Chapter 9: Group Theory
PART I A Guide to the Paradigmatical Cases (Episodes) Presented in this Chapter
PART II Data and Analysis
In the following I present the factual and interpretive accounts and conclusions for the 8 Episodes of the table in Part I. In Part III then I synthesise the findings of Part II related to Analysis and briefly discuss the wider cognitive issues that are presented in the overall synthesis of the data analysis in Chapter 10.
(i) A Gradually Revealing Example of the Linguistic and Conceptual Dimensions of Difficulty With Order of an Element, Generating <g> and the Group Operation
(ii) A Novice's Inquiry on the Concept of Equivalence Class and of Coset: Bestowing Meaning Through Ambivalent Uses of Geometrical Metaphors
(iii) A Contrast Between Expert and Novice Approaches to Proof: The Fine Details of a Lateralisation of Cases in GRF5.6
(iv) A Novice's Struggle for a Meaningful Interpretation of the Definitions of Centraliser and Conjugacy Class: Request For Examples and For a Teleological Rationale Behind the Definitions
(v) A Controversial Step Into Mathematical Maturity. A Novice Realises the Pitfalls of Pretentious Formalism Through a Conflict Between Ordinary and Formal Language
(vi) The First Isomorphism Theorem as a Container of Compressed Conceptual Group-Theoretical Obstacles
(vii) A Frustrating Vicious Circle of a Novice's Struggle to Construct a Meaning of a Coset
(viii) An Example of the Tension Between Novice and Expert Approaches to Mathematical Reasoning: The Need to Learn How to Achieve Mathematical Resonance by Creatively Co-ordinating and Manipulating Relevant Knowledge
PART III A Synthesis of the Findings in the Area of Group Theory. Indications for the Cross-Topical Synthesis in Chapter 10