Gifted Issues Discussion homepage Forums Learning Environments Conceptual mathematics

Just found this on the CNN website. It's a piece about a conceptually based approach to teaching maths. I guess these approaches are seductive on the surface, but they break down when you look at them more closely.

For example, why must this method exclude long division? Isn't long division simply another valid approach? If so, then why can't they teach it? I don't understand this at all.

Also, their "conceptual" approach to multiplying may work for 88*5 (see article), but will likely break down for almost everyone for 59877.26*6475.458. <sigh> The gifted kids will have figured this out on their own, and the others won't have learned how to multiply the old-fashioned way and so won't be able to solve the problem without a calculator.

Math Fad

It's like they're going to the other extreme from too much drilling.

Val

Yes, Val. I'm so happy that someone else saw this.

I read this article on CNN and had to laugh. I thought I was a lone, secret rebel in teaching my kid math the old-fashioned way. DS8 has Everyday Math in his PS. While it is not too terrible for most subjects (fractions are introduced in 1st grade, lots of geometry and 3-D shapes, and tons of word problems for math.. to name a few), it does a horrible, horrible job of teaching division in 3rd. The emphasis is on getting a "ballpark estimate" first, before explaining to the kids how do actually do division. For example, if the problem was to divide 529 by 13, they would emphasis that it is about 40. (in a very hand-waving way). Our problem arose in that DS had to have a firm understanding of size and scale, or he would start out trying out too small of a number for the ballpark estimate and get frustrated and quit. (13x5, no too small... 13x7, no too small.. this was a long, long approach to get to 13x40!!)

So after about 25 minutes of sheer frustration, I finally said look... here is the easy way, and showed him long division. He could do all of the problems easily after that.

I understand the importance of being able to do rough math in your head quickly. But maybe this should be a refinement AFTER the basic concept has been mastered.

Oh and Everyday Math teaches multiplication using two different method (as an extra way to confuse the kiddos!)... the lattice method and the partial products method. Neither are made for multiplying large numbers.

Is anyone else stuck with this type of math program? Our school has been using it for 4 or 5 years now, and the scores on the state achievement tests appear to be going down in math proficiency.

I try to expose my dd8 to as much math as I can from different sources. She is currently working on CTY's Math Olympiad (approaches to problem solving), Life of Fred (beginning Algebra), CML sample problems etc. She is also working on probability and statistics.

Although it seems like we are all over the place, the truth is that we for the most part follow the classical path in mathematics and we always come back to the core. She is free to explore and taste higher level math than what she is currently working, but not at the expense of the basic skills, but rather in addition to.

As much as I like some of the aspects of Conceptual Mathematics, I also believe in memorizing times tables, learning long division and learning how to multiply as well as other basic arithmetic. I try to expose my dd to number theory and higher concept math, but basic arithmetic is still the foundation on which everything else is built upon. I have tried to make sure that foundation is strong. I think it gives her more freedom to explore new ideas.

One of the benefits of being highly gifted is the ease with which they understand and absorb new things. They don't have to be limited to one method over the other. The fact that they learn everything so much faster than ND kids, gives them a lot of extra time to play with new concepts/ideas. They just have that much more time.

Dottie,
I like the word problems that Everyday Math seems to emphasize. They do a wonderful job of getting kids used to picking the facts out of a story in order to solve a math question. That is a skill which will become very useful when planes start flying at 550 miles per hour with a northwest wind blowing 15 miles per hour <smile>... or with physics word problems. And they do a great job of introducing ideas early on in a very general way... like fractions. But sometimes I think they have decided that the whole, big picture for something like division is too complex for the wee little minds, and that they need to approach the topic from a circuitous manner. That is the only issue that I have.

DS's school does a fair amount of time drills. I don't know if this is supplemented by the school or if it is part of the Everyday Math curriculum.

I'm not sure I love "Everyday Math," and I can't imagine not teaching long division at all. That's weird. But I do like conceptual math for my conceptual kid. I'm glad that I can teach him how he learns best as an individual. Memorizing times tables at 6 was killing his love of math. Learning concetual geometry got him excited to do math again, so I see the benefits of the big picture.

BUT (and it's a BIIIIIIG "BUT"), I think teaching a roomful of kids at all levels of ability is a TOTALLY different animal than teaching one GT kid at home, where we can adapt as needed and fill in gaps when we need to. I think the more methods the school can use to reach kids, the more like they are to reach all of 'em. Not all kids respond well to "big picture" math, and I think teaching algorithms is necessary, too.

I just don't understand the false dichotomy of the "math wars". The standard algorithms are just methods for solving problems. I don't think we should be teaching kids ANY algorithms without explanation. We can explain the standard algorithms just as other methods in Everyday Math are explained. What's different? They should be a part of everyone's problem solving tool box.

I agree CathyA. They make a false dichotomy. But as in everything, it has to be polarized...there is never a middle ground. Well, some schools have found it by modifying EM. A friend's school does that and that district has had great results w/ EM and the kids love it. OUr district modifies it (well at least his teacher did, I didn't find other teachers who did what she did) so there was only the standard algorithms in 2nd grade anyway.

The problem I've seen w/ EM is that they are using mental math algorithms used in Asian countries for written work. It's just plain incorrect. Many of the algorithms in EM are the basis for mental math in RightStart and Singapore Math but they are for mental math, not written math.

Example:
56+32 - mentally you'd do 56+30=86, 86+2=88

EM algorithm:
56
+32
______
80
8
______
88

That makes no sense to me. Rather than giving kids a strong foundation in place value, I think it's confusing after you've just spent a year looking at:
6
+2
----
8

so now the kids see:
6
+2
---
0


Here's a link to the EM algorithms.
http://www.math.nyu.edu/~braams/links/em-arith.html

Sing it, sister! I especially like this sentence:

Also, EM is not EM is not EM.... in the article the mom complained they got no books home or any explanations. We got sheets home explaining it as well as the Homelinks book which the homework sheets comes from. I think as in any curriculum, it may not necessarily be the curriculum but it's implementation. As good as Singapore math is, many drop it b/c it doesn't work for them either b/c they are not implementing it correctly or it's not a suitable fit for that particular child. The big thing w/ EM is supposed to be the games...that's where the kids practice and cement the facts. Well, guess what the teacher cuts out b/c of lack of time? the games. In one district, the parents received a letter saying it was the parents responsibility to drill the math facts at home and play the games. We also got a book with game ideas to play a few times each week. I hear the same story with RightStart math - it's too conceptual, my kid doesn't get it etc but when asked if they play the games "Uh no, we don't have time to play the games."

Good point, Dazey. You're not the first I've heard to proffer that criticism of the EM implementation. You can't cut out the practice opportunities and then be surprised that the system breaks down.