Comments

Congratulations! This is great!

I'm telling you: with kids, nothing is written in stone. But the verdict's still out for adults.

-- CarolynJohnston - 14 Jun 2005

Boy, that's for sure!

I've got to get the Wayne Wickelgren stuff posted -- about most kids not liking to learn math, even when they're good at it.

-- CatherineJohnson - 14 Jun 2005

When my daughter tells me she hates math, my response is always the same. "Well, I have good news for you. You don't have to like it. You just have to know how to do it." She's stopped telling me she hates math. We shouldn't be so concerned with whether kids like or hate something. I hated history and English, but you either toe the line or get bad grades, and I didn't want bad grades. In terms of math, kids hate it when they can't do it. When my daughter catches on to something, she likes doing it. Math is not easy sometimes and it takes work, and that message should also be imparted to children. Not that it's impossible; but that it can be difficult, and that we all had to work at it. When math isn't taught properly, then kids are not able to do it, and then they hate it. I've been talking to various adults lately who fit the description NCTM wrote about in the Jay Mathews' Post column of May 31 in which they talked about adults groaning when they heard the familiar story problem about distance, rate and speed. (A man starts out at 9 AM at 15 mph, etc etc). The adults I talked to said they hated those problems because they couldn't do them. When pressed, they admitted their teachers were not very good. This is not a definitive sample by any means. I lucked out and had a very good algebra teacher who gave us very good instruction on how to solve story problems. As a result, I liked them. The fact that I ended up majoring in math may or may not be coincidental. Barry Garelick

-- BarryGarelick - 14 Jun 2005

When my daughter tells me she hates math, my response is always the same. "Well, I have good news for you. You don't have to like it. You just have to know how to do it."

I love it!

In terms of math, kids hate it when they can't do it. When my daughter catches on to something, she likes doing it. Math is not easy sometimes and it takes work, and that message should also be imparted to children.

Absolutely, and this is a very important area to talk about -- one of the joys of math at the elementary level, which is being stripped away by constructivists, I believe -- is the joy of repetition.

Children like 'structure' . . . and structure is, at heart, repetition.

The whole idea that children should be exposed to constant novelty in mathematics at the age of 6 is simply wrong when it comes to promoting appreciation of the subject, a stated goal of the NCTM, I believe. (I haven't checked--)

Solving a problem 'in more than one way' may be pedagogically sound, or it may not; this is a complex and fascinating area.

But requiring children to solve-a-problem-in-more-than-one-way will not increase children's liking for math.

For children, repetition is fun; constant novelty is not.

Children are the ultimate Who Moved My Cheese people.

-- CatherineJohnson - 14 Jun 2005

"You don't have to like it. You just have to know how to do it."

I agree 100 percent. When did schools start rejecting this philosophy? I said to one teacher that I wanted my son to know the value of hard work and that for many valuable things in life, the payoff is way down the road. She gave me a funny look. My son is taking piano lessons and is required to practice his scales, arpeggios, and fingerings using Hanon. Can one ever play Chopin without technical skills and lots of practice? Is it OK just to understand(?) Chopin (as a pianist), but not play it very well? Or, is true understanding indelibly linked with technical skill? One ed school professor told me once that he understands all about soccer, even as a referee, but he can't play it at all, as if this understanding is all that the school needs to provide. The problem is that I want my son out on the field, not in the stands. Then again, the question is: Do you really understand something that you cannot do? The ed school professor was trying to say that understanding is understanding and skills are just rote. I completely disagree.

Actually, when my son was born, I told my mother that I wanted 3 things for him in life: 1. To care about other people. 2. To know the value of hard work. and 3. To be happy. Her response was that if he did numbers 1 and 2, then number 3 will take care of itself.

"When my daughter catches on to something, she likes doing it. Math is not easy sometimes and it takes work, and that message should also be imparted to children."

Exactly! The general refrain is that long ago, kids did poorly in math because it was taught incorrectly. We now know what and how to teach. Could it be that kids do (and did) poorly in math because it is concrete, exacting, cumulative and requires practice? Math is unlike any other subject; one poor teacher or a few unmastered methods and it can be all over. The joke is that the old way was all skill and no understanding and the new way is all understanding and no skill. Poor understanding can be overcome, but lack of skills cannot. Lack of understanding was due to poor teaching, but lack of skill is now part of the curriculum.

"When pressed, they admitted their teachers were not very good."

Schools can't admit to this nowadays because the whole premise of NCTM math is that what was taught and how it was taught was the problem. Do parents think that NCTM math has found some magic way to do word problems with more understanding and less practice?

-- SteveH - 14 Jun 2005

"Solving a problem 'in more than one way' may be pedagogically sound, or it may not; this is a complex and fascinating area."

If Everyday Math (as an example), thinks that doing things in different ways is helpful, then why do they completely avoid the standard algorithms (the best ways)? While doing Singapore Math with my son at home, he ends up doing a number of things in different ways than his EM at school. This can be helpful, or it can be an overload of the brain. Is it helpful to teach kids the Lattice Method, Partial Products, and the traditional algorithm? Probably not, unless you want them to see algebraically how they all work and how they are related. To do this properly would require knowledge that they don't already have. I'm not sure that this would be the best use of time even in a later grade.

NCTM has this real hang-up with doing things in more than one way, as if this isn't common in mathematics. Math and engineering are all about solving complex problems in different (presumably better) ways. The key word is "better". Why would an engineer use an older technique when a newer, better one exists. The technical literature is filled with friendly competition between groups vying to come up with better solutions. Some methods follow different paths of development, each with their own adherents. This competition is fascinating and I have spent a lot of time following developments from one technical paper to the next. The point is that there may be many ways to solve a problem, but the goal is to find an easy or best way. I can't tell you how excited I was when I found out how to apply line integrals using a very simple algorithm. (I don't think it's possible for me to rediscover Green's Theorem.) No more Simpson's Rule! This is now a tool that I use in all sort of creative ways. For learning, it may be important to learn the history of development and to learn different ways to do a task, but the goal is to add the best skills to your mathematical toolbox. NCTM math seems to think that the process is important, not the toolbox.

My specialty is geometric modeling and computer graphics. For some problems, there is a well-defined, tried, and true way of solving the problem. You would be crazy to do it any other way. As the problems get larger or different, there will be many paths towards a solution. Math, however, has never been about rote solutions of complex problems. It's about developing your mathematical toolbox of standard techniques (well mastered) that you can apply to a variety of complex situations. It may seem like math is just "rote" when learning the basic mathematical skills or tools, but there better be a good reason for spending a lot of time having the kids learn various methods or creating their own method.

Math and engineering are very creative fields. You just have to get through all of the basics. It's fine that reform math methods want to make this process easier or more interesting, but they waste a lot of time trying to show that there is more than one way to do the basics and that mastered skills are not very important.

-- SteveH - 14 Jun 2005

Steve--I've got to run, but when I get back I'll pull your observations about the competition to find better ways up front. I've had a similar email from a friend who works with engineers.

-- CatherineJohnson - 14 Jun 2005