Linear Algebra Teaching and Learning

The book presents the findings of our work that §investigated the effects §of visual representations on learning and teaching §of abstract concepts. Our work compared two first §year linear algebra classes; one is §traditional group and the other is experimental §group who used the geometric §representations of basic abstract linear algebra §concepts. §We documented differences in student §understanding of vector space concepts, and §consequently, §evaluated the strength and weakness of both §approaches. §§The experimental group performed significantly §better than the traditional group in tasks involving §only conceptual knowledge. The most noticeable §differences in understanding were found in applying §basic vector space concepts to linear §transformations, and in finding bases for §subspaces by recognizing vectors as the objects of §subspaces. No significant evidence was found to §support the belief that the experimental group §performed less well than the traditional group in §questions that required procedural knowledge. The book presents the findings of our work that §investigated the effects §of visual representations on learning and teaching §of abstract concepts. Our work compared two first §year linear algebra classes; one is §traditional group and the other is experimental §group who used the geometric §representations of basic abstract linear algebra §concepts. §We documented differences in student §understanding of vector space concepts, and §consequently, §evaluated the strength and weakness of both §approaches. §The experimental group performed significantly §better than the traditional group in tasks involving §only conceptual knowledge. The most noticeable §differences in understanding were found in applying §basic vector space concepts to linear §transformations, and in finding bases for §subspaces by recognizing vectors as the objects of §subspaces. No significant evidence was found to §support the belief that the experimental group §performed less well than the traditional group in §questions that required procedural knowledge.