Senior Numeracy Pilot Project 2005

Workshops OneIntroduction to Project

Stages, Diagnostics Testing

1

Learning Outcomes for this workshop.

• Teachers will develop an understanding of the developmental stages within the Number Framework

• Teachers will gain an understanding of the Numeracy Assessment tool

This project is all about teacher professional development and what happens in the mathematics classroom.

2

History• Ministry Taskforce report

1995• Count Me In Too Australia• Trialled in New Zealand 2000• Australian model adapted to

suit NZ students and framework extended

• Numeracy projects 2001 ENP ANP NEST

• 2002/3/4 ENP ANP INP SNP

3

Strategy is about how children solve number problems, in particular the mental processes they use.

Creates new knowledge through use

Strategy Knowledge

Provides foundation for strategies

Knowledge considers the key items of knowledge that children need to acquire.

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I buy 36 bales of hay at 44.50 each. How much do I pay? Explain how you got your answer. What strategy did you use? What knowledge did you need?

Typical Numeracy Project Plan

Workshop One:The Number Framework and The Diagnostic Assessment

Workshop Two:Getting Started,Knowledge & introduction to teaching model

Workshop Three:Addition & Subtraction strategy tchg

Workshop Four:Multiplication, Division and Fractions

Workshop Five:Evaluation

Visit One:Modelling Assessment

Visit Two:Knowledge Teaching with Whole Class. Strategy teaching with group.

Visit Three:Knowledge observedStrategies modelled

Visit Four:Observation of teaching

Diagnostic Assessment of Students (Initial)

Diagnostic Assessment of Students (Final)

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What could change this year?

• Groups for maths, up to three• Planning will reflect needs of groups• Cooperative planning, Quality learning circles• Lessons will consist of more parts:

Warm Up – Strategy –Practice – Games –Warm Down• Learning Outcomes will be shared with children before lessons.• A daily mathematics reflection recorded in books • Materials – Imaging – Number Properties scenario.• Type of questions. Open ended.• Listening to student responses.

• This is an excellent opportunity to try something new. It will not be an easy journey but it will be a rewarding one.

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Opening the Door...

• The Teaching Model

ExisitingKnowledge &

Strategies

Using Materials

Using Images of Materials

Noticing then Using Properties of Numbers

New Knowledge & Strategies

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Stages of DevelopmentStage 0 Emergent

Stage 1 1 – 1 counting

Stage 2 Counting from 1 on Materials

Stage 3 Counting from 1 by Imaging

Stage 4 Advanced Counting

Stage 5 Early Additive

Stage 6 Advanced Additive/Early Multiplicative

Stage 7 Advanced Multiplicative/Early Proportional

Stage 8 Advanced Proportional 8

Emergent

STRATEGY• This child is

unable to count a set of objects

KNOWLEDGE• Rote count to 5 at

least.

9

One To One Counting

STRATEGY• Count a set of

objects to 10 by one to one matching

KNOWLEDGE• Rote count to 10 at

least

10

Counting from one on Materials

STRATEGY• Solve simple addition

and subtraction problems to 20 by counting all the objects.

KNOWLEDGE• Rote count to 20 at

least• Instant recognition of

patterns to 5 including finger patterns

• Forward and backward number word sequence 0 – 20

• Order numbers to 20• Numbers before and

after in the range 1 - 20

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Counting From One By Imaging

STRATEGY• Solve addition and

subtraction problems to 20 by counting all the objects and or numbers in my head.

KNOWLEDGE• Instant recognition of

patterns to 10 including finger patterns

• Ordering numbers 0-20• Forward and backward

word sequence in the range 0 –20

• Say the number before and after a given number in the range 0-20

12

Advanced Counting

STRATEGY• Solve addition and

subtraction problems by counting on or back in my head from the largest number using supporting materials then moving to imagery.

• Solve addition and subtraction problems by counting on in 10’s and 1’s.

• Solve multiplication problems by skip counting in 2s, 5s 10s.

KNOWLEDGE• Recognising numbers 0 –

100• Ordering numbers 0-100• Forward and backward

word sequence 0-100• Numbers before and after

a given number from 0-100• Skip count in 2s, 5,s 10s

forwards and backwards.

13

Early Additive Part Whole

STRATEGY• Solve addition and

subtraction problems in their head by working out the answer from basic facts they know.

• Solve addition and subtraction problems with 2 or 3 numbers using groupings of 10 and 100.

• Use addition strategies to solve multiplication strategies

KNOWLEDGE• Recall doubles to 20 and

corresponding halves• Recall the names for 10 • Recall the teen numbers• Skip count in 2s,5s, 10s

forwards and backwards

14

Advanced Additive Part Whole

STRATEGYChoose from: • Compensation• Place Value• Compatible numbers• Reversibility• Equal Additions• Decomposition to solve + and - problems.Use pencil and paper or calculator to

work out answers where the numbers are large or untidy

Carry out column + and – with whole numbers of up to 4 digits.

Solve multiplication and division problems using known strategies eg doubling, rounding.

KNOWLEDGE• Identify numbers 0-1000• Forward and backward sequence

by 1,10,100 to 1000• Order numbers from 0-1000• Recall + and - facts to 20• Recall multiplication facts for 2, 5,

and 10 times tables.

15

Advanced Multiplicative Part Whole

STRATEGY• Solve +, - , x and ÷

problems with whole numbers (and decimals) using a range of strategies.

• Solve problems involving fractions, decimals, proportions and ratios using multiplication and division strategies

KNOWLEDGE• Identify, order and say

forward and backward number sequence from 0 –1000000

• Recall multiplication and division facts.

• Order fractions, including those greater than 1.

16

Advanced Proportional Part Whole

STRATEGY• Choose appropriately

from a broad range of strategies to +, -, x and ÷ fractions and decimals.

KNOWLEDGE• Know equivalent

proportions for unit fractions with numbers to 100 and 1000

• Know fraction, decimal, % conversion for unit fractions.

• Order decimals to 3 places.

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Numeracy Project Assessment -

• NumPA is a diagnostic tool. • The interview consists of two main parts; strategy

questions and knowledge questions.• NumPA is an individual interview with children.

This is necessary for two reasons: – Uncovering mental strategies involves finding out how

they solve number problems.– The interview process is invaluable for developing the

teacher’s knowledge about each child’s mathematical understandings.

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Purpose of Strategy Window

To assist teachers in being able to:

• Focus on uncovering student thinking.

• Determine which interview form to administer through the use of careful questioning.

• Save time.

19

Prompts

To uncover thinking after the student responds:

• How did you get the answer?• What numbers came into your head?• Where did you start counting?• What did you start with?• What numbers came next?• What did you do with the numbers?

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Numeracy Project Assessment - NumPA  

Strategy Sections of the Assessment Addition and Subtraction  - windowMultiplication and Division (Forms B & C only)Fractions (Forms B & C only)

Knowledge Sections of the AssessmentNumeral IdentificationForward and Backward Whole Number Sequence and Order Using Fractions, Decimals & Percentages (Forms B & C only)Grouping / Place Value  

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Short Term Plan

• To knowledge test the students in my class and record results.

• To interview the students in my class to gain insights as to how they think.

• To establish a better understanding of what my students know about mathematics.

• To use this data to inform my teaching.