Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, 2017) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments examining…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…

Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…

Using multitrait, multimethod data, and confirmatory factor analysis, the current study examined the effects of arithmetic item formatting and the possibility that across formats, abilities other than arithmetic may contribute to children's answers. Measurement hypotheses were guided by several leading theories of arithmetic cognition. With a…

Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a…

The ability to do arithmetic calculations is essential to school-based learning and skill development in an information rich society. Arithmetic is a basic academic skill that is needed for learning which includes the skills such as counting, calculating, reasoning etc. that are used for performing mathematical calculations. Unfortunately, many…

An alternating treatments design was used to compare the effects of baseline, interspersed brief problems, and interspersed brief problems plus token reinforcement on students' endurance while completing math worksheets. By pairing the completion of brief problems with token reinforcement, the role of problem completion as a conditioned reinforcer…

How can it be explained that, aside from inter-individual differences, pupils in certain classes are more responsive than others to the formal aspects of a problem that has been set? The author puts forward the hypothesis that teachers differ in their ability to operate relevant variations in the conception of problems. The differences in…