Predicting the actual performance of strategy use with self-report questionnaires is difficult, especially among elementary school children. Nevertheless, due to the simplicity of self-report questionnaires, it is desirable to identify one that can predict children's performance of actual strategy use. This study investigated whether a self-report…

Children with intellectual disabilities experience well-documented challenges in the development of problem-solving, particularly related to mathematical word-problem solving. Such challenges are related to both linguistic and conceptual skills. While interventions to assist children in developing conceptual skills are well reported, linguistic…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

Background: Given the context of low attainment in primary mathematics in South Africa, improving learners' understanding of multiplicative reasoning is important as it underpins much of later mathematics. Aim: Within a broader research programme aiming to improve Foundation Phase (Grades 1-3, 7-9-year-olds) learners' mathematical performance, the…

The purpose of this study was to assess student knowledge of numeric, visual and algebraic representations. A definite gap between arithmetic and algebra has been documented in the research. The researchers' goal was to identify a link between the two. Using four "Guess My Number" problems, seventh and tenth grade students were asked to write…

In Singapore, primary school students are taught to use bar diagrams to represent known and unknown values in algebraic word problems. However, little is known about students' understanding of these graphical representations. We investigated whether students use and think of the bar diagrams in a concrete or a more abstract fashion. We also…

This study investigated the modes of representations generated by kindergarteners and first graders while solving standard and problematic problems in mathematics. Furthermore, it examined the influence of pupils' visual representations on the breach of the didactical contract rules in problem solving. The sample of the study consisted of 38…

In this research work we explored the nature of 9-12 year old pupils' responses to probabilistic problems with tree diagrams. It was found that a large percentage of pupils failed to respond correctly even to very simple problems that demanded the identification of "possible routes/paths" in figures with tree diagrams/mazes. The results…