Numeracy tests and what they assess

Types of numeracy tests

There are generally two types of assessments.

Norm-referenced tests

Norm-referenced tests compare a student's abilities with others. Each task or test has a range of average scores for students who do not have learning difficulties with that task or test. If a student's score is within this range their outcomes will be described as average. If it's well below this range, it may indicate a learning difficulty or disability, such as dyscalculia.

Students' outcomes are measured as raw scores and then converted to standard scores, percentile ranks, a stanine score, or an age/year level norm. For more information, visit Interpreting assessment data.

Criterion-referenced tests

Criterion-referenced tests assess specific skills or knowledge without comparing a particular student to others. They do not tell you about a student’s performance in an expected range, but whether the student has achieved certain criteria.

Examples include tests that assess how well students can apply procedures they've been taught in maths.

Assessment tools

The Insight Assessment Platform features information and online tools to help teachers assess the progress and learning needs of all learners, including those with learning difficulties.

Some of the tests mentioned below may incur a cost. Your school may be able to purchase these tests as part of the wide range of practices and school activities supported through Tier 2 school-level funding: 'purchasing specific equipment, adaptive technology, devices or materials to support learning'. You can find more information (in the Guidance section) on Disability Inclusion Funding and Support: Policy.

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 refer 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 8 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.

Observations of a student's performance during numeracy learning and numeracy interviews

Observing how students approach numeracy learning and tasks and the thinking they use provides useful data for decision making. The quality of observational data is determined by what you observe and how, and the anecdotal records, checklists and rating scales you use.

The schedule for early number assessment

Structured interviews with students about numeracy, such as the Schedule for Early Number Assessment (SENA), provide valuable information about a student's approach to numeracy learning and numeracy learning difficulty.

The interview can tell you:

what students know and can do independently and with scaffolding
their level of engagement with numeracy tasks, motivation, self-efficacy and persistence
how they overcome barriers and obstacles in learning
their use of cognitive strategies
their use of metacognition for numeracy.

SENA 1 assesses a student's knowledge and skill in the areas of:

numeral identification
forward and backward counting by saying number word sequences
subitising and use of counting strategies
early addition and subtraction
multiplication and division.

SENA 2 assesses a student's knowledge and skill in the areas of:

early arithmetical strategies
numeral identification of numbers greater than 1,000
counting by 10s and 100s from any number
combining and partitioning to 20
place value 10s and ones
multiplication and division to multiplication and division as operations
area multiplication.

SENA helps you to interpret the numeracy strategies being used by each student in each area. The developmental trajectory for each area on SENA 1 is as follows:

numeral identification: four levels (emergent, numbers 1–10, numbers 1–20 and numbers 1–100)
forward and backward counting by saying number word sequences: six levels (emergent, initial 1–10, intermediate 1–10, facile 1–10, facile 1–30 and facile 1–100)
subitising and use of counting strategies: three levels (emergent, perceptual, conceptual)
early addition and subtraction; five levels (emergent, perceptual, figurative, counting on and back, facile)
multiplication and division: three levels (unable to form groups, able to form groups, able to find the total by).

This protocol assesses both the quality or sophistication of the student's forward counting for each range of numbers and the highest range to which the student can apply it.

Use SENA to understand a student's numeracy learning difficulty

SENA can help you to understand the nature of a student's numeracy learning difficulty. For example:

SENA is a criterion-referenced test. You can match a student's performance on each section of the SENA 1 and 2 with achievement standards on the Victorian Curriculum F–10: Mathematics. The highest level achieved by a student in each area will help you in deciding whether the student has a numeracy learning difficulty.
You can create a numeracy profile for a student who has a numeracy learning difficulty by collating their outcomes for each section of the SENA 1 or 2 on the Individual Analysis Sheet and comparing their performance with content descriptors on the Victorian Curriculum F–10: Mathematics.
Mapping the student's outcomes on the SENA onto the Victorian Curriculum F–10: Mathematics will indicate the areas of numeracy in which the student shows delay. You can also look for evidence of more general delay in other areas of learning and development.

You can find more information on mathematics and numeracy assessment on Mathematics Teaching Toolkit.

- 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.

P-12 school

Updated 1 February 2024