A deep understanding of fraction concepts and operations is necessary if pre-service teachers (PSTs) are to present the concepts in multiple forms to learners. Such an understanding needs to be grounded in rich conceptual knowledge. In the present study, we explore the development of this understanding by supporting a cohort of 103 PSTs, who had…

Basic multiplication fact fluency is an expected outcome of most third grade classrooms throughout the United States. Students need to know their multiplication facts. This statement does not seem to be under question; it is more about how will students learn their multiplication facts. The purpose of this study was to investigate the use of…

This study examined pre-service elementary teachers' change in their understanding of fraction operations while taking a mathematics methods course. Specifically, their explanations and justifications for common algorithms for multiplication and division of fractions were coded using an existing framework (SOLO; Biggs, 1999) for the assessment of…

Background: Specialized content knowledge (SCK) is a type of mathematical content knowledge specifically needed for teaching. This type of knowledge, although serving as a critical component for preservice teacher education, is often challenging to develop with preservice elementary teachers (PTs). The purpose of this study is to investigate PTs'…

Many children in the U.S. initially come to understand the equal sign operationally, as a symbol meaning "add up the numbers" rather than relationally, as an indication that the two sides of an equation share a common value. According to a change-resistance account (McNeil & Alibali, 2005b), children's operational ways of thinking…

Deficiencies in mathematics standardized test scores prompted school district policymakers to consider implementing a program designed to increase students' basic multiplication fact skills. This study was an evaluation of the Math Factual Operations for Understanding program. The program, marketed with a martial arts theme, was intended to…

Formative instruction on multiplication primarily focuses on rote memorization. This leads to factual fluency, but also develops a narrow view of multiplication and hinders the development of conceptual understanding. Theory and research recommend the concurrent development of conceptual understanding and factual fluency during the initial stages…

Background: The research on diagrammatic representations highlights their importance for the teaching and learning of mathematics. However, the empirical evidence to support their use in the classroom is mixed and somewhat lacking. Purpose: The aim of this study was to develop the use of diagrammatic representations of mathematical concepts in…

This study purposed to determine the effect of an endogenously designed instructional game on conceptual understanding of the associative and distributive properties of multiplication. Additional this study sought to investigate if performance on measures of conceptual understanding taken prior to and after game play could serve as predictors of…

Action research (AR) is defined by Macintyre to be: "an investigation, where, as a result of rigorous self-appraisal of current practice, the researcher focuses on a problem,or a topic or an issue which needs to be explained, and on the basis of information, plans, implements, then evaluates an action then draws conclusions on the basis of…

Mathematics and art are often considered opposites in the traditional curriculum. In this project with fourth graders, mathematics and art provided a springboard for using fractions, in particular, the multiplication of fractions, using Chinese kites. The project began with a discussion of, "What does an artist really do in a mathematics…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference presents the following research reports: (1) Text Talk, Body Talk, Table Talk: A Design of Ratio and Proportion as Classroom Parallel Events (Dor Abrahamson); (2) Generalizing the Context and Generalising the Calculation (Janet Ainley); (3) Interview…

The purpose of this practicum was to increase motivation and self-confidence of grade four students in mathematics achievement. Measured were the increase in the number of students displaying mastery of the times-tables, increase in the number of students making a gain on a math post-test, and increase in the number of students liking mathematics.…