Search results for "Teaching and learning of linear and abstract algebra"
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Delineating Aspects of Understanding Eigentheory through Assessment Development
2018
International audience; In this report, we share insights we have gained from developing an assessment for documenting students' understanding of eigentheory. We explain the literature and theory that influenced the assessment's development and share question examples. We frame our results in terms of three eigentheory settings (Ax = λx, (A - λI)x = 0, and eigenspaces) and four interpretations (numeric, algebraic, geometric, and verbal). Results from our analysis include students' reasoning being influenced by setting, insights into students' struggle with understanding eigenspaces, and the importance of making connections between and across various interpretations.
Tasks for enriching the understanding of the concept of linear span
2018
International audience; The concept of linear span is one of the first abstract notions that students encounter in a course on Linear Algebra. Using the theoretical construct of concept image and concept definition (Tall & Vinner, 1981) along with observations about teaching and learning Linear Algebra, we present two tasks designed to enrich students' concept image regarding linear span. These tasks could be included in a problem workshop of an introductory university course on Linear Algebra. Each task is carefully created and/or selected so as to foster the ground for potential conflict factors to arise and be confronted. A preliminary evaluation shows that the tasks are well received by…