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Geometry and Saxon

Geometry in the Saxon Series

Geometry is integrated in the Saxon textbooks. The Algebra One-Half and Algebra I have extensive work in shape classification, and in perimeter, area, and volume, some of it influential. Angle and line classifications and relationships, and proof, begin in the Algebra II book and are carried on in the Geometry/ Trigonometry/ Algebra III book (aka GTA-III, aka Advanced Mathematics). In this respect, students study geometry in the same way that higher-achieving countries do, as a natural part of the mathematics curriculum. Few countries require a dedicated course.

As a teacher, I enjoy the dedicated course. That’s not necessarily what students need, of course. The dedicated course is required in many places. When I represented Saxon at conferences, teachers often asked for a recommendation for such a book. I recommended Geometry for Enjoyment and Challenge, revised edition, ISBN 0-88343-916-6, by Richard Rhoad et al., McDougal Littell, publisher, copyright 1984. Two of the three authors were top coaches of interscholastic mathematics contests in suburban Chicago. The book features much ongoing review a la Saxon, with some arithmetic, some probability, and some algebra in each assignment. Copies are hard to find.

I also recommend a very tough geometry book by Weeks and Adkins, A Course in Geometry, published in 1960 or so, since republished by Bates Publishing. This was the work of two teachers at Phillips Exeter Academy, and reflected 65 years of teaching experience. The book is a great mix of numerical and proof exercises. I recall using this book when I was in high school, in part because I would read a problem, draw what I thought was intended, re-read the problem, and realize that I needed to redraw. But by the time I had the drawing under control, I had figured out what was needed to solve or prove. Most books these days have things already drawn, and I question this. Books with drawings sell better, but that’s not the point any more than my teacher preferences.

If a student or a class of students are willing to work, they can cover the three Saxon books (Algebra I, Algebra II, and GTA-III) in three years and be ready for a good calculus course. One might ask how this is possible when the standard curriculum takes four years. Any savy teacher knows, and my dissertation research demonstrated, that the bulk of the standard algebra two course is algebra one repeated, since the standard approach is one idea today, another tomorrow, in one ear and out the other. (Also: one tree today, another tree tomorrow, and never the forest -- until the final exam, too late.) Saxon students remember and synthesize on their own. Every day is a new tree and then a review of the forest. Just common sense.

Our youngest son grew up with this, and, before starting calculus, asked to have a dedicated trig course. I gave him Paul Forester’s book. He did a chapter a day until the last chapter, which involved complex variables. That took a week. He went on to ace an advanced calculus course at a good community college and then tutor in the math and science lab, starting when he was 16. He graduated from UT-Austin in Petroleum Engineering with highest honors, having slept (literally) through a differential equations midterm and scored the top grade on the final, the only other course grade. He is now a third-year med student at a good school, earning top grades, happily married, enjoying music and sports and church, and doing community volunteer work. Saxon and MATHCOUNTS have served him well.

I’m at 940-574-2190 in the evenings and weekends. I am looking for people who might want to help with the War on Learning book, if only to help proofread. My wife already knows what I’m going to say, etc.