Division by zero is often unclear and confusing, and teachers at various grade levels may encounter difficulties in conveying this concept to their students. The concept of dividing by zero plays a crucial role in developing an understanding of certain mathematical concepts, such as rational numbers and the relationship between multiplication and…

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…

In this study, we analyzed the imprecise (i.e., less mathematically precise) responses that 148 third- to fifth-grade Chinese students made on selected-response problems that were part of a spontaneous mathematical focusing task, the Quantitative Relations Test for Chinese Children (QRTC[superscript 2]). The purpose for this analysis was to…

A design experiment with 18 students in a regular seventh grade math class was conducted to investigate how to differentiate instruction for students' diverse ways of thinking during a 26-day unit on proportional reasoning. The class included students operating with three different multiplicative concepts that have been found to influence rational…

Inquiry-based instruction is a student-centered approach to teaching that focuses on active learning (Barron and Darling-Hammond 2008) in which students engage with "tasks that promote reasoning and problem solving" (NCTM 2014). Specifically, such tasks encourage a variety of solution strategies and stimulate use of the NCTM Process…

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…

A description is given of a lesson on two digit multiplication with nine-year olds that utilizes trial and error and partitioning of the problem in a discovery type approach. (MN)

This issue of the journal contains abstracts and critical comments for ten published reports of research in mathematics education. The reports concern teaching probability and estimation of measurements through microcomputer games, mental addition, use of calculators at the intermediate level, logical reasoning hierarchies, two approaches to the…

An editorial and abstracts for 12 research reports are contained in this issue. The editorial by Robert E. Reys focuses on the dangers of publishing poor research. The abstracts, each with a critique, concern research on a game for logical reasoning, wait-time and sex differences, vocabulary instruction on ratio and proportion, male-female…