This study is an extension to the ongoing research on secondary mathematics teachers’ knowledge. This study focused on the concepts of logarithms and logarithmic functions. Several research studies have confirmed that high-school and undergraduate students have a very poor knowledge of logarithms and logarithmic functions. One of the possible reasons for students’ difficulties could be an insufficient teachers’ knowledge of this subject domain. As of yet, t here has not been research into teachers’ knowledge of logarithms. This study was an attempt to fill this gap. The deeper understanding of teachers’ knowledge, particularly subject matter content knowledge and related pedagogical skills, leads towards improvement of instructional approaches for more effective teacher training. The questions posed in this study are: What is pre-service secondary mathematics teachers’ knowledge of logarithms and logarithmic functions? What is the relationship between their subject matter content knowledge and pedagogical content knowledge? What do the designed tasks reveal about the nature of teachers’ knowledge? To what extent are these tasks effective and useful as data collection tools for research in mathematics education? This study identified that pre-service teachers are aware of possible difficulties of teaching or learning the concepts of logarithms and logarithmic functions. However, their insufficient subject matter content knowledge disallowed participants to explain why the situations prompted by their own questions were indeed problematic and important. On the whole, the pre-service teachers’ displayed a relatively weak content knowledge of logarithms and logarithmic functions, exemplified by weak subject matter content knowledge and related pedagogical content knowledge. Another goal of this research was to determine the effectiveness of the research methodology developed and used in this study. I designed a unique research task, called the Job Interview, and utilized another research task, known as the Math Play. These activities allowed me to investigate pre-service teachers’ knowledge from many different sources that yielded very diverse information about the participants’ knowledge. Also, these tasks proved to be important learning activities. They allowed pre-service teachers to re-examine high school mathematics content and reflect on their practice, while keeping in focus students’ meaningful learning.
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