MATHEMATICS
PLAY AND FIND OUT ABOUT MATH: Easy Activities for Young Children, by Janice VanCleave. How long is five seconds? How can I draw a star? How much is one-half of something? Is my foot a foot long? I wonder … How can I do a math trick? These are just a few of the questions to be explored and learned about in this book. Your children may not know the words fraction and symmetry, but they will discover the concepts from these easy-to-do projects — and they’ll have fun doing it. Concepts covered are counting, numbers, addition and subtraction from 1 to 10, fractions (the concept of one-half), time, shapes, patterns, measurements, and quantities. All measurements are in given in standard and metric. (Why not learn both and be mathematically bilingual?) The projects use household materials and are designed for parent participation, but many activities can be just started by you. Easy, clear directions. Great illustrations. 50 simple activities. This book is part of an early-learning series that includes similar learning activities about science, nature, and the human body. $12.95. A 10.36
PATTERNS IN ARITHMETIC, by Suki Glenn, is the best introduction to mathematics and arithmetic I’ve seen. I like the Usborne math books and they are very good for children to work with, but I would start with this one first and use the Usborne books for practice and reinforcement if it’s needed. This book was developed at the Farm School, a development and research school affiliated with the University of California at Irvine. The book is about the exploration of mathematical concepts. Its approach is to encourage the child to do the discovering, as opposed to the normal approach of “teaching” concepts. Glenn’s method is very hands-on, and her excellent understanding of child development makes each lesson, game, or concept a process that happens very naturally. Her excellent ideas for exploring concepts with your child will make it fun for you too. You already have many of the materials needed, but you will need to purchase Cuisenaire rods and a set of base-ten blocks. Ages 5 to 8. Pattern Press, P.O. Box 2737, Fallbrook, CA 92088; members.aol.com/patternpr. Also found used for better prices on Amazon.
HOW MUCH, HOW MANY, HOW FAR, HOW HEAVY, HOW LONG, HOW TALL IS 1,000?, by Helen Nolan. Nolan has made great fun out of exploring the concepts of big, small, short, tall, distance, and more. Emphasis is on estimation rather than counting. Fun! Ages 5 to 9. $6.95 or less on Amazon.
SAXON MATH. John Saxon’s now-famous math books may be the only ones making full use of an “incremental” approach to learning — the introduction of topics in bits and pieces, which permits complete assimilation of one facet of a concept before the next is introduced, along with continuous review of all material learned previously.
We first learned of “the Saxon method” in 1985 from an article in Reader’s Digest. We bought a copy of Algebra ½, tried it, and were very favorably impressed. Since then, we have used most of the other Saxon math books, with fairly remarkable results. Two of our four children, who had seemed to have almost no mathematical aptitudes, gained a basic understanding (and even a little interest) in a very short time. On the other hand, the only “advanced” math studied by our daughter Karen, the only one of our children ever to be officially tested, was in an outdated, out-of-print copy of High School Subjects Self- Taught, and later she scored very high in the national SSAT (and was accepted by a college with only our high school diploma and no other official credentials).
For mastering advanced math, especially if it will have application in sciences such as chemistry (which is emphasized in some Saxon books), or if you’re going to need a lot of math to get into college, Saxon’s method may be the best — but many people are mastering math without ever seeing a Saxon book. A $15 book that covers all the basic math principles, with enough drill and practice to know whether or not you’re going to be a nuclear physicist, may be sufficient; it’s a lot easier on the wallet, and may be a lot easier on the student.
In his last edition of The Home School Source Book, Donn said we were no longer recommending or selling the Saxon math books. I’ve had second thoughts spawned by the tutoring I’ve done.
You can’t explain math clearly to anyone if you don’t understand it yourself. In an effort to educate myself enough to tutor, I looked at a number of textbooks. I talked with math teachers and had to accord them a lot of respect; it seems that some of them, too, are victims of the system. In search of the perfect textbook, schools frequently change textbooks from year to year. The methods of explaining math, if any,
vary from text to text. As one teacher told me, many teachers have their own way of teaching various math concepts and prefer that math books be written without any specific methods. Publishers, being well aware of the large profit margin in producing textbooks, are all too happy to accommodate these teachers.
I ordered some used Saxon books, and not only did I find them helpful, but they worked miracles for my students. Yes, we had to work at the basic tables. Boring? Yes, but within a short time my students were seeing progress as well as the reasoning behind learning the tables. The explanations and examples in the books were clear to me as well as to my students. Unfortunately, they were so good that I no longer have students paying to provide me with extra goodies.
Saxon’s K-3 program, originally developed “especially for classroom use,” was very difficult to adapt to individual use, but don’t let that frighten you. The special “home study kit” for individual use in kindergarten comes with the hefty price of $55. Now add $85 for first grade, $87.50 for second grade, and $90 for third grade, and although you didn’t grow up using Saxon math, you don’t need a calculator, a degree in mathematics, or a special course in financial management to know that the Saxon folks must think homeschoolers have bottomless pockets! (Those prices do not include the recommended manipulatives.) Fortunately, the prices drop with the more advanced books.
We won’t sell the Saxon K-3 courses because I object to the pricing, and because you can find cheap workbooks and make your own manipulatives. For the remaining grades I do suggest the Saxon books if you are trying to follow a prescribed school curriculum or if your own math skills are weak. Used Saxon books are readily available on many homeschooling websites. Make sure the textbook and answer books are for the same editions. Ages 8 through high school. Also found on Amazon and www.fes.follett.com.
MAKING CENTS: Every Kid’s Guide to Making Money, by Elizabeth Wilkinson. A Brown Paper School Book. How can kids have fun making money in their spare time? By starting with this book, which gives a kid’s-eye view of money, where it started, what it represents, how it’s spent, and (best of all) how to earn it — all in a book the kids will enjoy reading. Ages 10 to 12. New and used from Amazon.
Big Ideas for Small Mathematicians, by Ann Kajander. My essay about math in The Lifetime Learning Companion discusses the difference between arithmetic and mathematics. In case you haven’t read the book, the difference is simple. Arithmetic is the actual computation. Mathematics is the study of the concepts. If your kids aren’t enjoying arithmetic, try switching your focus to the mathematical concepts behind the computation. This book is what you need, and it’s been designed for use in schools and at home. Tackling the activities can be fun even if the kids (or you) don’t understand the math behind them. You’ll learn about Pythagoras, tessellations, and tetrahedral fractals — all without being a math genius yourself. You can take my word for this: I have a tendency to be mathphobic, and even I would have fun and learn doing these activities. Here are just a few of the chapter headings: Squares and Odd Numbers, Straw Structures, Party Fractions, Kaleidoscope, Moebius Strip, Balloons and Dice Game, 3-D Tic Tac Toe. Ages 6 to 11. $19.95. $17.00 from Brook Farm Books.