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.