In this paper we analyze the outcomes of a design experiment that sought to improve the multiplicative reasoning of 12-13 year-old learners across two schools in a South African context of low performance. Using a hybrid theoretical base in Realistic Mathematics Education, variation theory and analogical reasoning, a short-term intervention…

This study investigated the developmental influence of collaborative games, in the form of game-based worksheets, on the performance and attitudes of sixth-graders in the mathematics classroom. It is posited that games have the potential to enhance learning through positive emotional experiences. Non-digital game-based learning methodologies are…

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…

Middle-grades mathematics prospective teachers (PSTs) participated in three iterations of a design experiment that explored their current conceptualizations of integer and binomial multiplication; this study analyzed whether that knowledge changed after engaging in a series of scaffolded tasks while using area models as concrete manipulatives.…

This study is part of a larger project exploring students' thinking of Dynamic Measurement (DYME), an approach to area measurement that engages students in dynamic digital experiences of measuring rectangular surfaces through sweeping lengths. The goal of this study was to evaluate the extent to which students could bridge the mathematical…

Making connections during math instruction is a recommended practice, but may increase the difficulty of the lesson. We used an avatar video instructor to qualitatively examine the role of linking multiple representations for 24 middle school students learning algebra. Students were taught how to solve polynomial multiplication problems, such as…

This quantitative, quasi-experimental study investigated the effect of the Mathletics.com technology on basic multiplication fact fluency in fourth grade students in the Middle East. The treatment group received three weeks of scheduled time using Mathletics.com, while the control group practiced multiplication facts using only traditional…

Children who struggle in mathematics have a limited understanding of the foundational processes of mathematics. A lack of conceptual understanding causes students to fall behind as they progress through the core curriculum. Children at high risk for developing mathematics disabilities fail to gain numeracy knowledge. The purpose of this case study…

This study examined preservice elementary teachers' change in their understanding of fraction operations while taking a mathematics methods course focused on grades 3-5. The preservice teachers (n = 48) completed an assessment before and after the course's unit on the teaching and learning of fractions. Specifically, the preservice teachers were…

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…

The purposes of this study were to (a) investigate the efficacy of a core fraction intervention program on understanding and calculation skill and (b) isolate the effects of different forms of fraction word-problem (WP) intervention. At-risk fourth graders (n = 213) were randomly assigned to the school's business-as-usual program, or one of two…

The purposes of this study were to (a) investigate the efficacy of a core fraction intervention program on understanding and calculation skill and (b) isolate the effects of different forms of fraction word-problem (WP) intervention delivered as part of the larger program. At-risk 4th graders (n = 213) were randomly assigned at the individual…

The Common Core Mathematics Standards have raised expectations for schools and students in the United States. These standards demand much deeper content knowledge from teachers of mathematics and their students. Given the increasingly diverse student population in today's classrooms and shortage of qualified special education teachers,…

The present study extends recent advances coordinating research on cognition and psychometric modeling around fractions. Recent research has demonstrated that the Diagnosing Teachers' Multiplicative Reasoning Fractions survey provides information about distinct components necessary for reasoning in terms of quantities when solving fraction…

This design study investigated the use of multiplication and division problems to help 5-year-old children develop an early understanding of multiplication and division. One teacher and her class of 15 5-year-old children were involved in a collaborative partnership with the researchers. The design study was conducted over two 4-week periods in…