Developing Pre-Service Teachers' Technological Pedagogical Content Knowledge for Teaching Mathematics with the Geometer's Sketchpad through Lesson Study

By Meng, Chew Cheng; Sam, Lim Chap | Journal of Education and Learning, March 2013 | Go to article overview

Developing Pre-Service Teachers' Technological Pedagogical Content Knowledge for Teaching Mathematics with the Geometer's Sketchpad through Lesson Study


Meng, Chew Cheng, Sam, Lim Chap, Journal of Education and Learning


Abstract

The purpose of this study was to develop pre-service secondary teachers' technological pedagogical content knowledge (TPACK) for teaching mathematics with The Geometer's Sketchpad (GSP) through Lesson Study (LS). Specifically, a single-group pretest-posttest design was employed to examine whether there was a significant difference in the pre-service secondary teachers' TPACK for teaching mathematics with GSP after engaging in LS which was incorporated into the mathematics teaching methods course during the first semester of the 2011/2012 academic session in a Malaysian public university. Forty-six pre-service secondary teachers who enrolled in the course completed both the pretest and posttest questionnaires on teachers' TPACK for teaching mathematics with GSP. The results of the paired-samples t-test indicated that there was a significant difference in the pre-service secondary teachers' TPACK for teaching mathematics with GSP for all the subscales after engaging in LS.

Keywords: TPACK, the Geometer's sketchpad, lesson study, pre-service teachers, secondary mathematics

1. Introduction

1.1 Background of the Study

GSP is a type of dynamic geometry software for constructing and investigating mathematical objects, not just in geometry. For example, in Algebra, students can use GSP to investigate gradients and equations of straight lines, properties of parabolas, and many other important Algebra topics. In Statistics, students can employ GSP to investigate concepts of mean, standard deviation and variance. In Trigonometry, GSP can be used to investigate trigonometric functions (Chanan, 2000). In addition, according to Finzer and Jackiw (1998, p. 2), GSP "can best foster mathematical inquiry and learning through 'dynamic manipulation' experiments." This is because students can directly manipulate mathematical objects represented on the screen and the mathematical objects stay coherent and whole at all times as they are dragged. Besides, students feel that they are involved with the objects they are manipulating and they can focus on how to achieve their mathematical goals, instead of how to use GSP.

In fact, research has shown that teaching mathematics with GSP enhances students' learning of plane geometry (e.g., Choi, 1996; Driskell, 2004; Thompson, 2006; Chew & Lim, 2010) and solid geometry (e.g., July, 2001; McClintock et al., 2002; Chew, 2007). Furthermore, teaching mathematics with GSP which is "based on experimentation, observation, data recording and conjecturing" (Olive, 2000, p. 3) encourages "a process of discovery that more closely reflects the way mathematics is invented" (Bennett, 1999, p. viii). This inquiry-based approach to teaching mathematics with GSP should "give students the opportunity to engage in mathematics as mathematicians, not merely as passive recipients of others mathematical knowledge" (Olive, 2000, pp. 3-4).

In view of its importance, the Ministry of Education Malaysia advocates the use of GSP in the teaching and learning of mathematics (Ministry of Education Malaysia, 2003). However, a brief survey study conducted by Kasmawati (2006) on 151 secondary mathematics teachers in the state of Penang showed that 26% of the teachers had attended GSP training courses but only 2% had used GSP to teach mathematics in the classroom. The two main reasons given by the mathematics teachers were lack of skills and confidence as well as lack of time to prepare a GSP sketch to use GSP to teach mathematics in the classroom.

In order for teachers to effectively use technology in their teaching, they need to develop TPACK for teaching with the technology (Neiss, 2005). Mishra and Koehler (2006) conceptualized TPACK as the integration of teachers' knowledge of content, pedagogy and technology and it is needed to effectively use technology to teach specific subject matter. More specifically, Shafer (2008) showed that teachers need TPACK for teaching mathematics with GSP in order to effectively plan and implement a GSP lesson in the classroom. …

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