This paper reports findings related to the pursuit of describing a lived knowing for teaching mathematics. Specifically, we used an enactivist perspective to describe the knowing exhibited by three experienced high school teachers in their instructional actions while leading whole-class instruction on the topic of the equations of exponential…

Incorporating open-ended real-world tasks enhances students' access to mathematical and real-life knowledge and maximizes learning experiences. This article examines how a secondary mathematics teacher used an open-ended problem on distributing pay raises to teach mathematical concepts and fairness to students. The teacher's actions exemplify…

Mathematical concepts have been a consensus goal for decades, yet there is little consensus on what is meant by the terms "mathematical concept" and "mathematical understanding." This article attempts to discuss these terms in a way that can be of practical use to teachers. Greater clarity on "mathematical concept"…

The present study compared Japanese and U.S. preschool children's knowledge of geometric shapes. The main goal was to explore if differences in shape-naming conventions in Japanese and English could explain differences in children's understanding of geometric shapes. In ancient Chinese-based languages (e.g., Japanese), all standard 2D shapes…

This design-based research project explored how various design features of AR-based learning environments (ARLE) influence students' mathematics self-efficacy and learning of kinematics. Specifically, five ARLEs with different design features were developed and implemented with 136 seventh-grade students in two rounds. Data were gathered from pre-…

To this date, few standardized tests measuring students' performance with regards to statistics exist. Only four tests have been proposed for college or university students. The goal of the present study is to investigate these tests. University professors or instructors experienced in teaching statistics were asked to list the concepts they think…

Trigonometric derivatives are fundamental in both mathematics and physics, yet their correct application, particularly the distinction between radians and degrees, remains a significant challenge for college students worldwide. This study identifies a widespread "blind spot" in understanding trigonometric derivatives and their…

There is mixed evidence as to whether concrete manipulatives (e.g., toy animals) are better than abstract manipulatives (e.g., counters) for teaching mathematical concepts to children. Concreteness is defined as the amount of extraneous information a manipulative provides, and in this study we aimed to unpick which dimensions of concreteness…

Technology, in particular augmented reality (AR), has the potential to greatly enhance interactive learning environments for mathematics in both classrooms and other teaching environments. The purpose of the present study was to investigate existing literature on AR in mathematics education. We selected papers from 10 databases, Scopus, Web of…

With the objective of identifying intrinsic forms of mathematical production in complex analysis (CA), this study presents an analysis of the mathematical activity of five original works that contributed to the development of Cauchy's integral theorem. The analysis of the mathematical activity was carried out through the identification of the…

From literature, we know that making the connections between mathematics and physics is not trivial for most students, even at the advanced level. In the specific context of partial derivatives in thermodynamics, research suggests that making explicit connections between the mathematics and the physics is necessary to foster student understanding.…

We discuss student conceptions of improper integrals and infinity in the context of a second-semester calculus course (in a three-course sequence). Our observations stem from a sequence of activities used in an online course over a three-day period. Throughout the enactment of these activities, students are challenged to develop conceptions of…

In this study, it is aimed to examine the perceptions of the mathematics teacher candidates regarding the concept of fraction. 32 teacher candidates participated in the research carried out in the screening model. The word association test was used as a data collection tool and the obtained data were analyzed by content analysis method. According…

The empirical data in this study are from a series of two lessons on measurement implemented in seven classes with 119 six-year-old students in Sweden. Both problem solving and problem posing were shown to be important in early mathematics when students in this study worked on one problem-solving task and one problem-posing task on measurement. As…

We explore how the concept of abstraction, which is central to mathematical activity, can lead to detachment or attachment to land, nature, culture, language, and heritage in Indigenous contexts. We wonder if students detach themselves from mathematics because they feel mathematics asking them to detach themselves from people and places to whom…