Post on 04-Jan-2016
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.
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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.
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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.