Lead Teacher Workshop 3

Purpose of this session is…

Share and discuss examples of mid-year reporting to parents.

Continue to explore the mathematics behind the National Standards with a focus on Statistics.

Effective Mathematics Pedagogy - engaging learners in mathematics.

Mathwire.com

Release the Prisoners Game

who will free their prisoners first? Students use subtraction facts to find the difference of two dice. Directions, plus both the 6-sided dice and 12-sided dice, gameboards are included so teachers can target subtraction practice while helping students develop an intuitive appreciation of

probability.

Overview (8.45 – 11.45)

•Any current issues?

•Share report examples

•Module: Engaging Learners in Mathematics – rich tasks

• Morning Tea (10.10-10.30)

•Unpacking Statistics in the Standards

•What’s new – keep updated

Mid Year Reports

•Successes •Feedback from parents•Possible modifications for the next report

•Review the report examples

Reviewing written reports

Reporting achievement in relation to National Standards

Experiencing difficulties

Working towards the

standard

Working at the standard

Working above the standard

Working well above

Well below Below At Above Well above

Working below

Working at Working above

“Harry is working_____ the National Standard for his age”

The Points of Difference between the Standards:In your groups, compare the curriculum and

the standards;

• When you sit the curriculum next to the standards what do you notice?

• How is the growth in level 2 described in the ‘After 3 Years’ and the ‘End of Year 4’ standards? Record points of difference and progression – capture critical concepts.

• Record any points requiring clarification – vocabulary, concept development.

• Complete the process with the Year 5 and 6 standards.

Curriculum Level 2: Stage 5After 3 Years at School At the end of Year 4.

Apply basic addition facts and knowledge of place value and symmetry to:-Combine or partition whole numbers.- find fractions of sets, shapes and quantities.

Create and continue sequential patterns with one or two variables by identifying the unit of repeat.

Continue sequential patterns and number patters based on simple addition or subtraction.

Apply basic addition and subtraction facts, simple multiplication facts and knowledge of place value and symmetry to:-Combine or partition whole numbers.-Find fractions of sets, shapes, and quantities.

Create, continue and give the rule for sequential patterns with two variables.

Create and continue spatial patterns and number patterns based on repeated addition or subtraction.

• Part-whole using addition facts, e.g. 18 + 8

• Place value units without renaming, e.g. 40 + 50 = 90, 42 + 21 = 63and 87 – 30 = 57, 87 – 35 = 52

• Multiplication using addition facts, e.g. 8 + 8 as 2 x 8, 6 tens as 6 x 10 ,

•Part whole using subtraction facts, e.g. 37 - 9 and simple connection between add/sub e.g.14 - 6 = ? solved using 7+7.

• Place value with simple renaming,e.g. 49 + 24 = and 73 – 9

• Multiplication using halving,e.g.14 ÷ 2 = 7 as 7 + 7 =14, doubling, and simple known facts e.g. .2 x 6 = 12 so 3 x 6 = 18 (adding on).

Curriculum Level 3: Stage 6By the End of Year 5 By the End of Year 6

Apply additive and simple multiplicative strategies and knowledge of symmetry to:-Combine or partition whole numbers-Find fractions of sets, shapes and quantities

Create, continue and predict further members of sequential patterns with two variables.

Describe spatial and number patterns using rules that involve spatial features, repeated addition or subtraction with simple multiplication.

Apply additive and simple multiplicative strategies flexibly to:-Combine or partition whole numbers including performing mixed operations and using addition and subtraction as inverse operations.-Find fractions of sets, shapes and quantities.

Determine members of a sequential patterns, given their ordinal positions.

Describe spatial and number patterns using:-Tables and graphs-Rules that involve spatial features, repeated addition or subtraction, and simple multiplication.

• Solves 53 – 26 by subtracting in parts. For example: 53 – 6 = 47, 47 – 20 = 27, OR 53 – 20 = 33, 33 – 6 = 27.

• Solves 53 – 26 using a tidy number. For example: 53 – 30 = 23, 23 + 4 = 27.

• Continue and predict the next few members in a sequential pattern.

• Uses inverse relationships to solve 53- 26. For example: 26 + 4 = 30, 30 + 23 = 53 OR 26 + 26 = 52, so 26 + 27 = 53.

•Determine or predict the sequential pattern given any ordinal position.

•Use of tables and graphs to solve spatial and number patterns.

Module 7 & 9Engaging learners with mathematics

http://nzcurriculum.tki.org.nz/National-Standards/Professional-development/Professional-learning-modules/Overview

Effective Teaching Cycle

Assess

Analyse data

Plan

Teach

Practice/Apply

Assessment in the NZC

“The primary purpose of assessment is to improve students’ learning and teachers’ teaching as both student and teacher respond to the information that it provides……”

The New Zealand Curriculum, p.39

Assessment of learning

Assessment for learning

Formative Assessment – Dylan WiliamProfessor of Educational Assessment at the University of London. Also works with

Paul Black – co-authors of Inside the Black Boxhttp://www.ltscotland.org.uk/learningaboutlearning/aboutlal/biogs/

biogdylanwiliam.asp .

Discuss…

• Main points that you found of interest• How you do / might implement these

ideas into your school.

Should formative assessment be recorded?If so – how?• Modelling book• Teachers feedback comments in student books• On planning units• Other anecdotal notebook• Self/peer assessment in maths diaries

The expectations defined by the standards include how a student solves a given problem, not only the student’s ability to solve it so….

•Provide tasks with multiple possible solution strategies

Using Different Problem Types

Different Problem Types

1. Martin opened his book and noticed that the sum of the two pages was 157.

What page numbers were showing?

2. 78 + 79 =

Open ended problems are something they need to think about, not simply a disguised way of practising already demonstrated algorithms

open-ended

procedural

• It must be accessible to everyone at the start.• It needs to allow further challenges and be extendable.• It should invite learners to make decisions.• It should involve learners in speculating, hypothesis

making and testing, proving and explaining, reflecting, interpreting.

• It should not restrict learners from searching in other directions.

• It should promote discussion and communication.• It should encourage originality/invention.• It should encourage 'what if' and 'what if not' questions.• It should have an element of surprise.• It should be enjoyable.Ahmed (1987), page 20

How do teachers engage students in rich tasks?

However, keeping mathematics interesting and fun should not be at the expense of content.

Posing and answering questions

Gathering, sorting and displaying

Communicating findings

Mathematics Statistics

Exploration of and use of patterns and relationships in… quantities, space and time

Set answer

Exploration of and use of patterns and relationships in… data

No definitive answer

How is Statistics different in the new curriculum?

• Data is still key• Enquiry cycle (PPDAC)• Verbs

– Posing, gathering, sorting, displaying, communicating, displaying, using

• Specific graph types not mentioned

Problem

• Statistical investigation cycle• Has at its heart a starting point based on a

problem.• Data driven or Question driven

CensusAtSchool

http:///

www.censusatschool.org.nz

Leonardo da Vinci (1452-1519) was a scientist and an artist. In 1492 he drew this picture. Can you see how the man is standingIn a circle and a square? Leonardo thought that The span of someone’s arms is equal to theirheight. Why do you think he was interested in working out body proportions?

Do you think Leonardo’s theories still work today?

Are you a Masterpiece?

Plan

– What variables do we need to collect?– How shall we pose the survey questions.– Who shall we ask / how many?– How will we know when we have asked everyone?– How are we going to record and collect the data?

Data cards

Leisure activity

Arm span

No. of members in your family

Height

Year 1-3 teachers collect this data on yellow cardsYear 4-6 on blue cards

Brainstorm all possible questions from the available information on the data cards.

Problem Question Types• Summary (Years 1- 8)

– A description of the data, usually a single data sete.g. “What is the most common birth month in our

class”

• Comparison (Y5 onwards)– Comparing two (or more) sets of data across a

common variable, e.g. “Do females typically live longer than males?”

• Relationship (Y7 onwards)– Interrelationship between two paired variables,e.g.“Does watching a lot of TV increase your IQ?”

Classifying

Sort / classify the questions according to the following categories:

• Summary• Comparison • Relationship

Category Data

Numerical Data

Time-Series Data

Analysis

• Make a graph using your data cards that will help you to answer your question.

• Describe the graph identifying patterns and trends in context.

• Remember the context. If I cover any labels can I still tell what the graphs are showing?

Analysis• Use I notice… as a starter for statements.

• For category variables: (e.g. birth month etc)– Shape– The most common category, the least common category,

other categories of interest– Anything unusual, or of interest

• For measurement variables: (e.g. bed time)– Shape – Spread (difference between lowest & highest values)– Middle group(s)– Anything unusual, or of interest

Relationship Question

• Are you a masterpiece?

• What is the relationship between your height and arm span?

Statistics in the NZC and Standards

Highlight the difference in progression from Y1 to Y8

Circle any vocabulary that you are unsure of.

Collecting category data using post it notes

Leisure activity

= Reading

Collecting bivariate data using post it notes

Leisure activity

= Reading

Leisure activity

= Playing sport

Girls Boys

Collecting multivariate data using post it notes

What school subject do you most enjoy teaching?

What time did you go to bed last night?

What school subject did you most enjoy at school as a child?

Birth month

Analysis: Key words for describing data display

Shape Middle Spread

Clump (s)

gap,

symmetrical, rectangular,

most of the data is, a few points are

Same/different

The middle of the data is …..

about..,

between,

higher/lower

Close together, spread out,

evenly spread, mostly between,

less/more spread out than…

Describing Categories

Most (N.B. “most” must be more than half), least, some, all, more than, less than, more than half, about half, roughly a quarter, a lot, not many, a few, most popular, least popular, most typical, least typical

• I notice that the most common birth month is August with 5 people in the group.

• I notice the least common birth months are January and November with no one in the group born in these months.

• I notice that four months have four people born in them, they are May, June, October and December.

• I notice that the Winter months have the most people born in them, 12 people. Spring has the least number of people born with only 5 people born then.

( )count

1

2

3

4

5

6

Birth_monthFebruary March April May June July August September October December

PAT Y6 Question (time-series data)

Emma went for a run from home. She stopped for a while and then walked home. Which graph shows how far from home she was during her journey?

Greater Heights (FIO 2-3, pg.4)Dot plots are used to show number data that

comes from counting or measuring.

1. What is the same and/or different about the girls’ and boys’ data?

2. How might Ahere’s idea of finding the ‘middle’ help answer Tim’s question “I wonder if the boys are taller than the girls?”.

3. Do you agree or disagree with Ahere’s statement? Support your views with at least three statements based on the data.

Useful Websites:

http://www.stats.govt.nz/

http://www.babynamewizard.com/

Gender: femaleAge: 12Height: 155 cmArm span: 155 cmTravel: walkTime: 10 - 20Lunch: ran

Gender: maleAge: 12Height: 163 cm Arm span: 163 cmTravel: walkTime: less 10Lunch: ran

Resources:• www.nzmaths.co.nz (Second tier material, statistics units)

• www.censusatschool.org.nz

• Figure It Out Statistics,

• Data Cards:

And remember…98% of all statistics

are made up!

E- AsTTle Update:All schools are welcome to access the software

• Either as a pen & paper test or as an online assessment tool.

• 1000 schools are presently participating and there is some spaces left to join.

• There is PD available

• Classroom management systems are being improved to assist schools with reporting in relation to National Standards.

What’s New – Keeping up to date•Last week’s announcement- $36m allocation used over 4 years to give special teaching for children, redesign of teacher development. Experts appointed to work with schools•E-asttle being recalibrated now (free PD until end of the year)•4 main SMS systems have been enhanced-more still to come. Basic changes are free.•Junior assessment tool being trialled at present.•Pilot intervention programmes for Accelerating Learning in Mathematics

Thought for the day

Remember that frequently…

The student knows more than the teacher about what he has learned even though he knows less about what he was taught.

 Just because you’ve taught it doesn’t mean

they’ve learned it!