## A math-schooled mind is a chloroformed mind

Thursday, January 24th, 2019

For decades since Benezet’s time, educators have debated about the best ways to teach mathematics in schools:

There was the new math, the new new math, and so on. Nothing has worked. There are lots of reasons for this, one of which is that the people who teach in elementary schools are not mathematicians. Most of them are math phobic, just like most people in the larger culture. They, after all, are themselves products of the school system, and one thing the school system does well is to generate a lasting fear and loathing of mathematics in most people who pass through it. No matter what textbooks or worksheets or lesson plans the higher-ups devise for them, the teachers teach math by rote, in the only way they can, and they just pray that no smart-alec student asks them a question such as “Why do we do it that way?” or “What good is this?” The students, of course, pick up on their teachers’ fear, and they learn not to ask or even to think about such questions. They learn to be dumb. They learn, as Benezet would have put it, that a math-schooled mind is a chloroformed mind.

In an article published in 2005, Patricia Clark Kenschaft, a professor of mathematics at Montclair State University, described her experiences of going into elementary schools and talking with teachers about math. In one visit to a K-6 elementary school in New Jersey she discovered that not a single teacher, out of the fifty that she met with, knew how to find the area of a rectangle.[2] They taught multiplication, but none of them knew that multiplication is used to find the area of a rectangle. Their most common guess was that you add the length and the width to get the area. Their excuse for not knowing was that they did not need to teach about areas of rectangles; that came later in the curriculum. But the fact that they couldn’t figure out that multiplication is used to find the area was evidence to Kenschaft that they didn’t really know what multiplication is or what it is for. She also found that although the teachers knew and taught the algorithm for multiplying one two-digit number by another, none of them could explain why that algorithm works.

The school that Kenschaft visited happened to be in a very poor district, with mostly African American kids, so at first she figured that the worst teachers must have been assigned to that school, and she theorized that this was why African Americans do even more poorly than white Americans on math tests. But then she went into some schools in wealthy districts, with mostly white kids, and found that the mathematics knowledge of teachers there was equally pathetic. She concluded that nobody could be learning much math in school and, “It appears that the higher scores of the affluent districts are not due to superior teaching but to the supplementary informal ‘home schooling’ of children.”

It must be the supplementary informal home schooling…

1. Schmendrick says:

Can’t testify for anyone but myself, but in my case yes, it was the “supplementary informal home schooling.” I went to school in an allegedly very good school district in suburban southern California, but had absolutely cruddy math teachers. My 7th grade math teacher, for example, had been a life-time english teacher until he pissed off the wrong administrator and got reassigned to us. He was incredibly nice and taught me quite a lot about baseball, but knew absolutely nothing about pre-algebra or geometry, or even the order of operations. My dad (a Ph.D. in nuclear engineering) tried to make up for the shortfall by going over my homework with me. I’m still no great shakes at math (and never got more than middling grades in anything above trigonometry), but I’m halfway competent at day-to-day stuff and am a dab hand at excel. I’m confident that it’s almost entirely down to my dad.

2. Graham says:

I went to public school in Ontario in the 70s and 80s and have no idea if the methods used to teach us qualified as old math or new math in terms of those systems in the US. I was aware of “new math” mainly from despairing references by TV and comic strip characters.

I never did as well in math as in word-based subjects, and certainly was not going to do math at university level. I can come to no real conclusion as to whether that is a matter of humans having innate tendencies toward or abilities with math, or is purely a matter of instruction method. I lean hard toward the former, since so many other things about a person’s abilities seems to have a major hereditary component, and even tendencies and interests in subjects seem to resist shaping.

But I’m open to instruction based arguments. I instinctively question them in other areas, but with math I’m not so sure.

I am unconvinced any method would have made be more inclined to it, but comments on an earlier post made me wonder. I tended to 70s in math or sometimes less, where I made 80s-90s elsewhere.

I don’t quite get the problem with the basic symbols of arithmetic notation or see why one would need to change them, especially to a purely brackets based system. That seems more confusing. I see more of a problem when it comes to order of operations, though in the end it just seems like a hierarchy one would have to accept and internalize, since one would be needed, and I’m not sure standard notation fails unless someone will here point out that it becomes hopeless in trig or calculus. Or is relevant. It never seemed a problem in HS algebra.

One thing I dimly remember from junior grades was having difficulty internalizing the system for doing subtraction on paper. Addition, easy peasy. Multiplication too.

Division was interesting. Somehow I got taught a method for short division first, then struggled when they wanted to make us use long division, then struggled anew later when they wanted us to use short division. No idea whether that was old math versus new, or just a skewed curriculum unsure what to teach first.

All basic stuff, but I’m not sure whether the method or notation was the problem, or just me.

One thing for sure, I could be taken as far as algebra in 12th grade, but no farther, and I could not solve those equations today.

If there’s something in education that could make math more intuitive than that for the likes of me, then I’d listen even now.

3. Graham says:

I rather thought the point of educating every kid with a bit of everything, the eternal answer to that snotty question about “when am I ever going to use this in life?” or “I am not interested in this, why can’t I study what I want?” would be fourfold:

1. You must be exposed to as much as possible and tried and tested in it, so that we may as much as possible catch the fire in those who can be interested in each aspect of knowledge.

2. You must be exposed to as much as possible so that you come out with some lingering notion of what humanity has accomplished, and be aware of as much as possible so that you can look up information or seek help from the right sources later.

3. You must be exposed to as much as possible so that you have some idea of the scale and glory of the human achievement, the possibility that you might someday have something to offer through using it in your life, your duty to preserve it, or to take any chance to add to it.

4. You must be brought to understand the scale of your own ignorance compared to the total of what humanity has learned and thought.

4. David Foster says:

““What good is this?”

A math professor I knew was asked this question by a student…

Professor: You use it to make the atomic bomb.
Student: HOW do you use it to make the atomic bomb.
Professor: That’s classified!

5. CVLR says:

“It must be the supplementary informal home schooling…”

In my experience, this is literally true.