Example of how to unpack a student's numeracy learning difficulty

To unpack Ben's numeracy learning difficulty, you first need to get an accurate picture of their current numeracy abilities and maths knowledge and skills.  

For a student in Year 6 the Victorian Curriculum F–10: Mathematics and the National Numeracy Learning Progression, which both describe the range of skills to cover, would recommend you collect current assessment information about Ben's abilities in the following three strands and substrands:

• Number and Algebra: number and place value, counting processes, additive strategies, multiplicative strategies, interpreting fractions, proportional thinking, number patterns and algebraic thinking, understanding money
• Measurement and Geometry: understanding units of measurement, understanding geometric properties, positioning and locating, measuring time
• Statistics and Probability: understanding chance, interpreting and presenting data.

You can collect two types of data. First, you can observe how Ben does various types of numeracy tasks in the classroom and list those they can demonstrate satisfactorily, the tasks that challenge them and the context in each case. Note which strand each task belongs to and the substrand involved.

Monitor whether Ben demonstrates particular difficulties consistently and over a significant period or whether they occur infrequently and Ben's performance is generally appropriate. You can begin to collect observational data about Ben's maths learning by:

• noting the types of maths tasks Ben can do well and those that challenge them. What computational strategies is Ben using for problem solving (for example, counting individual numbers or more sophisticated approaches)?
  
• asking Ben to 'think out loud' as they work through maths tasks that challenge them
• noting whether outcomes improve when you modify the teaching or context in particular ways
• noting whether Ben can do tasks from the same substrands typical of a years 4 or 5 level.

For any substrand you teach, observe how well Ben:  

• understands and links maths concepts, and can transfer procedural knowledge from one problem to a similar problem
  
• recalls and uses mathematical understanding and procedures fluently
• applies understanding in problem-solving
• reasons logically about numeracy patterns and uses various thinking strategies selectively
• learns and uses the maths language and symbolism
• manages and directs their learning activity
• engages with maths tasks and has self-efficacy as a maths learner.

The second step is to collect data using specific numeracy assessment tools that describe Ben's ability for each strand or area in terms of typical Year 6 skill levels. Some tools will describe Ben's skill in each area as a standard score, percentile rank or stanine score. Other tools will describe it in terms of the curriculum level that matches ability.  

You can find more information on Numeracy tests and what they assess.  

Interpret Ben's outcomes for these assessments by noting how their knowledge and skills in each area compares to a typical Year 6 cohort. Ben might achieve in the average range or higher for some tasks and below average in others.  

If Ben's standard score is in:  

• the sixteenth to twenty-fourth percentile range, or at least one standard deviation below the mean for their year or age level, then Ben may be at risk of a learning difficulty in that area.
• the third to fifteenth percentile range, or between one and two standard deviations below the mean for their year or age level, Ben is likely to have a learning difficulty in that area.
• the second percentile range or lower, or at least two standard deviations below the mean for their year level or age, Ben probably has a learning difficulty due to a specific learning disability (such as dyscalculia).

For these descriptions to be accurate, Ben needs to demonstrate these difficulties consistently for an extended period and the cohort that they are being compared to must be typical of students for that level.  

The Victorian Curriculum F–10: Mathematics and the National Numeracy Learning Progressions describe students' outcomes in terms of curriculum points or numeracy indicators. The substrands in which Ben's highest level is at least one year level below their current year level are indicative of a learning difficulty in that strand.  

You can find more information on Mathematics Teaching Toolkit.  

The third step is to compare Ben's ability on the various strands and substrands of numeracy.

You are looking for patterns in numeracy outcomes. Ben may show typical or average ability in some areas and lower ability in others. This helps you identify the strands of numeracy Ben has in place (the appropriate level of development) and those that need further work.  

You also want an indication of Ben's highest level of skill in each strand and substrand. You may want to know, for example, whether their performance in a substrand is at a Year 4 or 5 level. You can get this information in several ways.  

• Some tests will give you a separate standard score for each strand or substrand. Scores in the lowest twenty-fifth percentile range, or at least one standard deviation below the mean for Ben's year or age level, will require further attention.
• Some tests identify tasks that assess years 4 or 5 skills. You can note Ben's outcomes on the year 4 or 5 level items that are in the same substrand as the Year 6 items they answered incorrectly.
• Other tests have a separate test form for each year level. In this case, you can ask Ben to complete the Year 5 or Year 4 forms. These will indicate whether Ben can answer correctly earlier year items that match the Year 6 items they answered incorrectly.
• Some tests link each item directly with curriculum points. This tells you directly the highest level in a substrand Ben has achieved.
• Use the observational data you collected about Ben's maths learning in the classroom and categorise the tasks they could complete successfully in terms curriculum points or progressions.

It's useful to collate these data so that you can interpret them more easily and see patterns. Organising them in a table can help you identify skill and knowledge for each substrand. Include information you have collected about the curriculum points Ben has achieved and their scores for the strands and substrands.

The fourth step helps you identify possible causes of Ben's underachievement and target those areas in your teaching.

You want to determine whether Ben's underachievement is due to:  

• general delayed development in learning. This can be caused by a range of developmental issues, such as sensory, physical, language, intellectual, emotional, environmental or socio-economic factors.
• a specific learning disability such as dyscalculia. Individuals have difficulty learning maths facts and procedures, recognising the relationship between symbolic and non-symbolic forms of number (for example, 'seven' and/or '7' and a corresponding number line or array of dots).
• and have trouble understanding quantities and concepts like more and less, or smallest and biggest. They also have difficulties making number comparisons (for example, that 12 is greater than 10).

Analysis of Ben's assessment data will indicate which cause is more likely and what that means for your follow-up teaching plan.  

Evidence for delayed development cause

To examine evidence for the delayed development cause, you can analyse Ben's learning in other areas. We know that Ben has dyspraxia. Given the critical role of motor ability and strategic action in children's general development, it is likely that this has affected aspects of Ben's physical, language, intellectual and emotional development and capacity to respond to their environment. These aspects can impact on Ben's ability to make the maths learning progress of same-age peers.  

Detailed information about Ben's delayed development may be available in their school records.  Ben's parents may have described earlier development, acquisition of milestones and obstacles and barriers encountered. There may also be reports from health and medical professionals such as psychologists, speech pathologists, developmental physiotherapists or paediatricians that examine the impact of dyspraxia on Ben's learning capacity.  

Delayed developmental issues can impact on maths outcomes across the three strands. They can also have a more specific impact, for example, the student may be able to understand maths concepts and procedures fluently but not use them in problem-solving. Alternatively, you may also see the opposite pattern where a student can solve real-life maths problems but not recall the underpinning concepts and procedures fluently. It's recommended for any student that you compare the particular maths tasks they can answer correctly with those that they cannot.  

Evidence for the dyscalculia cause

Although it is unlikely, it is possible that the dyspraxia has not impacted the development of Ben's general learning capacity and that underachievement is limited to numeracy and due to dyscalculia. In this case, you would expect:  

• learning ability in other areas to be in at least the average range
• maths outcomes in areas that did not draw on numeracy skills to be better developed than those that require numeracy skills.

Students with dyscalculia have specific difficulty understanding and using number concepts and skills. These make up the areas of number and place value and counting processes and are the pre-requisites to learning maths knowledge and skills in other areas, for example, understanding units of measurement and interpreting and representing data.

Because these are components of other areas, it is often difficult to identify their direct impact in maths tasks at the Year 6 level. You can see their influence more clearly when you analyse how Ben works through tasks and note the components in a task that challenge them.  

You can find more information on Learning Difficulties in Numeracy (5 videos).