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# Comparison: a general or specific problem of children with mathematical difficulties?

Joanka Vloo

#### Introduction and objective

About seven to fifteen percent of the children in school have a specific disability within the domain of mathematics. Several studies show a relation between number sense and arithmetic competences. Number sense is the understanding and flexible use of digits and can be studied with digit comparison tasks. Children with arithmetic difficulties usually underperform on these tasks. However, it is not clear whether this deficit is caused by a specific problem in processing digits or a general problem with comparing symbols, such as digits or letters. The current study investigated whether children with specific arithmetic difficulties have a specific problem with comparing digits or a problem with comparing in general.

#### Method

In this study, 66 children with arithmetic difficulties ( Mage = 11.29) and 103 children without arithmetic difficulties ( Mage = 10.73) in grade 5 to 8 of primary school participated . The children performed two different tasks on a computer: one for the comparison of digits and one for the comparison of letters. In the comparison of digits task, children had to indicate which digit (2 to 8) was the highest and in the comparison of letters task, they had to indicate which letter (I, J, L, N, O, P, U, T) was closest to ‘Z’. One variable was created based on the accuracy and reaction speed, a higher score indicating a lower performance. The arithmetic performance was measured using the ‘Tempo Test Rekenen (TTR)’ (Rapidity Test Arithmetic)’. The results were analyzed using independent t-test, Pearsons correlation and multiple regression models. First it was checked if children with specific arithmetic problems show a deficit in both digit and letter comparisons. Then, it was analyzed if there is a relation between the digit and letter comparison and arithmetic performance.

#### Results

Children with arithmetical difficulties perform significantly lower than children without arithmetical difficulties on the digit comparison task t(143)= 2.99, p < .01, d = .48, but not on the letter comparison task t(139) = 1.58, p = .12, d = .26. The digit comparison task is a significant predictor of arithmetic performance of children with arithmetical difficulties, β = -.28, t(52) = -2.11, p = .04, but the letter comparison task is not a significant predictor in combination with digit comparison, β = -.21, t(52) = -1.55, p = .13, and not on its own, r = -.17, p = .11.

#### Conclusion and recommendations

It can be concluded that children with arithmetical difficulties have a specific problem with comparing digits, rather than a general problem. Therefore, interventions should focus on comparing digits. Further studies are needed to look further into the underlying processes of digit comparison in which children with arithmetical difficulties show a deficit, to study how number sense and arithmetical skills should be taught. Perhaps the ordering of digits is an underlying problem for these children, which could lead to deficits in performing digit comparison tasks.

By: Joanka Vloo

Supervised by: Dr. Anne van Hoogmoed en Dr. Laura Batstra