With so much attention focused on students who have a difficult time reading, it may be easy to forget that having a learning disability (LD) in the area of mathematics can be equally impairing. We use numbers every day, from counting out the number of apples we are buying, to knowing how much we owe to the shopkeeper, from getting home on time, to measuring out the ingredients to make dinner. Having early difficulties with numbers can lead to lifelong difficulties.

Like in reading, a disorder in mathematics is not a heterogeneous condition. Some individuals with mathematical LDs may have good conceptual understanding of mathematics but poor calculation ability (e.g., they may answer 2 x 5 = 25 or not be able to borrow). Other students may be great with math calculations but have poor conceptual understanding. Another student may not understand the vocabulary used in a word problem.

## Mathematical Competencies

The common diagnostic practice is to assess several aspects of mathematical ability to determine if any of the areas fall below a critical point which would indicate individuals having significant difficulties.

The common areas in math that are assessed on the standardized test are as follows:

1. Number sense (e.g. understanding of numbers, their magnitude, and relationships)
2. Memorization of arithmetic facts (e.g. having memorized the times tables or math formulas such as area)
3. Accurate calculation (e.g. the knowledge of and ability to carry out the procedural aspects of mathematics such as adding two numbers together, fractions, long division, trigonometry),
4. Fluent calculation (e.g. the speed at which one is able to perform simple mathematical computations such as adding, subtracting, and multiplication),
5. Accurate math reasoning and application (e.g. the ability to tell time, convert currencies, extract information from a chart or diagram, complete word problems, and calculate statistics).

## Achievement Tests

The standardized tests used in assessment have been created in such a way that for each age and graded level a normal distribution of scores can be seen. A normal distribution means that we can expect the majority of students to score a little above or a little below the average. As we move towards more extreme results (either very high or very low), we would see fewer students achieving those scores.

Results of standardized normed reference tests are often given in percentiles. A percentile is a person's relative position to a normal distribution. If I scored at the 31st percentile, that means I did as well or better than 31% of the normal distribution. Another way to say this is if 100 same age people were sampled and I scored at the 31st percentile means I did as well or better than 31 out of the 100 people on that test. The average range is between the 25th and the 75th percentile. For a disability in mathematics, the cutoff point is often established between the 10th and the 15th percentile.

The following are the main academic tests that are used in the assessment of a math LD:

• Wechsler Individual Achievement Test – Third Edition (WIAT III)
• Kaufman Test of Education Achievement – Third Edition (KTEA-3)
• Woodcock-Johnson IV Test of Achievement (WJ IV ACH)
• KeyMath3

## Other Considerations

However, diagnoses are not based on test scores alone.

• First, the individual must have experienced these difficulties with math for a period of at least six months to two years.
• Secondly, there must be noticeable impairment resulting from the challenges with math. In school, this is typically seen as either low marks in mathematics or a student spending an excessive amount of time trying to keep up with the mathematical curriculum.
• Thirdly, the difficulties cannot be attributed to other causes, such as lack of schooling, intellectual disabilities, uncorrected visual or auditory acuity, and lack of proficiency in the language of academic instruction. It is also important to ensure the student has an understanding of mathematical terminology (e.g. knows the mathematical vocabulary such as sum, more, add, increase by, all mean addition).

In Ontario, the Ministry of Education also has another component that is required for the identification of LDs related to mathematics. For identification, there needs to be a cognitive explanation for why the student is having difficulties in mathematics.

The current research in mathematics LDs (e.g. scoring at or below the 10th or 15th percentile on the standardized math test and having mathematical impairment for at least six months) does not point to a singular common explanation for why a person has difficulties learning math. There are many different cognitive processes that could explain why one has a mathematical disability including working memory, processing speed, executive functioning, abstract spatial reasoning, and others.

## Predictors

Research in this area is still ongoing, however, in recent years, it has been shown that difficulty acquiring certain early skills can be used to predict which students are at risk of developing further mathematical difficulties.

Numerical magnitude is the ability to say which of two numbers or which grouping of items, is larger. This task enlists a behavioural signature called the numerical distance effect (NDE), where individuals are faster and more accurate when the numerical distance between the numbers increases. Numerical magnitude is a powerful predictor of a student’s arithmetic development.

Numerical magnitude provides the foundations for our understanding and allows for the ability to estimate, and understand what is happening to numbers as we add or subtract. Research that has been done in Ontario is showing that numerical magnitude tasks have been able to predict mathematical outcomes on standardized mathematic numeric operation tests. This is an exciting finding, as it provides educators with an early screening tool to identify children at-risk of having a mathematical LD.

## Criteria for a Math LD Diagnosis

There's still much to be learnt in the area of mathematics LDs. However, one thing is for sure; LDs do not fall into discrete categories

If a student is presented with a math problem that they do not get right, it does not conclude they have a math LD. This student could instead be struggling due to an LD that affects their ability to read, making it difficult to find and comprehend important information within the problem. Alternatively, the student may be unable to remember necessary formulas due to poor working memory.

To be diagnosed with an LD in math students must meet the following criteria:

• the student has tested between the 10th and 15th percentile on a standardized assessment;
• the student has experienced difficulties for at least six months;
• the student has experienced a noticeable impairment due to their difficulties;
• the impairment cannot be attributed to any other causes, and
• there is a cognitive explanation for the difficulties experienced.

Only when all the criteria are met, can a student be accurately diagnosed with a math LD.