This study focuses on computer-based formative assessment for supporting problem solving and reasoning in mathematics. To be able to assist students who find themselves in difficulties, the software suggested descriptions - diagnoses - of the encountered difficulty the students could choose from. Thereafter, the software provided metacognitive and…

The aim of this study is to explore the judgments and reasoning in probabilistic tasks that require comparing two probabilities either with or without introducing an additional degree of uncertainty. The reasoning associated with the task having an additional condition of uncertainty has not been discussed in previous studies. The 66 undergraduate…

Students' opportunities to struggle with mathematical ideas have long been considered paramount to learning. However, there's little research on how teachers; (1) draw on and make sense of the discourses of perseverance; (2) enact it in classroom; and (3) develop an expansive view of perseverance. To contribute to these lines of research, we build…

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…

Applying and adapting a variety of appropriate heuristic strategies is one of the accepted standards of problem solving (NCTM, 2000). Thinking through a solution to a non-routine mathematical task, experts in problem solving call into play many sophisticated strategies (almost) without conscious efforts, while novices need to be taught how to do…

Presents thinking-aloud protocols from secondary pupils solving arithmetic story and geometrical problems and analyzes their protocols by using interpretation models founded on a general problem-solving model. A word problem solving simulation is also used to further explicate processes pupils use to solve mathematical tasks. (Author/MBR)