Students enjoy constructivist math in Ossining, New York, writes Samuel Freedman in the NY Times. But the kid who learned math in the traditional way in Catholic school is way ahead.

Worried that students fell behind in math in the upper grades, Ossining looked for a new math curriculum.

A math consultant, Dr. Benjamin Lindeman, prepared an audit that took as a starting point, a veritable first principle, the notions that “sitting and listening to the teacher” or “memorization and drill and practice” were failed methods.

Quite understandably, Ossining administrators decided to choose only from those curriculums bearing the imprimaturs of the National Science Foundation and the math teachers’ council – all of which just happened to be more or less constructivist.

The vast majority of the town’s elementary school teachers, after all, did not possess or claim any expertise in math; virtually all of them held degrees in education, special education, or reading education, and were more confident in their judgment, and more able to resist cant and dogma, in the humanities rather than in math. No rational person could blame them for assuming that the support of the National Science Foundation and the National Council of Teachers of Mathematics for a given curriculum should have amounted to what Jewish tradition calls a hechsher – proof a product is kosher.

This is a first-rate analysis of the problem, though it doesn’t pick a right answer.

“A math consultant, Dr. Benjamin Lindeman, prepared an audit that took as a starting point, a veritable first principle, the notions that “sitting and listening to the teacher” or “memorization and drill and practice” were failed methods.”

Of course. The usual ed school progressive, self-serving analysis and assumptions.

“The vast majority of the town’s elementary school teachers, after all, did not possess or claim any expertise in math; virtually all of them held degrees in education, special education, or reading education, and were more confident in their judgment, and more able to resist cant and dogma, in the humanities rather than in math.”

Of course again. Where are the high school math teachers? They are the ones who have at least some math background and have to deal with all of the poorly prepared students. They should be yelling and screaming. I know from personal experience that our lower school did not want any parental (professional) assistance in helping them select a math curriculum.

TERC! Quick, open a Kumon Math center. At least TERC is better (barely) than MathLand which they use in our public schools.

“Yet it is impossible not to be haunted by the image of Jimmy doing 23 times 16 while everyone else was charting multiples of two, and not to wonder if he knew something nobody else in the room did.”

There are many parts to this issue.

1. What material is covered in each grade.

2. How is the material taught or presented.

3. What (exactly) are the kinds of problems each student can do at the end of the year.

4. How much practice is expected of the student.

5. What kind of testing is done in class. (not state testing)

6. What level of knowledge and performance must the student meet before he/she can continue to the next grade.

Obviously, the TERC class teaches using different methods, but it also covers less material and has lower expectations. It is easy to get distracted by a discussion about direct teaching versus discovery learning methods when all you have to do is compare the types of problems each student has to solve by the end of the year. That will tell you all you need to know about who has the better mathematical ability. You can have all of the “reasoning” ability in the world, but if you can’t do the problems, it means squat.

rant mode on –

Arrrrghhh, this is what I’ve been yelling about for sooooo long. This is soooooooo stupid, these self-serving, self-righteous, pompous edufakers, quit experimenting with our kids. “Old school” has worked for years and years and years – the ‘new’ methods are slower, and the results are still in doubt.

Like I’ve said before, I can take most any kid getting C’s in Catholic schools and they will get A’s in public schools. Take most A students from a public school, put them in a Catholic school and in most cases they will need tutoring to catch up with where the class is at. Very few of them will be doing A work within a year, because so much more is expected of them and they aren’t use to having to do that amount and quality of work.

Memorization and drill work, I can’t tell you about all the ‘new’ methods, but history shows that memorization and drill works. Quit making the kids experimental hamsters. The folks need to stand up to all these stupid, simple ‘new’ math programs – force phonics, drill in math, learning REALLY hasn’t changed folks.

rant mode off –

You may now return to the regularly scheduled program.

When you’re in a hole, dig harder. Yup, “Dr”. (Ed.D. no doubt) Lindeman, that’ll really get you somewhere.

Investigations may be the worst of these awful curricula. (Priceless summary on the “Mathematically Correct” website: “The use of this program in our public schools is a strong argument for vouchers.”) Not surprising that a district that clearly has no idea what it’s doing would end up with the worst possible option. When in God’s name does this madness stop? How many kids’ futures have to be crippled before it stops? And the biggest crime is that it’s the kids from disadvantaged families who suffer the most- they don’t have parents who can just go ahead and teach them properly regardless of the school’s dereliction.

We pulled our older kid (and hence the younger one) out of public schools because of the crappy math curriculum. I can’t remember what the program was called, but it was horrifyingly bad. It’s a big struggle even in private school, because elementary teachers just don’t know any math, and so they don’t really want to teach it. Our kids are doing quite advanced work in school in “language arts” (the 8th grader is really doing college level work in English ), but there is no way that they would be doing comparable work in math if my wife and I weren’t taking care of this.

The idea that a first course in calculus by the end of high school is high achievement for a select few is actually depressing, and the “Stand and Deliver” story shows that it’s expecting much too little. But filling kids’ heads with this kind of “whole math mush” and precluding even the best students from learning any math infuriates me.

In liberal Minnesota, we are fortunate to have some friends in higher ed who lend their math expertise to those of us with kids in “fuzzy math.” Check out Dr. Lawrence Gray’s perspective at http://www.edwatch.org/drgray.htm. We also have some very active parents who have successfully battled these new new math programs, and brought back traditional math instruction to K-12.

While I could see the value of constructivist education on a subject like sciences, where experiementation is common, it is more than worthless in mathematics. Two plus two is four, and always will be. Children need to learn the basic facts of mathematics, and there’s really no reason to construct a different framework of knowledge. There is only one answer!

One idea behind construtivist math — an idea which is pathetically misguided — is that mathematics is in some sense discovered, and so we should teach kids how to discover things for themselves. While it is true that mathematics is discovered (or invented, if you prefer), it’s essential to know things first. The fact is that all of the good math teachers I’ve ever had (most of them in college and graduate school) engaged students so that they “discovered” things while being taught them using a curriculum that was of the old-fashioned kind.

I don’t believe that anyone can teach anything with the 2 constructivist curricula that I’ve seen, since they were both full of mistakes, nonsense, and worse.

You know, upon re-reading of this item, this part stands out to me (no more ranting, I think) – “…The vast majority of the town’s elementary school teachers, after all, did not possess or claim any expertise in math…” – Well, wait a minute, we’re talking 4th grade math folks. As I recall, we’re still in multiplcation, division, adding and subtracting. If you can’t teach that stuff, it means you didn’t learn it well enough yourself.

I don’t have ANY kind of teaching creditials (nor do I ever wish to get any) but I KNOW that I can teach – I use to tutor, and it was algebra. I use physical props, I draw it on paper, I use whatever means are necessary to get the idea across. I use to tutor in college (algebra) and I am helping my daughter in her freshman high school algebra classes. Folks, we’re back to basics here, if a grown man or woman who went all the way through and is now a qualified teacher, can’t teach 4th grade math, we REALLY need to re-assess what we allow to be minimum qualifications for teachers.

I have problems with both sides:

My own math education focussed a lot on the sorts of drills and straight equation solving side of math. I was good at it, if I do say so myself – I have a good memory for numbers, and once you learn each type of equation, its just memory and attention to detail to solve it.

I started to then pursue a higher education in math and was totally bogged down. I was VERY bad at the sorts of proofs that are required in say, proving why the short cuts we use in calculus work. I gave up pretty quickly, and moved on to writing and sociology, where my math background made statistics a bit easier.

I wonder, though, if those sorts of proofs had been part of my early education, whether I would have been able to go further than I did.

Day-to-day problems are best solved with the rote memorization stuff, but there is a lot of bad sociology and economics out there, for example, because the people who try to analyze the statistics don’t know enough about the concepts to apply the right tests. They just use the standard tests, often incorrectly.

mike from oregon wrote:

“Arrrrghhh, this is what I’ve been yelling about for sooooo long. This is soooooooo stupid, these self-serving, self-righteous, pompous edufakers, quit experimenting with our kids.”

Actually, the problem is educators are NOT experimenting with our kids. If they had bothered to do an experiment of say 10,000 kids randomly assigned to either a traditional math curriculum or a constructivist curriculum, we would KNOW which was better. By purporting to KNOW which is better without experimental studies, the educrats are more akin to purveyors of snake oil. The snake oil might be good for you but we have to take it on faith. That faith is in short supply given the history of education in the US over the last few decades. When they do studies to test their theories that give high quality results, we won’t have to have this type of debate.

Left in Texas, your comment really is beyond the range of this discussion, which is about the teaching of arithmetic in elementary school. But here’s something for you to worry about. Traditionally, geometry is the high school math course in which the concept of rigorous proof is first introduced. But I understand that the current trend in geometry curricula is to deemphasize proofs, or in extreme cases even to neglect them altogether.

Stephen,

I guess my point was, that maybe if I had learned a slightly more constructivist approach to math early on, proofs might have been easier later in life. Maybe not, either.

To me, it sounds like the debates between phonics and whole language – pure forms of either don’t work so well, although pure whole language is somewhat more disastrous, from what I’ve read.