Studies that address preservice teachers' knowledge of area measurement emphasize their lack of knowledge and their tendency towards the use of formulas, without offering a body of knowledge that helps to address such difficulties. This study offers an approximation of the mathematical knowledge necessary for preservice teachers to solve area…

This article uses a cultural-developmental framework to illuminate the interplay between collective and individual activity in the mathematical reasoning displayed in a university Masters level lesson on fractals. During whole class and small group discussions, eleven students, guided by an instructor, engage in inductive reasoning about the area…

One goal of inquiry-oriented instruction is student engagement with others' mathematical ideas. This paper analyzes a relatively short episode in which students engaged with others' ideas; the instructor facilitated engagement in order to support students in making mathematical progress. Students expressed some bafflement pertaining to the…

The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

Understanding fraction as a quantity has been identified as a key developmental understanding. In this study, students in Grades 5, 8, and 11 were asked to compare the areas of two halves of the same square--a rectangle and a right triangle. Findings from this study suggest that students who understand fraction as a quantity use reasoning related…

This article suggests a tool for analysing diagrams in mathematical texts. The starting point for this tool is Halliday's Systemic Functional Grammar (SFG), which considered language as a social practice. Kress and Van Leeuwen (2006) applied Halliday's SFG to images, suggesting a grammar for reading images. Morgan (1996) adopted Halliday's SFG and…

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become "thinkable" the…

The purpose of this study was to examine geometry interventions for students with learning disabilities. We synthesized nine intervention studies by focusing on the geometry concepts and skills taught to students with learning disabilities, intervention types used, instructional components embedded, and the methodological rigor of the studies.…

This paper presents research on the argumentation that preservice teachers perform when designing and teaching geometry. Argumentation is associated with speech acts carrying didactical intentions. This research study features of preservice teachers' argumentation when explaining geometry tasks both to peers, during preparation and discussion of…

The aim of this study is to examine the geometric thinking levels of middle school mathematics preservice teachers regarding the problem situations regarding the concept of social distance according to the SOLO taxonomy. The research was conducted using the special case method, one of the qualitative research methods. The working group, studying…

This note outlines some connections between projective geometry and some designs used in clinical trials in the health sciences. The connections are not immediately obvious but they widen the scope for enrichment work at both the senior high school level and for capstone subjects at the undergraduate level.

The literature reports preservice teachers' overuse of proportionality when solving geometric similarity problems with nonproportional relationships. Changing this type of error is reported as difficult even after applying certain interventions. As a solution to this type of error, this study used augmented reality activities to facilitate the…

Extended reality experiences for mathematics teachers can allow them to understand both pedagogy and the mathematics itself in new ways. In this study, the authors explored a virtual reality simulation for learning about geometric shapes, where teachers could engage in joint, shared manipulation of holograms in three dimensions. The authors…

In the 21st century we live in, technology is developing rapidly. Inevitably, the technologies used in almost every area of daily life will also reflect in the field of education. Educational technologies, which enable students to grasp abstract concepts more easily and facilitate the teaching process for teachers, have increased their impact in…

This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…