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Back in the good old days, when I was teaching Calculus to undergrads, I remember two types of students: those who could calculate, and those who couldn't. Now, certainly there are other skills which are important for the study of higher mathematics. There's creativity, and imagination, both of which feed into visualization and abstraction. But without the ability to calculate, to do simple arithmetic quickly and easily, the other skills are handicapped.
I had students who could grasp difficult concepts, could creatively plan methods of attack on complex problems, or could abstract fundamental truths from seemingly unrelated data. But they couldn't bring those tools to bear in their full strength, because they had a weak foundation in arithmetic. And they were often slow in following my reasoning on the board, because they were still hung up on a simple factoring that occurred two paragraphs earlier ("Dr. Fulton, where did that come from?"). I had students who got Calculus. They truly understood the conceptual picture. But they struggled solving problems, simply because of arithmetic. Why? I don't know exactly. I can only guess that they were allowed to use calculators throughout grade school, and they missed out on the reflexive training for arithmetic. That's a heartbreaking situation, because it's not easily fixable at a later stage. No Calculus student wants to be told to go back and review multiplication tables.
We mentioned one flash card technique that we've used in our "Shoot-the-Number" post, involving Nerf guns. It involved the child saying the answer, and then shooting it on the number chart if he was right. As he improves, make him get 5 in a row before he can take a shot. Then make him get 5 in a row in under 10 seconds. It's like weightlifting. Keep making it harder, tougher, faster. You want the arithmetic to be reflexive.
Another technique we've used is the trampoline. A child gets to keep jumping on the trampoline, as long as they're doing the flash cards and getting them right. Once they've missed, say, three cards, it's time to get off. Choose an activity your kid enjoys, and do likewise. If you have children of different age levels, you can teach multiple kids at once. We just did this yesterday. One child held up a card, a younger child pronounced the numbers on the card (for number recognition), and an older child answered the multiplication problem. Meanwhile, the child holding up the card was also getting a review. Sometimes, it is useful to call out the card to your child, without letting them see it. It's different, and it will slow them down at first. But it's good. It's important to be able to do mathematics without necessarily relying upon optical signals. It builds visualization. There are many, many variations that can be done with flash cards. Be creative. But be consistent. Use them regularly. They're a good, cheap tool in building an arithmetical foundation that will last... ...to Calculus, and beyond!
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2 Comments
This puzzle was sent to us by a family member. It requires either a little algebra, or else a little "guess-and-check" work. 
We hear it all the time.
"My child's so smart! My child's a genius! He's brilliant! So creative!" And then follows the inevitable... "But I can't teach him anything, because he just won't sit still!" (We use "he" and "him" throughout this post, because this problem overwhelmingly happens to boys - including our own. Our girls were model students for us. They listened attentively to every word. They sat still, and did their work most of the time. We thought we were master teachers. And then our boys came along...)
Now, what should the questions be? Well, it depends on the age of your child. The sky's the limit. Any question with an answer from 1 to 100 will suffice.
Examples: 1) When your child is just learning numbers, point to a number on the chart, and have him pronounce it. If he's correct, have him shoot it. 2) Flash cards are great for this! Just have your kid tell you the correct answer out loud before shooting, because Nerf guns are rather imprecise. 3) Do Flash cards without the cards. Meaning, don't show the card to your child, but instead say it aloud to him. It's a good skill to be able to add or subtract or multiply without seeing the numbers on paper. 4) Do word problems. Your child is more likely to fight through the frustration that comes from word problems, if there's the chance to take a shot afterwards. 5) This isn't math, but it's a bonus. Use it for geography. Put a world map on the wall (or a country map, or a state map, etc.), and have them shoot certain countries or oceans as you call them out. This is surprisingly fun. So much so, that the teacher has even been known to take up arms a time or two. (Those European countries are downright devilish to hit on a world map. Good luck shooting Switzerland with a Nerf gun.) Okay, now some will say "Yeah, those sound fine, but it's much more efficient to just have them say the answers out loud to me, or write them on paper. We can go much quicker that way." Guess what? They're right! And if your kid is able to sit still and concentrate well enough for your liking, then by all means do what's most efficient. Our girls did great in that regimen. And we intend to get our boys to that point, as well. But at this stage for our boys, well, it just ain't happenin'! And we're gonna do what works. Even if it's not the most efficient technique. Oh, and even if your child doesn't need "Shoot-the-Number" to stay on task, it's kinda fun to offer it anyway on special occasions. Our daughters don't need it, but they're not averse to pulling the trigger, by any means! Just be warned. A stray projectile sometimes (often?) manages to strike the teacher. By accident, of course.
If you like our puzzles and explanations, please visit our store and check out our problem-solving and logic puzzle books!
This post may contain affiliate links for which we will earn compensation should you choose to make a purchase. We are disclosing this information in accordance with the Federal Trade Commission’s 16 CFR Part 255, Guides Concerning the Use of Endorsements and Testimonials in Advertising. Thank you for your support of The Math Profs.  Four people (Bob, Jim, Ken, and Travis) are participating in a parade. They are each riding a different vehicle (on a float, in a golf cart, on a bike, or in a truck bed), and wearing a different costume (sheep, baseball uniform, clown, or bear). Match each person with the appropriate vehicle and costume.
 Full tutorial found here.
This puzzle was taken directly from Book 3 of our "Grids For Kids" logic puzzle series. If you like our puzzles and explanations, please visit our store and check out our problem-solving and logic puzzle books! |
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February 2021
CategoriesAuthorsBrian and Melanie Fulton both earned doctoral degrees in mathematics at Virginia Tech. They formerly taught math at the university level, and now run a hobby farm while accuracy-checking collegiate mathematics texts. They homeschool their four children, frequently employing the aid of chicken, dairy goat, cat, and dog tutors. |
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