- Jim Nance

Saxon is good at getting across to students of all ages and abilities the skills required for solving most types of math problems. If you desire to train students to work math problems and do well on math tests, as well as to give them a basic foundation in fundamental math, then Saxon will suit your purposes well. The constant repetition helps to engrave the methods into the students’ minds, the large number of problems in each daily assignment teaches them diligence and makes them comfortable and confident in attacking their math assignments. The problems being all of the same general type helps prevent some confusion and bewilderment. Many students feel that Saxon makes math fun, or at least easy.

However, if you desire to teach children how to approach math problems they have never seen before, and to apply math to the real world (including the sciences), and fundamentally to think about mathematics the way we believe that truly educated students should, then Saxon is often more of a hindrance than a help. We need to ask whether high school students should find math easy. Should they not rather struggle through much of it? Should they not be bewildered with problems of types they have never seen before (rather than problems they saw worked out on the previous page), pondering them and searching them out, only then to discover (with joy!) that they can indeed take the fundamental concepts and solve the problem on their own? Saxon too often removes that thrill of discovery and replaces it with the mere satisfaction of getting the homework done and getting most of the answers correct.

This may explain why I think Saxon is fine for elementary students. Saxon’s aim of making math skills automatic is very appropriate for Grammar-stage math (i.e. arithmetic). At this age they need to get the basics down: multiplication tables, methods of long division, telling time, adding money, graphing ordered pairs, and so on. The fact that they are doing math and finding answers is thrill enough. The methods of Saxon seem to fit well with this stage of the Trivium. But as young people move into the Dialectic stage, they begin to feel that simply knowing the answers is not enough. They begin to ask why the answers are the way they are, why the methods work the way they do, and how they can know that the methods are true. At this age they begin to delight more in the wonder, beauty and power of abstraction rather than the comfort and confidence of the concrete. Many of them, for example, find a special joy in writing proofs of geometry (at which Saxon is appallingly weak). I believe that Saxon artificially extends the methods of the Grammar stage into the Dialectic and Rhetoric years. And though the students get used to it and can work within it, they usually do not delight in it as they should.

Saxon math, with its constant repetition and multiple problems every day, teaches students to look for “the trick” to solve this or that particular problem, rather than giving them the tools of learning so that they can tackle any kind of problem. It trains students so that they can do well on tests, but it does not teach them how to learn math on their own.

Saxon is also weak on application, believing that the students should learn all the math skills before they begin applying any of them. This again is appropriate for younger students, but not high schoolers.

At Logos, we first began to discover this from three different directions. First, we felt that the Saxon texts did not teach the skills of geometry. Saxon included too few geometry problems, and failed miserably to show that any geometric proof can be solved using the axioms, theorems and definitions. Saxon’s approach rather was to introduce, for example, the proof that the interior angles in a triangle add up to 180 degrees, and then to require the students to write that proof, over and over again. This does not teach students that geometry by its nature is a creative art. They do not learn that the only thing that stands in the way of solving any proof is their own inexperience and maturing creative skills. Instead, they are merely trained how to solve that one proof, and the next, and the next, ad nauseam.

Second, we found that our students were inexplicably unable to take what they had apparently learned in math class and apply it to science class. They should have been able to take the lessons on vectors from Trig and apply it to adding forces in Physics. But they couldn’t; it was as if they had never seen vectors before. When questioned, their response was, “But these don’t look like the problems in the Saxon book.”

Third, when our graduates began to take math classes in college, our high hopes of hearing of the successes of our former “math wizards” were regularly disappointed. Instead, we often heard this comment, among others: “The teacher wants us to solve problems that he hasn’t shown us how to do.” When I responded that they should be able to approach unfamiliar problems using the concepts that they had learned, they finally made it clear to me that I had not taught them concepts; I had merely taught them techniques. Sure, they knew how to solve problems. But they had not learned how to learn.

Recognizing this, at Logos we now use the Scott-Foresman (UCSMP) math curriculum in our Freshman and Sophomore math classes (Geometry and Advanced Algebra), and the Houghton Mifflin math curriculum (Pre-Calculus and Calculus) in our Junior and Senior math classes. These texts approach higher-level math in a more appropriate way than Saxon: the lessons teach the fundamental concepts, give good examples, then require the students to apply the concepts to problems different from the examples. Many of the problems are directly applicable to the real world, as opposed to Saxon’s word problems which are more artificially contrived. And they approach the concepts in a logical, linear manner, each lesson usually being built directly on the foundation of the previous one.

Our primary goal is different from Saxon’s. His stated goal is high scores on the math portion of standardized tests. Our goal is to teach students how to think about math. To be honest, as a result of these changes math has sometimes been more difficult for our students. They are forced to think, and to struggle through unfamiliar territory. But this gives us the opportunity to help them learn how to overcome the struggle on their own. We have seen good success in our math program over the years since we have made the switch away from Saxon in the Secondary. We are glad we did.

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Jim B. Nance recieved his B.S. in Mechanical Engineering from Washington State University in 1984. After working for the Boeing Aircraft Company, Jim started teaching at Logos School in Moscow, Idaho in 1990. Jim teaches Logic, Rhetoric, Calculus, Physics, and Christian Doctrine. He is an elder at Christ Church. Jim and his wife Giselle have four children, all of whom attend Logos School.

Jim is author of Logos School’s expanded, corrected, completely Redesigned logic curriculum, and Classical Rhetoric curriculum.