This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…

The purpose of this study was to deconstruct the relationship between visual static models and students' written solutions to fraction problems using a large sample of students' solutions. Participants in the study included 162 third-grade and 209 fourth-grade students from 17 different classrooms. Students' written responses to open-ended tasks…

We examine how rectangular array model can support students' spatial structuring in learning multiplication. To begin, we define what we mean by spatial structuring as the mental operation of constructing an organization or form for an object or set of objects. For that reason, the eggs problem was chosen as the starting point in which the…

Self-efficacy beliefs in mathematics, as a dimension of the affective domain, are related with students' performance on solving tasks and mainly on overcoming cognitive obstacles. The present study investigated the interrelations of cognitive performance on geometry and young students' self-efficacy beliefs about using representations for solving…

Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use…

This article describes the use of the book "Inchworm and a Half" to stimulate children's investigations in measurement and number. During a two-day lesson children used physical models and visual representations to develop measurement skills and explore equivalent relationships.