Learning multiplication: An integrated analysis of the multiplication ability of primary school children and the difficulty of single digit and multidigit multiplication problems

• Multiplication ability and multiplication problems were analyzed in primary school.
• Three groups appeared: Single digit solvers, multidigit solvers and high performers.
• The difficulty of single digit problems can be explained well with known effects.
• Computational efficiency, memory strength and network efficiency models were compared.
• For multidigit problems, other effects were found, such as the number of operations.

In this study the mental multiplication ability of primary school children and the difficulty structure of all single digit and 469 multidigit multiplication problems, each solved tens of thousands of times in a web-based practice program, were investigated.Child analyses indicated three groups: single digit problem solvers, multidigit problem solvers, and high performers. Within-grade ability differences were very large.In the item analyses, previously identified effects in single digit multiplication, such as the problem size effect and the tie effect, were replicated in one integrated analysis. Data from two tasks were contrasted: one in which children used predominantly computational strategies, and one in which they are expected to rely mostly on retrieval. In both tasks we found most support for the computational efficiency model. Finally, exploratory analyses on the difficulty of multidigit problems suggest that children rely on the base 10 structure of our number system.