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Math Q & A with Cafi Cohen
Math Q & A with Cafi Cohen
Cafi Cohen is best known for her books on teen homeschoolers and college admissions including, Homeschooling: The Teen Years and Homeschoolers' College Admissions Handbook. What follows is a transcript of a Q&A with Cafi that took place during a Homefires' Virtual Conference from March 12th - March 16th, 2001.
Q: Is it really important to know your Math Facts? When it comes to math, is it more important that students know how to figure out the answers, even if using calculators, if they aren't great at memorizing facts?
A: I think "math facts" are extremely important - as important as knowing the alphabet and one hundred most common "sight" words. What's more, my definition of "math facts" is broader than most. In it I include all addition, subtraction, multiplication, and division "facts" up through "12," squares of numbers up through 15, and at least 10 common percentage-decimal-fraction conversions (e.g. 1/2=0.5=50%). We should never use calculators for calculations more quickly and accurately done in our heads.
That said, teaching and learning math facts is not a one-time thing. It's something that has to be continued and reinforced over anywhere from 3-8 years. As our children increase their math facts mastery, certainly they can keep "moving along". No reason not to learn about perimeters or fractions or even simple algebraic equations, for example, just because we only know our multiplication facts up through 5.
Facts are important. Just as important is the learning when and how to use the facts, "how to figure things out," as you put it. Don't give up on the math facts, AND don't hold your children back even if they cannot recite every fact. The two things go hand in hand, and often take several years. Just be persistent and get as much math in as you can.
Q: How do I help my child memorize Multiplication Facts?
A: I'm a BIG fan of math games. One you can try today is called Math War. There are several variations. Simply remove the face cards from a deck of cards. This leaves you with the numbers 1-10. Deal the cards out evenly to two or more players. Each player turns the first two cards up on his or her stack, multiplies the two cards, and states the product (results of the multiplication). High product takes all cards. If one player says an erroneous product and the other player(s) notices, the erroneous player loses the face up cards, even if she has a high product. If the products are equal, everyone puts three cards face down, followed by one face up. High face-up card takes all. You can begin with a simpler version of this game, with just the cards 1(ace) through 5 or just 1 (ace), 2, 5, and 10.
Also, have your child practice counting by 2's, 3's, 4's, 5's, 6's, 7's, 8's, 9's, and 10's -- not all of these at once, just introduce a new one every week or so. Finally, model why multiplication works. Use home made manipulatives, such as dried beans or pennies to show why 3 X 4 = 4 X 3.
Q: My daughter hates math - any ideas? Our homeschool day takes a turn for the worse when it is "math time". My 13-year-old daughter doesn't struggle with it, but she becomes angry and upset and fights me about doing it. I think it's important — especially when it comes time for college entrance exams. Any recommendations?
A: I agree that math is very important — not only for college entrance examinations (the math portion of these acts as a social filter, IMHO), but also for life. Too many people do not understand the vagaries of mortgages, compound interest, even simple percentages.
We required very few things of our children, in fact only five things. Math through trigonometry was one of those things.
That said, have you tried Saxon Math? I think how you use Saxon is very important and can make or break a child's success with the program. We found it vital to provide a steady diet of math complements to any math textbook learning.
Straight textbook math would probably make me hate "math time" also (and I like math). Of course, Saxon is not the best program for everyone. Make sure that you and your daughter choose a program together. This makes the audience much more receptive!
Don't be afraid to take a "math break" for a month or two to figure all of this out. Play math games, read about the history of ancient numbering systems, do some logic puzzles instead for a while.
Q: Did you say you skipped every other lesson in Saxon Math? How did you cover all the material with skipping every other lesson? Does this mean you went through a book in "half" the time?
A: Sure, we probably did go through the books in "half" the time if you want to count actual days we spent on Saxon. We didn't skip every other lesson, we skipped every other problem set. Big difference. Because my children had such a heavy dose of the things I describe as "math complements" (unit study math, mental math, math games, consumer & real life math, math history), their textbook math was much easier for them.
Q: Abeka or Saxon Math? My daughter is in 4th grade. She had previously attended a Christian School where they used a complete Abeka program. As this is our first year homeschooling, we used the same curriculum. I was thinking about changing to Saxon math. I had her do the online placement testing and it said we should use Saxon 8/7. After seeing this, I felt a bit unsure about whether to change her from Abeka. How do you feel these two curriculum compare?
A: Abeka is probably the most challenging traditional math program on the market. ABeka grade four contains material similar to grade 5 and 6 material in other programs. Adding to the confusion, the Saxon 76, 87, Algebra 1/2 books contain 80-90% of the same material, and it's only necessary for most folks to do one of these volumes.
As homeschoolers, we stopped worrying about grade level designations, and you should consider that also. What's important is to find a program which eventually your daughter can use on her own, without your help -- so you don't have to relearn trigonometry, should it come to that. Does Abeka strike you as a program that could become self-instructional at higher levels?
If you and your daughter are comfortable with your current program, don't change. If you are not comfortable, consider many alternatives, not just Saxon.
Q: Would you give us a list of some family board games that a family could learn from and enjoy?
A: We really like Monopoly (mental math), Scrabble (vocabulary & spelling), and chess (critical thinking).
A couple of other games that have always been a big hit around here are:
24-Game. It's basically a stack of cards, each card containing 4 numbers that have to add/subtract/multiply/divide up to 24. It now comes in about 10 variations, making it the ideal maintain-your-mental-math skills game.
SET. I don't know what to classify this as except as critical thinking. My teenagers loved it, especially once they could regularly beat us. You can play the online SET daily puzzle.
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