From: T. Esh
To: Teacher2Teacher Public Discussion
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 wrong. 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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