Review of math textbooks by Harold Jacobs

by Susan Richman

Open up any of Harold Jacobs' math text books and browse a bit--Elementary Algebra, Geometry, or Mathematics a Human Endeavor. I don't think you'll be able to just close the cover with a polite yawn very quickly. First you might be pulled in by the cartoons, real cartoons from Peanuts, the New Yorker Magazine, B.C., and other sources, that all have math as their topic in one way or another. You'll soon be chuckling and flipping through to look for more. You'll find them. Jokes like this--a small boy is reading a newspaper with the following article:

Toledo, Apr 19 (UPS) Professor T.B. Murray, world famous philosopher-mathematician, writing in the prestigious literary magazine, "You and the Idaho Potato," claims to have solved the problem of feeding 220,000,000 Americans. "The solution," writes the Professor, "Is to move the decimal point seven digits to the left." Feeding twenty-two people "should be a snap," Prof. Murray said.

But more than just fun, the cartoon is tied to the lesson at hand, which is on scientific notation. My kids love to leaf through these books to find the good cartoons--even Molly (6) enjoys them! Even Hannah at 2 1/2 likes to look through them, and whenever she sees a cartoon, says very excitedly, "There's an Algebra!" (I don't think she'll have math anxiety at any rate...)

But if you look beyond the cartoons, you'll find something else, too. Harold Jacobs writes in understandable interesting and engaging English. Math text books seem notorious for thinking that normal language should be left at the door when the topic is simultaneous equations or coordinate graphing or exponential equations. Directions are often given in choppy outline sentences or flow-chart mini-phrases, I guess trying not to "handicap" the student who might not be able to read very well. But Jacobs is refreshingly different--he writes with a voice you can hear, and draws the student into the topic by first creating a specific vignette or story.

For example, when introducing exponential functions in algebra, Jacobs opens with a cartoon from the New Yorker that has a woman saying to a man at a cocktail party of highbrows, referring to another man who's sitting alone on a couch, "His knowledge is doubling every ten years, and it's making him jumpy." Next Jacobs helps us see what this comment could really mean mathematically: the man would have twice as much knowledge in 10 years, four times as much knowledge in 20 years, eight times as much knowledge in 30 years. A table is constructed, and equation created that summarizes this data, and soon a graph is created. Then generalizations about exponential functions in general are made, and comments on their wide usefulness and applicability in science and sociology (populations can grow exponentially with time). Then come the exercises for the student to work, the humorous "knowledge doubling" image firmly in mind.

I also like the order of material presented. It makes good sense to me and is different from many other books. In Elementary Algebra, Jacobs introduces graphing very early on, by Chapter 2, something that the Saxon books, for one, do not get to until a third of the way through Algebra I. Graphing is a very important part of algebra, and it makes good sense to me to bring it in right away.

These books also share the main advantage of the Saxon books--regular review of all concepts. After each lesson in Elementary Algebra, there are four sets of exercises. Set I is the review set, usually not many problems, but just enough to make sure you haven't forgotten writing formulas from tables of data just because you've now moved on to learn about equations in two variables. The student or teacher can choose between doing Set II and Set III, as they are basically the same type (Set II answers are in the back of the student's book). And Set IV is often our favorite--here is one challenging problem that really requires creative thought. Here's an example of this type of problem:

The following problem was invented by a man named Mahavira, who lived in southern India more than a thousand years ago. The price of 9 citrons and 7 wood apples is 107; the price of 7 citrons and 9 wood apples is 101. Tell me quickly the price of a citron and of a wood apple. Can you figure out what the two prices are?

Jacobs often brings in problems in Set IV that are historical, showing students a bit of the intrigue of math history along with a problem solving challenge. He has problems from Roman times, puzzles from turn of the century recreational math books, and even one from the English poet Samuel Taylor Coleridge.

Jacob's book Mathematics: A Human Endeavor was written for several audiences, but primarily for college general math courses for students who felt they were lousy in math. It is subtitled, A Book for Those who Think they Don't Like the Subject, making it a sort of graduate version of Marilyn Burns very popular and good book for elementary students, The I Hate Mathematics Book. This book is also very accessible to much younger students (Jacob at 9 and Jesse at 12 love it, and even Molly at 6 can do some of the logic problems). The topics range widely: number tricks and deductive reasoning, graphing the path of billiard balls, number sequences such as the Fibonacci sequence , functions and their graphs, large numbers and logarithms, polygons and symmetry (helping the student learn to construct many exciting models of polyhedra--what my kids call "geodesics"), mathematical curves (including ingenious ways to fold these curves with a piece of paper, and problems exploring the logarithmic spiral of the chambered nautilus shell, and even how to draw the beautiful curves called cycloids, which we all know from these children's drawings sets with little toothed plastic gears that fit into larger plastic circles and you whirl the thing around to make a pattern), probability and chance, and topology. Always there are experiments to do, and intriguing problems that help you learn about the world we live in.

I hope you'll decide to take a look at these books, especially if you have junior or senior high age young people at home, and especially if you want to turn them away from a fear or dislike of mathematics.



Query about Jacob's vs. Saxon's Textbooks

from Linda Butler (Utah)

Have you ever compared the Saxon Math books with the Harold Jacobs books that John Holt recommended? [Editor's note from Susan: We carry the Jacobs' text in our catalog, along with teachers guides.] I have been able to pick up each of these (public school discards!): Saxon Algebra 1/2 which we used last year, Algebra 1 and Algebra 2; and Jacob's Elementary Algebra, Geometry (but they tore out the answers in the backboo, hiss!), and Mathematics: A Human Endeavor. My personal impression of the books is that Jacobs is more "right brained" in that he tells stories, shows pictures, and explains things a lot. Saxon seems more "left brained" in that he gives you "just the facts, m'am." I have tried to get my daughter Jessica to look through the books and pick one she thinks she would like, but that is too overwhelming for her. I think I would enjoy using Jacobs' books to teach with, but I don't even know what age (grade, maturity level) they are aimed at. I am NOT a math person (I was until 7th grade when a sexist teacher made me "realize" that girls were no good at math, no way, no how). I don't even know which of the Jacobs' books is to be used first. So any ideas, comparisons, impressions, hints, helps you can give me regarding this would be greatly, immensely appreciated.

Response from Susan Richman

I think Linda hit it right on the head in her characterization of the two different math series. I think Jacobs is indeed the much more engaging author, the one who goes out of his way to help students see the why and the intrigue of math--to see the reason for all this stuff, and the pattern that links it altogether. He takes the time to give a bit of the story behind math topics, the history and color of the subject not just the dry procedures for solving particular types of exercises. Saxon does have a bit of a sense of humor some folks tell me, but I think it's pretty limited. The book is routine, and depends much more on just rote learning and repetition rather than helping students understand the why (and for some students once they really understand the why, drill ad-nauseum is NOT necessary because they can always easily remember the what because they understand where it comes from).

So parents need to think about what type of student they have -- do your kids thrive best on routine that doesn't ask for very much original thought or give much fun, or do your kids need something more to learn best? I personally know kids who prefer the Saxon books after trying Jacobs--and I know of many kids who find the Saxon books deadly boring and mind-numbing but who perk up to math when using the Jacobs books. And think of who you are as a parent teacher-- which book will inspire you a bit? Both books can be used effectively by students on their own if you need your kids to do that. My daughter Molly is quite successfully working through Elementary Algebra by Jacobs now on her own, with input from me when she needs help or wants to discuss thingswith the two older boys I did each lesson with them and usually worked the problem sets along with them also to get myself back in gear for the subject.

As far as grade/age levels for Jacobs' books, that all depends on the student. All the books are designed for normal high school students, though I've certainly met bright junior high kids who are doing great with them. Human Endeavor is often used as a freshman college course for the non-math student, as a way of helping the student get a broad background in many useful and intriguing math topics-- and to help the student learn to appreciate math and see the human side of it while really working with the subject in new ways. In fact, one of Harold Jacobs' missions as a math teacher was to try to show students who thought they hated math that it really isn't so bad, that math can even be, well, engaging and interesting.

The sequence should probably be Elementary Algebra, Geometry, and then Mathematics: A Human Endeavor. But there is plenty in Human Endeavor that even a bright upper elementary student could grasp and enjoy. In fact that book can be done sort of piece- meal if you want to-- the units are pretty much self-contained and don't really depend too much on other previous work in that text. The other two books are definitely sequential, and would best be worked in order. The Elementary Algebra book is actually three books in one-- it's got pre-algebra for those who haven't had it yet, and as far as I can see it has everything that both Saxon Algebra I and Algebra II have (this is not based on a really in depth check, just a quick browse through). You don't need extra tests, as there are summary reviews at the end of each chapter, as well as mid-term and final exams right in the books. We now carry the teacher's guides for all three books, so you have access to all the answers, as well as some extra teaching material if needed.

Both the Saxon books and the Jacobs books have well-defined lessons, with clear beginnings and endings, making it easy to give assignments that are realistic and easy to understand. Both have regular review of all earlier topics. Both are comprehensive and cover required and expected material. Both seem to help students do very well on standardized tests. The difference really is in tone and approach-- and you're the only one who knows which will be best for your family.


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