- Photo courtesy of jin.thai
When I do interviews or speak to groups about math, one of the things I worry about is that people will expect me to do math tricks. And I worry about this for good reason. I can’t multiply two three-digit numbers in my head. I don’t know π to the 100th decimal place. Heck, I can’t always remember what 9 x 8 is!
There are plenty of folks out there who have these abilities, and god bless ‘em. It’s not my schtick. In fact, while I think these tricks are pretty nifty, I’m not so keen on people learning them, at the expense of gaining a deeper understanding of the math behind them. This goes for kids and adults.
This is what I write about in one my first posts as the math expert for MSN.com’s site for parents, Mom’s Homeroom. Over the next several months, I’ll write articles and develop activities designed to give parents the tools they need to help their kids succeed in math. (Other experts address reading, social skills, homework and study habits and parental involvement.) One of my first posts, 5 Cool Math Tricks You Didn’t Know, looks at some neat shortcuts for basic math facts — like multiplying any number by 11 or finding out if a number is divisible by 3.
The twist is that I show readers why these tricks work. But this is a step that most folks skip altogether. My friend, Felice Shore, who is an assistant professor and co-assistant chair of Towson University’s math department, explains why it’s critical to master the math behind the magic.
“The important mathematics [in third and fourth grade] is still about building understanding of relationships between numbers — the very reasons behind math facts. Once you show them the trick, it’ll most likely just shut down their thinking.”
That goes for grownups, too. If you’re brushing up on some basic math skills, don’t just memorize facts or use nifty tricks. When you take a little time to look beyond a quick answer, you will likely learn a great deal more. And as we all know, this can extend to other applications and concepts.
Math is often described as a set of building blocks stacked on one another — the foundation must be there to move into more complex concepts and more difficult applications.
But it’s also a web. What you learn about multiplication applies to division, which applies to factors and multiples, which applies to fractions. Sometimes, a concept that passes you by can be better understood later on when the idea shows up again. In other words, you might just learn your 12s times tables,when you’re applying measurement conversions (12″ = 1′). Tricks just might keep you from deeper understanding.
So whether you’re trying to get good at math on the fly or helping your child remember that 9 x 8 = 72, be careful with the tricks. They just might keep you or your child from learning much bigger concepts.
Do you depend on math tricks? If you’re a teacher, what do you think of students using math tricks?
I think math tricks are counterproductive for two reasons. First, they do cause children to shut down their thinking. Second, students get them confused and don’t know when to use what trick. Some of the worst I’ve seen are the poems to learn individual multiplication facts. Examples – http://www.superteacherworksheets.com/multiplication-poems.html
I think the most useless one I heard was while I was working with a student on subtraction. Our problem was 15 – 9. I was trying to help the student determine the relationship between 10 and 9 to understand that subtracting 9 resulted in an answer 1 more than subtracting 10. Another helpful adult heard our conversation and decided to come over and share a trick. She said it was a great trick when subtracting 9, but it only works when subtracting 9 from a number less than 20. She told the student to add the tens digit and the ones digit of the starting number. Example: 16 – 9 is 1+6 or 7. Grr! I’m hoping the student forgot that one quickly, which is highly likely to be the case.
I am thoroughly convinced that relational thinking is the key to students becoming mathematicians, and that Cognitively Guided Instruction is the key to developing relational thinking. Second grade example – http://www.suedowning.blogspot.com/2012/03/marvelous-math-play-date.html
These kids have not only figured out the 5s by understanding the relationship to the 10s. They knew how to quickly determine the 9s by subtracting from the product of the number and 10. They also knew they could manipulate the numbers by dividing one by a number and multiplying the other by the same number.
Great thoughts here. I look forward to learning more about Cognitively Guided Instruction. I agree that relational thinking is the key for many students. I also think that we need to be open to a lot of different ways of thinking. Perhaps looking at the relationships between concepts addresses more of those differences. I think it certainly is more inclusive than memorization or tricks!
I’ve always thought of my brain as a series of hooks. When I get new information, I automatically look for the hook it belongs on. So multiplying by five belongs on the multiply by 10 hook (and vice versa). One-fourth belongs on the 1/2 hook, which also includes 1/8 and 1/16. (I use those all of the time for sewing.) For me that’s relational thinking. But when I tell people about that, I often get a “wow, she’s nuts!” look. Maybe I just think too hard about things.
Laura
I like your hook concept and I don’t believe you think too hard. CGI encourages children to solve math problems in a way that makes sense to them and then to explain their thinking. Here is some more information – http://www.wcer.wisc.edu/news/coverstories/cgi_math_encourages_ingenuity.php
This link is the first 25 pages of a book written by the authors of the CGI book. You may be surprised when you read about the misconceptions students have about the equal sign. I discovered that was a major issue with a struggling 2nd grade student I am tutoring.
http://books.heinemann.com/shared/onlineresources/e00565/chapter2.pdf
I partially blame my lack of more complex math skills on the fact that we learned by memorization in school. If i don’t have a firm grasp on why, I struggle to retain information. Which is probably why I’m great with finance and practical stuff, regardless of the complexity but still occasionally add on my fingers and have to really think about the times tables!
I had such a hard time with memorization myself. It wasn’t until I figured out how to understand the concepts behind the math –sometimes with the help of a teacher, sometimes on my own — that I started excelling in more complex math.
I think this was such a huge reason that I ultimately went into math education. I desperately wanted to share the ideas and counteract the memorization stuff.