Why is it difficult to multiply? The types of learning disorders that impair multiplication table knowledge
Read the full dissertation (in Hebrew)…
One of the main mathematical skills learned in elementary school is the ability to remember arithmetic facts, such as the multiplication table, and to retrieve them from long-term memory without relying on calculation strategies. Learning the multiplication table is a challenge that creates considerable difficulty for many children. Nevertheless, to date, the origins of this difficulty were not examined systematically, certainly not while considering that these origins may be different for different children.
To find the origins of difficulty in multiplication-table knowledge, and to identify the learning disorders that underlie this difficulty, the present study assessed in detail the performance of 19 adults aged 22-45 who had poor knowledge of the multiplication table. Each participant performed a series of tasks to detect the presence of cognitive disorders in several mechanisms – long-term memory, short-term memory, working memory, attention, and sensitivity to proactive interference; to detect emotional difficulties – math anxiety and general anxiety; and to detect difficulties whose origin is educational – insufficient learning during primary school. We compared the participants’ performance to a control group with typical knowledge of the multiplication table.
We found that difficulty in learning the multiplication table – essentially, dyscalculia – is a very heterogeneous phenomenon. No single origin could explain the difficulty for all participants, not even for most of them. Cognitive deficits could explain the difficulty for 12/19 participants, with each specific deficit accounting for 2-8 participants. Additionally, for 7 participants the difficulty seems to have arisen from insufficient learning at school, and for 6 of them, this was the only explanation for the difficulty. Finally, there were 12 participants with high anxiety levels, suggesting an emotional origin of the difficulty.
Previous studies, which examined dyscalculia at the group level, linked poor multiplication fact knowledge with poor performance of long-term memory, or with high susceptibility to proactive interference. In contrast, the present study, which examined each participant individually, pointed to neither of these factors as a major predictor of poor multiplication fact knowledge. Only 2 of the 19 participants showed poor long-term memory abilities, and only 5 showed high sensitivity to proactive interference.
Overall, this study shows that calculation difficulties do not necessarily originate in domain-specific mathematical or numerical mechanisms – they may arise from deficits in domain-general mechanisms such as memory and attention. In fact, the difficulties of 18 of the 19 participants could be explained without assuming a deficit in a domain-specific mathematical mechanism.
The study also emphasizes how important it is to assess the precise origin of difficulty for each person. Even when different individuals exhibit an apparently-homogeneous learning disorder, such as poor knowledge of arithmetic facts, the difficulty may have different origins in different individuals. Precise assessment of the origin of difficulty would hopefully allow to provide targeted treatment and effective teaching to each child.