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textbooks and software
Posted:
Mar 17, 1995 3:35 PM
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This is not an unbiased note as I am an author of UCSMP geometry published
by ScottForesman. (I do not, however, receive royalties on sales.)
Most geometry textbooks will do quite nicely in conjunction with Sketchpad,
Cabri II, or other geometry drawing programs. Art Mabbot gives the
strength of Serra's Discovering Geometry in that the approach is inductive
and lets the students create their own conjectures. Of course, with good
teaching, any class of students can be helped to create their own
conjectures regardless of the text using software.
The strength of UCSMP Geometry is first of all in the emphasis on
transformations. Transformations provide for average students a more
intuitive and meaningful approach to congruenced and similarity. They are
also powerful in that transformations apply to any shape whatsoever so that
different definitions are not needed for congruence of triangles vs.
congruence of quadrilaterals. The dynamic software makes the teaching of
transformations so rich as you see the dynamism of the software directly
put into the mathematical (and functional) language of transformations.
Seeing figures reflected over the composite of two intersecting lines to
get a rotation is just beautiful. The payoff of geometric transformations
in the analysis of functions and data will be made even more easily and
impressive with Sketchpad 3.0 and Cabri II.
Second of all, UCSMP Geometry does do proof and an axiomatic geometric
system while also have explicit lessons on conjecturing. Thus students see
the relationship of technology enabling conjectures and then going from
conjectures to proof. The role of induction, deduction, argument, proof,
and convincing of others need to be address in Geometry and technology and
a good text and, most importantly, good teaching helps students to begin to
feel their way among these distinctions.
As the nature of geometry becomes more dynamic, it is incumbent upon all of
us to realize the strengths and limitations of all texts. Texts serve as
resources for students and teachers (Clearly there are many geometric
results which will not be created by students or which are deemed
"important" by outside experts, society, testmakers....). Geometry
software is also a resource to allow for exploration, verification, and
visual modelling. It does not necessarily strengthen these resources by
having them completely in sync. (Nor does it strengthen them to completely
independent.)
Anyway, a lot of choosing a text depends on the type of students at the
school, the goals of the course and the program, the demeanor of the math
department members, and the view that individuals have of mathematics. All
students should be exposed to geometry software, but the balance of
technology, textbook, and other pedagogies is best decided at the local
level.
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