The concept of intellectual need, which proposes that learning is the result of students wrestling with a problem that is unsolvable by their current knowledge, has been used in instructional design for many years. However, prior research has not described a way to empirically determine whether, and to what extent, students experience intellectual…

High dropout rates in the first year of undergraduate studies are an expression of the secondary-tertiary transition problem and they seem to be particularly high in those degree programs where specialized mathematics courses are taught in the first year of study. Research shows that students' difficulties during the transition period cannot be…

This paper has two main goals: first, to analyze current research related with transition to identify the foci being produced and reproduced by research through a literature review and, second, to map the connections between circulating discourses to unfold the discursive network that supports them via an intensive reading. Specifically, we are…

This paper investigates the connection between the spiral teaching method and mathematical rigor in K-12 education. Defining rigor as a balanced integration of conceptual understanding, application, and procedural fluency (contrasting it with rote learning), the paper posits that the spiral approach cultivates this rigor. By revisiting…

In this article we report on a study focused on revealing and categorizing the arguments that preservice mathematics teachers put forward when they are asked about why mathematics is taught, which is a question closely related to the justification problem in mathematics education. Another focus of the study is the identification of myths within…

Supporting young students in developing meanings for the set-theoretic function definition is emphasized in 6th-12th grade curricula around the world. In prior work, we have highlighted how covariational reasoning supports college students in constructing relationships that afford considering mathematical properties important for a set-theoretic…