Sinclair, Nathalie (2008). The History of the Geometry Curriculum in the United States. Reviewed by David W. Henderson, Cornell University

Sinclair, Nathalie (2008). The History of the Geometry Curriculum in the United States. Charlotte, NC: Information Age Publishing, Inc. Pp. vii + 105         ISBN 98-1-59311-696-5 Reviewed by David W. Henderson Cornell University August 19, 2008 This book is useful for anyone involved with the school geometry curriculum: Teachers, administrators, curriculum writers, and teacher educators. I fit into the last two categories and I learned a lot from reading the book. There are many facts presented in the book which surprised me; I suspect that they will also surprise you. I suggest that you take the following “quiz” and then check your answers at the end. Count your answer correct if it is within 15 years (either side) of the correct answer. Before reading this book I would have only gotten one correct! Quiz: When did a prominent educator who influenced school teaching insist “that students learn through activities and concrete objects […] and that they should be free to pursue their own interests and draw their own conclusions”. When was a geometry text published that “took very seriously the idea that students should construct their own mathematics”. When were the first national commissions to attempt to “standardize the school geometry curriculum”? In what year did “teachers frequently cited the expense of equipment as well as the increased time required to prepare laboratory-based classes.” When was the publication of a geometry textbook that integrated high algebra and geometry. In what year did an Mathematical Association of America sponsored a national committee to give “national expression to the movement for reform in the teaching of mathematics.” When did the first national committee recommend transformational geometry? When did transformational geometry first get implemented in a high school text book? By what year, “the new emphasis on meaning and understanding had become so strong that some schools were neglecting the development of basic skills.” The author details the historical development of many issues in the teaching of geometry, including: The use of technology Straightedge/compass constructions Two column proofs “Flaws” in Euclid The (sometimes) conflicting goals of deductive reasoning, informal reasoning, applications, vocabulary. Connections between algebra and geometry The use of pictures and diagrams (some texts have none) Calls for the fusion of plane and solid geometry which resulted in the demise of most solid geometry. Standards in school geometry Uses of motion and transformations in geometry In addition, there are numerous useful bibliographic references (10 pages of them). My main complaint about the book is the figure and pictures. Most of them are of poor visual quality primarily because of low resolution. In some, it is not clear what is being illustrated. For example, Figure 3.8 (page 62) is labeled “Bhaskara’s ‘Behold!’ proof of the Pythagorean theorem” but there is not enough included to see the proof. Answers: 1 (1850s), 2 (1876), 3 (1892), 4 (about 1907), 5 (1910), 6 (1923), 7 (1923), 8 (1971), 9 (1956). About the Reviewer David W. Henderson, is a Professor of Mathematics at Cornell University and a faculty member of the Graduate Field of Education. He directs theses in both mathematics and mathematics education. His work is the field he labels “educational mathematics” which is the study of those aspects of mathematics that impinge on the teaching and learning of mathematics. He has written five undergraduate geometry texts and is currently involved in high school curriculum development with the Algebra Project (www.algebra.org).