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…

Many instructional strategies that appear to improve learners' performance during training may not realize adequate posttest performance or transfer to a job. The converse has been found to be true as well: Instructional strategies that appear to slow the learner's progress during training often lead to better posttraining or transfer performance.…

In this research we present the use of some technologies in problem solving activities (at different secondary school grades), aimed at finding a model for a geometric configuration, and representing this model in various ways: through a construction, through a Cartesian graph, etc. The task is part of a teaching experiment, in which students used…

When contexts are framed expansively, students are positioned as actively contributing to larger conversations that extend across time, places, and people. A set of recent studies provides empirical evidence that the expansive framing of contexts can foster transfer. In this article, we present five potentially complementary explanations for how…

The self-teaching hypothesis proposes that orthographic learning takes place via phonological decoding in meaningful texts, that is, in context. Context is proposed to be important in learning to read, especially when decoding is only partial. However, little research has directly explored this hypothesis. The current study looked at the effect of…

This paper gives an account of a teaching experiment on absolute value inequalities, whose aim was to identify characteristics of an approach that would realize the potential of the topic to develop theoretical thinking in students enrolled in prerequisite mathematics courses at a large, urban North American university. The potential is…

Comparative studies of forward and backward chaining have led some to suggest that sensitivity to each teaching procedure may be idiosyncratic across learners and tasks. The purposes of the current study were threefold. First, we assessed differential sensitivity to each chaining procedure within children when presented with multiple learning…

In two experiments, participants made inferences from weather maps, before and after they received instruction about relevant meteorological principles. Different versions of the maps showed either task-relevant information alone, or both task-relevant and task-irrelevant information. Participants improved on the inference task after instruction,…

Two experiments were conducted to determine whether explicit instruction focusing on metaphorical collocations would promote the incidental noticing of similar phrases by English learners during a subsequent reading task. Noticing was operationalized using the remember-know protocol and learning was measured on a fill-in-the-blanks test. In…

Children with mathematics difficulties suffer from working memory deficits. This study investigated the deficit profile of phonological storage and executive functions in working memory among children with mathematics difficulties. Based on multiple instruments and two assessment points, 68 children were screened out of 805 fifth graders. Of these…