Our goal in this research was to understand the specific challenges middle-school students face when engaging in mathematical problem-solving by using executive function (i.e., shifting, updating, and inhibiting) of working memory as a functional construct for the analysis. Using modified talk-aloud protocols, real-time naturalistic analysis of…

This article considers two small groups of students in the same Grade 8 mathematics classroom whose approaches to the same mathematical problem result in very different experiences. Using videotapes and written transcripts, an analysis of the groups' working processes was undertaken using Sawyer's pre-existing structures required for the presence…

The design of technology tools has the potential to dramatically influence how students interact with tools, and these interactions, in turn, may influence students' mathematical problem solving. To better understand these interactions, we analyzed eighth grade students' problem solving as they used a java applet designed to specifically accompany…

In individual interviews, 220 students in grades 4, 6, 8, and 9 were given one task, and 72 eighth graders were given three tasks to answer two questions: (a) Is a square the unit of measurement for an area for students in grades 4-8? and (b) Does a square have a space-covering characteristic for students in grade 8? The answers to both questions…