# DISKRE

How relevant is intelligence (discrepancy) to the phenomenon and definition of dyscalculia?

PublicationsAccording to the World Health Organization’s (WHO; ICD-10) definition and diagnostic criteria of the "specific disorder of arithmetical skills" a child’s mathematical performance must be significantly below the level of general intelligence (discrepancy criterion) to be diagnosed with dyscalculia. Although this discrepancy between low mathematical achievement and general intelligence has been criticized empirically and theoretically, it still is applied in many countries, including Germany. In contrast to the WHO, the American Psychological Association (APA) has rejected this criterion in its revised definition of “specific learning disorder with impairments in mathematics” and in its new definition and diagnostic criteria (DSM-5) the focus is on symptoms such as difficulties in mastering number sense and number facts.

Consequently, the question arises as to whether the discrepancy criterion is still relevant in defining dyscalculia according to criteria of the WHO.

## Objectives

#### Do the cognitive patterns in low-performing children in mathematics differ according to whether or not they reach the IQ-achievement discrepancy?

The performance of children with dyscalculia and those without was assessed in several domain-specific (e.g., basic numerical processing, arithmetic facts) and domain-general (working memory) areas to establish criteria for defining and diagnosing dyscalculia, to determine the importance of such criteria for mathematical achievement in general, and to ascertain whether various factors are specific to meeting the discrepancy or not.

While identifying specific cognitive patterns in children who reach the discrepancy may shed light on the importance of the discrepancy criterion in defining dyscalculia (as suggested by WHO) identifying similar cognitive patterns in both groups of low-performing children in mathematics may require a symptom-based diagnostic procedure, as suggested by the APA.

To establish whether different performances in the areas mentioned above were related to intelligence, two control groups of average-achieving peers in mathematics matched for intelligence were assessed. It was taken into account that children who do not reach the IQ-achievement gap usually have a slightly lower IQ than those who do.

## Methods

To recruit children with dyscalculia and those without, the mathematical performance, literacy skills, and intelligence (non-verbal, figural) of 1900 children were assessed with standardized classroom tests at the end of grade 2. Children were classified as having dyscalculia when they had less than 1 standard deviation (SD) below average in mathematics and performed at least on average in literacy.

Children with dyscalculia were divided into two groups: those who reached the IQ-achievement discrepancy (at least 1.2 SD between IQ and achievement in mathematics) and those who did not. Children with average performance in mathematics and literacy were assigned to one of the two control groups depending on their intelligence. This resulted in a two (intelligence) by two (mathematical achievement) design.

The performance of the 175 children who took part in the study on tasks related to working memory, arithmetic fact retrieval, basic numerical skills, and word problems was assessed over a period of two years.

## Results

Our findings indicate the importance of retrieving correct arithmetic facts as well as visual-spatial working memory for mathematical achievement irrespective of intelligence and IQ-discrepancy, thus not indicating specific patterns in children reaching the IQ-achievement discrepancy.

With such results we recommend that the definition and procedure for diagnosing dyscalculia be symptom-based (as done by the APA) rather than dependent on the discrepancy criterion (as suggested by the WHO).

## Contact

# DISKRE

How relevant is intelligence (discrepancy) to the phenomenon and definition of dyscalculia? Differential effects of fact retrieval promotion on children with mathematical difficulties

PublicationsIn the first phase of the project we investigated whether cognitive patterns in working memory, basic numerical processing and arithmetic fact retrieval in children with dyscalculia differed between those who reached the IQ-achievement discrepancy, which is demanded by the World Health Organization in its diagnostic criteria (WHO; ICD-10) and those who did not.

Results indicated that all the children underachieving in mathematics had difficulties in retrieving arithmetic facts and in visual-spatial working memory tasks irrespective of intelligence. Therefore, in the second phase of the project a computer-based training session promoting knowledge of arithmetic facts through drill and practice with pictorial representations is constructed and its effectiveness is evaluated.

## Objectives

### Do drill and practice promote arithmetic fact knowledge in children with mathematical difficulties?

To be able to provide effective intervention for children with mathematical difficulties, we determine whether the training sessions we develop promote retrieval of arithmetic facts, a skill which might be transferable to other areas of mathematics (e.g., addition with higher number ranges or word problems).

### Do children with mathematical difficulties who reach the IQ-achievement discrepancy respond differently to the intervention than their peers who do not reach the discrepancy?

Children with mathematical difficulties have difficulties retrieving arithmetic facts irrespective of their intelligence, nevertheless the question remains as to whether different levels of intelligence could result in different responses to the intervention. Therefore, we investigate whether children with mathematical difficulties who reach the discrepancy and those who do not respond differently to the tasks in the intervention, indicating the need for different interventions among sub-groups.

## Methods

In a longitudinal study, the effects of computer-based training sessions promoting knowledge of arithmetic facts in children with mathematical difficulties who reach and in those who do not reach the IQ-achievement discrepancy as well as in two control groups of average-achieving peers matched for intelligence is explored. We use a pre-post study design and control training sessions in order to determine specific effects. The arithmetic fact training sessions are designed as drill and practice exercises. Children reproduce repeatedly arithmetic facts (additions up to 20) that flash quickly on the computer screen and are represented pictorially when being entered by the children. By repeatedly reproducing the additions it is assumed that the children’s representations are strengthened in long-term memory and can be retrieved easily and correctly later.

Performance on arithmetic fact retrieval is evaluated at the beginning and end of the training sessions.

Working memory tasks and standardized curriculum-based tests in mathematics containing tasks on addition with higher number ranges and word problems are further administered to all children during the pre- and post-tests.

All participants also take part in a control training session involving a spot-the-difference task. The order of the training sessions is random.