This research consists of teacher interviews, student interviews, and classroom observations, all based around the mathematical content area of combinatorics. Combinatorics is a part of discrete mathematics concerning the ordering and grouping of distinct elements. The data are used in four separate analyses. The first provides evidence that…

Researchers have speculated that children find it more difficult to acquire conceptual understanding of the inverse relation between multiplication and division than that between addition and subtraction. We reviewed research on children and adults' use of shortcut procedures that make use of the inverse relation on two kinds of problems:…

An idempotent satisfies the equation x[superscript 2] = x. In ordinary arithmetic, this is so easy to solve it's boring. We delight the mathematical palette here, topping idempotents off with modular arithmetic and a series of exercises determining for which n there are more than two idempotents (mod n) and exactly how many there are.

Several studies on learning mathematics for rural area's student indicate that students have difficulty in understanding the concept of division operation. Students are more likely to be introduced by the use of the formula without involving the concept itself and learning division separate the concrete situation of learning process. This…

This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies…

This study examines how collective activity related to multiplication evolved over several class sessions in an elementary mathematics content course that was designed to foster prospective elementary teachers' number-sense development. We document how the class drew on as-if-shared ideas to make sense of multidigit multiplication in terms of…

A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible…

Developing fluency in arithmetic facts is instrumental to mathematics learning. This study compares the effects of two practice conditions on children's fluency in simple multiplication facts. Third and fourth graders in the Netherlands (N = 282) practised in either a conventional "recall" condition where they produced answers to…

The purpose of this study was to better understand how students with learning disabilities, including those who struggle specifically with mathematics, engage with fraction computation. In particular, we examined error patterns, the influence of like and unlike denominators on these patterns, and correct solution methods. Although skill-related…

Over the last two decades, students in Singapore consistently scored above students from other nations on the Trends in International Mathematics and Science Study (TIMSS; Provasnik et al., 2012). In contrast, students in the United States have not performed as well on international and national mathematics assessments and students with…

The purpose of this study was to explore problem solving with kindergarten students. This line of inquiry is highly significant given that Common Core State Standards emphasize deep, conceptual understanding in mathematics as well as problem solving in kindergarten. However, there is little research on problem solving with kindergarten students.…

This study aimed to examine the relations among property strategies, working memory, and multiplication tasks with 101 Chinese fourth-grade students. Two multiplication property strategies (associative and distributive) were compared with no strategy and demonstrated differentiated effects on students' accuracy and reaction time. Associative…

The purpose of the present study was to examine the effectiveness of a strategic training program for improving students' performance in solving multiplication problems. The participants were 3 third graders with math difficulties. In this teaching experiment, microgenetic analysis was used to analyze improvement in students' strategic development…

The 43rd meeting of Canadian Mathematics Education Study Group (CMESG) was held at St. Francis Xavier University in Antigonish, Nova Scotia (May 31-June 4, 2019). This meeting marked only the third time CMESG/GCEDM (Groupe Canadien d'Étude en Didactique des Mathématiques) had been held in Nova Scotia (1996, 2003), and the first time it had been…

This paper shares research from a pilot study in which young children were introduced to multiplication and division problems in their first year of school. The focus was on building children's conceptual understanding of the idea of "repeated groups" as a fundamental aspect of multiplication and its relation to division. The particular…