Investigations in Math
February 21, 2008
I hadn’t heard about the new new math until reading the Washington Post’s article Parents Rise Up Against a New Approach to Math.
The program de-emphasizes memorization and drills and pushes students to use more creative ways to find answers, such as drawing pictures, playing games and using objects. Prince William officials say “Investigations,” which cost the county more than $1 million, teaches students why an answer is correct, prepares them for algebraic concepts on the SAT and increases passing rates on state exams.
Carol Knight, Prince William’s math supervisor, said that when children break down numbers into multiples of 10 and 100, their understanding of place value and “number sense” increases.
“Memorization will only carry you so far,” Knight said. “With ‘Investigations,’ kids understand the real values of the numbers and are not doing shortcuts. When they multiply 23 times 5, they’ll do five 20s to get 100, and then add five 3s to get 15, and they put that all together and get 115. What they’ve done is made actual use of the numbers.”
The parents in Prince William are upset because the new method is apparently very confusing compared to the rote memorization we used. But I remember the basic arithmetic being a real problem for me, not only in elementary school but further on into high school and then college. Trigonometry had me staying after school every day for almost an entire semester for additional work with the teacher before I could pass it. I had to repeat linear algebra in college and never passed vector geometry despite trying twice.
At a certain point the math became too heavy for my shaky math understanding — built primarily on faith and memorization — to support. I think that’s because when I learned my multiplication tables I also learned math was memorizing rules about how numbers operated.
Just from the gloss the Post offers above, it seems like the Investigations approach would have worked for me better. I have always been very impatient with rote memorization, scoring much better on analytical questions instead of fact-recall. This confused the aforementioned trig teacher. I could do trigonometric proofs all day. In fact, I was probably the only student in class who enjoyed doing proofs. But I still made basic errors in long division. (Long division is still pretty much magic to me. I have no idea why it gives the correct answer.)
I suspect the current No Child Left Behind standardized testing regime would have been an twelve year horror show for me.
This new program strikes me as a deeper way to study math — one that would have, if I had learned it, engaged my analytical sense early on and actually made me interested in what I was doing. But apparently it’s not working for many other kids, so I’d like to hear more about it. Have any of you brushed up against the new new math? What’s it really like?
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February 21st, 2008 at 7:26 am
I recall reading an article — perhaps it was in the Post as well — that dealt with people in another district revolting against “new” math. The reason was slower learning, I believe. Such analysis takes time; memorization takes a few evenings.
I think the approach is a great idea, used in moderation. Start out that way; let the kids get a feel for how it works; then slowly switch to memorization. Those that have problems memorizing things will have some built-in assistance; those who memorize well will have the skill if they need it.
There’s an irony in it as well:
If we were using the metric system like the rest of the industrialized world, this would be reinforced at every turn.
February 21st, 2008 at 7:31 am
An addendum:
I think this would have appealed to you because, in part, you were a motivated student, even in the Melvinmeister’s class. I can think of a dozen students in my own classes who, I believe, would have great difficulty with this kind of analytical thinking, in part because it hasn’t been modeled for them, and in part because they’re not motivated enough to withstand a few moments of confusion while on the path to Greater Knowledge. I substituted for some math teachers when we first came back to the States, and when I tried teaching some of them tricks like that (multiply 62 x 32 first by doing 60 x 30…), they were frustrated by the lack of immediate clarity. My own students now, many of them, flat out ask for worksheets and packets, saying, “We just want to read the story and answer question.” That’s the ELA equivalent to learning your times table.
February 21st, 2008 at 10:41 am
That’s interesting, because that example given is exactly the way I’ve always done math in my head. I never did memorize the multiplication table fully, and developed this method of doing math on my own. Scott does it, too, but his method is slightly different than mine and confusing to me. I think this would have worked for both of us, though, if they taught math that way when we were in school.
February 21st, 2008 at 12:40 pm
I think it’s great that they are trying this. If they can teach kids the real properties of numbers, and how they work, they’ll understand that there really are no tricks to solving basic math problems like the article shows. They’ll understand they can break things down analytically and come up with correct answers in different ways, and, most importantly why they can do that.
I also love that they want the kids to come to an answer and then think about whether that answer makes sense. If you studied engineering in college, that’s one of the first thing that gets drilled into your head. If you’re solving a circuit and need to determine the value of a resistor, for example, and your answer is 100 milliOhms, you better go back and try again. The sooner they teach that concept, the better, IMHO.
The only downside I see is that some kids just aren’t going to get math. Teach it the old way, or this way, it’s a lost cause. I can tell you, if this were English we were talking about, that’s the way I would be. My brain simply isn’t geared toward understanding proper sentence structure, prepositions, and other stuff like that (if you read my posts, I’m sure you’ll agree). It’s just completely uninteresting to me. That’s why in our house, I do the calculations, my better half does the writing.
Most likely there’s also a percentage of students that will actually understand math this way as opposed to the traditional way, and the opposite is true as well. So, that’s probably a wash in the grand scheme.
February 21st, 2008 at 2:27 pm
I grew up in Montgomery County Public Schools and to some extent, we already learned in this way. I remember the math specialist in my elementary school had a collection of little blocks. There were singles, and sets of 10 glued together. We learned how to group the 10s together to get larger groupings.
I never had to memorize formulas for test. They were always given to us, because if we didn’t know how to use the formula, we still wouldn’t get the problem correct. Of course I had a very hard time when I got to college, because I didn’t know how to memorize formulas and suddenly had to start doing it.
On the other hand, one of my friends insists that she always had to memorize formulas. We were both in honors classes, so I don’t know why my teachers made her memorize and mine didn’t.
February 21st, 2008 at 7:50 pm
I majored in math and did very well. I think it’s great that there are new methods available to students and have always been happy that there’s more than one way to solve a problem.
That being said, I’ve been stymied, more than once, by my elementary-school-aged daughter’s homework. It’s not the homework, and it’s not the methods … it’s how these methods are explained. It isn’t being done well, in my opinion, and having new methods just causes more problems if the students have to learn more than one of them.
I don’t suppose there’s a way to teach the methods without having students try them out, but I keep thinking there ought to be a way to teach them BETTER. When the school sends home a “help sheet” for parents, and a reasonably-intelligent parent who happened to major in math can barely translate the mumbo-jumbo and either too-technical or fancified language therein, it quite frankly doesn’t seem like an improvement over rote memorization.
Can’t “intuitive” mathematics be communicated simply?
February 26th, 2008 at 6:35 pm
I was taught under the “old” new math — still don’t know my multiplication tables by heart. But hey, I learned to count to 99 on my fingers!