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ROLE OF MATHEMATICS TEACHER IN USING TECHNOLOGY
Abstract
Investigating the effect technology has on the secondary mathematics classroom instruction has been a growing topic in mathematics education since calculators and computers became readily available to students and teachers. Most of the focus has been on students' use of technology to enhance their mathematical knowledge, while teacher use of technology during instruction has had limited research attention. The purpose of this study was to further understand the emergence of the roles of facilitator and mediator when secondary mathematics teachers used technology during instruction. Conceptual and procedural mathematical activities affected the participants' role while teaching with technology. An emergent theme of the source of mathematical activities, internal or external, helped illuminate the development of teacher roles while using technology. Procedural mathematical activities were found to only contain external sources of mathematical activities while conceptual mathematical activities contained both internal and external sources. A connection was established while comparing the source of mathematical activities with the teachers' roles while using technology. The analysis indicated that the facilitator role was only observed when teachers' had conceptual mathematical activities that involved internal sources. When an external source was observed, the teachers' role was found to be that of a mediator.
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The recent development of powerful new technologies such as dynamic geometry software (DGS) with drag capability has made possible the continuous variation of geometric configurations and allows one to quickly and easily investigate whether particular conjectures are true or not. Because of the inductive nature of the DGS, the experimental-theoretical gap that exists in the acquisition and justification of geometrical knowledge becomes an important pedagogical concern. In this article we discuss the implications of the development of this new software for the teaching of proof and making proof meaningful to students. We describe how three prospective primary school teachers explored problems in geometry and how their constructions and conjectures led them see proofs in DGS.
Generalization and proof are defining activities within mathematics, yet the focus of "school" proof has often been on form
over meaning, on established results rather than exploration and discovery. Computer-based microworlds offer opportunities
for students to notice and describe patterns, formulate generalizations, and generate and test mathematics conjectures. This
paper examines the work of a group of middle and high school students who used a microworld for transformation geometry to
investigate the composition of reflections. The students‘conjectures are described in terms of a learning paths chart for
the task, as well as through a detailed analysis of the work of one pair of students. A general scheme for describing informal
exploration and reasoning prior to formal proof is offered, and the role of social support in the learning of proof is discussed.
The last decade has seen the development in France of a significant body of research into the teaching and learning of mathematics
in CAS environments. As part of this, French researchers have reflected on issues of ‘instrumentation’, and the dialectics
between conceptual and technical work in mathematics. The reflection presented here is more than a personal one – it is based
on the collaboration and dialogues that I have been involved in during the nineties. After a short introduction, I briefly
present the main theoretical frameworks which we have used and developed in the French research: the anthropological approach
in didactics initiated by Chevallard, and the theory of instrumentation developed in cognitive ergonomics. Turning to the
CAS research, I show how these frameworks have allowed us to approach important issues as regards the educational use of CAS
technology, focusing on the following points: the unexpected complexity of instrumental genesis, the mathematical needs of
instrumentation, the status of instrumented techniques, the problems arising from their connection with paper & pencil techniques,
and their institutional management.
Presents a study designed to explore whether a student's use of the graphing calculator during instruction will affect their concept of function, how students' participation in a conceptual change assignment affects their concept of function, and how the graphing calculator and the conceptual change assignment interact with one another to influence concept formation. (DDR)
Preservice teachers' pedagogical content knowledge (PCK) development was investigated with respect to integrating technology. Four components of PCK were adapted to describe technology-enhanced PCK (TPCK). The study examined the TPCK of student teachers in a multi-dimensional science and mathematics teacher preparation program that integrated teaching and learning with technology throughout the program. Five cases described the difficulties and successes of student teachers teaching with technology in molding their TPCK. Student teachers view of the integration of technology and the nature of the discipline was identified as an important aspect of the development of TPCK.
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