In mathematics education, representations are used in place of mathematical structures, ideas, or relationships to concretize, transform, and represent them. When students interact with these representations, they engage in various cognitive activities such as thinking, reasoning, understanding, remembering, problem-solving, attention, and…

This study examined whether students were reaching automaticity with single digit multiplication facts. A fourteen question interview was used to collect data. The first three questions asked the student basic information about themselves and their current math teacher. The next seven questions were math facts. The math facts chosen for the…

This study investigated how middle school students leverage information about bound Latin roots (e.g., "voc" in "advocate" and "vociferous") to infer meanings of unfamiliar words, and how instruction may facilitate morphological analysis using roots. A dynamic assessment of morphological analysis was administered to…

This study investigated how middle school students leverage information about bound Latin roots (e.g., voc in "advocate" and "vociferous") to infer meanings of unfamiliar words, and how instruction may facilitate morphological analysis using roots. A dynamic assessment of morphological analysis was administered to 29 sixth…

Numerous authors have reviewed research to determine which skills are considered fundamental to successful academic and social outcomes for students (Hattie, Briggs, & Purdie, 1996; Masten & Coatworth, 1998; Wang, Haertel, & Walberg, 1994; Zins, Weissberg, Wang, & Walberg, 2004). These skills include: (1) cognitive and…

This dissertation analyzes differences found in Spanish-speaking middle school and high school students in algebra-based problem solving. It identifies the accuracy differences between word problems presented in English, Spanish and numerically based problems. The study also explores accuracy differences between each subgroup of Spanish-speaking…

This study investigated the relationship between 3 ability-based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems…

This article explores the thinking behind students' thinking. (Contains 2 endnotes.)

In this article, the author presents an innovative approach to teaching multiplication facts for children in middle school or younger. After introducing the dangers of some contradictions that persist, relating a brief summary of related research and guidelines regarding math facts and their relation to strategic approaches to more complex math,…

SpringBoard is a comprehensive instructional program in English language arts and mathematics that reflects powerful, research-based understandings about how people learn. This report presents a model of learning based on cognitive science with particular attention to the role of memory and language. The instructional framework of strategic…