1/28/2022

Today I write to share my experience for people thinking about homeschooling using Saxon Calculus. I homeschooled my first daughter using Saxon Calculus, Second Edition. I have decided to try using the first edition for subsequent teaching rather than the second edition. I was dissatisfied with the second edition for reasons mentioned below.

My calculus background: I took Saxon Calculus (First Edition) in high school, and I had no problems. Enjoyed it. In college, I have no idea what book I used for Calculus I, but I had no issues whatsoever earning my A.

Calculus Curriculum Terminology (AB? BC? Calculus I? Calculus II?)

When you choose a calculus curriculum for homeschool or high school, it gets a little confusing and you need to know some terminology. This is what I know, which may be corrected if you know more.

The terms “AB” and “BC” are terms made up by the makers of the Advanced Placement (AP) tests. (The makers and sellers of the AP tests are called the College Board.)

The terms Calculus I and Calculus II (and Calculus III) are traditional terms used by colleges. Calculus I usually covers differentials and limits, some basic integration. Calculus II covers more integration techniques, series/sequence. (Calculus III is multi-variate and not single variable.)

If students do AP’s AB calculus, then they get the equivalent of about what is covered in college Calculus I. And if students do AP BC calculus, then they roughly get the equivalent of college Calculus I plus Calculus II.

I wonder why the AP producers did not use the traditional terminology. Does anyone know? (The initial idea of AP may have been sound, but where it has gone today seems wrong for sincere seekers of learning.)

I Picked the Second Edition Saxon

For our first go-round with calculus in our homeschool, I selected Saxon’s Calculus with Trigonometry and Analytic Geometry, Second Edition. My public high school when I was a student used Saxon Calculus, First Edition, which is about equivalent, from what I understand, to college level Calculus I. I chose the Second Edition for my daughter based on all the reviews saying that it was better, more comprehensive, and prepared a student better for the AP exam.

I was taught calculus in high school using Saxon Calculus, First Edition. And I don’t remember that book being as hard as my daughter’s Saxon Calculus, Second Edition book. The second edition has made significant edits to make it correlate with the AP exam, which covers approximately college level Calculus I and Calculus II.

My daughter does not anticipate taking the AP calculus test, nor does she plan to study mathematics (beyond potentially needed prerequisites) in college. I wish sorely I had tracked down the first edition Saxon edition I was trained on for my first daughter. But all the reviews said that the second edition was the way to go. And I was worried that my daughter would be taking classes with kids who had AP classes, so the college calculus class might be geared to the knowledge those kids came to college classes with. So I selected the second edition, which is also much easier to come by than the first edition of the book.

In hindsight, I am now aware that basic college calculus is basic college calculus, and the first edition would have been just fine for our purposes. Although the scope of many college subjects has progressed by 2022, say computer technology or molecular biology, basic Calculus I has not.

Why Choose Saxon Calculus at all?

1. Information comes in small bite-sized bits rather than tackling complex material all at once.
2. The explanations are thorough and written with good, understandable prose.
3. The practice problems are cumulative, really promoting retention.
4. With mastery of the lessons, you have a good, solid understanding and improved long-term retention.
5. The page layout is simple and flows. Many new texts have “busy” graphic layouts, not Saxon.

Cons of the Second Edition:

1. There is too much material in the second edition. There are 148 problem sets. (In the first edition, there are just 117 problem sets.) Also, there are more problems in each problem set in the new edition than the old edition. It actually states that the second edition is to be a three semester class. I guess that’s fine. But since my student isn’t interested in mathematics or other hard-core math related fields and she’s not taking the AP test, she could have done just fine with the first edition’s lesser quantity material, which states is to be covered in two semesters. And then, if by chance after that, she loved calculus, we could have found another text to use for advanced study.
2. It expects students to have a complex understanding of “arithmetic series,” much deeper than was presented by the Saxon algebra and advanced mathematics texts we used prior to Calculus. (I do not know if perhaps we lack understanding of the needed advanced arithmetic series information because we used older algebra/advanced mathematics editions. Maybe the new Saxon algebra texts cover arithmetic series really well? The old ones teach it at a very basic, introductory level. NOT the level this second edition calculus book demands!) So we had to spend a lot of time learning this to be able to proceed.
3. Some of the trigonometry equations required were also not presented as thoroughly in prior texts as this book “assumes” its student will have. So you had to go back and learn these.
4. Not enough supplemental practice problems to do if a student struggles with a particular concept.
5. When something is not understood, then cross-referencing with other resources is difficult. Why? Because Saxon presents learning in little pieces sporadically as you travel through the lessons. Other resources present it all-out in a discrete unit. Saxon doesn’t always call the new little pieces that are learned along the way by names that will help you cross reference to another text when you get stuck. Make sense?
6. I guess maybe I just feel like they tried to introduce calculus “theory” and understanding too early in the lesson sequence of the book. I actually kind of enjoyed it because I had some (limited) calculus background, and I was getting to learn exactly what this calculus stuff was “doing!” But my daughter did not like that. She just needed to get comfortable with DOING the work, and then the theory might have sunk in better later in the text. But I feel like the new edition wanted to teach the kids the why early on. If you read about John Saxon’s teaching theory, he didn’t believe in teaching the why and the theory too early in his math books. It can bog down learning. I feel like the book was trying to set the user up for the more complex Calculus II topics (BC), but my user just needed to get comfortable with this new style of math! So again, I suspect I would have been happier with the first edition which doesn’t cover as much Calculus II and setting up of theory for it–then supplementing at the end of we wanted to do more advanced calculus.

Supplemental Resources We Used:

Calculus textbook by Larson and Edwards

On-line tutoring

Khan Academy videos

Calculus for Everyone by Mitch Stokes

Essential Calculus Skills Practice Workbook, Chris McMullen, PhD

CLEP Calculus

Miscellaneous Thoughts

1. I will use the first edition for my next student, which from experience I feel does a great job with limits, derivatives, and basic integrals without bogging the learner down like the second edition does. My daughters are leaning towards health-related sciences, and they will only need one basic college calculus class. (I went to medical school. My kids are considering that. Some medical schools don’t even require math. Some don’t require calculus. Check the schools you want for prerequisites!) I really do prefer Saxon’s teaching methods, so I want to stick with Saxon. But my students do not need the more advanced topics that the second edition has made revisions to accommodate. The first edition covers basic college calculus preparation quite well without the extra fluff for AP exams. If my daughters wish to proceed to Calculus II one day, the first edition is adequate to help them do well in their Calculus I college class and give them a very strong foundation to move on.
2. We found an on-line tutor to help us periodically. He was displeased with the sequence of the Saxon second edition book and made no bones about expressing his irritation about it with us. (Kind of stated, “Too much, too early. Why so early? It’ll just depress students.”) I know that there are on-line classes which use the second edition for homeschoolers, and if I used the second edition again, I would use one of those actual classes rather than try to teach it on my own. Those math-minded people would do a better job knowing how to teach any gaps and how to skip unnecessary lessons and problems without interrupting the flow of the cumulative Saxon program. We had to use many extra resources and time as we sifted through this. (I do not consider it wasted time…but my daughter complained a lot…but I think it taught her how to fend for herself in the academic world to get what she needed.)
3. Another homeschooling family I know used the second edition of Calculus, and their daughter liked it a lot. Different strokes for different folks. That student likes computer programming and math. My daughter does advanced math because I make her and she might need a calculus class in college as a prerequisite for her graduate school plans (and plus I know she can do it).
4. My daughter has transitioned well to calculus-based physics.
5. Good luck to you whatever you decide! Have fun with it. If you’re at the this point, your child is about to graduate and move on! This is what you prepared them for! Watch them fly!