Senior Numeracy Pilot Project 2005 Workshops One Introduction 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. 4 I buy 36 bales of hay at 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 observed Strategies modelled Visit Four: Observation of teaching Diagnostic Assessment of Students (Initial) Diagnostic Assessment of Students (Final) 5

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. 6

Opening the Door... The Teaching Model 7

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 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

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

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. 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 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. 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 – 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. 17

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. 18

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? 20

Numeracy Project Assessment - NumPA Strategy Sections of the Assessment Addition and Subtraction - window Multiplication and Division (Forms B & C only) Fractions (Forms B & C only) Knowledge Sections of the Assessment Numeral Identification Forward and Backward Whole Number Sequence and Order Using Fractions, Decimals & Percentages (Forms B & C only) Grouping / Place Value 21

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.