
But first let's get them to know that 7*7 is 49. Memorization won't hurt. There are other good curricula out there. |
We're talking third grade here, and most kids are average. I will say that if you look at the folks that win those Fields Medals, they have a way of coming from Russia and France. They don't use EDM there. That abstract stuff should never be presented to young children. The most important thing is to get everyone over a certain level. After that, you can start to select the promising kids and take them aside, but I can tell you that that happens after (way after) third grade. BTW, the ones with the medals, they memorized. |
How do you know they are not presented with "abstract concepts," even though they don't use EDM? Moreover, I think very few people are arguing that kids should not memorize; the question, rather, is what else can they learn at the same time? Mathematics is fascinating and powerful and creative, but it's hard to realize that if you associate it solely with mindless drill. |
A little odd that you start your post by talking about how most kids are average, and curricula should be aimed at them, and then go on to make an argument based on success at producing a handful of the top mathematical minds in the world. Is your point that the bulk of the distribution needs to memorize, or that memorizing gets one to the upper tail of the upper tail of the upper tail of the distribution? I think you're wrong in either case. My guess is most of the ones with the medals didn't memorize: they had an inherent grasp of the logic underlying these basic calculations, and so it came to them almost as second nature without hours of joyless memorization. BTW, the inherent grasp of the underlying logic that they guys with the medals have is the same logic that programs like EDM try to produce in those of us living to the left of the uppermost part of the upper tail of the distribution. |
Do you know any of them? |
There is a high frequency of French and Russian Fields Medal winners. I will do a little research and find out what their natioanl math curricula are like. |
Do I personally know any Fields Medal winners? No. Do I know alot of people with PhDs in math and physics from high-powered universities? Yes. It's an occupational hazard. Let's do a little modelling and see where it leads us. Let's suppose that the typical mathematician gets his PhD at 27, toils for 40 years, and retires at 67 to sip sherry in the faculty club and fall asleep reading the obituaries. That puts the mid-point of his professional career at age 47. For most of them, would you guess the most productive part of their career is in the first half or the second half? In particular, for those very select few who win medals or are otherwise considered at the very top of their discipline, is the work for which they are honored likely to have been conducted in the first half or the second half of their careers? You know the answer as well as I do. Now, is that pattern consistent with a model where mathematical wisdom comes from the slow accretion of facts or is it more consistent with a model where wisdom comes from extraordinary intuition and insight that leads to an explosion of discovery (and then too often peters out)? And does that suggest that the people who win the awards did so because they spent alot of time studying their multiplication tables, or because they were (figuratively, though some might say literally) touched by the hand of God? Now let me put it another way: when you read a paper that really impresses you, one that you really wish you had authored, do you say to yourself "I could have written that paper if I had memorized more facts," or do you marvel at the intuition that produced it? |
Absolutely. 5 minutes a day of basic math facts drill. What's the big deal. |
I don't think the usual rap on Everyday Math is that it doesn't teach fluent retrieval of math facts. I've read two big complaints: first, that it doesn't teach the conventional algorithms for problem solving, so kids can get confused, or not gain mastery of the quickest way to solve a problem, and, second, that it spirals so aggressively that kids who love math are left frustrated that they had to move on before they had exhausted a topic and/or bored when they keep coming back to something they have already learned. |
bump |
Isn't this different for different learning styles, and if so, isn't it better to learn the broader themes without being bogged down in the mundane? |
I am also a mathematician. The multiplication table is one of the few things in math that need to be memorized, and the sooner the better. |
Thanks for your input. Based on what I've seen here, I thought less time spent on memorization was themain complaint. The second issue in particular does sound like a real problem. |
The presence of EM programs at Beauvoir and GDS were reasons why we did not apply to these schools. We had EM in DCPS and found it highly unsatisfying. The problem about not teaching conventional algorithms is a serious one. As a person who tutored basic maths extensively, I could see that many of the EM "ways" of doing problems were causing mistakes in computation. They are unwieldy and slow and hard to review for errors. In addition, although these alternative algorithms could have been used to show the basic underlying math computation works (i.e. principles of commutative or additive properties in math), the teachers were so math illiterate, they couldn't actually explain to the kids why they were using these algorithms or why they worked, thus negating their teaching value. IMO, if a kid tried to use EM to solve real math problems on a timed test, he wouldn't do very well... Also the EM alternatives would be terrible (IMO) for kids with attention/organization problems. The spiraling is also a serious problem. Most kids need repetition in problems to see their mistakes and correct them. In learning double digit addition/subtraction, one needs to make mistakes in carrying and computation. The process of do, get it wrong, figure out why and redo is very important. There is not enough repetition for kids to get this. The spiraling means that each pass thru a concept is shallow, and the next pass doesn't help because the kids didn't really get it the first time. It's as if someone was trying to teach you to throw a football in a nice tight spiral, but you're only allowed to try it yourself 4 times once a month, and nobody ever watches you and explains after you fail why you failed. When you get a chance to throw another 4 times the next month, you've forgotten how you're supposed to do it anyway, so you have to start all over, but since you only get 4 throws, you still don't get it.... |
Ex-Beauvoir parent here. I don't think Beauvoir has a strong math curriculum either but I don't have a major problem with EM. I think that it's fine to have multiple strategies for teaching kids math in the early years since there are different learning styles. The kid then can use his/her own approach to doing math. While EM needs more repetition, that's easy to supplement at home or as homework (or do Kumon). I think Beauvoir could have done more to reinforce basic math facts for kids who struggle with them. But for kids who have the concepts and the facts down, Beauvoir was very weak (and resistant) in offering extensions of those concepts - thus boredom for some the kids on that end of the spectrum. |