In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

This article reports on a research project that examined the ways that 10-year-old students, who were using Scratch for coding, engaged with mathematical ideas. Interactive software is emerging that has cross-curricula implications and facilitates thinking in rich, problem-solving environments. Scratch, a free-to-use graphical programming…

As classrooms begin to adopt a greater number of digital technologies such as computers and tablets, it is important for educators to understand how effective such tools can be in aiding in the delivery of instruction to students who struggle in mathematics, such as those identified with a learning disability in mathematics. One digital-based…

In this study, it was aimed to examine the relation between seventh-grade students' quadrilaterals achievement levels and Van Hiele geometric thinking levels. Survey method was used. The sample of the study was 160 students from the three different districts of Kayseri, as Melikgazi, Incesu, and Tomarza. Van Hiele geometric thinking test and…

In the present study, the aim was to investigate 9th grade students' geometrical figure apprehension. To this end, the Figure Apprehension Cognitive Processes Test (FACPT), constructed by the researchers of the study, was administered to 51 ninth grade students, with whom clinical interviews were also conducted. As a result of the data analysed,…

As a component of a course on geometry for preservice elementary teachers (PSTs), we derive area formulas for a variety of polygons including triangles, quadrilaterals, and both regular and irregular shapes whose areas can be measured empirically using decomposition. Decomposing a circle to justify why its area can be measured using the standard…

This article reports on a study that explored how a group of in-service mathematics teachers integrated ethnomathematics approaches into the teaching and learning of geometry. The study used a convergent parallel mixed-methods design, which combined both quantitative and qualitative methods, to provide a deeper understanding of how the…

We report on the construction, validation, and implementation of an instrument for measuring students' strategic knowledge about drawing for geometry modelling problems, namely, the "strategic knowledge about drawing scale." We conducted a qualitative study and a quantitative study to validate the proposed construction and interpretation…

In this paper we display an example of how educational software Geogebra can be used as a tool for the STEM education. Geogebra is used in the process of introducing students in high school to mathematical models of materials science. Scientific results from materials science experiments were used for mathematical modelling and learning about the…

Inquiry-based learning (IBL) is a pedagogical approach in which students address complex, ill-structured problems set in authentic contexts. While IBL is gaining ground in Australia as an instructional practice, there has been little research that considers implications for student motivation and engagement. Expectancy-value theory (Eccles and…

This article explores the process of finding the Fermat point for a triangle ABC in three dimensions. Three examples are presented in detail using geometrical methods. A delightfully simple general method is then presented that requires only the comparison of coordinates of the vertices A, B and C.

The concepts and instruments required for the teaching and learning of geometric optics are introduced in the didactic process without a proper didactic transposition. This claim is secured by the ample evidence of both wide- and deep-rooted alternative concepts on the topic. Didactic transposition is a theory that comes from a reflection on the…

In this brief article Elana Reiser describes her favorite lesson that combines popular culture with mathematics in a way that motivates student thinking and participation. Exploring open-ended problems, students may feel uneasy at first, but working in small groups often leads them to experiment with a variety of solutions. Reiser explains that…

The article is dedicated to solving extrema problems in teaching mathematics, without using calculus. We present and discuss a wide variety of mathematical extrema tasks where the extrema are obtained and find their solutions without resorting to differential. Particular attention is paid to the role of arithmetic and geometric means inequality in…

This article uses parts of qualitative data from the first author's study that focused on exploring Pirie and Kieren's process of "folding back," revisiting previously held understandings of a concept for its extended understanding in order to solve the problem of enhancing Grade 10 learners' reasoning in geometry. In South Africa,…