This book considers the views of participants in the process of becoming a mathematician, that is, the students and the graduates. This book investigates the people who carry out mathematics rather than the topics of mathematics. Learning is about change in a person, the development of an identity and ways of interacting with the world. It investigates more generally the development of mathematical scientists for a variety of workplaces, and includes the experiences of those who were not successful in the transition to the workplace as mathematicians. The research presented is based on interviews, observations and surveys of students and graduates as they are finding their identity as a mathematician. The book contains material from the research carried out in South Africa, Northern Ireland, Canada and Brunei as well as Australia.
1.Introduction: How Does a Person Become a Mathematician? -- What This Book Is About -- Why Is Mathematics Important? -- How People Come to Work with Mathematics -- Learning Mathematics -- Researching the Experience of Learning and Working with Mathematics -- Dramatis Personae -- References -- 2.How Do Mathematics Students Think of Mathematics? - A First Look -- Introduction -- Previous Investigation of Views of Mathematics -- Our Study of Students' Conceptions of Mathematics -- Conceptions of Mathematics -- (1).Mathematics Is About Components -- (2).Mathematics Is About Models -- (3).Mathematics Is About Life -- Discussion -- Implications for Teaching and Learning -- And What About Students Who Are Not Mathematics Majors? -- Summary and Looking Forward -- References -- 3.How Do Mathematics Students Go About Learning Mathematics? - A First Look -- Introduction -- Previous Investigation of Views of Learning Mathematics -- Our Study of Students' Conceptions of Learning Mathematics -- Conceptions of Learning Mathematics -- (1).Techniques Orientation -- (2).Subject Orientation -- (3).Life Orientation -- Discussion -- Implications for Teaching and Learning -- Summary and Looking Forward -- References -- 4.What Do Mathematics Students Say About Mathematics Internationally? -- Introduction -- The Methodology of Our Study -- Results from the Survey - Conceptions of Mathematics -- (0).Mathematics Is About Numbers -- (1).Mathematics Is About Components -- (2a).Mathematics Is About Modelling -- (2b).Mathematics Is About the Abstract -- (3).Mathematics Is About Life -- Results from the Survey - Future Use of Mathematics -- Factors Associated with Broader Conceptions of Mathematics -- Discussion -- Implications for Teaching and Learning -- Summary and Looking Forward -- References -- 5.How Can We Track Our Students' Progress Towards Becoming Mathematicians? -- Introduction -- Questionnaire-Based Studies of Students' Conceptions of Mathematics -- Our Questionnaire Study -- Results - Conceptions of Mathematics -- Results - Future Use of Mathematics -- Discussion and Implications for Teaching and Learning -- Summary and Looking Forward -- References -- 6.What Is the Contribution of Mathematics to Graduates' Professional Working Life? -- Introduction -- Studies of Transition from Study to Professional Work from the Viewpoint of Graduates -- Our Studies with Graduates -- Contributions - Technical and Generic Skills, Personal Characteristics and Identity -- Contributions - Problem Solving and Logical Thinking -- (1).Specific Mathematical Problems -- (2).Problems in a Work Context -- (3).Problems in Life Generally -- Discussion -- Implications for Teaching and Learning -- Summary and Looking Forward -- References -- 7.What Is the Role of Communication in Mathematics Graduates' Transition to Professional Work? -- Introduction -- Mathematical Discourse -- Becoming a Communicator of Mathematics -- The Methodology of Our Study -- The Importance of Communication for Recent Graduates -- Conceptions of Mathematical Communication -- (1).Jargon and Notation -- (2).Concepts and Thinking -- (3).Strength -- Learning Mathematical Communication Skills -- (1).Trial and Error -- (2).Mediated by Others and Outside Situations -- (3).Active, Detached Observation -- Discussion -- Summary and Looking Forward -- References -- 8.What University Curriculum Best Helps Students to Become Mathematicians? -- Introduction -- The Philosophy of Tertiary Mathematics Curriculum -- The Practice of Curriculum in Tertiary Mathematics -- The Message from Undergraduate Learners of Mathematics -- Broadening the View of Professional Skills and Dispositions -- The Message from Mathematics Graduates -- Discussion -- Summary and Looking Forward -- References -- 9.How Can Professional Development Contribute to University Mathematics Teaching? -- Introduction -- What Is Professional Development? -- Professional Development in University Mathematics -- An Action Research Model of Professional Development -- Peer Tutoring as a Model of Professional Development -- Professional Development Based on Professional Standards -- Sociological Models of Professional Development -- Discussion -- Summary and Looking Forward -- References -- 10.Conclusion: Becoming a Mathematician - Revisited -- Introduction -- A Summary of the Main Ideas -- Learning from Our Students -- Paul's Interview -- Heather's Interview -- Being and Becoming -- What We Can Do -- References -- Appendices -- Appendix 1 Short Form of Conceptions of Mathematics Survey -- Appendix 2 Mathematical Communication Outcomes -- Appendix 3 Australian Professional Development Framework.