GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the "two square difference identity" expressed for the square, which is a flat polygon, made with different approaches.…

The aim of this study is to examine 8th grade students' Van Hiele geometry thinking levels, proof writing and justification skills. The research was carried out with sixteen eighth grade students of a private school in Sivas. Participants were selected based on an easily accessible sample. The data were collected from the students who participated…

The aim of this study is to characterize ways of reasoning and arguing that first year university mathematics students exhibit in problem-solving activities from a course that emphasizes the importance of formulating conjectures and the search for different ways to support or validate them. The use of a Dynamic Geometry System in the…

Mathematical justifications offer an approach to which students deepen and extend their mathematical thinking. This process has the potential to enhance students' conceptual understanding. Mathematical practices and process standards ask students to use critical thinking skills to justify their reasoning, but this is usually seen as proofs in high…

Proof, as a central and integral part of mathematics, is an essential component of mathematical education and is considered as the basic procedure for revealing the truth of mathematical propositions and for teaching productive reasoning as part of human civilization. Is there therefore room for conjectures in mathematics? In this paper after…

In this study, it is aimed to reveal what kind of relationship exists between prospective teachers' thinking structures and their level of writing proofs. This study was carried out as a case study. The study was carried out with 82 prospective teachers enrolled in the Department of Secondary School Mathematics Teaching of a state university…

This study was conducted to examine whether newly enrolled 9th grade students were ready to directly engage in the theoretical discursive process from the perspective of Duval's Cognitive Model. The sample of the study was comprised of 51 newly enrolled 9th grade students between the ages of 14 and 15, who had not received any prior geometry…

The need to develop consistent theoretical frameworks for the teaching and learning of discrete mathematics, specifically of graph theory, has attracted the attention of the researchers in mathematics education. Responding to this demand, the scope of the Van Hiele model has been extended to the field of graphs through a proposal of four levels of…

Access to body-based resources has been shown to augment cognitive processes, but not all movements equally aid reasoning. Interactive technologies, like dynamic geometry systems (DGS), potentially amplify the link between movement and geometric representation, thereby deepening students' understanding of geometric properties. This study…

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition…

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the "cognitive relevance" of particular body states to associated math concepts. We test competing models of action-cognition…

We argue that examples can do more than serve the purpose of illustrating the truth of an existential statement or disconfirming the truth of a universal statement. Our argument is relevant to the use of technology in classroom assessment. A central challenge of computer-assisted assessment is to develop ways of collecting rich and complex data…

Increasing students' exposure to mathematical reasoning (Lannin, Ellis, & Elliot, 2011) has been a constant call from mathematics education reform efforts. However, studies have raised concerns about whether teachers are prepared to teach reasoning. This paper explores one aspect of reasoning, refutations, by examining the geometric…

A theoretical model describing young students' (Grades 1-3) functional-thinking modes was formulated and validated empirically (n = 345), hypothesizing that young students' functional-thinking modes consist of recursive patterning, covariational thinking, correspondence-particular, and correspondence-general factors. Data analysis suggested that…

Thinking development processes among high-school students is an important and significant issue that has been widely investigated (Leviathan, 2012; Ball, 1996; De Risi, 2015). A few studies discuss the development of mathematical thinking as this field contains additional difficulties to the traditional factors, teachers, students, and parents,…