Abstract
The study aimed to expose how pre-service teachers perceived the value of an inquiry-based geometrical task with dynamic geometry software for increasing and deepening their understanding of the task itself, and for heightening their mathematical, pedagogical, and technological knowledge in the case of reflection and transformation. Twenty-seven pre-service teachers studying to become middle-school (junior high) mathematics teachers were assigned an inquiry-based geometrical task to explore – both by conventional, low-tech means (paper and pencil) and then in a dynamic geometry software (DGS) environment – the properties of objects formed by reflections in polygons (triangles and quadrilaterals) and to offer conjectures and proofs regarding the final polygon’s shape and area concerning the original. The results show that the majority of participants indicated that DGS provided a valuable instrument for revising and expanding their knowledge, that the assignment demonstrated the value that technological tools have in teaching and learning processes, and the importance of adapting learning tasks in geometry to a dynamic geometry environment for expanding and deepening geometrical and pedagogical knowledge and reasoning skills.
Highlights
Mathematics Teachers’ KnowledgeOver the past few decades, scholars in the field of mathematics education have been surveying and characterizing the type of knowledge that is essential for mathematics teachers.Relying on Shulman’s (1986) work, which suggests that teachers require unique types of knowledge and that defined two key concepts to describe them – subject matter knowledge and pedagogical content knowledge – Ball and Bass (2003) tried to characterize the knowledge required for mathematics teachers
The above formed the framework for the present study, which was to investigate the perceptions pre-service mathematics teachers have about the development of their technological content knowledge and technological pedagogical knowledge during their coping with inquiry-geometrical task
The worksheets showed that even though students might have offered a correct conjecture, their proofs were often incorrect because they relied on manual sketches to identify the shape of the reflected polygon and predicted the area ratios based on visual reckoning and not on precise calculations using the sides and angles. (The students who did offer the correct conjecture performed the proper calculations.)
Summary
Over the past few decades, scholars in the field of mathematics education have been surveying and characterizing the type of knowledge that is essential for mathematics teachers. TPACK encompasses the intersection of the basic types of knowledge that teachers require to integrate technologies into their teaching no matter what the content area. It includes an understanding of the representation of concepts using technology; pedagogical techniques that use technologies in constructive ways to teach content; knowledge about what makes concepts difficult or easy to learn; appreciation of how technology can help students solve tasks; and knowledge of how technology can be used to develop new knowledge based on existing knowledge. The above formed the framework for the present study, which was to investigate the perceptions pre-service mathematics teachers have about the development of their technological content knowledge and technological pedagogical knowledge during their coping with inquiry-geometrical task. A point, P, is selected within rhombus ABCD and reflected through the midpoints of the sides of ABCD to obtain points K, L, M, and N, which form the vertices of the reflected quadrilateral
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