In this article, the authors focus on students constructing observations of patterns to understand how surfaces affect the motion of an object. Students will use the patterns they observe to predict future motion of marbles (NGSS Lead States 2013). Students then apply their learning by engaging in an engineering task. By giving students a task to…

Pattern generalisation has become an important feature of mathematics classrooms around the globe. Sometimes these activities focus purely on given numerical terms, but the use of pictorial or figural patterns is now becoming part of the standard repertoire for such generalisation exercises. From a pedagogic point of view, the investigation of…

Task analytic theories of graph comprehension account for the perceptual and conceptual processes required to extract specific information from graphs. Comparatively, the processes underlying information integration have received less attention. We propose a new framework for information integration that highlights visual integration and cognitive…

This article introduces "expertise-based training" (XBT) as an instructional design theory that draws on the theories, findings, and methods of expertise research in order to create instructional strategies that can hasten the development of advanced learners into experts. The central tenants of XBT are: 1) Key cognitive sub-skills that…