The purpose of this study was to describe the standard process of mathematical reasoning in learning on pyramid volume concepts. The study was a study with descriptive qualitative approach, carried out by peer teaching in the classroom. The subjects of this research were Class B Postgraduate 2018 (S2) students, State University of Malang. The…

In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the "philosophy of mathematical practice." In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice…

There is evidence that spatial thinking is malleable, and that spatial and mathematical skills are associated (Mix et al. [2016] "Journal of Experimental Psychology: General," 145, 1206; Mix et al. [2017] "Journal of Cognition and Development," 18, 465; Uttal et al. [2013] "Psychological Bulletin," 139, 352). However,…

A growing body of research supports writing as a means to learn mathematics. Although introductory courses have benefited the most from the spread of this mode of learning, writing may be promoted in advanced courses. This paper reports on writing tasks in a complex analysis course where the primary goal was for students to investigate…

This article examines the mathematical activity of five-year-old Liam to explore the difference between the mathematics games designed for children and the children's games that emerge through playful activity. We propose that this distinction is a salient one for teachers observing mathematical play for evidence of mathematical sense making.

This article describes an inquiry-oriented real analysis classroom in which students were guided to discover mathematics for themselves. To support student inquiry, the framework of "five practices" from K-12 education was used. To illustrate this framework, two case examples are given from actual discussions that took place in this…

In recent years, several researchers have tried to use stories and games as a starting point for learning mathematics. This is allegedly able to increase students' mathematical abilities and make learning mathematics more enjoyable. Therefore, this research is aimed to design a mathematics learning trajectory in pattern number using…

Empirical studies of angle, angle measure, and radian angle measure have primarily focused on documenting students' and teachers' conceptions. Representations of angle measure have the potential to inform and build on these conceptions. To gain insight into the concept of radian angle measure from a curricular perspective, I investigated the…

This paper offers instructional interventions designed to support undergraduate math students' understanding of two forms of representations of Calculus concepts, mathematical language and graphs. We first discuss issues in students' understanding of mathematical language and graphs related to Calculus concepts. Then, we describe tasks, which are…

Mathematics educators view the equals sign as a bidirectional relation symbol, but the authors have observed that students might not have such flexibility in their understanding of the equals sign. The authors have observed that students have a hard time viewing mathematical properties (for example, log (MN) = log (M) log (N)) with bidirectional…

Literature has already shown that gestures play a relevant role in classroom interactions between students and teacher. We integrate the perspective of Theory of Semiotic Mediation with the notion of Semiotic Bundle to illustrate how gestures can be used as "pivot signs" in semiotic chains. This means that gestures can be performed by…

The mathematics curricula of countries such as the United States, Singapore, Australia and New Zealand have started to incorporate the teaching of algebra in early childhood education. From this perspective, our study has two objectives: (a) to design a learning trajectory and teaching itinerary introducing patterns for children between the ages…

Research has explored the use of simulations for education and training, and attention is turning to how they might support learning in school subjects such as mathematics and science. However, existing studies have mostly concentrated on older students, and if simulations help build knowledge useful for solving problems "within" the…

We report on findings from two one-on-one teaching experiments with prospective middle school teachers (PTs). The focus of each teaching experiment was on identifying and explicating the mental processes and types of intermediate, supporting reasoning that each PT used in their development of combinatorial reasoning. The teaching experiments were…

This study explored the use of Indigenous storytelling in the planning and teaching of mathematical content. In collaboration with Indigenous and non-Indigenous educators, a culturally inclusive mathematical lesson was developed, implemented, and reviewed in an elementary school in Northern Ontario. This study used a culturally authentic approach…