Q&A #918

Teachers' Lounge Discussion: Geometry Textbook "Discovering Geometry" by Michael Serra

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From: T. Esh

To: Teacher2Teacher Public Discussion
Date: 2006120501:40:24
Subject: Inductive Failure

My experience with the "Discovering Geometry" book has been to clean
up the mess that Serra makes with otherwise intelligent students.

The inductive approach to teaching only works when there is a standard
to gauge against.  Expecting students to generate answers without the
tools to do so is an exercise in futility and self-reinforcing
conjecture, which all too often is incorrect.  The book asks for the
student to supply the definitions they need.  This means the students
are forced to do thousands of years' worth of math reasoning in a very
short time, and gives little to no feedback as to whether or not that
reasoning is accurate.

That's the real problem.  Induction itself can be valuable, especially
with proofs.  That said, you cannot learn induction with a
lassaiz-faire approach, and expect it to come out correct.  You cannot
learn induction with no guidance, no milestones.

I've had to deal with two years' worth of students who have learned
almost no geometry from this book, but have instead learned to hate
math, inductive reasoning, and geometry.

Textbooks should provide information, and the application for that
information.  Teaching inductive reasoning is a course of study in and
of itself, and trying to shoehorn a full fledged Geometry class into
the Inducive Approach is a failure in this textbook's responsibility
to teach the subject at hand; Geometry.

Perhaps the counter to that premise might be that teachers should do
the teaching.  Fair enough.  Most teachers, however, do not.  Also,
the inductive approach is time intensive, and must be tailored to
individual students.  When the teacher spends all of the class time
telling the students why their approach was wrong from the previous
assignment, instead of actually teaching new material, something is

It is not teaching induction to set students up to fail, and then make
them relearn the material.  Students simply do not have time for this
nonsense.  There are too many demands on their time, and learning and
relearning the material is a huge waste of teachers' time, students'
time, and everyone else's time who has to clean up the mess left by
poor teaching practices.

Geometry needs to be taught, and this book and the teachers I've seen
use it are not teaching.  They are not promoting understanding, they
are promoting confusion and frustration.

Save induction for a course on its own, and please get back to
teaching Geometry.

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