This paper reports from a case study which explores kindergarten children's mathematical abstraction in a teaching--learning activity about reflection symmetry. From a dialectical perspective, abstraction is here conceived as a process, as a genuine part of human activity, where the learner establishes "a point of view from which the concrete…

Successful analogical reasoning requires an analogue in a source domain to have high degrees of structural and surface similarity with a learning task in a target domain. It also requires learners to have sufficient source- and target-domain knowledge. We review the literature and speculate that "less" might create "more"; in…

Teaching and learning is a growing field of research and practice globally, and increasing investments are being made in developing academics as teachers. An inability to adequately account for disciplinary knowledge can lead to academic development inputs that are unable to fully address the needs of students, educators, or disciplines…

This study examined student actions, interpretations, and language in respect to questions raised regarding tabular, graphical, and algebraic representations in the context of functions. The purpose was to investigate students' interpretations and specific ways of working within table, graph, and the algebraic on notions fundamental to a…

This theory-into-practice paper integrates Tomasello's concept of Joint Attentional Frames and well-known ideas related to the work of Russian psychologist, Lev Vygotsky, with more recent ideas from social semiotics. Classroom procedures for incorporating student-created Joint Attentional Frames into literacy lessons are explained by links to…

This case study deals with a solitary learner's process of mathematical justification during her investigation of bifurcation points in dynamic systems. Her motivation to justify the bifurcation points drove the learning process. Methodologically, our analysis used the nested epistemic actions model for abstraction in context. In previous work, we…

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

Discussion of students' prior knowledge and its effect on analogical reasoning focuses on four case studies of high school and college students that were designed to determine factors important for success in overcoming misconceptions via analogical reasoning. Explanatory models are explained, and abstract transfer versus explanatory model…