Calculus With Trigonometry and Analytic Geometry (Saxon Calculus)

Our children used Saxon from 54 to 87, then moved on to advanced math, calculus and physics and they have excelled with this method. Although my background doesn't include an emphasis in math, my husband's education and professional life is steeped in mathematics. He's enthusiastic about Saxon because it creates a strong foundation in the subject.

Admittedly, solving 30+ problems a lesson can be a challenge, however, this process increases one's speed and accuracy over time and as my daughter said, it helped her "to make peace with math." Math is like learning how to play a musical instrument; it takes practice and self-discipline, but it's well worth the effort. Understanding math, like being proficient at reading and writing, is one of those practical skills that make life so much easier.

Using this incremental method of learning made homeschooling through high school a breeze and our college-age children sailed through their college math courses as well. In hindsight, it would be easy to choose it again.

This book teaches the advanced topics of calculus in a manner that one does no learn one day and forget in a month. The Saxon series learning premise is that of an 'incremental development', which means once a skill is acquired and it is practiced, another fascet is added, and then another until you have a full understanding of the material. This book is great for anyone at all who wants to learn Calculus; not just students. It is recommended that the book "Advanced Mathematics" should preceed this because the first part "Calculus" quickly reviews all the topics in that book. So, I say get the book and try it; it is the best way to learn Calculus!

The bottom line: if you want an "unfair" advantage over other math students, or if you are a teacher who wants your math students to have an "unfair" advantage, use the Saxon advanced math texts.

In essence, Saxon texts teach advanced math as a language. At present, all other serious texts teach advanced math as a formalism, a grammar. Analogously, other advanced math books present examples of the present tense the first week, then examples of nouns the second, etc. By contrast, Saxon texts make you speak sentences using the present tense every day, throughout the year.

The newer Saxon-style "language" instructional paradigm is far more consistent with consensus empirical cognitive research than is the traditional math formalism/grammar model, as well as probably being more consistent with your own intuition and past experience: grammar books may be very good at describing a language, but they are inherently not very good at training you to speak it.

The Saxon calculus text is tough, accurate, and makes profuse use of "classic" problems to teach. It just doesn't look like a grammar book, or even aspire to be one. That is apparently sufficient to bewilder, even repulse, some math educators.

Saxon detractors suspicious of its basic pedagogy are welcome to perform the mountains of painstaking basic research that would be necessary to overturn fundamental tenets in cognitive science, such as the general superiority of "distributed" (Saxon-style) practice over "massed" (traditional-style) practice. The Nobel prizes critics would garner would of course be mere icing on the cake.

But it's actually easy to demolish the fundamental argument of Saxon critics. Once people understand that other serious advanced math texts are really grammar books, Saxon critics have lost, since the average person already knows that grammar books inherently suck.

In a perfect world, all advanced math texts would simply accept the Saxon-style "language" model as obviously the superior pedagogy, and we consumers would benefit as publishers competed to produce the best possible realizations of that inherently superior model. At present, however, especially at the advanced level, the Saxon texts are the only game in town, and fine ones, at that. This gives students and teachers willing to use the Saxon texts an "unfair" advantage over their peers.

Excellent printed introductions on how to teach and learn advanced math in Saxon are available for download from the Saxon website. The most important point can be noted here: in Saxon, you are learning to "speak" math. Every single Saxon problem, in every problem set, exists solely to force you to be as fluent in as many aspects of math as possible at that time. Therefore, you can't skip any problems, or skip around in the book. If you did, you'd either be cheating yourself of opportunities to "speak" at your current highest level, or stretching yourself too thin.

A Saxon year is devoted exclusively to grammar-in-use, to "speaking" math. A point or two of math "grammar" is introduced briefly and quickly each lesson, and understanding is built up not through more explanation but through repeated and gradually more sophisticated use of the concept in problems over the following days, weeks, or even months. Introductory calculus teachers are definitely not accustomed to that way of teaching, and college-level teachers who dared to use a "language"-paradigm introductory calculus text like Saxon might be at special risk for merciless ridicule from colleagues, but something much less philosophical could also be a factor in teacher resistance to the Saxon-style approach.

Grammar books are not pedagogies, so a teacher who uses a grammar book still has to decide how to teach the grammar. Accordingly, many American math teachers are accustomed to a lot of pedagogical control. On a given day, they will pick and choose the specific problems students will do, or skip around in the text, omit or expand the development of topics, drop the textbook completely or use it merely as a "resource," and/or give elaborate lectures and demonstrations. Saxon texts, being an actual pedagogy and not a grammar of "topics," don't allow any of that.

A Saxon teacher's goal is to help every single student "speak" math each day by doing every single problem in the problem set for that day. Period. Since a Saxon text asks teachers, even more than students, to behave very differently in the classroom, a Saxon text should always be adopted voluntarily, never imposed. The unknowing, and especially, the unwilling, would wreak havoc. Learning a "language"-paradigm math text using traditional methods would be like having the football coach teach you violin. You would not enjoy the results.

Of course, there will always be a place for grammar-style math texts -- as reference manuals, once students have solidly learned the grammar-in-use.

I have no connection to the Saxon people, but I have used the Saxon texts with my own children and therefore know them intimately. As I've implied, while the Saxon books are very good, it's improbable that they represent the ultimate realization of the inherently superior "language" model, and I wish there were lots of worthy competitors. However, especially at the advanced level, the Saxon texts currently have no competition. At present, they're the only "language"-paradigm texts available.

It's a free country. If, despite considerable basic science to the contrary, you think that grammar books are swell at teaching languages; or if you believe that a language paradigm is irrelevant to mathematics instruction, since math is a beautiful formalism that only second-rate engineering students would ever deploy as a grammar-in-use; or if you simply enjoy the pedagogical autonomy that traditional introductory calculus texts allow you to exercise, then there are a plethora of math grammars to choose from. For the rest of us, there's Saxon.