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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.
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.