Magda Praet

Cognitive phenotype of mathematical learning disabilities: what can we learn from siblings?

The sensitivity of number sense as cognitive phenotype for mathematical learning disabilities (MLD) was assessed in siblings of children with MLD (n = 9) and age matched children without family members with MLD (n = 63). A number line estimation paradigm was used as a measure of childrens early number sense. In line with the triple code model of Dehaene (1992), three different presentation formats were presented. The results of the study confirmed that number line estimation was related to early arithmetic achievement in kindergarten. In addition siblings were less proficient in number line placements compared to non-siblings, with a larger effect size for symbolic and especially number word estimation compared to the non-symbolic results. Siblings also differed from non-siblings on procedural and conceptual counting skills and logical thinking in kindergarten. Moreover MLD had a familial aggregation, since about three out of five sibling girls had clinical scores on an Early Numeracy Test in kindergarten, pointing to a risk to develop MLD themselves. Implications of the study to our understanding of MLD are discussed.

Enhancing Mathematical Skills Through Interventions with Virtual Manipulatives

In this chapter, we report the findings from a randomized controlled trial investigating the effect of using virtual manipulatives to improve preschool students’ early mathematics skills. One hundred thirty-two preschool children were randomly assigned to nine sessions of adaptive computerized counting or comparison with virtual manipulatives, or to a typical instruction control group. Children in both experimental intervention groups, including children with poor calculation skills at the start of the intervention, performed better than controls not using virtual manipulatives on early mathematics tasks at the posttest. In addition, the effects of the training held six months later with the counting intervention improving number knowledge and mental arithmetic performance, and the comparison intervention only enhancing the number knowledge proficiency in Grade 1. The effect of virtual manipulatives was present in empathic children, thinkers, persisters, dreamers, rebels and promoters according to the Kahler Process Communication Model. In addition children in both experimental groups became more adventurous after the training. We discuss the value of these short interventions with virtual manipulatives in preschool as a forward-looking approach to enhance arithmetic proficiency.

Number Sense in Siblings of Children with Mathematical Learning Disabilities: A Longitudinal Study

Number sense, counting and logical thinking were assessed in 14 siblings of children with Mathematical Learning Disabilities (MLD) and in 41 age matched children without family members with MLD. The children were tested in kindergarten and followed up in grade 1. A 0-100 number line estimation paradigm with three formats (Arabic digits, dots and number) was used as a measure of number sense. Results reveal that siblings of children with MLD are less proficient in number line placements compared to non-siblings, with both groups having a logarithmic representation in kindergarten and grade 1. Siblings also differ from non siblings on procedural and conceptual counting knowledge and logical thinking in kindergarten. In addition, our findings suggest that nnumber line estimation in kindergarten is especially predictive for untimed procedural calculation performances in grade 1, whereas procedural counting knowledge is related to timed fact retrieval skills in grade 1. Our findings also reveal that MLD had a familial aggregation. Clinical siblings especially differ from non-clinical siblings on the estimation with Arabic numbers (in kindergarten and grade 1) and number words (in grade 1), pointing to the fact that especially symbolic number line estimation tasks on a 0-100 scale can be used as screeners for MLD. Implications for the understanding and diagnosis of MLD are discussed.