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