Many students encounter difficulty in their transition to advanced mathematical thinking. Such difficulty may be explained by a lack of understanding of many concepts taught in early school years, especially multiplicative reasoning. Advanced mathematical thinking depends on the development of multiplicative reasoning. The purpose of this study…

The purpose of this study was to investigate prospective mathematics teachers' knowledge of common conceptions and misconceptions that sixth and seventh grade students had about multiplication of fractions. In addition, prospective teachers' knowledge of the sources of these misconceptions and strategies they knew to overcome these misconceptions…

Contemporary teachers need instructional practices that are (a) powerful enough to meet the needs of a rapidly diversifying student population, (b) feasible to implement on a classwide basis, and (c) socially acceptable to them and their pupils. Classwide peer tutoring (CWPT) is one such instructional practice. In addition to describing CWPT, its…

Researchers have documented the positive effects of classwide peer tutoring on academic performance, engagement, and other social behaviors of students with and without disabilities. Commonly, in classwide peer tutoring, students are paired and the class is divided in half. Points are awarded for tutoring behavior and academic responding during…

This quasi-experimental study aims to streamline cognitive models on fraction multiplication and division that contain the most worthwhile features of other existing models. Its exploratory nature and its approach to proof elicitation can be used to help establish its effectiveness in building students' understanding of fractions as compared to…

Adaptive learning techniques have typically scheduled practice using learners' accuracy and item presentation history. We describe an adaptive learning system (Adaptive Response Time Based Sequencing--ARTS) that uses both accuracy and response time (RT) as direct inputs into sequencing. Response times are used to assess learning strength and to…

In this third of a series of four articles, the author deconstructs the primary national strategy's approach to written multiplication. The approach to multiplication, as set out on pages 12 to 15 of the primary national strategy's "Guidance paper" "Calculation" (DfES, 2007), is divided into six stages: (1) mental…

This study examined effectiveness of simultaneous prompting system in teaching students with cognitive impairment to automate recall of multiplication facts. A multiple probes design with multiple sets of math facts and replicated across multiple subjects was used to assess effectiveness of simultaneous prompting on recall of basic multiplication…

The National Mathematics Advisory Panel, established under the Bush Administration, was created to improve teaching and learning of mathematics in the United States. One component of the study was focused on teachers and professional development opportunities. They found that the majority of professional development studies available were mostly…

This submission contains the Proceedings of the 2013 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Brock University in St. Catharines, Ontario. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

In this study, the authors wish to explore the use of visual representations in facilitating the understanding of multiplication. In doing so, they examine the different aspects of multiplication that they can access through different representations. In addition, they draw on a study that they have been carrying out looking at pupils' actual use…

This article describes a number of multiplication algorithms from different cultures around the world: Hindu, Egyptian, Russian, Japanese, and Chinese. Students can learn these algorithms and better understand the operation and properties of multiplication.

People remember information better if they generate the information while studying rather than read the information. However, prior research has not investigated whether this generation effect extends to related but unstudied items and has not been conducted in classroom settings. We compared third graders' success on studied and unstudied…

This article describes the positive impact of Montessori manipulative materials on four seventh grade students who qualified for academic intervention services because of previous low state test scores in mathematics. This mathematics technique for teaching multi-digit multiplication uses a placemat-sized quilt with different color-coded squares…

Structured multisensory drills and activities used to teach the multiplication tables to a hyperactive boy are described. (CL)