Is not Like the Old Days

And that’s what makes it

Awesome

Teaching Mathematics

Just because you don’t see numbers doesn’t mean it’s not math.........

Just a few different ways...Measurement- What units would you measure the length of the dock in?Numeration- Estimate how many steps it would take to fall into the water.Probability- If the weather is exactly like it is in the picture four out of every five days then how likely is the going to be weather bad? Even in the examples above it is both graphics and the written word that is becoming the vehicle for math instruction and communication. When used properly Language is just as important as written numbers in the understanding and application of mathematics.

Playing with blocks isn’t just play but a chance to engage in learning

“The development of mathematical knowledge

is a gradual process. A continuous, cohesive program built throughout the grades is necessary to help students develop an understanding of the “big ideas” of mathematics-that is, the interrelated concepts that form a framework for learning mathematics in a coherent way.”

(The Ontario Curriculum, Grades 1-8:Mathematics,2005, p.4)

What are these Big Ideas that everyone keeps talking about?

The whole concept of the “Big Idea” is that in the past teachers taught one strand of math at a time and never strayed outside of whatever that was. Now teachers are encouraged to come up with applications preferably ones that have a basis in real life. To try and encompass as many strands as are required to cover the idea and not restrict themselves to a single strand. An example of this would be the slide of the dock earlier in the presentation on the variety of strands that could be accessed from one real life picture.

Math Works Best When it Makes Personal and Practical Connections

Providing mathematics problems with situations and contexts that are meaningful to all students (e.g., problems that reflect students’ interests, home-life experiences, and cultural backgrounds and that arouse their curiosity and the spirit of enquiry);

The following statement is taken from The Ontario Ministry of Educations document A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6

Manipulatives

Pencil and paper are no longer the only tools required to do mathematics. Any opportunity for students to use hands on tools/manipulatives and computer assistive technology is no longer just a good idea, it’s an essential part of effective learning.

Then and Now

When we went to school• The Teacher showed one

example and then we did twenty more

• The example on the board was the only acceptable way to do the question

• A computational device was our fingers

• The only way we showed we knew what we were doing was by having the correct answer on the page

• Feedback from our work was either a red check or an X

What they do now • Teachers not only model several

examples but also talk about what they are thinking while solving the examples

• A Variety of problem solving techniques are not only acceptable but encouraged

• The use of Calculators and computer software used to enhance learning

• Students write in journals which offers a more accurate look into their mathematical ideas and they receive descriptive feedback from it

• The process used to solve the question is in many cases more important than the end result

How Can I Help at Home•Let them see you doing math. Whether that’s writing a cheque, calculating the cost of something or counting how many forks are needed •Use their math expertise regardless how vast or limited it is to help out with some part of daily family life. This will empower them not only to know they are a valued member of the family but that they used their knowledge to help.•Watch your kids play and if the moment presents itself to add in some math then go for it. Exploration through play is a very powerful learning style and kids will learn that learning can be fun•Let them be the teacher. Have your child teach you the math concept that they are working on. This is a great way to consolidate ideas and create a dialogue between you and your child around math•Try whenever possible to give real life applications and connections to whatever your child is doing. Whether that’s being able to measure a space for a new deck or to know how much change you should be getting back from ten dollars. When real life connections are made understanding is far greater.

The Seven Skills that Make Better Problem Solvers

1-Problem Solving and Inquiry-The thirst to want to know why and the confidence to try a variety of strategies2-Reasoning and Proving-The ability to make connections and suppositions during problem solving3-Reflecting-The ability to think about how a student is going about a solution and determine if that choice of strategy was useful one4-Selecting Tools and Computational Strategies- The ability to choose the correct tools and problem solving methods to be successful5-Connecting-The ability to use previous knowledge to make connections as well as being able to bridge between concrete and theoretical examples6-Representing-The ability to represent mathematical ideas through pictures, diagrams, numbers words and symbols7-Communicating-The ability to explain mathematical ideas both orally, visually and in written form The following ideas are taken from The Ontario Ministry of Educations document A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6

Journals aren’t Just for Language Class Anymore

Math journals allow students and especially teachers to be even more accurate and descriptive in their feedback when communicating about math. This allows both groups to have a better chance of meeting their target goals. Math journaling can be described using the following metaphor: A person asks you for directions and you are almost positive that you know where they need to go but can’t tell them because your not absolutely positive and don’t want to be wrong. You apologize to them by saying “I know how to get there myself but I just can’t explain it.” Allowing students to write and communicate in their journal allows them a whole different avenue to describe their thoughts. In relation to the metaphor I’ll bet if the person sketched in a rough map on paper with a couple of ideas to go with it the person would have gotten much closer to if not exactly where they needed to go.

Constructivism

When we teach by asking questions that allow students to formulate their own ideas and ways of seeing a mathematical task we call this the Constructivist approach . Constructivism is a philosophy of learning founded on the premise that, by reflecting on our experiences, we construct our own understanding of the world we live in. Each of us generates our own “rules” and “mental models,” which we use to make sense of our experiences. Learning, therefore, is simply the process of adjusting our mental models to accommodate new experiences.Jacqueline and Martin Brooks, The Case for Constructivist Classrooms.

As adults being taught new work tasks we often don’t truly become comfortable and or efficient with those tasks until we find ways to make it make sense to ourselves. This is the essence of the constructivist model.

Mathematical Beliefs When I start the conversation that I am far more interested in

how my students arrived at their final answer than the answer itself they stare at me not believing a word I'm telling them. It's at this point that I use one of my favourite analogies: I have them visualize that they are in a maze and that when they show their work it's the same thing as the students being able to mark their trail. If they find that they've gone down a path that didn't work then they could easily use their trail and come back to a place they recognize and then go off in a different direction. No work means no trail and no real way of keeping track where they are which makes their chances of getting out far more limited.

Trust and Inquiry " Effective classroom communication requires a supportive and respectful

environment that makes all members of the class feel comfortable when they speak and when they question, react to, and elaborate on the statements of their classmates and the teacher." The Ontario Curriculum Mathematics. 2005 pg 17.

This excerpt only outlines the framework of what an effective classroom needs. In order for students to be willing to take risks they must be able to trust in the idea that they will not be ridiculed for their ideas. When students know that they can say or write virtually whatever is on their mind and know that they will be supported they can stretch farther and be receptive to so much more. So whether that is in pairs, groups, whole class or writing in their journals when students have a fostered sense of confidence they are able to be more successful. This is the atmosphere that is expected and one that we are all working toward using in our class.

Questions

Why isn’t my child using their textbook very often?

In an inquiry based classroom math texts are used far more for as a starting off point than the are the primary source. Much like in language we use a dictionary and a thesaurus we don’t use these resources as the main part of the writing process.

Questions

Why isn’t there more memorization of math facts?

Studies have shown that when children learn solely by rote that their ability to problem solve and use the information becomes very limited. In most cases the students have great difficulty applying the same knowledge to different applications.