Estimation is such an important yet sometimes overlooked skill. Enhancing estimation skills through exposing students to enumeration ('how many') problems where they are required to estimate before calculating is a critical aspect of developing number sense (Reys et al., 2012). This article describes a 'how many' problem undertaken with a small…

This is the first of two articles on the use of a written multiplication algorithm and the mathematics that underpins it. In this first article, the authors present a brief overview of research by mathematics educators and then provide a small selection of some of the many student work samples they have collected during their research into…

The aim of this research is to determine the different types of resources, regarding the thinking styles, used by mathematics teachers to create an a-didactical situation using a video-game from an essential resource. In this research embedded mixed method was used. Participants were ten teacher-student-researchers, studying at the master degree…

Mathematics is necessary to enable children to gain the knowledge and skills required for daily life, it teaches them how to solve a problem, enables them to gain ways of thinking and prepares them for the future. The prejudice developed towards mathematics affects the students' perceptions related to the mentioned course. The students' low…

As three-dimensional (3D) printing technology is fast becoming more affordable and accessible, calculus instructors can now consider using 3D printing and 3D printed models to actively engage students in core concepts relating to objects in R[superscript 3]. This article describes three lessons for a multivariable calculus class in which students…

This paper summarizes the experiences of two mathematics faculty members who participated in an in-house study abroad program. Descriptions of math courses taught abroad are given, as well as how students were recruited, courses were designed, and the environment was incorporated. Tips for mathematics faculty wanting to offer study abroad are…

Mathematics textbooks play a very important role in mathematics education and textbook tasks are used by students for practice to a large extent. Since the nature of the tasks may influence the way students think it is important that the textbooks provide a balance of a variety of tasks. The analyses of the requirements in textbook tasks contain…

Research Findings: We evaluated the score stability of the Mathematical Quality of Instruction (MQI), an observational measure of mathematics instruction. Three raters each scored, independently, 100 video-recorded lessons taught by 20 kindergarten teachers in the spring. Using generalizability theory analyses, we decomposed the MQI's score…

Early childhood provides a time of crucial growth in all developmental domains. Prekindergarten is an optimal time for young children to use objects of play as a medium to explore new cognitive concepts, including mathematical structure. Mathematical structure plays an important role in providing students a means to reason about mathematics,…

In our research, we focused on the design of assessment instruments for measuring teachers' mathematical knowledge for teaching geometry. Since 1987 when Lee Shulman conceptualized pedagogical content knowledge, different research groups have expanded on this construct and developed their own measurement instruments. The strengths and limitations…

In an undergraduate analysis course taught by one of the authors, three prompts are regularly given: (i) What do we know? (ii) What do we need to show? (iii) Let's draw a picture. We focus on the third prompt and its role in helping students develop their confidence in learning how to construct proofs. Specific examples of visual models and their…

I examined how well a self-diagnosis activity engages students in knowledge-integration processes, and its impact on students' mathematical achievements. The self-diagnosis activity requires students to self-diagnose their solutions to problems that they have solved on their own--namely, to identify where they went wrong and to explain the nature…

Myths about early education abound. Many beliefs people hold about early math have a grain of truth in them, but as a whole are not true--they are largely myths. But the myths persist, and many harm children. In this article, we address ubiquitous math myths that may be negatively affecting many young students. We conclude that avoiding the myths…

Research indicates that standards-based mathematics instruction positively supports students' academic development. Although standards documents identify accepted best practices, they do not speak to the impact that students' expectations of the mathematics classroom has on the successful implementation of standards-based instruction at the…

International surveys repeatedly showed that Japanese children were good at mathematics but disliking it. We hypothesized there were a considerable number of "fake math-dislikes" among Japanese students who claimed they disliked mathematics explicitly but accepted it implicitly. To examine this hypothesis, we administered questionnaires…