Chapter 8: Linear Algebra
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 the Part I. In Part III then I synthesise the findings of Part II related to Linear Algebra and briefly discuss the wider cognitive issues that are presented in the overall synthesis of the data analysis in Chapter 10.
(i) Constructing the Span of Various Sets as an Example of the Generating Procedure of Spanning and the Debatable Value of the Metaphor of the Plane
(ii) The Contrast Between Algorithmic Ability and Conceptual and Contextual Understanding: Applying the Subspace Test and Looking for the Zero Element of ÂÂ
(iii) Spanning Sets and the Struggle for a Meaningful Metaphor
(iv) Constructing Bases For Various Vector Spaces: the Inadequate Targeting of Essential Intuitive Ideas and Induction Into the Notational Language of Advanced Mathematical Thinking
(v) dim(X+Y)=dimX+dimY-dim(XÇ Y) and the Varying Persuasion of Mathematical Arguments
(vi) Looking for the 'Usual' Basis of P3(Â): Decontextualised Knowledge and the Ambiguous Nature of 1
(vii) Transforming 'beautifully literary' Intuitions Into Mathematical Formalism
(viii) Leading Didactical Style as a Potential Propagator of Passive Learning. Resisting the Contingency of Multiple Answers to a Mathematical Question
PART III A Synthesis of the Findings in the Area of Linear Algebra. Indications for the Cross-Topical Synthesis in Chapter 10