Mathematical representation includes the process of transforming problems or ideas into new forms, including changing pictures or physical models into symbols, words, or sentences that can facilitate students in solving mathematical problems. Pythagorean Theorem material is widely used in analytic geometry, so this material becomes important for…

This paper reports the multimodal resources that attached to students' reasoning in the reinvention of specific geometric linear transformations (like reflections according to the axes, projections onto axes and composition of reflections) in a dynamic geometry environment. Following the design heuristics of Realistic Mathematics Education, we…

This paper focuses on problem solving and problem posing in mathematics education with 6-year-olds. After working on a problem-solving activity, the young students were asked to pose a "similar" task to a friend. This article explores how the students interpret the notion of "similar." To be able to pose a problem-solving task…

The purpose of this study is to investigate how students' in senior grade of the high school participate in and interpret the transformational geometry activities integrated with cultural context. 5 students in senior grade participated in this study, all of whom live in Aydin district of Turkey. The main design of the study is qualitative.…

Learning and teaching function transformation has a significant place since it provides new opportunities for learners to use, reflect and discover knowledge related to the concept of function. This study's main goals related to the importance of learning function transformation are to examine pre-service mathematics teachers' (PMTs) mental…

One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

This article describes a geometrical solution to a problem that is usually solved geometrically as an example of how alternative solutions may enrich the teaching and learning of mathematics. (Contains 11 figures.)

Contractions play a considerable role in the theory of fractals. However, it is not easy to find contractions which are not similitudes. In this study, it is shown by counter examples that an affine transformation of the plane carrying a given triangle onto another triangle may not be a contraction even if it contracts edges, heights or medians.…

Concept image and concept definition is an important construct in mathematics education. Its use, however, has been limited to cognitive studies. This article revisits concept image in the context of research on undergraduate students' understanding of the derivative which regards the context of learning as paramount. The literature, mainly on…

For two given vectors of the three-dimensional Euclidean space we investigate the problem of identifying all rotations that transform them into each other. For this purpose we consider three types of rotation matrices to obtain a complete characterization. Finally some attention is paid to the problem of obtaining all rotations taking two vectors…

An easy way to present the uniqueness of the square root of a positive semidefinite matrix is given.

Students learn more when they attempt to make sense of a mathematical situation they face. For example, a question like why square root of 25 is not + or - 5. Providing the intermediate steps and the reasoning of a technique with graphs can help make better sense of mathematics.