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.

Blueprint for Literacy Success Using strategies rather than items of knowledge is important in reading and writing acquisition because it leads to independence. Once children know how to use appropriate strategies in their reading and writing, they are able to learn a little more about reading and writing every time they read and write. Using strategies rather than items of knowledge is important in mathematics acquisition because it leads to independence. Once children know how to use appropriate strategies in their mathematics, they are able to learn a little more about mathematics every time they do mathematics.

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 Development Stage 0Emergent Stage 11 – 1 counting Stage 2Counting from 1 on Materials Stage 3Counting from 1 by Imaging Stage 4Advanced Counting Stage 5Early Additive Stage 6Advanced Additive/Early Multiplicative Stage 7 Advanced Multiplicative/Early Proportional Stage 8Advanced 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

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 Forward and backward word sequence Numbers before and after a given number from 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 STRATEGY Choose 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 Forward and backward sequence by 1,10,100 to 1000 Order numbers from 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 – 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?