This article looks at a simple geometry problem that also involves some reasoning about number combinations, and show how it was used in a Year 7 classroom. The problem is accessible to students with a wide range of abilities, and provides scope for stimulating extensive discussion and reasoning in the classroom, as well as an opportunity for…

The Monty Hall dilemma (MHD) is a counterintuitive probability problem in which participants often use misleading heuristics, such as the equiprobability bias. Finding the optimal solution to the MHD requires inhibition of these heuristics. In the current study, we investigated the relation between participants' equiprobability bias and their MHD…

Since 1950, the Prisoner's Dilemma has intrigued economists and amused fans of mathematics. It presents a situation in which two players acting to their own advantage do not do as well together as two players whose actions oppose their individual interests--hence, the dilemma. Variations of the Prisoner's Dilemma have appeared in diverse…

This article reports on a longitudinal observation study about students' development in their use of procedures to calculate instantaneous rate of change. Different procedures for solving tasks on rate of change are taught in mathematics and physics classes, and together they form a repertoire. Our study took an actor-oriented perspective, which…

People need the idea of transformation geometry in order to understand the nature and environment they live in. The teachers should provide learning environments towards perceptual understanding in symmetry training and development practice skills of the students. In order to make up such a learning environment, teachers should have information…

Building on common assumptions in theories of interest and mathematics education, this experimental study examined the effect of context personalization based on individual preferences, group personalization, and example choice with preselected popular examples on middle school students' situational interest and performance in mathematics.…

This study examined pre-service primary school teachers' performance in posing problems that require knowledge of problem-solving strategies. Quantitative and qualitative methods were combined. The 120 participants were asked to pose a problem that could be solved by using the find-a-pattern a particular problem-solving strategy. After that,…

Within mathematics teaching, ways to help students resolve proportional reasoning problems remains a topical issue. This study sought to investigate how a simple innovative procedure could be introduced to enhance skill acquisition. In two classroom-based experiments, 12-year-old students were asked to solve proportional reasoning mathematics…

As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a…

Problem solving has long been a focus of research and curriculum reform (Kilpatrick 1985; Lester 1994; NCTM 1989, 2000; CCSSI 2010). The importance of problem solving is not new, but the Common Core introduced the idea of making sense of problems and persevering in solving them (CCSSI 2010, p. 6) as an aspect of problem solving. Perseverance is…

This note describes a course designed to prepare community college instructors and K-12 teachers for teaching foundational aspects of quantitative reasoning. A body of literature on quantitative reasoning and quantitative literacy informed the course design. The note describes the course content, which includes engaging in case studies, reading…

Drawing comparisons between students' alternative solution strategies to a single mathematics problem is a powerful yet challenging instructional practice. We examined 80 preservice teachers' when asked to design a short lesson when given a problem and two student solutions--one correct and one incorrect. These micro-teaching events were…

As a self described lesson collector, author Charles Lovett enjoys gathering "interesting" lessons and teasing them apart to find out what makes them "tick", particularly the pedagogy. He often wonders what decisions the teacher made that generated such an interesting and successful learning environment. Here he describes a…

Using expository text and examples available in 10 college textbooks we identify two conceptions of angles, trigonometric functions, and inverse trigonometric functions that rely on either a static or a dynamic definition of angle. Although the textbooks favor a conception of trigonometric functions that is based on a dynamic conception of angle,…

The concept of fractions is perceived as one of the most difficult areas in school mathematics to learn and teach. The most frequently mentioned factors contributing to the complexity is fractions having five interrelated constructs: part-whole, ratio, operator, quotient, and measure. In this study, we used this framework to investigate the…