Numeracy 2003

Presented by JB

2003

“To be numerate is to have the ability and inclination to

use mathematics effectively in our lives – at home, at work and in the

community.”

Curriculum Update 45 Ministry of Education 2001

Ministry Philosophy

• Research based

• Dynamic and evolutionary

• Teachers are key figures in change

• Focus is to improve student performance through teacher professional development

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 ENP ANP INP SNP

Learning Outcomes• Teachers will gain an awareness of

the New Zealand Number Framework and Assessment Tool.

• Teachers will develop an understanding of the progression of student’s number acquisition.

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.

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

Emergent

STRATEGY• This child is

unable to count a set of objects

KNOWLEDGE• Rote count to 5 at

least.

One To One Counting

STRATEGY• Count a set of

objects to 10 by one to one matching

KNOWLEDGE• Rote count to 10 at

least

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

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

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.

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

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.

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.

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.

Stage and Behavioural Indicators

• When testing students you will observe their strategies and knowledge within the framework stages of development.

• This is what they can do now.• Strategy teaching begins with

consolidation at students highest current stage before moving them into the next stage.

Numeracy Project Assessment -NumPA

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

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.

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?Allow maximum of 10 seconds thinking time .• What are you trying to do?