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Geometry-A Guided Inquiry
is a very special textbook!
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Of
all the Geometry texts I have used over the past 30 years, this one
stands out as by far the richest, most intuitive, and most interesting.
This text is unique.
- Most geometry
textbooks present a long list of facts about geometric figures
organized in a rigid logical order, working generally from simple
to more complex. Applications of these facts may or may not be
made clear to the student.Geometry: A Guided
Inquiry starts by posing interesting geometric problems (puzzles).
Clusters of geometric facts are presented, as needed, in the process
of solving these problems. The usefulness and relevance of the
new facts are therefore apparent from the moment they are introduced.Most geometry textbooks, especially those written under
the influence of the "New Math" era of the 1960s, put
heavy emphasis on precise use of technical vocabulary and mathematical
notation.
- Geometry: A Guided Inquiry emphasizes the underlying
geometric and mathematical ideas and works to help the student
understand them intuitively as well as logically. Overemphasis
on technical vocabulary and complex notation can actually stand
in the way of understanding, so the authors use simplified vocabulary
and notation wherever possible.
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- Most geometry textbooks start each problem set with lots of
routine, repetitive problems, gradually working up to an interesting
problem or two at the end of the assignment.
- Geometry: A Guided Inquiry puts the best problems right up
front! From the very beginning the student is given problems worth solving.Most geometry textbooks read like they were written by a committee
following a prescribed agenda. Most in fact are! The life is squeezed
out of the narrative in the process.
- Geometry: A Guided Inquiry has a distinct sense of authorship.
The authors are good mathematicians, good teachers, and good writers.
Their joy in the pursuit of mathematics shows through their writing.
Geometry: A Guided Inquiry makes
frequent use of compass, protractor and ruler activities, data tables,
guess and check methods, model-building, and other techniques of intuitive
exploration in preparation for general solutions. (The Geometer's Sketchpad
adds a new dimension to the opportunities for exploration with dynamic
illustrations.)Each chapter begins with a "Central Problem" that provides the focus and motivates the
discussion in that chapter. The Central section presents
all the essential new material. Along the way you will be led to a solution
of the Central Problem and explore its connections with other topics.
After the Central section is a Review section, and each
of the first seven chapters are followed with a short Algebra Review
that stresses algebra topics related to the current work.
Next comes the best part.
Each chapter has an open ended Projects section with problems that
are extensions to the material in the Central section, sometimes
carrying the discussion in new directions. (The Project sections include
some of the most interesting material in the text!) In a classroom
setting, where students work at their own pace, the faster students would
work on the Project section while the slower students are finishing
the Central and Review sections. In a home study environment
you should read through the whole Project section and work on as
many of the project problems as possible. If you find the work easy, rather
than going faster, you should instead take more time and go deeper!
Home Study Companion
The Home Study Companion supplements the textbook in several
important ways:
- It provides complete, worked out solutions (not just answers)
to all problems in the Central and Project sections
of the text.
- It provides additional commentary to supplement the presentation
of the text, much as the lecture portion of a traditional course
supplements the text.
- It provides a collection of nearly 300 demonstrations using The
Geometer's Sketchpad covering most of the main concepts, and
many additional explorations, in the Central and Projects
sections of each chapter.
- Geometry: A Guided
Inquiry was written long before the current obsession with
standardized testing, and it marches to a different drummer.
It covers many fascinating
topics you will see in no other high school Geometry textbook.
The selection of topics in the text is excellent, but the authors'
choice of topics (in 1970) did not anticipate every choice of
the Academic Standards Commission at the end of the century. Therefore the Home Study Companion adds Extensions to
the chapters, as needed, to cover these additional topics. The
text plus extensions cover the standards for California and nearly
all other states. (Students not affected by mandatory statewide
testing can treat the extensions as optional topics.)
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The Geometer's Sketchpad
The Geometer's
Sketchpad was not available when Geometry: A Guided Inquiry
was written, but it is the kind of tool that fits perfectly with
the educational philosophy of the text. Students can use The
Geometer's Sketchpad to experiment with geometric constructions,
but unlike pencil-and-paper constructions they can alter or animate
their constructions to see how they behave dynamically. Collections
of demonstrations accompany the Central and Project
sections of each chapter.
In addition, a lab
section has been added to the Home Study Companion with
tutorials for using The Geometer's Sketchpad. Students are encouraged
to learn to use The Geometer's Sketchpad as a tool in its
own right. It is a wonderful tool for both exploration and creativity.
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