The objective of this article is to describe types of mathematical reasoning evidenced by a middle school mathematics teacher, when answering two generalization questions in a figural pattern generalization task, related to quadratic sequences. Reasoning is delimited from teacher's arguments, reconstructed from a theoretical-methodological…

This paper explores strategies for teachers to work with science conceptions, both those consistent and those inconsistent with western science understanding. It emphasises the value of teachers checking their own and their students' prior understanding of concepts to be learnt. A past approach of educators has been to replace old beliefs with new…

There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…

We are currently at an exciting juncture in developing effective means for assessing so-called 21st-century skills in an innovative yet reliable fashion. One of these avenues leads through the world of "epistemic games" (Shaffer, 2006a), which are games designed to give learners the rich experience of professional practica within a discipline.…

This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns,…

Researchers have regarded inductive reasoning as one of the seven primary mental abilities that account for human intelligent behaviours. Researchers have also shown that inductive reasoning ability is one of the best predictors for academic performance. Modelling of inductive reasoning is therefore an important issue for providing adaptivity in…

This paper outlines a model of cognitive functioning and remedial direction, based upon an information integration approach and work in neuropsychology. The approach, used primarily with low-achieving and learning-disabled students, utilizes "bridging tasks" which are paired with specific global cognitive tasks to promote generalization…

Many significant changes in perspective have to take place before efforts to learn the content and capabilities of children's minds can hold much sway in educational testing. The language of testing, especially of high stakes testing, remains firmly in the realm of "behaviors", "performance" and "competency" defined…