Learning progressions detail the incremental steps that students take as they learn to master a skill. These progressions are based on developmental research about how students learn and how their thinking develops as a result of instruction. A typical progression not only describes the stages that students must master, but it also shows what…

In this paper, we describe our learning progressions approach to early algebra research that involves the coordination of a curricular framework, an instructional sequence, written assessments, and levels of sophistication describing the development of students' thinking. We focus in particular on what we have learning through this approach about…

This article promotes the use of mathematically appropriate, engaging and challenging tasks to support learning that is worthwhile. The authors share insights from a three-lesson design experiment and the three tasks along with the results from their implementation are explored.

Mobile devices have been increasingly utilized in informal learning because of their high degree of portability; mobile guide systems (or electronic guidebooks) have also been adopted in museum learning, including those that combine learning strategies and the general audio-visual guide systems. To gain a deeper understanding of the features and…

Graphical representations (GRs) of the learning content are often used for instruction (Ainsworth, 2006). When used in learning technology, GRs can be especially useful since they allow for interactions across representations that are physically impossible, for instance by dragging and dropping symbolic statements into a chart that automatically…

Teaching and learning are time-dependant processes. It can be hypothesised that the content coherence during a teaching sequence is an important factor of learning. In this perspective, it is of great interest to follow the occurrences of a notion and the development of its meanings in the classroom discourse, all along the various sessions of a…

Magnitude is assumed to be represented along a holistic mental number line in adults. However, the authors recently observed a unit-decade compatibility effect for 2-digit numbers that is inconsistent with this "holisticness" assumption (H.-C. Nuerk, U. Weger, & K. Willmes, 2001). This study used the compatibility effect to examine whether the…

This annotated bibliography is a compilation of the research on programed instruction conducted in the United States since 1954. The introduction describes the field; looks back over the research and reviews some of its conclusions; answers the question whether students learn from programmed instruction; explains the characteristic variables; and…