When, how, and why students use conceptual knowledge during math problem solving is not well understood. We propose that when solving routine problems, students are more likely to recruit conceptual knowledge if their procedural knowledge is weak than if it is strong, and that in this context, metacognitive processes, specifically feelings of…

The aim of the study was to determine the arithmetic and algebraic problem-solving approaches of prospective mathematics teachers in the Department of Elementary Mathematics Education, and mathematics teachers in secondary schools. The study adopted mixed methods research design using exploratory sequential pattern. The participants of the study…

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

In this paper, we investigate the mathematical, social and affective nature of children's engagement with "TouchCounts," a multitouch application for counting and doing arithmetic. In order to study these dimensions of engagement in a way that recognizes their fundamental intertwinement, we use rhythm as a primary unit of analysis.…

In this paper we investigated the contribution of a dynamic testing procedure, including multiple graduated prompts protocols, in identifying differences in need for instruction of second grade children (N = 120) with arithmetic difficulties. The training was adaptive and prompts were provided according to one of six protocols, each focusing on a…