About six per cent of children have significant difficulty learning mathematics, including remembering arithmetic facts and performing calculations. While research has revealed multiple deficits as candidate causes for mathematical difficulties (MDs) and probable subtypes, the cognitive profiles of these subtypes are not fully understood, and it has not yet been determined whether children may move in or out of these subtypes over time. 

A study by Dr Winnie Chan Wai-lan, Assistant Professor at the Department of Special Education and Counselling, The Education University of Hong Kong, set out to (1) discover the cognitive profiles of subtypes of MDs and (2) assess the stability of these subtypes in the first two years of elementary school (P1 and P2). It adopted the commonly used definition of MDs: the 25th percentile cut-off based on mathematical achievement. 

The first phase of the study included a representative sample of 565 P1 Chinese-speaking children from six primary schools in Hong Kong. All participants completed a mathematical achievement test and a number of domain-general and domain-specific tasks in P1 and P2. They also completed a nonverbal intelligence test in P1 and four mathematical tasks in P2.

We used a data-driven, clustering approach to group children with MDs into subtypes according to shared deficits. Our study included a more comprehensive range of cognitive variables than previous studies and used cleaner samples by subtyping for each grade separately. For each child, we compared the memberships of subtypes across P1 and P2 to evaluate their stability over time.

Using this cluster analyse, we found five distinctive subtypes among children with MDs over the first two years of primary school: (1) number sense deficit, (2) numerosity coding deficit, (3) symbolic deficit subtype, (4) working memory subtype, and (5) a mild difficulty group. These subtypes showed moderate stability. Some subtypes appeared to be somewhat stable over time, some developed into another profile of deficits, and some emerged only at later points in the children’s development. 

The number sense deficit group was the most distinct cluster identified in both grades. They had a severe deficit in approximate number system, but average performance in all other cognitive domains.  Children in the numerosity coding deficit group had difficulty processing exact numerosities. Children in the symbolic deficit group had deficits in both enumeration and number line and weaknesses in working memory capacity in P1. In P2, their number line deficit became more severe and their enumeration difficulty less severe. They also had weaknesses in visuospatial working memory and number comparison. Children in the working memory deficit group had deficient visuospatial working memory and weak working memory.  

The discovery of five distinctive MDs subtypes in this study has several important practical implications: (1) Children with persistent difficulties in learning mathematics may exhibit a variety of cognitive deficits, which supports the multiple deficit view for MDs, so MD assessment should cover a comprehensive range of cognitive skills; (2) MD subtypes can change and warrant reassessment over time; and (3) understanding the cognitive profiles of different subtypes of MDs can help researchers and educators devise intervention strategies that build on what the children can do and help them improve in areas in which they are struggling.

The study was co-conducted by Dr Chan and Dr Terry Wong Tin-Yau at the Department of Psychology, The University of Hong Kong. To learn more about the project please click here.