Doctor of Philosophy / Department of Physics / N. Sanjay Rebello / Calculus is used across many physics topics from introductory to upper-division level college courses. The concepts of differentiation and integration are important tools for solving real world problems. Using calculus or any mathematical tool in physics is much more complex than the straightforward application of the equations and algorithms that students often encounter in math classes. Research in physics education has reported students’ lack of ability to transfer their calculus knowledge to physics problem solving. In the past, studies often focused on what students fail to do with less focus on their underlying cognition. However, when solving physics problems requiring the use of integration, their reasoning about mathematics and physics concepts has not yet been carefully and systematically studied. Hence the main purpose of this qualitative study is to investigate student thinking in-depth and provide deeper insights into student reasoning in physics problem solving from multiple perspectives. I propose a conceptual framework by integrating aspects of several theoretical constructs from the literature to help us understand our observations of student work as they solve physics problems that require the use of integration. I combined elements of three important theoretical constructs: mathematical resources or symbolic forms, which are the small pieces of knowledge elements associated with students’ use of mathematical ideas; conceptual metaphors, which describe the systematic mapping of knowledge across multiple conceptual domains – typically from concrete source domain to abstract target domain; and conceptual blending, which describes the construction of new learning by integrating knowledge in different mental spaces. I collected data from group teaching/learning interviews as students solved physics problems requiring setting up integrals. Participants were recruited from a second-semester calculus-based physics course. I conducted qualitative analysis of the videotaped student conversations and their written work. The main contributions of this research include (1) providing evidence for the existence of symbolic forms in students’ reasoning about differentials and integrals, (2) identifying conceptual metaphors involved in student reasoning about differentials and integrals, (3) categorizing the different ways in which students integrate their mathematics and physics knowledge in the context of solving physics integration problems, (4)exploring the use of hypothetical debate problems in shifting students’ framing of physics problem solving requiring mathematics.

D.Ed.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science Johannesburg 2016. / This dissertation investigates grit “passion and perseverance” for a long-term goal and growth mindset in grade 11 high school students as they code a non-trivial pro-gramming project in Java over a six-week period. Students are often challenged by the complexities of programming and can be overwhelmed when they encounter errors causing them to give up and not persevere. The programming project includes scaffolding with frequent feedback to increase the motivation of students. The study used mixed methods research that used both quantitative and qualitative data to find answers to the research questions. Whilst the correlation between grit, mindset and the project results were moderate, that students submitted their project numerous times showed an indication to perseverance. The data gathered from the interviews further indicated that the students’ perseverance led them to employ their own prob-lem-solving strategies when they encounter problems. / MT 2017

A research report submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg in fulfilment of the partial requirement of the degree of Master of Science. Johannesburg, 2012 / Campaigns to educate people on how to use and manage energy responsibly are on the agenda of energy producers, Non-Governmental Organisations (NGO) and the government of South Africa. Until recently, publications on energy conservation programmes to inform these groups on best practice have been non-existent. This paper reports on an energy conservation programme, “Energy Dialogues” primarily aimed at offering information as well as influencing pro-environmental attitudes and consequently the behaviour of grade 11 learners in the Gauteng province of South Africa. The Energy Dialogues was conducted in a non-formal learning environment. Learners on the programme were challenged to propose various forms of ‘action taking’ to promote Energy Dialogues amongst their peers, in their school, at home, and in their community. Seven out of twenty schools met the challenge. The research project captured the social interaction among learners during the “Energy Dialogues” programme. A survey confirmed that learners still possess alternative ideas with regards to energy use and management after classroom instruction. While learners have significant knowledge of the causes and consequences of poor energy usage, this does not translate into change in behaviour. Creating an environment of group learning may influence the learners’ lifestyle choices. Learners are more inclined to align themselves with the values of a group. An active learning framework of the Energy Dialogues gave learners an opportunity to take personal responsibility for the environment. They redefined their culture, physically engaged in activity and spoke the language of the educator. While the learners’ visit to DEC was a one-time occurrence, and the findings cannot be generalised, this study may inform future longitudinal research which would offer information of the causal relationships of the components influencing sustainable practices.

Solving proportion problems in schools is a very difficult task for most children. Too often children are taught to use techniques for solving fractions when working with ratio and proportion problems. Although these techniques may prove useful for obtaining a solution to a proportion problem, they do not provide rich learning opportunities for students to construct proportional relationships. Individual interviews, problem solving episodes, and personal journals were the primary tools used in collecting data for this study. The problem solving episodes became the key components in observing and interacting with the participants as they solved ratio and proportion problems. The researcher found that individuals must have many elaborated constructions to solve proportion tasks. Without these elaborated constructions the individual is unable to effectively coordinate the information needed to solve proportion tasks. That is, the individual is unable to reason proportionally. Another outcome of this study was the importance of finding meaningful and doable proportion tasks for the informants to complete. Unexpected outcomes of the study included the effect of engaging in problem solving on the identity of the child and the role of language in giving meaning to the tasks. / Typescript. / "Summer Semester, 1992." / "Submitted to the Department of Curriculum and Instruction in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisor: Grayson H. Wheatley, Professor Directing Dissertation. / Includes bibliographical references.

Thesis advisor: Ina V.S. Mullis / The eTIMSS mathematics PSIs were a new and pioneering effort to capitalize on the computer- and tablet-based mode of assessment delivery introduced in the eTIMSS 2019 assessments at the fourth and eighth grades. The PSIs were scenario-based mathematics problem solving tasks intended to enhance measurement of mathematics problem solving and reasoning skills and increase student engagement and motivation in the assessment. These unique tasks were designed to measure the same mathematics content as the rest of the mathematics items in the eTIMSS 2019 assessments, but because of their novelty, there was a question about whether the PSIs achieved this goal and could be reported together with the regular TIMSS mathematics items. Following a full-scale field test in 30 countries completed in May 2018, this dissertation conducted an in-depth investigation of the validity of the eTIMSS 2019 mathematics PSIs with the goals of informing analysis and reporting plans for TIMSS 2019 and providing insights for future assessments aspiring to capitalize on digital technology. This investigation involved three key tasks: 1) examining and documenting the methods and procedures used to develop the PSIs and promote validity by design, 2) investigating the characteristics of the PSIs in terms of the content coverage and fidelity of student responses, and 3) using the eTIMSS field test data to evaluate the internal structure of the PSIs. The results indicate that the PSIs are well-aligned with the TIMSS 2019 Mathematics Framework and elicited the intended interactions from students. The regular and PSI items were found to measure the same unidimensional construct, and therefore can be validly reported together on the TIMSS 2019 achievement scale. The lessons TIMSS learned in developing the PSIs for eTIMSS 2019 and suggestions for the future also are discussed. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Research, Measurement and Evaluation.

by Lee Fong Lok. / Chinese title: / Bibliography: leaves 103-111 / Thesis (M.A.Ed.)--Chinese University of Hong Kong

by Wong Ka-Ming. / Thesis (M.A.Ed.)--Chinese University of Hong Kong, 1989. / Bibliography: leaves 164-173.

by Cheng Kar Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves [195-199] / ABSTRACT / Chapter CHAPTER 1 --- INTRODUCTION --- p.1 / Chapter 1.1 --- Problem --- p.2 / Chapter 1 .2 --- Approach --- p.3 / Chapter 1.2.1 --- Programming Approach --- p.4 / Chapter 1.2.2 --- Specification Approach --- p.5 / Chapter 1.3 --- Thesis Organization --- p.11 / Chapter CHAPTER 2 --- MODEL SPECIFICATION APPROACH --- p.12 / Chapter 2 .1 --- Overview --- p.14 / Chapter 2.2 --- Compilation Phases --- p.17 / Chapter 2.3 --- Array Graph --- p.22 / Chapter 2.4 --- Scheduling --- p.25 / Chapter CHAPTER 3 --- SURVEY --- p.31 / Chapter 3.1 --- Goodenough's Proposal --- p.31 / Chapter 3.2 --- Exception Handling Models --- p.34 / Chapter 3.3 --- Programming Languages --- p.40 / Chapter 3.4 --- Data-Oriented Exception Handling --- p.49 / Chapter 3.5 --- Specification Languages --- p.50 / Chapter CHAPTER 4 --- EXCEPTION HANDLING SPECIFICATION --- p.55 / Chapter 4.1 --- Data-Oriented Exceptions Specification --- p.55 / Chapter 4.2 --- Assertions for Exception Handling --- p.59 / Chapter 4.2.1 --- User-defined Exception Condition Assertion --- p.61 / Chapter 4.2.2 --- Fatal Condition Assertion --- p.62 / Chapter 4.2.3 --- Replacement Assertion --- p.64 / Chapter 4.2.3.1 --- Scenario 1: Immediate Replacement --- p.68 / Chapter 4.2.3.2 --- Scenario 2: Direct Dependency --- p.71 / Chapter 4.2.3.3 --- Scenario 3: Indirect Dependency --- p.72 / Chapter 4.2.3.4 --- Scenario 4: Lower Dimensionality --- p.74 / Chapter 4.2.4 --- Message Vector Assertion --- p.76 / Chapter CHAPTER 5 --- ARRAY GRAPH FOR EXCEPTION HANDLING --- p.78 / Chapter 5.1 --- Subgraph Embedding --- p.78 / Chapter 5.1.1 --- User-Defined Exception Conditions --- p.80 / Chapter 5.1.2 --- Fatal Conditions --- p.82 / Chapter 5.1.3 --- Pre-Defined Exception Conditions --- p.83 / Chapter 5.1.4 --- Replacement Assertions --- p.85 / Chapter 5.1.5 --- Message Vector Assertions --- p.89 / Chapter 5.2 --- Data Dependency Interpretation --- p.91 / Chapter 5.2.1 --- Immediate Replacement --- p.92 / Chapter 5.2.2 --- Direct Dependency --- p.92 / Chapter 5.2.3 --- Indirect Dependency --- p.93 / Chapter 5.2.4 --- Shared Data Variable --- p.99 / Chapter CHAPTER 6 --- SCHEDULING FOR EXCEPTION HANDLING --- p.104 / Chapter 6.1 --- Backward Path Tracing --- p.106 / Chapter 6.1.1 --- Forward Versus Backward Tracing --- p.106 / Chapter 6.1.2 --- Assertion-Marking Strategy --- p.113 / Chapter 6.2 --- Grain Scheduling --- p.116 / Chapter 6.2.1 --- New Constraints --- p.120 / Chapter 6.3 --- Delayed Exception Raise Event --- p.125 / Chapter 6.4 --- Enhancement of Scheduling Algorithm --- p.126 / Chapter 6.5 --- Control Flow Issues --- p.128 / Chapter 6.5.1 --- Immediate Replacement --- p.130 / Chapter 6.5.2 --- Direct Dependency --- p.131 / Chapter 6.5.3 --- Indirect Dependency --- p.132 / Chapter 6.5.4 --- Lower Dimensionality --- p.133 / Chapter CHAPTER 7 --- MORE COMPLICATED SCHEDULING --- p.135 / Chapter 7.1 --- Multiple Exception Handling Assertions --- p.137 / Chapter 7.1.1 --- Overlapped Scopes of Exception Grain --- p.138 / Chapter 7.1.2 --- Priorities in Scheduling --- p.156 / Chapter 7.2 --- Single Replacement Assertion --- p.160 / Chapter 7.2.1 --- Multiple Exception Conditions --- p.160 / Chapter 7.2.2 --- Conditional Replacement --- p.163 / Chapter 7 .3 --- Loop Optimization --- p.164 / Chapter 7.4 --- Modifications to the Scheduling Algorithm --- p.177 / Chapter 7.5 --- Implementation --- p.180 / Chapter 7.5.1 --- Syntax Checking --- p.180 / Chapter 7.5.2 --- Array Graph Construction --- p.182 / Chapter 7.5.3 --- Array Graph Analysis --- p.185 / Chapter 7.5.4 --- Generation of Schedule with Exception Handling Subgraph --- p.186 / Chapter CHAPTER 8 --- CONCLUSIONS --- p.187 / Chapter 8 .1 --- Future Work --- p.188 / APPENDIX / Chapter 1. --- Backward Tracing/Assertion Marking Strategy / REFERENCE

Yeung Kam-chuen Anthony. / Title also in Chinese. / Thesis (M.A.Ed.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 137-144. / ACKNOWLEDGEMENTS --- p.ii / ABSTRACT --- p.iv / LIST OF TABLES --- p.viii / LIST OF FIGURES --- p.xiii / CHAPTER / Chapter 1. --- Introduction --- p.1 / Context of the study problem --- p.1 / Statement of the Problem --- p.3 / Significance of the Study --- p.4 / Chapter 2. --- Review of Literature --- p.8 / From Concept Formation to Problem Solving --- p.8 / About Problem Solving --- p.12 / Information-processing Theory of Human Problem Solving --- p.16 / The Nature of Social Science Problems --- p.28 / Domain-specific Knowledge in Social Science Problem Solving --- p.31 / Social Science Problem Solving Strategies --- p.38 / Chapter 3. --- The Social Science Problem-solving Model --- p.40 / Early Development of the Social Science Problem-solving Model --- p.40 / The Problem-solving- reasoning Model --- p.41 / Chapter 4. --- Research Design --- p.48 / Statement of Hypotheses --- p.48 / Operational Definitions of Variables --- p.52 / Subjects --- p.57 / Instruments --- p.62 / Procedures --- p.71 / Chapter 5. --- Results and Discussion --- p.78 / Statistical Analysis of Data --- p.79 / Qualitative Analysis of Data --- p.108 / Discussion --- p.119 / Chapter 6. --- Conclusions and Recommendations --- p.130 / Conclusions --- p.130 / Implications --- p.132 / Limitations --- p.135 / Recommendations --- p.136 / BIBLIOGRAPHY --- p.137 / APPENDIX / Chapter 1. --- The Knowledge Test --- p.145 / Chapter 2. --- "The ""Locating a Ball Pen Factory"" Problem" --- p.150 / Chapter 3. --- "The ""Locating an Oil Refinery"" Problem" --- p.153