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Valid and invalid verbal definitions Mathematical notations were used in 4% of the definitions. Three percent of these definitions were valid but 1% invalid. Sample definitions are presented below.
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The purpose of this study is to reveal the concept definitions and examples of pre-service elementary
mathematics teachers regarding sets. In this context, students’ formal definitions, personal definitions and examples in sets were investigated. Concept of equal sets, subsets, union, intersection, compliment, and difference were considered as basi...
Citations
... Instead of providing deeply mathematical explanations, the teachers gave answers at a general level of mathematical knowledge that someone engaged in mathematics could answer. In the researches, it is seen that pre-service mathematics teachers do not perform conceptual learning regarding "The Basic Concepts of Sets" and they have difficulty in making the formal definition of the concepts (Doruk & Çiltaş, 2020;Fischbein & Baltsan, 1999;Speer et al., 2015;Zehir et al., 2008). In this study, we can express the erroneous or incomplete information that teachers have about the concepts of "Set, Universal Set, Infinite Set" and "Equal Set" as follows: ...
This study investigates first-year undergraduate students of Primary Education Mathematics Teacher Education's knowledge and understanding of rotational symmetry in geometric shapes. Three students participated in this study, which was designed within the framework of a one-to-one teaching experiment (a qualitative research method) in the fall semester of the 2020-2021 academic year. A total of four one-to-one clinical interviews were conducted with the students once a week for an average of one hour and fifteen minutes each. Researchers recorded the sessions with a video camera and kept a log of observations. The data were analyzed and interpreted using continuous analysis and retrospective analysis. Each abstraction type and level of rotational symmetry was assigned indicators based on the results. According to the results, a student at Piaget's experimental abstraction level related to rotational symmetry before the teaching experiment reached the third level of reflective abstraction. Another student at experimental abstraction reached the level of reflective abstraction at level 2; the student who was not at any level reached the level of reflective abstraction at level 1. Students can undertake reflective abstraction by improving their knowledge and understanding of rotational symmetry by using daily life examples and making rotational symmetric drawings in the classroom. Consequently, daily life examples should be used more often in geometry lessons and students should be encouraged to draw more. Additionally, it was suggested that new research be conducted to support student abstraction based on Piaget's reflective abstraction theory.
The purpose of this research; it is to reveal the knowledge and understanding of the first year undergraduate students of Primary School Mathematics Teacher Education about rotational symmetry in a given geometric figure by examining them. This research, which was designed within the framework of one-to-one teaching experiment, one of the qualitative research approaches; it was conducted with three students in the fall semester of the 2020-2021 academic year. The data of the research; it was collected by video recording and researcher diary of four clinical interviews with all students one- on-one once a week. Continuous analysis and retrospective analysis were used in the analysis and interpretation of the research data. Based on the research findings; parameters have been determined for each of the abstraction types and levels related to the concept of rotational symmetry. Based on the research findings; it has been determined progresses regarding the concept of rotational symmetry. A student at the experimental abstraction level of Piaget's abstraction level reached the 3rd level reflective abstraction level after the teaching experiment the other student at the experimental abstraction level reached the 2nd level reflective abstraction level. And the student who did not have any level reached the 1st level reflective abstraction level. It has been determined that making use of daily life examples and making rotationally symmetrical drawings in rotational symmetry teaching are extremely important for students to develop their knowledge and understanding of the concept of rotational symmetry and make reflective abstraction.
In this paper, we provide a conceptual framework of the central aspects of mathematical definitions discussed in the mathematics education literature. Based on a systematic literature review, we found that characterizations of definitions in the mathematics education literature can be classified into five main themes: requirements, preferred features, role and function, nature, and types of definition. Within each theme, a refined set of aspects was found by means of inductive coding. We discuss each aspect and point out areas where we believe further research is needed. The framework can be used both as a research tool and a didactical tool, as it highlights many aspects of mathematical definitions that call for attention by teachers and researchers.
