Why study three-dimensional geometry?
Motivation:
á The non-traditional activities that include
three-dimensional geometry topics can motivate students who see geometry as a
set of abstract rules and definitions.
á Three-dimensional geometry lends itself easily to
discovery learning which also stimulates and maintains motivation.
History:
á Three-dimensional geometry can also provide a
historical context for the history-oriented student. For example, presenting a
historical perspective on the Platonic and Archimedean solids can motivate
certain students.
Everyday Interactions:
á Three-dimensional geometry enhances studentsŐ
intuitive geometry usually generated from interactions with their environments.
Reinforcement:
á Three-dimensional geometry can expand, enhance, and
reinforce studentsŐ knowledge of Euclidean geometry that is traditionally
taught in high school.
Refinement:
á Three-dimensional geometry can aid in the development
or refinement of studentsŐ spatial sense, perception, and visualization.
á Three-dimensional geometry enhances spatial abilities.
Spatial ability can affect how much of a studentŐs focus is given to the entire
act of learning. If a student lacks a component crucial to spatial sense then
he/she may not be able to devote his/her entire attention to the learning of
other geometric ideas and concepts. Seven components of spatial sense
identified as having Ňgreatest relevance to academic developmentÓ (Del Grande,
p. 127) are: eye-motor coordination,
figure-ground perception, perceptual constancy, position-in-space perception,
perception of spatial relationships, visual discrimination, and visual memory.
Foundations:
á Early experience with three-dimensional geometry
provides a solid foundation for higher level mathematics, including calculus, group
theory, and topology. It can also lay a foundation for other disciplines such
as computer science and chemistry.
Confidence:
á Working with physical models in three-dimensional
geometry can increase student mathematical confidence with abstract concepts.
Another way to study
traditional ideas of mathematics:
á Three-dimensional geometry can be studied in a
non-abstract fashion that still maintains the rigor associated with traditional
geometry.