Literature on student ideas about circuits largely focuses on misunderstandings and difficulties, with seminal papers framing student thinking as stable, difficult to change, and connected to incorrect ontological categorizations of current as a thing rather than a process. In this paper, we analyzed 417 student responses to a conceptual question…

Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

According to Geary's evolutionary approach, humans are able to easily acquire primary knowledge and, with more efforts, secondary knowledge. The present study investigates how primary knowledge contents can facilitate the learning of formal logical rules, i.e., secondary knowledge. Framing formal logical problems in evolutionary salient contexts…

Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

This article describes part of a study in which researchers designed lesson sequences based around using a string number line to help teachers support children's development of relative thinking and understanding of linear scale. In the first year of the study, eight teachers of Years 3-5 participated in four one-day professional development…