The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

Instruction often starts with an explanation of a concept or principle before students are presented with problems to be solved. Recent research indicates that reversing this widely used tell-and-practice sequence (T&P) so that exploratory problem-solving precedes the instructional explanation (i.e., PS-I) might be more beneficial. We aimed to…

This article examines the process of shifting to a "Physics First" sequence in science course offerings in three school districts in the United States. This curricular sequence reverses the more common U.S. high school sequence of biology/chemistry/physics, and has gained substantial support in the physics education community over the…

The paper presents and analyses a sequence of events that preceded an insight solution to a challenging problem in the context of numerical sequences. A three­week long solution process by a pair of ninth­-grade students is analysed by means of the theory of shifts of attention. The goal for this article is to reveal the potential of this theory…

Educators and researchers have long been interested in determinants of access to honors level and college prep courses in high school. Factors influencing access to upper level mathematics courses are particularly important because of the hierarchical and sequential nature of this subject and because students who finish high school with only lower…