanding in mathematics identified by the DEECD website and based upon the work of Professor Seimon, provided the framework for the literature review above. The framework covers both primary and secondary schooling but I would like to adapt the metaphor by Howe et al. (2010) about mathematics being a chain of ideas to my conclusion. What Howe et al. (2010) suggested was that it was important for teachers to anticipate the different parts of the chain when teaching a particular [mathematical] concept. With this in mind it would be educational to follow some of the misunderstandings from Level 6 through to Level 1 if possible. Misunderstandings with multiplicative thinking have far-‐reaching consequences for students with adverse learning outcomes being seen at Levels 6, 5, 4 and 3. Another serious weakness, showing up in Levels 6, 5 and 3, is an over-‐reliance on rules and a concomitant weakness in conceptual understanding. Proportional misunderstandings at Level 6 first arise in Level 4 where misunderstandings occur around rational numbers. Weaknesses in additional thinking at Level 3 can be traced to problems with counting in Level 1.


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Bibliography for chapter 21 Booker, G., Bond, D., Briggs, J., & Davey, G. (1998). Teaching Primary Mathematics: Second edition. Australia: Longman. Chapin, S. H., & Johnson, A. (2000). Math Matters: Understanding the math you teach, Grades K-‐6. California: Math Solutions Publications. Howe, C., Nunes, T., & Bryant, p. (2010). Rational number and proportional reasoning using intensive quantities to promote achievement in mathematics and science. International Journal of Science and Mathematics Education, 9, 393-‐417. Seimon, D. (2006). Assessment for Common Misunderstandings. Prepared for the Victorian Department of Education and Early Childhood Development. http://www.education.vic.gov.au/studentlearning/teachingresources/maths/common/default.htm retrieved August 6, 2011. Warren, E., & Cooper, T. (2009). Developing mathematics understanding and abstraction: The case of equivalence in the elementary years. Mathematics Education Research Journal, 21(2) 76-‐95.


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Willis, S. G., (2002) Crossing borders: learning to count. The Australian Educational Researcher, 29(2), 115-‐129.


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CONCLUSION TO THINKING MATHEMATICALLY Innumeracy has serious consequences for the individual. It is associated with: . Poverty . Low-‐skilled employment and unemployment . Lack of engagement with school . Poor money management . Low confidence and self-‐esteem, and . Criminal behaviour I am extremely concerned about the chronological, grade-‐based, ‘cover-‐the-‐content’ approach to mathematical teaching. I think such an approach is ultimately destructive for students. Unlike all the other ways of thinking discussed in this book which are more about frameworks and approaches, learning mathematics is so conceptual, so centred upon the student, that they must set the pace for their own learning. Pushing an idea onto the child before they are ready to hear it, or before they have mastered the previous big idea in the chain is absurd.


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SECTION SIX – SIX WAYS OF THINKING

The Six Rs were the kick-‐off point for this book because I wanted to explore, researching, retelling and reasoning, three parts of my own home-‐grown pedagogy in greater detail. At about the same time as I began writing the rollout of the new Australian national curriculum had begun, and the Victorian government, my employer, had moved towards a model for greater accountability of school leaders. Curriculum, as envisaged by the national curriculum, my own state department of education, and reflected by large schools with specialist staff, is extremely difficult to replicate in a small school like mine (1.5 generalist teachers). Up until now I had the Six Rs, and it had stood the test of time, but now the goal posts were changing and I realised I needed a more coherent curriculum for my middle and upper

Thinking Aesthetically -‐-‐-‐-‐-‐-‐|-‐-‐-‐-‐-‐ Thinking scientifically Thinking with language -‐-‐-‐ Thinking mathematically Thinking Systematically -‐-‐-‐-‐|-‐-‐-‐-‐-‐ Situated Thinking


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primary school students that made sense in my teaching context. I began by writing about the work of specialist teachers chapter by chapter. In the course of my writing I came to the realisation that I had had identified six ways of thinking (see above). These were thinking approaches that are diametrically opposed to each other (shown as italics vs. regular font) and yet generalist teachers are expected to seamlessly deliver in all areas. Two ways of thinking, thinking with language and thinking mathematically, are arguably more important in primary school than the other four (shown in bold) and relate to the three Rs of reading, writing and arithmetic. Thinking aesthetically versus scientifically, and thinking systematically versus situated thinking all relate to the remain Rs, in the Six Rs of reasoning, researching and retelling. What I have suggested in this book is that an overcrowded curriculum, especially that dealing with middle-‐year’s students, can be reduced to the six ways of thinking. The reason I ‘think’ this way, no pun intended, is that content is so easy to access now-‐days, and there is so much of it, that it is no longer the raison d'être for the basis of a curriculum. Another point I would make, and it is the


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reason for this book, that appropriate levels of content knowledge are not always available in a school’s teaching staff. So anticipating that content knowledge is available to anyone with access to the internet, ways of thinking about that content are much more useful, especially to the generalist teacher delivering a specialist subject, than particular knowledge of a content area. I am suggesting to you that if you get across the ways of thinking you will be a more than useful generalist, teaching in a specialist subject, or specialist teaching outside your method. Let’s look at these ways of thinking from a delivery perspective in terms of departments for bigger schools and domains for teachers. Let’s start with, ‘thinking with language’ and then, ‘thinking mathematically’. Both ways of thinking require of its students to succeed at a functional level, hence the terms literacy and numeracy, and then go far beyond this basic functionality to develop ways of thinking.

Thinking with language Without a doubt this is one of the most important departments/domains within our school curriculum that is underpinned by ways of thinking. Quite simply, illiteracy predicts such poor outcomes for the individual that every attempt must be made to prevent this from happening. At the other end of the


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spectrum, thinking with a foreign language is correlated with a number of benefits. Rather than being separate departments/domains in our school curriculum they should work together and integrate their efforts for the benefit of students. In Victorian primary schools it is generally expected that literacy will take up the first two hours of each day. I have no issue with that except to suggest that LOTE and ESL be incorporated within that two hours and that history, along with quality fiction of course, provide the vehicle for delivery for literacy. Learning English is about learning conventions and rules and relentless practice and a LOTE will provide an alternative perspective for the rules and conventions of language while history, provides an authentic reason for language. One can anticipate a team-‐teaching scenario in larger schools where English, LOTE and history teachers, along with input from the ESL teacher, combine to deliver contextually relevant units of work to their students. Generalist teachers can fit into these groups and she be prepared to teach at the functional literacy level at least. Individual teachers can’t team-‐teach but they can integrate the subjects.


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To think with language is to use the language frame ones thinking. With respect to writing, the choice of words, the structure of the sentence, the arrangement of ideas in a paragraph, and awareness of your audience in longer text. As a reader you learn to decode words, follow the meaning of a sentence, see the big idea in a paragraph, and work with an author as you read a text. Speaking & listening can be enacted formally and informally following many of the same conventions and rules of writing and reading.

Thinking mathematically For much the same reason as illiteracy needs to be avoided, innumeracy predicts very poor outcomes for the individual, and it too needs our best efforts to avoid such an outcome for our students. However, unlike literacy where relentless practice is required to learn the rules and conventions, numeracy relies upon conceptual understanding and these have to be built up over time and owned by the student. For this reason I think it is appropriate to abandon ‘teaching’ grade-‐based chronological content-‐based mathematics and move to self-‐paced on-‐line learning along with diagnostic testing and direct instruction around class and individual weaknesses. As I make this recommendation, I can’t help but be aware of the fact that mathematics teachers are in short supply in Australia, and that in


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this area, many students have teachers who lack either a strong content background, or the confidence to ‘teach’ mathematics. I would argue that ‘tutoring’, with an appropriate understanding of common misconceptions in mathematics, is a more effective approach. It is an entirely different way of teaching mathematics. So looking at the structure of the maths department/domain I see it as being comprised of tutors and teachers, hopefully with specialist knowledge of functional numeracy and more advanced mathematics. These staff may specialise in different levels of schooling but I would anticipate that their students may be representative of a range of grades. Movement between the levels would not wait until the end of the school year but happen as and when on-‐line content is completed. Regular diagnostic testing would take place and depending on the conceptual difficulty, teachers would offer lessons for students to choose to attend. These lessons could be on-‐line too. It is a different way of delivering mathematics to the middle years. One final point before moving on: I want to highlight that functional numeracy is not the same as thinking mathematically. Functional numeracy is really about arithmetic. Good skills in arithmetic reduce the cognitive load of


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students thinking mathematically. For mine, I would much rather have a grade eight student with a solid grounding in grade seven level concepts than the same student with a just a patchy understanding at a range of levels. The first student would, in my opinion, be functionally numerate for the world of non-‐professional work and life as a citizen. I would have even greater confidence in the future of this student if s/he had successfully completed a financial literacy unit. Financial literacy comes up in the next section about situated thinking.

Situated thinking In third place of importance I place situated thinking because all of the subjects within it are relevant to the lives of your students irrespective of their eventual profession, trade or occupation. Like functional literacy and functional numeracy situated thinking is about practical, useful and purposeful learning for life. Situated thinking subjects are about agency, how your students think and act in their own world and their place in that world. Unlike all the other ways of thinking, the individual student and their context, is central to this approach. Thinking about maintaining personal, interpersonal, nutritional and financial health is based on the self. Our department/domain concerned with situated thinking would seem, on the face of it,


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a disparate group. In Australia, only the PE teachers have mandated work to do, and thus, may expect specific time in the school week to do it. However, IT, home economics and financial literacy could easily be combined, as could the health part of H&PE. A situated thinking curriculum combined with functional levels of thinking with language, and thinking mathematically might be considered a bare minimum of learning, a three Rs if you will of readin’ & ‘ritin’, ‘rithmatic, and ‘real’ life, and what a shame it would be if schools delivered such a spare and practical curriculum. All teachers experience life, and so all generalist teachers are qualified to at least tackle this way of thinking. I would be looking to employ para-‐professional staff and some parents too. Remember, this is a functional-‐level of thinking. I think the final three ways of thinking, aesthetic, scientific and systematic cannot be ranked based upon their functionality, although I am certain that the proponents of each method could make an argument that they are functional. Aesthetic thinking is about making products and using processes and evaluating these. Surely this is practical? Thinking scientifically is about asking questions and gathering evidence and explaining the evidence in light of what we


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know and don’t know. I reckon that has practical applications, don’t you? Finally, thinking systematically is about looking from the outside in, its about the big picture and finding order in what appears to be chaos and how humans, and our planet, are affected by both natural and man-‐made phenomena, and why there rarely are simple solutions to complex problems. Surely, that kind of appreciation of our world is of practical use to the individual? So, in alphabetical order only, let’s look at the final three ways of thinking more closely.

Thinking aesthetically It might seem odd on the face of it to combine performance and visual art with technology and information technology, but each is about product and process and each, dare I say is about appreciation for a beautiful, or eminently suited-‐for-‐purpose object. The difference between art and technology is in the intent with art being more iterative than technology however, I argued that the amount of forward planning or simple thinking on your feet can change with the complexity on an art project, and the skill, knowledge and experience of the technician. There is a lot of overlap between commercial art and technology, especially where IT is being used.


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I believe students should ‘make’ things and not just essays, or reports, or power points. They should make models and artefacts, useful and more abstract objects. They should show an appreciation for the process too because sometimes, solutions to life’s problems can have unanticipated consequences. Look at DDT pesticide. Our aesthetic department/domain need appropriate spaces to work in and tools and materials to work with. The discussions by teachers in this department about the student’s ability to conceive and idea and see it through, to use the materials and tools in conventional and novel ways and, to reflect upon the work and object in a way that is emotional and pragmatic at the same time. School productions are more obvious vehicle for these subjects to come together for a common purpose.

Thinking systematically It is in this department/domain we will find the specialist backgrounds for many of our generalists, the civics teachers, the economics majors and the geographers. I should not neglect the environmental educationalists be they working for the environment (environmental studies) or learning about the environment (the environmental scientists).


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This is a department/domain concerned with the planet and the people on it. It covers natural phenomena as well as man-‐made forces. Politics, civic rights and civil responsibilities are covered and we should not overlook the sustainable future agenda. This is a department/domain that appreciates and solves problems, maybe only on the desktop, but it is about THE BIG PICTURE, and thank goodness for that. An inward looking, self-‐centred citizenry neither demonstrates empathy for others nor concern beyond the practical day-‐to-‐day issues of their own life. Thinking systematically is diametrically opposite to situated thinking. This is a department/domain that practically cries out for team-‐teaching and/or integrated learning.

Thinking scientifically Thinking scientifically is opposite to thinking aesthetically. And yet, science can be beautiful. An idea or theory can be beautiful. We should not forget that technology is often derived from science. Art may take ‘evidence’ and respond to it in an entirely different way from what might be done by a scientist creating a model to explain the phenomena. An artist or technologist is much more likely to intervene in the process in order to achieve the desired outcome or, just to see what happens next without any expectations.


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By focussing on scientific method rather scientific content as I have, I have created a teaching and learning scenario that might be tackled by a team of specialist science teachers and generalists. Our specialist may work with the class and the generalist teacher from time to time look at what has been done so far and to formulate experiments to be carried out by the class and generalist teacher in the interim. At the same time deliver teaching around the big ideas. This could be done in person or on-‐line.

Curriculum outlines FOR THE GENERALIST CLASSROOM Term 1 Thinking mathematically / Thinking with language / Situated Thinking Term 2 Thinking mathematically / Thinking with language / Thinking Systematically Term 3 Thinking mathematically / Thinking with language / Thinking Scientifically Term 4 Thinking mathematically / Thinking with language / Thinking Aesthetically


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Could it be this easy? Maybe it is and maybe it should be. Which means we still need those national and state curriculum documents but as a menu to choose from filled with guidelines for what is appropriate at a particular grade level in a particular subject. If grades and subjects reflect the reality of your school then well and good. If it does not, as it does not for me then perhaps this simple curriculum outline will work well enough and not need a whole bunch of people with specialist teaching knowledge to deliver it. FOR THE SMALL PRIMARY SCHOOL Term 1 Thinking mathematically / Thinking with language . Situated Thinking (infants) . Thinking Systematically (middle school) . Thinking Scientifically (upper school) Term 2 Thinking mathematically / Thinking with language . Thinking Systematically (infants) . Thinking Scientifically (middle school)


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. Situated Thinking (upper school) Term 3 Thinking mathematically / Thinking with language . Thinking Scientifically (infants) . Situated Thinking (middle school) . Thinking Systematically (upper school) Term 4 Thinking mathematically / Thinking with language / Thinking Aesthetically We are often told that schools need more autonomy but all too often this autonomy gives you the ‘freedom’ to choose the school cleaner. It does not give you the autonomy you want, the autonomy that would resonate with your skill, knowledge and expertise. That is the autonomy to choose the curriculum and pedagogy to be utilised in your school. FOR THE LARGER PRIMARY AND SMALLER SECONDARY SCHOOLS Term 1 Thinking mathematically / Thinking with language


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. Situated Thinking (infants) (7) . Thinking Systematically (1-‐2) (8) . Thinking Scientifically (3-‐4) (9) . Thinking Aesthetically (5-‐6) (10) Term 2 Thinking mathematically / Thinking with language . Thinking Aesthetically (infants) (7) . Situated Thinking (1-‐2) (8) . Thinking Systematically (3-‐4) (9) . Thinking Scientifically (5-‐6) (10) Term 3 Thinking mathematically / Thinking with language . Thinking Scientifically (infants) (7) . Thinking Aesthetically (1-‐2) (8) . Situated Thinking (3-‐4) (9) . Thinking Systematically (5-‐6) (10)


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Term 4 Thinking mathematically / Thinking with language . Thinking Systematically (infants) (7) . Thinking Scientifically (1-‐2) (8) . Thinking Aesthetically (3-‐4) (9) . Situated Thinking (5-‐6) (10) The simple curriculums I have proposed above provides lots of room to engage your students in the work they will do. It allows you, the teacher and educational manager, to provide context appropriate learning to your students. And, if I might make one final suggestion, the topics within each way of thinking need not run for the entire term. There could be a number of topics, embedded in a particular way of thinking that can be dealt with over the course of a term.

In closing The writing of this book has taken all of 60 days to complete. 60 days of researching, retelling and reasoning. Not to mention framing my thinking and sharing it with you through language. It has been a good way to use up some long service leave.


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My one hope is that you do get something out of the book. I know I did. You may not agree with me, but that isn’t important, what is important is that you will have reflected upon your own professional practice. I guess my own experience, researching and writing this book, shows just how accessible content is and it would not be appropriate to close, without acknowledging the wonderful resource known as the Internet. More significant webpages have links to them at the end of each chapter, but many did not, providing only small pieces of information. The websites that provided most of the small pieces was Wikipedia and Ask.com. I would also like to thank my daughter, Kate, a middle-‐years teacher with a business degree teaching at a local secondary school. Kate has taught business and many other subjects in her time. She was able to answer a few critical questions not otherwise apparent on websites. Where my part came in was in the filtering and distilling of this content and formulating a new ‘whole’, which you are reading now. So any mistakes you see are mine. If you got this far, well done. I guess you liked it. I’m glad about that.


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About the author Peter Farrell came to teaching relatively late in his working life in 2001. Apart from one year in another small school as a beginning teacher, and one term in a larger school as the acting-‐principal, Peter has always worked at [Ourplace] Primary School, a small rural school in Victoria, Australia. Peter has an honours degree majoring in aquaculture with minors in plant biology and microbiology, a research masters degree in applied science (farming freshwater crayfish), and a graduate teaching diploma. Later on, he added a doctorate of education (about small school leadership) and a post-‐graduate certificate in primary mathematics teaching to his CV. When he is not writing, Peter likes to race sailboats, cruise in sailboats, and mess about in sailboats.

curriculum advice for generalist teachers in very small schools (2nd edition)

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