Numeracy tests and what they assess

The Mathematics Online Interview (MOI) assesses the mathematical understanding of students in Foundation to Year 2 using growth points or 'stepping stones', in the strands of Number and Algebra, and Measurement and Geometry. Conduct the interview one-on-one and refers to the growth points.

The assessment consists of 77 questions and takes approximately 30 to 45 minutes.

The MOI is mapped to the Victorian Curriculum F–10: Mathematics. Each task is linked to relevant achievement standards and content descriptors.

Sections of the MOI

• Section A: Counting
  
• Section B: Place Value
  
• Section C: Addition and Subtraction
  
• Section D: Multiplication and Division
  
• Section E: Time
  
• Section F: Length Measurement
• Section G: Mass Measurement
  
• Section H: Properties of Shape
• Section I: Visualisation
  

For more information, visit MOI user guide, tip sheet and support.

The Fraction and Decimals Online Interview (FDOI) assesses a student's knowledge, skills and behaviours about fractions, decimals, ratios and percentages. Designed for use with students in years 5 to 10 but valuable for assessing high-achieving students in Year 4 or below.

The FDOI consists of 54 questions, takes approximately 30 to 45 minutes, and should be conducted as a one-on-one interview. The FDOI is mapped to the Victorian Curriculum F–10: Mathematics. Each task is linked to relevant achievement standards and content descriptors.

Scaffolding Numeracy in the Middle Years provides teachers with access to assessment materials, learning plans, authentic tasks and the Learning and Assessment Framework.

Learning and Assessment Framework

The Learning and Assessment Framework (LAF) can be used to assess key ideas and strategies related to the development of a student's multiplicative thinking. Multiplicative thinking is characterised by:

• a capacity to work flexibly and efficiently with an extended range of numbers (larger whole numbers, decimals, common fractions, ratios and percentages)
  
• an ability to recognise and solve a range of problems involving multiplication or division including the direct and indirect proportion
  
• the means to communicate this effectively in a variety of ways (words, diagrams, symbolic expressions and written algorithms).
  

The LAF should be conducted as a one-on-one interview. Two assessment booklets can be downloaded and used to help measure a student's knowledge, skills and abilities against the framework. Each booklet contains:

• assessment tasks
  
• student score sheets
  
• scoring rubrics for each task
  
• raw score translator.
  

After conducting the assessment, use the score sheets, rubrics and raw score translator to score and locate your students in one of the eight zones of the LAF. Students may be located across several zones, so you may need to familiarise yourself with several areas of the framework.

The eight zones of the LAF

• Zone 1: Primitive Modelling
  
• Zone 2: Intuitive Modelling
  
• Zone 3: Sensing
  
• Zone 4: Strategy Exploring
  
• Zone 5: Strategy Refining
  
• Zone 6: Strategy Extending
  
• Zone 7: Connecting
  
• Zone 8: Reflective Knowing
  

The Assessment for Common Misunderstandings (ACM) tests a student's thinking about key aspects of Numbers.

A hierarchy of student responses is identified for each task and, for each of these, an interpretation of what the response might mean is provided with some practical ideas to address the learning needs identified.

The ACM should be used as a one-on-one interview. The assessment tasks take approximately 5–10 minutes each.

Assessment levels and key ideas

• Level 1 – Trusting the count
  
• Level 2 – Place-value
• Level 3 – Multiplicative thinking
• Level 4 – Partitioning
• Level 5 – Proportional reasoning
• Level 6 – Generalising.

Note: Levels refer to the Victorian Essential Learning Standards. They are progressively being updated to align with the Victorian Curriculum F–10: Mathematics.    

The Test of Early Mathematics Learning Ability, Third Edition (TEMA-3) assesses skills for ages 3–9 in the areas of:

• enumeration (perception of small numbers)
  
• number-comparison (perception of 'more', choosing the larger number)
  
• mathematics concepts (cardinality, number constancy, part-whole concept)
  
• counting, verbal counting
  
• calculation skills (non-verbal (concrete) addition and subtraction, modelling addition word problems)
  
• numerical literacy, reading and writing numerals
  
• recall of number facts and mental addition and subtraction.
  

The test comprises two sections, each with 72 items. It describes outcomes as a raw score, age and year-level equivalents, percentile rank and Maths Ability Score (standard score).

TEMA-3 is administered individually. It is not a timed test. It takes up to one hour and can be administered over several sessions.

Although it is a norm-referenced test, student responses to individual items can be very informative about number understanding.

TEMA-3 is also helpful when assessing older students to:

• identify students who are achieving below their expected level
  
• develop a student's numeracy learning profile by comparing their outcomes in particular aspects of mathematical knowledge, as well as identifying strengths and difficulties. For example, scores may suggest that a student finds place value challenging but is capable of mental addition.
  
• look for possible causes for a student's difficulty by comparing outcomes in formal maths, such as numerical literacy, number facts, concepts and calculations, with outcomes that assess informal concepts and skills in relative magnitude, counting, and calculation.
  
• assess and monitor a student's progress.
  

KeyMaths provides a comprehensive assessment of essential mathematical concepts and skills for ages 4.5 to 21. It covers maths content taught typically from kindergarten through to Year 9. It's comprised of 10 sub-tests grouped into three general areas:

Basic concepts (conceptual knowledge)

• Numeration
  
• Algebra
• Geometry
• Measurement
  
• Data analysis and probability.
  

Operations (computational skills)

• Mental computation and estimation
• Addition and subtraction
  
• Multiplication and division.
  

Applications (problem-solving)

• Foundations of problem-solving
  
• Applied problem-solving.
  

The test provides a student's sub-test scale scores, area scores and total test standard scores, percentiles, age and year-level equivalents and growth values. The average value of the standard scores for the test as a whole and each area at all ages is 100, with a standard deviation of 15. A standard score of less than 85 means the student is in the lowest fifteenth percentile range for their cohort.

KeyMaths guides you through the process of comparing standard scores for different areas and students and explains why identifying discrepancies between them is important.

Using KeyMaths to unpack a student's numeracy learning difficulty

KeyMaths can help you to unpack a student's numeracy learning difficulty. For example:

• Each student's total test score can be expressed as a standard score or a percentile and can be used to make age and developmental comparisons. These scores will also help to locate a student on a developmental continuum, such as the National Numeracy Learning Progressions and help you compare them to their peers.
  
• Create a numeracy profile for a student with a learning difficulty by analysing their standard scores across the three general areas. By interpreting this assessment information you will be able to identify patterns in their outcomes, as well as the types of knowledge and skills that need to be developed.
  
• KeyMaths assessments can help you to make inferences about the cause(s) of a student's numeracy learning difficulty. The skills assessed by each item are clearly specified and map to the Victorian Curriculum F–10: Mathematics. You can examine whether a student's performance across the various areas on the tests is typical of that of a younger student. This may indicate a developmental delay or identify foundation knowledge and skills that a student may not have learned previously.
  

You can also identify early signs or indicators that may suggest a learning disability or dyscalculia. The sub-tests with items that most closely assess informal enumeration skills are Numeration (1, 2, 3, 4, 5, 6, 7 and 8) and Algebra (1, 2 and 3). A student's outcomes in these sub-tests should be closely monitored.

Progressive Achievement Tests (PAT) Early Years Maths assesses the development of mathematical skills every six months during Foundation and Year 1. It focuses on numbers and targets measurement, geometry and statistics skills. It comprises four tests that increase in difficulty:

Start Foundation

Students count, combine and share collections, recognise and order digits under 20, complete simple patterns, interpret positional language, compare quantities, lengths and sizes, and name simple shapes and order objects.

Mid-Foundation

Students recognise and order digits 0–99, skip count by fives, solve simple problems involving addition, subtraction and sharing with numbers up to 50, interpret simple graphs, compare volume and mass, and identify common 3D shapes.

Mid-Year 1

Students recognise and order digits 0–999, identify and represent place value, solve simple problems involving addition, subtraction and sharing with numbers up to 100, represent problems with number sentences, complete four-element patterns with rotation, skip count backwards by twos, measure the length in centimetres, identify simple features of 3D shapes, and compare data in a simple table.

End Year 1

Students recognise and order digits 0–9,999 including using number lines, solve simple problems involving addition, repeated addition, subtraction and sharing with numbers up to 100, skip count by threes, identify 2D features in 3D shapes, insert, compare and combine data in simple graphs, identify the probability of events happening, and make simple interpretations of calendars.

PAT Early Years tests are administered online. Each test is made up of 30 questions and takes approximately 20–35 minutes to complete. Students should be given four to eight minutes of practice time.

Questions and instructions are provided via audio and written text. Students independently navigate through the tasks.

Outcomes are described using PAT scale scores. Each student's score is linked with their numeracy understanding and skill using the PAT Maths achievement band descriptions.

PAT scale scores are aligned with a numeracy learning continuum that describes what typical progress looks like. This continuum is extended to underpin PAT Maths Fourth Edition. This means you have a numeracy pathway along which you can monitor a student's progress through to Year 10. You can identify at any time the skills a student has mastered, those they are consolidating and those they will learn next.

Using PAT early years maths to unpack a student's numeracy learning difficulty

PAT Early Years Maths can help you to unpack a student's numeracy learning difficulty. For example:

• A student's score on each of the tests can be expressed as a standard patm score, a percentile rank and stanine. You can use these to determine the location of the student in comparison with their peer group (PAT Early Years Reference Groups). Once you know the band within which the student's score sits, you can obtain a description of the student's typical understanding and skill in number, algebra, measurement, geometry, statistics and probability (PAT Maths: Strands and achievement band descriptions).
  
• Use the data from the tests to create a numeracy profile for a student. The item difficulty for each test shows the location of each task in number, algebra, measurement, geometry and statistics (and probability for End Year 1). You can note which items the student answered correctly and their average score in each area.
• Use the items in the Start Foundation test that assess counting, combining and sharing collections, ordering numerals less than 20, completing simple patterns and comparing quantities, to indicate whether there may be a learning disability or dyscalculia. Some of the tasks are pre-Foundation.
  

You can examine whether a student's performance across the various areas on any of the tests is typical of that of a younger student. This could suggest that the cause of a student's numeracy difficulty is developmental delay.

PAT Maths Fourth Edition assessment focuses on number knowledge, strategies, algebra, geometry, measurement and statistics. PAT Maths is designed for years 3–10. There is an additional test that some schools use in Year 2.

The Dyscalculia Screener assesses a student's understanding of numerosities and the ability to apply them. It can be used with students aged six and up, although it is more reliable for students aged seven and above. It is administered individually and takes 15–30 minutes to complete.

The Dyscalculia Screener comprises four online tasks. Students respond to the tasks by pressing a designated computer key as quickly as possible. The computer records the time taken to respond to each item.

The four tasks are:

• Dot enumeration: the student sees a set of up to nine dots on one half of a screen and a numeral on the other. They decide whether the numeral matches the set of dots (How many spots are there? Does this match the number?).
  
• Number comparison: the student sees two numerals and selects the one that specifies more (Which number is more than the other?).
• Arithmetic achievement (addition and multiplication): the student sees an addition number sentence such as 3 + 5 = 9 and decides whether the answer is correct (Is this sum correct?). Students aged 10 or older also see multiplication number sentences.
• Simple reaction time: the student presses a computer key as quickly as possible as soon as they see a dot appear on the screen. (As soon as you see a black spot, press the right key with your right hand.) The time taken to do this task is used to adjust their reaction times for the preceding three tasks.
  

Student outcomes are expressed as standard scores with norms for each age group. These scores are automatically calculated and displayed by computer in a printable form.

Using the dyscalculia screener to understand a student's numeracy learning difficulty

The Dyscalculia Screener can help you to describe a student's numeracy profile by making clear the following patterns:    

• Lower performance on the achievement test than on the capacity tests suggests a numeracy learning difficulty.
  
• Lower performance on the capacity tests than on the achievement test suggests a specific learning disability (for example, dyscalculia)
  
• Significantly low performance on both capacity and achievement tests suggest a broad-based general numeracy learning difficulty.
  

These patterns can help to identify the causes of a student's numeracy difficulty and whether their results indicate dyscalculia. It's recommended you use the screener alongside a standardised test, such as the TEMA-3.

An important and very informative additional test that is easy to administer is the number line.

For very young students a 0–10 number line can be used. For mid-primary, a 0–100 number line is appropriate and for upper primary, 0–1,000 can be administered.    

A logarithmic function rather than a straight line is indicative of an ordinal understanding of numbers, but not of the ratio properties between numbers. Administering both 0–10 and 0–100 for mid-primary, or 0–100 and 0–1,000 for upper primary, can provide a progression towards a mature understanding of the mapping of symbols onto a non-symbolic format.

• Australian Council for Educational Research (ACER) (2013)PAT Early Years Maths Fourth Edition, ACER Press, Melbourne.
  
• Butterworth B (2003) Dyscalculia Screener, Nelson Publishing Company Limited, London.
  
• Conolly A (2010) KeyMaths-3 Diagnostic Assessment – Australian and New Zealand Language Adapted Edition, Third Edition, Pearson, Minneapolis, MN.
• Ginsburg H and Baroody A (2003) Test of Early Mathematics Ability – Third Edition, Pro-Ed, Austin, TX.
• Department of Education (1999) 'Schedule for Early Number Assessment (SENA)', Count Me In Too, Department of Education, Sydney, New South Wales.