1. A Guide to the New Assessment Tool for Primary Mathematics
Presented by Charlotte Wilkinson
©2018 NC Wilkinsons Ltd

2. Why To move beyond numeracy project stages
To make use of the learning progressions for mathematics (Developed originally for the PACT reporting tool)
To better implement the NZ Curriculum
Assess what you value and you are more likely to achieve what you value.
Numeracy project stages are not wrong but they have been replaced with something better able to assist the implementation of the NZ Curriculum.
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3. NZ Curriculum
In a range of meaningful contexts, students will be able to solve problems and model situations that require them to …… use their mathematics
This tool assesses the students ability to solve problems and model situations using words, pictures, diagrams and equations
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4. Assessment of Mathematics
Ability to use mathematics to solve problems
Mathematical knowledge and skills
Assessing mathematics requires more than one assessment
GLoSS and IKAN (the most ridiculous assessment ever invented!) – both summative snapshots
PAT and/or AssTle have a place for tracking trends and analysis of data could give some insights assuming students haven’t guessed or over thought the multiple choice type questions.
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5. Organisation Section 1 – Baseline – Mid Level 1
Section 2 – Early Level 1 – Upper Level 1
Section 3 – Upper Level 1 – Mid Level 2
Section 4 – Mid Level 2 – Early Level 3
Section 5 – Early Level 3 – Upper Level 3
Section 6 – Upper Level 3 – Upper Level 4
The six sections means there is teacher judgement to decide which section of the tool to use.
When the teacher knows the student then this should not be difficult.
For new student the teacher may use a combination of first impressions and student’s age.
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6. Evidence collected in each of the sections against the learning progressions.
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7. Level 1 – Individual Interview
Section 1 (7 questions)
Knowledge of:
Sorting
Naming shapes
Patterning
Counting
Numeral recognition
Making sets
Sequencing
Equal Grouping
Section 2 (6 questions)
Knowledge of
Counting
Sorting
Naming shapes
Patterning
Solving
Addition (within 10)
Subtraction (within 10)
Equal Sharing
These sections need to be carried out as individual interviews due to the age of the students most likely to be operating at these levels.
Paper and pencil is given to students in section 2 as their problem solving may involve drawing the problem (or student modelling with the counters).
They are also assessed on whether than can record the problem as an addition or subtraction equation using the operation symbols and the equals symbol.
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8. Level 2 – Guided Recording Individual or small group
Section 3 (9 questions)
Solving:
Addition type
Subtraction type
Multiplication type
Strategy thinking:
Counting on or early part/whole
Knowledge used:
Doubles,
Early place value
Fractions (equal parts)
Section 4 (8 questions)
Solving:
Addition/Subtraction type
Multiplication/Division type
Strategy thinking:
Early to advanced additive
Early multiplicative
Knowledge used
Place value
Recall +/- facts
Recall some x/÷ facts
Link between fractions, x ÷
Paper and pencil as students are asked to represent problems as addition or subtraction equations and a multiplication equation.
Paper and pencil also allows students to use problem solving strategies – draw a picture or diagram to assist the thinking.
From their recordings you are often able to see their thinking without having to ask for an explanation of their thinking. Also having a recording assists students to explain the thinking they have just done but talking to their recording.
Administration: Individual or sitting with a small group of students – each student working on their own piece of paper
Not all questions need to be done in one sitting.
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9. Level 3 & 4– recorded by student
Section 5 (8 questions)
Solving
Addition/Subtraction
Multiplication/Division
Strategy thinking
Advanced additive, multiplicative
Knowledge used
Recall of + - x ÷
Decimals
Perimeter
Volume
Ratios
Section 6 (6 questions)
Solving (including multi step)
Addition/Subtraction
Multiplication/Division
Strategy Thinking
Advanced additive, multiplicative & proportional
Knowledge Used:
Recall of + - x ÷
Decimals
Fractions
Percentages
Scales
These problems are becoming more complicated and pull in knowledge from other areas of mathematics (geometry & measurement)
Expect students to read the questions for themselves but then assist students to unpacking the problems if required. If knowledge of perimeter or volume is missing then explain what this is to the student making note there is no evidence for this measurement learning progression.
These questions can be completed over a number of mathematics lessons.
The ability to communicate problem solving through the written medium of words and equations for a third party to comprehend is a requirement of any written mathematics assessment. (See page 16 of the curriculum document – language across all learning areas)
Conferencing individual students will allow them to more fully explain their thinking by talking to their recordings.
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10. Multiple use of same section
For each of sections 2 – 6 there are four versions of the questions
To mitigate variations caused by change of context or question type only the numbers have been changed in each version.
Most teachers/classes will use one or two of the sections meaning teachers will become familiar with their sections of the assessment.
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11. Resources Required Section 1 Section 2 Student question booklet
Shape cards
Number cards
Counters
Student record sheet
Student question booklet
Shape cards
Counters
Student record card
Paper & pencil
Sections 3 – 6
Student questions – as a booklet or on individual cards
Student record card
Paper & pencil
Paper & pencil is required as students ability to solve problems is not an assessment of mental dexterity.
Solving problems involves making sense of a problem and communicating a solution.
Can the students interpret the problem by expressing it as an equation?
Students may record their thinking in diagrams (eg empty number line) this allows the teacher to see the thinking the student has used without having to ask them to explain their thinking. However it may still be necessary to uncover how a student thought about a solution by questioning. If you see a student counting on don’t ask them how they solved it!
Student questions can be given in booklet form – one question per page available as a download form the edify website. These could be printed on individual cards if required.
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12. Marking
For each question answered the response is coded to a specific learning progression set
Response
Progression
Unable to record addition statement
Symbols & Expressions Set 1
Records addition statement
Symbols & Expressions Set 2
Counts on
Additive Thinking Set 4
a = 42
= 42
b = 43
= 43
Additive Thinking Set 5
c = 44
= 44
d = 43
After each set of questions a table is provided to show where the response sits in terms of the learning progressions.
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13. A solutions chart for all questions in a particular assessment is available as a download.
(Mistake in first box Q4 has been noted by publishers!)
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14. The learning progressions can be found at https://lpf. education. govt
However find descriptions of the learning progressions cannot be found directly on this site but exemplars for each of the progressions can be found here or by downloading the learning progressions app.
Descriptions for the learning progressions can be found at under the Free Teaching Resources icon.
The progressions give the key progression outcomes for each strand – unfortunately they were not set against the curriculum levels (the PACT tool did this step)
The Minister for Education has requested that this alignment is made clear but as yet nothing has happened.
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15. I opened every exemplar and pulled out the key evidence shown for each set of the progressions.
I have then used the curriculum to make an alignment to the curriculum levels.
A copy of this chart (A3) is available from Members only (Subscription $30 individual (PayPal) or $275 for schools (Paypal or Invoice) adjusted for schools less than 9 teachers (Invoice only)
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16. Student best fit: ©2018 NC Wilkinsons Ltd AT Set 4 Set 5 S&E Set 1AT
Set 4
Set 5
S&E
Set 1
Set 2
Set 3
MT Set 2 MT
MT Set 4
MT Set 5 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9
Level 1
Level 2
AT:Set 4
AT:Set 5
MT: Set 2
MT: Set 3
MT: Set 4
MT: Set 5
S&E: Set 1
S&E: Set 2
S&E: Set 3
There will always be an element of teacher judgement so in school moderation is always best practice.
The Assessment book will give guidance to assist your decisions.
Final assessment is made against the curriculum levels.
Information from the MOE is that assessment should be against curriculum levels showing progress through the curriculum.
Student best fit:
Upper Level 1
Early Level 2
Mid level 2
Date
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17. For each section of each curriculum level there is a statement describing what the student can do now from the evidence of your teacher judgment.
A “where next?” statement giving the next learning steps is also provided along with where to find appropriate resources aligned to Pearson Mathematics
This appendix is printed in the book and also available as a download from the Primary Mathematics Assessment Tool on the Edify website.
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18. A schools profile sheet to show progression across the students time in the school using a range of assessment tools.
PMAT
PAT – central score band has been sectioned in score bands for each section of the curriculum using the number descriptors and adjoining curriculum level indicators in the PAT administration guide.
Wilkie Way Assessment Screen – with current scoring divided into smaller increments to match the upper, middle and early in each level.
Portfolio Evidence – school designed tasks undertaken each term and moderated by staff. (result of in school professional learning contract)
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19. A schools profile sheet to show progression across the students time in the school using a range of assessment tools.
PMAT
E asTTle – using advanced, proficient and basic to match upper, middle and early curriculum levels for number and the other strands
Wilkie Way Assessment Screen – with current scoring divided into smaller increments to match the upper, middle and early in each level.
Moving towards moderated tasks– school designed tasks undertaken each term and moderated by staff. (result of in school professional learning contract)
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20. Wilkie Way Assessment Screen
The screen is not timed. Students have as long as they require to show what they know.
Whole number place value
Addition & Subtraction – recall & solving by chosen method including mental & algorithm
Multiplication & Division – equal grouping, arrays, recall, solving by chosen method & algorithm
Fractions
Decimals (Level 3 & 4 only)
Even year and odd year version of each screen available from Or
Each pack has 35 student copies & a teacher guide
Further teacher guides available from Members Content Area.
Download an order form for details of discount for multiple copies of each pack
Single copies available for small schools.
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21. Student Management Systems
Systems can be altered to fit new measures
MOE information is indicating the move to using curriculum levels as a measure of progress in all learning areas. (National standards used curriculum levels)
A system should not stop us from making progress. When it requires changing it can be changed.
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22. Managing data Beagle Innovations
This NZ designed cloud based data management system will include PMAT in their suite of assessment tools to enable you to manipulate the data alongside other data for insights into each students achievement and learning needs.
Check out the website for further information.
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23. Where can I get my copy? www.edify.co.nz/shop/primary $119.00
All resources for making the kits available through a link from the above website.
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