| Let's start at the beginning, with motivation. | | | | curve, and so on. All of this is really easy if you |
| Competition and rewards, as much as some | | | | understand the concept of abstract value. But I |
| people like to knock them, were a big factor in | | | | guarantee you that a child who has always been |
| both Bill and me getting turned on to math. My | | | | able to stick manipulatives end-to-end or in a |
| dad offered me, at the age of five, a penny for | | | | square to solve a problem will be totally lost when |
| every page I completed in a set of math | | | | he runs into negative numbers, irrational numbers, |
| workbooks he bought me. After I had very | | | | or imaginary numbers. |
| quickly earned a buck, he declined to issue any | | | | Don't get stuck in the concrete, when you could |
| further remuneration, but by then I had learned | | | | teach your children abstract math thinking with |
| (1) I could do this! and (2) math was fun and | | | | your pocket change. |
| profitable! In Bill's case, his third-grade teacher had | | | | One more point about money: even kids who |
| her class copy out four pages of math problems | | | | struggle with numbers catch on very quickly |
| each week. Every Wednesday, they would have | | | | when those numbers have two decimal places |
| a timed math bee, filling in the problems. The first | | | | and dollar signs. I have yet to meet a kid who |
| person to get them all right was the winner. A | | | | can't learn to shop! Girls & Math Research shows |
| clickable ball-point pen (then costing around 5?) | | | | that American girls do noticeably worse than |
| was the prize. Bill only won about once every five | | | | American boys on standardized math tests. But |
| weeks, but that was enough to motivate him to | | | | not homeschooled girls! Our own daughter Sarah |
| start thinking about math as an exciting game. | | | | recently scored a perfect 80 out of 80 on the |
| The idea is to make a child's first math | | | | math portion of the PSAT. (I admit it, that was |
| experience a thrill. Some variations: do math | | | | bragging!) The better performance of |
| problems with M&Ms, and let them eat the | | | | homeschooled girls probably has to do with (1) |
| answers they get right. Let them do math with | | | | using math more in their everyday lives and (2) |
| pennies, and keep the change if they get the | | | | not being surrounded by boys who not-so-subtly |
| problem right. You won't want to keep doing this | | | | prefer cute airheads to smart young misses. As |
| for months at a time, as the kids will either get | | | | long as the parents expect their daughter to do |
| fat or rich, but as my dad found, it isn't necessary | | | | well in math, there should be nothing in the |
| to keep up these rewards once the children start | | | | homeschool environment to hold her back. |
| enjoying math for its own sake. | | | | One area that most girls do need extra help with, |
| The Barnum Software Quarter Mile program | | | | even at home: spatial skills. |
| brings just this surge of excitement. | | | | If I ask you to visualize a shape in your head, |
| Not only are kids drilling the math facts, they are | | | | then rotate it various ways, most guys can do |
| competing against their own previous best speeds. | | | | this with ease, but most gals can't. Two |
| This can be taken to a competitive level if you | | | | resources I have found that are a great help in |
| sign up for one of their International Math | | | | improving spatial skills are: F The Factory (Mac, |
| Tournaments. Our kids all enjoyed competing | | | | Win, Apple, and DOS versions available; $89.95) |
| very much, and it certainly gave them incentive | | | | and Factory Deluxe (Mac or Win CD; $89.95) |
| to practice! For a noncomputerized alternative, the | | | | software from Sunburst (1-800-321-7511). Or (for |
| Providence Project Calculadder timed math drill | | | | Mac only, $129.95) the Spatial Sense CD-ROM, |
| sheets also "rev" kids up and give them that | | | | which includes Factory, Super Factory, and Building |
| sense of progress. | | | | Perspective. Check them out on |
| The great beauty of math drill software is that | | | | www.sunburst.com. |
| you, the devoted parent, don't have to be there | | | | F The most excellent D.I.M.E. Blocks ($17) and |
| for the child to improve his skills. But if you prefer | | | | associated 3-D Build-Up books (three available for |
| to use traditional flashcard, here's a tip: let the | | | | $7 each) from Timberdoodle (1-360-426-0672). |
| child hold the cards he gets right, then run through | | | | This forms an entire mini-course in spatial skills, as |
| the deck again. Every time he gets a card, the | | | | you rotate and fit the odd-shaped blocks |
| number of facts to drill narrows down to those | | | | together. Oodles of fun, too! Puzzles & |
| that need the most work; and for some reason, | | | | Construction Puzzles and construction toys are |
| holding the cards make the child feel like a winner. | | | | another great way to develop your spatial skills. |
| He will count the cards he has gotten right so far | | | | Bill's mom was, and is, an avid puzzler, who also |
| (more math practice!) and calculate how many he | | | | bought him Tinkertoys and Erector sets. Oddly |
| has to go (yet more practice!), while feeling he | | | | enough, my parents also gave me tons of |
| has already succeeded at least in part. | | | | puzzles, and the very same building sets Bill grew |
| What Counts? Most of us have 10 fingers and 10 | | | | up with. |
| toes to count. But that gets old pretty fast. | | | | Today, "Erector" sets are called "Meccano," and |
| Try counting backwards, like a rocket lift-off | | | | products such as Duplo and Lego bricks are |
| countdown: "10, 9, 8, 7, 6, 5, 4, 3, 2, 1, BLAST | | | | mainstays of many homeschools. While Lego-like |
| OFF!" Little kids love it! Try learning to count in | | | | products are great for creativity, they only fit |
| several foreign languages. This is a great way to | | | | together in a few limited ways. For more |
| introduce the concept of other languages, and to | | | | advanced spatial and engineering skills, an |
| help kids keep their ability to make the sounds of | | | | up-to-date construction series such as |
| languages other than our own. It also teaches | | | | Fishertechnik (available from Timberdoodle: |
| them that "2" is "2," no matter what it's called. | | | | 1-360-426-0672) or the motorized Robotix kits |
| I have a dress with 20 buttons. This made it easy | | | | (available from Home Life: 1-800-346-6322) is |
| to practice counting with teeny-tiny ones on my | | | | what you need. |
| lap. Try counting flowers on the wallpaper, leaves | | | | A Word About Words One fact of mathematical |
| on a branch, cans on the shelf . . . whatever is | | | | life that nobody talks about is the nomenclature: |
| right there in front of you. Remember to make a | | | | the jargon mathematicians use. Getting a grip on |
| big excited fuss when the little one gets it right! | | | | the lingo as early as possible is a way for your |
| Math Manipulatives For the math facts, I still think | | | | child to "pre-digest" some of what he'll be |
| money makes the best math manipulatives. Coins | | | | encountering in later math courses. We were only |
| and bills aren't rods you can lay side by side, or | | | | kidding about the Baby's First Calculus course in |
| cubes you can snap together. | | | | our Homeschool Admirer parody section in this |
| For that very reason, they encourage abstract | | | | issue, because babies can't learn calculus. |
| math thinking skills. A dime doesn't look like it's | | | | However, young kids can learn calculus |
| worth more than a nickel; it just is worth more | | | | terminology. So go ahead: "integrate" these math |
| than a nickel. You have to assign a value of 10 to | | | | words into your daily life and help your children |
| the dime and 5 to the nickel. This is prealgebra | | | | "function" better as you push them to their |
| and advanced math at its most basic; assigning | | | | "limits"! (Note: the words in quotes are |
| values and making calculations based on those | | | | mathematical terms. I don't really think kids should |
| values. | | | | be pushed anywhere unless they're in a baby |
| A word more about the value of abstract thinking. | | | | carriage or wheelchair.) A great book I just found |
| The National Council of Teachers of Mathematics | | | | that can help you with this is G is for Googol, |
| has been for some time promoting the use of | | | | from Tricycle Press pictured on the first page of |
| hands-on math manipulatives designed to help | | | | this article ($15.95, 1-800-841-2665). This |
| children think about math concretely. "This five-rod | | | | "alphabet" book is not for teaching little kiddies to |
| is as long as five one-rods. I can see with my | | | | read. |
| eyes how many one-rods it takes to make a rod | | | | Instead, this 57-page, oversized, fully illustrated |
| of the same length as one five-rod." This is not | | | | hardcover is devoted to explaining advanced math |
| the way math manipulatives have worked | | | | to the young. |
| throughout history. The sheepherder who made a | | | | Starting with "A is for abacus," in which we see |
| knot in his string for every ten sheep, or the | | | | an abacus, learn its history, and see how it works, |
| abacus user who moved a bead to the top of his | | | | each letter stands for one or more important |
| abacus to indicate "five," were using the knot or | | | | topics beloved of mathematicians. I'm not talking |
| the bead to indicate abstract value. There is | | | | about wimpy stuff like addition or fractions, either. |
| nothing "ten-ish" about a knot, or "five-ish" about a | | | | Cast your ovoid oculars on this list: Abacus, |
| bead, any more than there is anything "ten-ish" | | | | Binary, Cubit, Diamond, Equilateral, Exponent, |
| about a dime or "five-ish" about a nickel. People | | | | Fibonacci, Googol, Googolplex, Hundred, "If," |
| had to think abstractly to handle the knots and | | | | Jupiter, Königsberg, Light-year, Möbius |
| beads. They couldn't just count up a number of | | | | Strip, Nature, Obtuse, Probability, Quantity and |
| one-rods to get the answer. | | | | Quality, Rhombicosidodecahedron, Symmetry, |
| A dime does not resemble ten pennies in the | | | | Tesselate, Unit, Venn Diagram, "When are we |
| least. A ten-rod resembles ten one-rods; maybe | | | | ever going to use this stuff, anyway?," X, Y-axis, |
| not in its color, but in having the exact same | | | | Zillion. |
| overall length and shape. Therefore, I encourage | | | | Each concept is explained in easy-reading detail, |
| you to use rods, cubes, and even cuter | | | | with full-color drawings and diagrams. As a bonus, |
| manipulatives such as the Delta Fast Food math | | | | for each letter you'll also find a list of other math |
| items reviewed elsewhere in this issue, to | | | | concepts starting with the letter in question. So A |
| demonstrate math principles, but not to work | | | | is for Abacus (the main entry), and also for acute, |
| math problems. Rather, try using coins, with all | | | | algebra, angle, art, architecture, area, asymmetry, |
| their different values. | | | | average, and axis. No definitions are provided for |
| Your kids will learn the most essential math skill of | | | | the bonus list, but any parent with a smidgen of |
| all, needed in all math from algebra on up - how | | | | mathematical training can use this list for |
| to solve problems where you can't simply count | | | | inspiration for further explanations and |
| your way to the answer. At the moment, it will | | | | explorations. |
| be a nickel standing for five pennies; later, it will | | | | Three last tips: (1) math puzzle books, available at |
| be x standing for a number; still later, it will be x | | | | bookstores and teacher's stores: (2) checkers, |
| standing for an entire statement including other | | | | and (3) chess. All are great, fun ways to improve |
| variables; later yet, it will be f(x) standing for a | | | | math thinking skills. Let's do it! |
| series, or a number set, or the area under a | | | | |