In this article, the authors present two activities in which students explore angles and related geometric properties in the context of dance, namely ballet. The activities have been successfully implemented in pre-service numeracy classes at Monash University's two-year, post-degree teacher education program (MTeach). Specifically, the activities…

In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students' difficulties when treating…

Although some students might struggle with problem posing, the positive effects on student learning and abilities may be far reaching for those who engage in this activity. Problem posing requires students to create their own problems rather than to solve problems posed by others. Problem posing is not regularly taught; however, reform proponent…

Practical problems that use mathematical concepts are among the highlights of any mathematics class, for better and for worse. Teachers are thrilled to show applications of new theoretical ideas, whereas most students dread "word problems." This article presents a sequence of three activities designed to get students to think about…

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

In this qualitative research, we studied difficulties that undergraduate students face while learning the concept of inner product space. Participants were 35 first-year mathematics students from Yildiz Technical University in the 2011 and 2012 academic years. We asked participants to solve 5 inner product space questions. Data were jointly…

Mathematical games are widely used in the primary classroom; however, not all games are equally valuable. How might teachers decide which specific games to introduce? The authors present five principles of educationally-rich games to help teachers address this issue. In so doing, they provide teachers with a usable framework to stimulate…

Desmos Battleship is an engaging activity in which students can improve their visualisation skills, and deepen their understanding of linear functions and circles by making connections between algebraic and graphical representations. The Desmos Battleship activity was used in a Saturday STEM (Science, Technology, Engineering, and Mathematics)…

This research examined the effects of two instructional treatments on training performance in solid volume measurement and potential effects on solving capacity and displaced volume problems by two related studies. Fifty-three fifth-graders from a public elementary school in Taipei, Taiwan, participated. In the Phase 1 study, the children (n = 27)…

Several researchers have documented prospective teachers' (PTs') conceptions of various mathematical topics. However, less is known about how PTs' conceptions develop. To address this gap, I designed two tasks with the goals of addressing the PTs' initial conceptions of multidigit whole numbers and helping them develop more sophisticated ones. I…

This study illustrates how mathematical communication and learning are inherently multimodal and embodied; hence, sight-disabled students are also able to conceptualize visuospatial information and mathematical concepts through tactile and auditory activities. Adapting a perceptuomotor integration approach, the study shows that the lack of access…

Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…

In that current study, pattern conversion ability of 25 pre-service mathematics teachers (producing figural patterns following number patterns) was investigated. During the study participants were asked to generate figural patterns based on those number patterns. The results of the study indicate that many participants could generate different…

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner. First, using geometrical software, we investigate four theorems that represent interesting geometrical properties,…

Mathematical conventions -- which account for the choices of mathematics community regarding definitions of concepts, their names and symbols -- are the focus of this paper. We introduce the task of unpacking, that is, offering plausible explanations and arguments for the choice of conventions. Using responses of four prospective teachers to the…