This page takes you through key questions and steps to help you understand the nature of a student's learning difficulties in numeracy.
Use the following questions and advice as a starting point before planning any adjustments in teaching or making recommendations as part of an
individual education plan (IEP).
The first step in unpacking a student's learning difficulty is to get an accurate picture of their current numeracy abilities and their maths knowledge and skills.
It's important that student data provides an overall assessment of the student's abilities and can be analysed in detail and describe what a student already knows and can do.
A student's outcomes for these assessments, coupled with observation data, can then be evaluated using the following questions:
- How do their current knowledge and skills compare to a typical student at this level?
- Are their outcomes indicative of a learning difficulty or disability (such as dyscalculia)?
- Has the student demonstrated this difficulty consistently and over a significant period?
Assessing a student's current knowledge and skills
Victorian Curriculum F–10: Mathematics provides a useful starting point for assessing a student's existing knowledge and skills, using three strands:
- Number and Algebra
- Measurement and Geometry
- Statistics and Probability.
Each strand has a set of substrands.
National Numeracy Learning Progressions can be used to create an accurate picture of a student's developmental level. Each area describes the sequence of knowledge and skills that a student needs to learn. For each area a student must learn to:
- understand, connect and apply mathematical concepts and structures of increasing complexity
- use mathematical understanding and procedures fluently to recall and apply it accurately, efficiently and flexibly
- reason logically and use various thinking strategies.
A student's outcomes in these areas can be measured using standard scores or percentile ranks. You can also locate their performance on the curriculum by describing the indicators that best match a student's outcomes.
Once you have a measure of a student's outcomes in each area, it's vital to note the areas in which a student has demonstrated capability and areas of challenge.
For more information, visit Numeracy tests and what they assess.
When trying to determine if a student has a learning difficulty it's helpful to start with their cohort or class. Do you feel that the class represents an average or typical distribution of student ability for the year level? If so, then compare students' outcomes using a normal distribution or bell curve.
If you are unsure if the class is typical, use the results of the entire year level or previous cohorts for comparison instead.
It's possible for a student to achieve in the average range or higher for some tasks and below average in others. However, if a student's overall scores in any area are in:
- the sixteenth to twenty-fourth percentile range, or at least one standard deviation below the mean for their year level or age, then they may be at risk of a learning difficulty.
- the third to fifteenth percentile range, or between one and two standard deviations below the mean for their year level or age, they are likely to have a learning difficulty.
- the second percentile range or lower, or at least two standard deviations below the mean for their year level or age, it is almost certain that they have a learning difficulty, and it is possible that they have a specific learning disability (such as dyscalculia).
For these descriptions to be accurate the student must have been demonstrating these difficulties consistently for an extended period and the cohort they are being compared to must be typical of students for that level.
Indicators of delayed development and learning disability
A student's learning difficulty may be caused by interruptions in their learning (such as extended time away from school) or other factors that have resulted in the delayed development of certain knowledge and skills, or they might be caused by a specific learning disability (such as dyscalculia).
Delayed development in numeracy and maths can be caused by sensory, physical, language, intellectual, emotional, environmental or socio-economic factors. Any of these developmental issues may impact on a student's numeracy learning and outcomes in maths.
Information about a student's delayed development may be available from your school. Families of students with learning difficulties may also have information about their child's development. There may also be reports from psychologists, speech pathologists or other health and medical professionals.
Students with dyscalculia have trouble understanding what numbers are and how they work. This ability is sometimes referred to as 'number sense'. Students with dyscalculia may, for example, struggle with telling analogue time. They may also:
- lack intuition about the relationship between symbolic forms of number, (that the word 'seven' and numeral '7' both mean the same thing) and relating symbolic forms to non-symbolic forms of numbers (for example, number lines or arrays of dots).
- have difficulties learning maths facts and procedures
- have trouble understanding quantities and concepts like more and less, or smallest and biggest
- have difficulties making number comparisons (for example, that 12 is greater than 10).
Apart from number sense, students with dyscalculia may also have difficulties interpreting and representing number and magnitude, specifically the ability to:
- rapidly and precisely enumerate (determine the number of) small sets of objects without needing to count them individually (subitising)
- efficiently compare the approximate magnitude of quantities (comparing approximate magnitude).
Differences in the brain that affect these foundational abilities contribute to difficulties with counting, reading and writing numbers, comparing the sizes of numbers and performing calculations. Students with dyscalculia typically have trouble with these core number abilities.
Students with non-neurological learning difficulties are unlikely to present with these issues.
You can find more information on:
Identifying a trend in a student's outcomes over time
To evaluate whether a student's outcomes are following a trend, collect data over an extended period and supplement this with data from their previous year. Determine if the student's performance is affected by environmental factors (such as sound, light, temperature), peer influence, or their location in the classroom (do they sit close to the board or at the back of the room, are they near additional noise or distractions such as an air conditioner, windows or corridor) when they engage in numeracy-related activities. Is their performance and confidence enhanced by using manipulatives or pictures?