**University of Washington Math Professor Letter**

**The following excerpts are from a letter written to the Seattle Public Schools by Dr. John Lee, a University of Washington mathematics professor**. Dr. Lee’s letter (dated March 4, 2009) represents his review of the textbooks being considered for adoption for Seattle Public High Schools. The 3 textbook finalists are: Discovering Series by Key Curriculum Press, Prentice-Hall, and CPM. Dr. Lee is also a parent in the Seattle Public School system. The letter in its entirety is included here for those interested however, his thoughts and impressions of the CPM texts specifically are included here for your review. Excerpts below:

**C***This book is, in a word, unsuitable. To be sure, it presents a wealth of nice inquiry activities that might help students to develop an intuitive understanding of geometric relationships. But the problems with the book so outweigh its positive aspects that adopting it would lead to disaster. Here are the main problems that I noticed with the book: • The organization of chapters is obscure. Many of the chapters have titles that suggest two or more completely different ideas thrown together (“Justification and Similarity,” “Proofs and Quadrilaterals”), and the chapters themselves did not give me any confidence that the authors had succeeded in integrating their disparate subjects into a coherent narrative. • There are virtually no mathematically coherent definitions. One absolute requirement for deductive reasoning is precise definitions: You cannot argue carefully about a concept if you don’t know exactly what it is. The descriptions that pass for “definitions” in this book are laughably vague, and many key concepts (such as angle) seem never to be defined at all. • Many (perhaps most?) important geometric facts are never stated precisely. Instead, it is left to the students to glean a generality from their inquiry activities and then state it themselves. I don’t dispute the usefulness of having students come up with their own versions of general statements based on guided experience; but it’s a rare student who is able to synthesize experience into a correct and precise statement of mathematical truth. • There are almost no proofs in this book. For a while, the book guides students through what it calls “justifications” (which I think are supposed to be reasonably convincing arguments without quite having the logical force of proof), but it never says exactly what a “justification” is or how students can distinguish a good one from a bad one. Then in Chapter 7, the book introduces the notion of “proof,” but never says exactly what a proof is or how it is supposed to be different from a “justification.” Most damningly, I could not find a single proof presented clearly and completely in the book; instead, students are supposed to construct their own. How can they possibly know how to construct a good proof if they’ve never seen one? • There are no postulates or axioms anywhere in the book, as far as I can tell. (There is no entry for either term in the index; and while there are glossary entries for both “axiom” and “proof,” they don’t have page references associated with them, unlike most of the other glossary terms.) This makes a mockery of the whole idea of proof, because a deductive proof has to be based on previously established results. If you try to prove anything without starting with some postulates, your argument will be either circular or too vague to be meaningful. If this book is adopted, I shudder for the intellectual fate of a generation of Seattle high-school students.*

**ollege Preparatory Mathematics: Geometry Connections**

*Like the geometry book from the same publisher, these books are completely unsuitable for a high-school algebra course. There are lots of nice hands-on activities here (algebra tiles, webs, generic rectangles, etc.), but very little in the way of clearly stated general principles. Many definitions of mathematical terms are utterly useless. For example, here are the definitions of relations and functions, two of the central concepts of algebra: “Each equation that relates inputs to outputs is called a relation; when a relation is functioning consistently and predictably, we call that relation a function.” Again, both definitions are circular, and the key terms used in them are not clearly explained (except by example). Exactly what does it mean for a relation to “function consistently and predictably”?*

**College Preparatory Mathematics: Algebra Connections and Algebra 2**
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