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Towards the Pedagogy of Risk: Teaching and Learning Risk in the Context of Secondary

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Towards the Pedagogy of Risk: Teaching and Learning Risk in the Context of Secondary Towards the Pedagogy of Risk: Teaching and Learning Risk in the Context of Secondary Mathematics by Nenad Radakovic A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Department of Curriculum, Teaching, and Learning Ontario Institute for Studies in Education University of Toronto © Copyright by Nenad Radakovic 2014 Towards the Pedagogy of Risk: Teaching and Learning Risk in the Context of Secondary Mathematics Nenad Radakovic Doctor of Philosophy, 2014 Department of Curriculum, Teaching, and Learning Ontario Institute for Studies in Education University of Toronto Abstract A qualitative case study was presented in order to explore an inquiry-based learning approach to teaching risk in two different grade 11 mathematics classes in an urban centre in Canada. The first class was in an all-boys independent school (23 boys) and the second class was in a publicly funded religious school (19 girls and 4 boys). The students were given an initial assessment in which they were asked about the safety of nuclear power plants and their knowledge of the Fukushima nuclear power plant accident. Following the initial assessment, the students participated in an activity with the purpose of determining the empirical probability of a nuclear power plant accident based on the authentic data found online. The second activity was then presented in order to determine the impact of a nuclear power plant accident and compare it to a coal power plant accident. The findings provide evidence that the students possess intuitive knowledge that risk of an event should be assessed by both its likelihood and its impact. The study confirms the Levinson et al. (2012) pedagogic model of risk in which individuals’ values and prior experiences together with representations and judgments of probability play a role in the estimation of risk. The study also expands on this model by suggesting that pedagogy of risk should include five components, namely: 1) knowledge, beliefs, and values, 2) judgment of impact, 3) judgment of probability, 4) representations, and 5) estimation of risk. These ii components do not necessarily appear in the instruction or students’ decision making in a chronological order; furthermore, they influence each other. For example, judgments about impact (deciding not to consider accidents with low impact into calculations) may influence the judgments about probability. The implication for mathematics education is that a meaningful instruction about risk should go beyond mathematical representations and reasoning and include other components of the pedagogy of risk. The study also illustrates the importance of reasoning about rational numbers (rates, ratios, and fractions) and their critical interpretation in the pedagogy of risk. Finally, the curricular expectations relevant to the pedagogy of risk from the Ontario secondary curriculum are identified. iii Acknowledgments I would like to thank my supervisor, Doug McDougall, for all of his support and advice, as well as my committee members, Clare Brett, Indigo Esmonde, David Booth, and Jim Hewitt. Special thanks to Professor Cynthia Langrall for agreeing to be the external examiner and for her comments and suggestions that have significantly improved the final product. I have been at OISE since 2006 and there have been many faculty members who have supported me in my journey first as an MA student and then as a PhD student. They include Gila Hanna, Rina Cohen, Eunice Jang, John Wallace, Brent Kilbourn, and Larry Bencze, among others. I am also grateful to the wonderful staff at OISE and would like to thank Terry Louisy, Janice Abdul Jabbar, Mary MacDonell, and Margaret Brennan. OISE, specifically the SMT community, feels like a family. I would like to mention my fellow students, including the members of the Zieg and PPL labs, and especially Susan (Mick’s cousin) Jagger, Limin Jao, Amy Gullage, and Erin Sperling. I would also like to thank my mom Ljiljana, sister Svetlana, and grandmother Danica for their love and support. Finally, I would like to thank Lauren for her love and for being there for me. I am looking forward to our life after the PhD. iv Abstract……………………………………………………………………………………….ii Acknowledgments…………………………………………………………………………....iv Table of Contents………………………………………………………………………….....v List of Tables………………………………………………………………………………...vii List of Figures………………………………………………………………………………...ix Chapter One: Introduction ........................................................................................................ 1 Research Context .................................................................................................................. 1 Purpose of the Study ............................................................................................................. 3 Significance of the Research ................................................................................................. 4 Background of the Researcher .............................................................................................. 5 Structure of the Thesis .......................................................................................................... 8 Chapter Two: Review of Literature ........................................................................................ 10 The Concept of Risk ........................................................................................................... 10 Cultural Perspectives ...................................................................................................... 11 Teaching and Learning of Risk ........................................................................................... 13 Deficit Theory of Risk .................................................................................................... 13 Pedagogic Model of Risk ................................................................................................ 20 Elements of the Pedagogic Model of Risk ...................................................................... 21 Probabilistic Judgments .................................................................................................. 22 Teaching Risk in the Classroom ..................................................................................... 32 Summary: Pedagogy of Risk .............................................................................................. 33 Chapter Three: Methodology .................................................................................................. 34 Classroom Research in Mathematics Education ................................................................. 34 Case Study Research ....................................................................................................... 36 Research Setting and Participants ....................................................................................... 37 Inquiry-Based Learning Approach ..................................................................................... 38 The Task: Safety of Nuclear Power Plants ..................................................................... 39 Data Collection ................................................................................................................... 42 Data Analysis ...................................................................................................................... 43 Ethical Considerations .................................................................................................... 49 Chapter Four: Findings ........................................................................................................... 50 Case One: Dale Academy ................................................................................................... 50 Students ........................................................................................................................... 51 Teacher ............................................................................................................................ 53 Initial Assessment ........................................................................................................... 53 v The First Nuclear Power Plant Activity .......................................................................... 59 Choosing the Website ..................................................................................................... 61 Estimating Empirical Probability .................................................................................... 62 Decisions Based on Probability ...................................................................................... 64 The Second Nuclear Power Plant Activity ..................................................................... 65 Case Two: St. Hubertus Secondary School ........................................................................ 72 Students ........................................................................................................................... 72 Teacher ............................................................................................................................ 74 Initial Assessment ............................................................................................................... 74 The First Nuclear Power Plant Activity .......................................................................... 79 The Second Nuclear Power Plant Activity ....................................................................
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