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The Impact of Problem-Based Learning on Pre-Service Teachers’ Development and Application of Their Mathematics Pedagogical Content Knowledge

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The Impact of Problem-Based Learning on Pre-Service Teachers’ Development and Application of Their Mathematics Pedagogical Content Knowledge The Impact of Problem-based Learning on Pre-service Teachers’ Development and Application of Their Mathematics Pedagogical Content Knowledge A Thesis submitted by David A. Martin B.Ed., Dip. T., M.Ed. Technology, M.Ed. Leadership For the award of Doctor of Philosophy 2017 Abstract The main aim of this study was to investigate the effectiveness of problem-based learning (PBL) compared to a traditional teacher-led instructional approach on pre-service teachers’ mathematics pedagogical content knowledge (PCK) and their ability to apply that knowledge. Predictors of teacher effectiveness in relation to student achievement are based on defined attributes, for example: (a) the ability to use a range of evidence-based teaching strategies (Dean, Hubbell, Pitler, & Stone, 2012; Hattie, 2009), such as those encompassed in the PBL framework as described by Hmelo-Silver and Barrows (2015) and Savery (2015); (b) the ability of a teacher to enact the PCK he or she possesses (Hattie, 2009; Hill, Ball, & Schilling, 2008; Hill, Rowan, & Ball, 2005; Shulman, 1986; Tatto & Senk, 2011) and (c) the level of confidence, and/or self-efficacy, a teacher maintains in his or her ability to teach (Bandura, 1977; Schunk, 1991; Tschannen-Moran & Hoy, 2001). Teachers who have high self-efficacy may also maintain the expectation that they can influence positive academic outcomes for their students (Bandura, 1986; Enochs, Smith, & Huinker, 2000). This type of cognitive belief is identified by Bandura (1977) as outcome expectancy. Although studies on PBL are numerous, an inspection of the literature did not reveal any which examined the specific characteristics noted above in pre-service teachers when PBL was introduced to the teaching context. As a result, this study aimed to investigate the impact specifically that closed loop PBL had in a tertiary mathematics education subject, compared to using a traditional teacher-led approach, on pre-service teachers’ mathematics PCK, their ability to enact their PCK, their self-efficacy for teaching mathematics and their mathematics teaching outcome expectancy. To measure pre- service teachers’ knowledge of mathematics PCK and their self-beliefs for teaching mathematics, a Mathematics Pedagogical Content Knowledge Instrument (MPCKI) and a Mathematics Teaching Efficacy Belief Instrument (MTEBI) were developed and used in a pilot study. The instruments were administered pre-intervention and post- intervention to both a control group (n=15), who received traditional instruction, and a treatment group (n=15) who were instructed using the closed loop PBL teaching method (the intervention). The outcomes of the pilot study provided insight into the need for i additional data to be collected from pre-service teachers’ end-of-semester exam questions (N=37) to measure specifically their ability to enact their mathematics PCK. Qualitative data were also collected in the form of semi-structured interview responses. The interviews, which were conducted at the end of the intervention, asked questions of the treatment group participants (n=17) relating to the impact PBL had on the development of their mathematics PCK, the ability to enact their PCK and their teaching beliefs. The analysis of the results of the MPCKI, which was designed as a multiple-choice survey instrument, did not demonstrate a significant difference between the two groups’ mathematics PCK. However, the analysis of the pre-service teachers’ constructed responses to the end-of-semester exam mathematics PCK-specific questions did demonstrate a significant difference between the two groups ability to enact their mathematics PCK. Furthermore, the qualitative data collected from the interview responses from the PBL treatment group indicated a unanimous satisfaction with being taught by the PBL method and a unanimous affirmative response when asked if they felt the closed loop PBL teaching method was more effective than traditional instruction in developing their mathematics PCK and their ability to enact their PCK. The results of the MTEBI analysis did not demonstrate a significant difference between the two groups’ self-efficacy for teaching and teaching outcome expectancy. However, an analysis of the interview transcripts from the PBL group of pre-service teachers revealed a new sense of confidence and teacher effectiveness, which, they felt will positively impact on their students’ academic success. It was hypothesised that the closed loop PBL method is a more effective pedagogical approach in teacher education compared to traditional teacher-led instruction for mathematics education. As the aim of teacher education is to enhance graduate teachers’ abilities to enact their mathematics PCK, simply put to be better mathematics teachers, it was concluded that closed loop PBL is a useful pedagogical strategy to afford them the confidence and skills to enact their personal mathematics PCK. Although the findings returned mixed results, most of the evidence supports closed loop PBL’s potential as a more effective pedagogical approach for developing pre-service teachers’ ability to enact mathematics PCK. ii Certification of Thesis This thesis is entirely the work of David A Martin except where otherwise acknowledged. The work is original and has not been previously submitted for any other award, except where acknowledged. Student and supervisors’ signatures of endorsement are held at USQ. Professor Romina Jamieson-Proctor Principal PhD Supervisor Professor Peter Albion Associate PhD Supervisor iii Acknowledgements The depths I have travelled to where a PhD candidate is taken has been made possible by both my supervisors and a number of colleagues. Firstly, I offer sincere gratitude to my Principal Supervisor, Professor Romina Jamieson-Proctor, for her continued support, advice and feedback. Her years of mentorship have enriched my ability to conduct quality research. I am obliged also to my Associate Supervisor, Professor Peter Albion, for his comprehensive reviews of my work and thesis. His expertise with PBL and high expectations for scholarly writing served my thesis well. I would like to thank Associate Professor Rosemary Callingham from the University of Tasmania and Dr Peter Grimbeek of Griffith University for sharing their specialised knowledge in using SPSS and Winsteps to conduct factor and Rasch item analyses. The professional development they provided enabled me to demonstrate an extra dimension of rigour and validity of the study’s quantitative instruments for measuring mathematics PCK in pre-service teachers. In terms of a support network I am grateful to two colleagues, Dr Trevor Black and Dr Sharon Louth, for the copious number of think tank sessions we engaged in over the years. During the sessions we discussed each other’s ideas, clarified concepts, cleared up misconceptions, and supported each other during the writing of our respective theses. I thank the School of Education professional and academic staff members at the University of Southern Queensland who supported my research endeavours and recognised my work as a sound contribution to the research of teaching and learning at the tertiary level. Most importantly, I would like to thank my wife April for her patience and support which allowed me both the freedom and time to pursue this endeavour, time which we would have otherwise spent together. I truly appreciate her sacrifice, selflessness, love and encouragement. iv Table of Contents Abstract ............................................................................................................................. i Certification of Thesis ..................................................................................................... iii Acknowledgements ......................................................................................................... iv List of Figures ............................................................................................................... viii List of Tables .................................................................................................................. ix Chapter 1 Introduction ..................................................................................................... 1 1.1 Overview ........................................................................................................... 1 1.2 The Research Problem and Aim of the Study ................................................... 1 1.3 Addressing the Research Problem ..................................................................... 3 1.4 Background to the Conceptualisation of the Study ........................................... 6 1.5 Chapter Summary .............................................................................................. 8 1.6 Structure of the Thesis ....................................................................................... 9 1.7 Glossary of Terms and Acronyms used throughout ........................................ 10 Chapter 2 Literature Review ......................................................................................... 13 2.1 Overview ......................................................................................................... 13 2.2 Attributes of Effective Teachers ...................................................................... 13 2.3 Content Knowledge ......................................................................................... 16 2.4 Pedagogical Knowledge .................................................................................
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