Binary operations are one of the fundamental structures underlying our number and algebraic systems. Yet, researchers have often left their role implicit as they model student understanding of abstract structures. In this paper, we directly analyze students' perceptions of the general binary operation via a two-phase study consisting of task-based…

Background/purpose: Understanding gifted students' perceptions by means of metaphors, carefully examining and interpreting them may help to guide the organization of training programs and the differentiation of educational content for gifted students. This study aims to reveal the perceptions of gifted students regarding science and mathematics…

Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing…

In this study, it was aimed both to examine middle school students' perceptions of the concept of pattern and to reveal if the metaphoric perceptions which the students created in relation to the concept of pattern changed according to the variable of grade level. The metaphors in relation to the concept were carried out via the…

The aim of this study is to evaluate the classroom teacher candidates' metaphorical perceptions about the mathematics course through the visuals they create. The sample of the study consists of 36 classroom teacher candidates studying at a state university in Istanbul. The case study, which is one of the qualitative research methods, was used as…

In this study, it is aimed to examine the perceptions of prospective mathematics teacher about the concept of "intelligent games" through metaphors. Phenomenology method was used in the research. The participants of the research consisted of a total of 218 prospective teachers who studied in Department of Elementary School Mathematics…

This research aims to determine the perceptions of middle school pre-service mathematics teachers regarding the concept of "mathematical thinking" through the usage of metaphors. The phenomenology method, which is one of the qualitative research methods, is adopted in this study. Data of the research was obtained by the pre-service…

Mathematically speaking, a "difference" is the result of a subtraction. However, when the number domain is extended from natural numbers to integers, the separation of the magnitude of a number from its value creates "different differences," where the connection to subtraction is no longer straightforward. Based on…

The purpose of this study is get opinions of students on the subject of mathematics. It is thought that determining the meaning of mathematics in students' minds, the things that students associate mathematics with and the things that come to their minds when you say mathematics is vital. In this way, it is thought that it can be possible to take…

Calculus is used across many physics topics from introductory to upper-division level college courses. The concepts of differentiation and integration are important tools for solving real world problems. Using calculus or any mathematical tool in physics is much more complex than the straightforward application of the equations and algorithms that…

This submission contains the Proceedings of the 2014 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of Alberta in Edmonton, Alberta. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

This paper reports on an exploratory study of the mathematical beliefs of a group of ninth and tenth grade students at a large, college preparatory, private school in the Southeastern United States. These beliefs were revealed using contemporary metaphor theory. A thematic analysis of the students' metaphors for mathematics indicated that students…

"Function", as it is understood today, formulates one of the most important concepts of mathematics. Nevertheless, many students do not sufficiently understand the abstract but comprehensive meaning of function and problems concerning its didactical metaphor are often confronted. The present study examines the interpretation of the…

The metaphorical nature of first-year calculus students' reasoning about limit concepts is explored using an instrumentalist approach. Analysis of written and verbal language reveals that, while these students used motion terminology profusely when discussing limits, it was typically not intended to signify actual motion and did not play a…

This study investigates middle school mathematics students' views and interpretations of graphical representations as they use graphs to answer algebraic questions--specifically, questions that require them to extrapolate information from graphs. From data gathered in videotaped interviews, students' verbal responses were analyzed as well as any…