What do we learn in school?

Sometimes I think about my old friend Pete. He was a real friendly guy, very tall, was a great person to have fun with. I think I met him in 7th grade or so, and last saw him when he was 22 or around there and he was doing pretty well at that time.

One day when he was around 21, he asked me to read to him a letter he had gotten, and so I did, and then he thanked me and admitted he didn't know how to read. I thought that was pretty interesting since he had graduated from high school without any problems and asked wow, how did you do that. He said it wasn't really an issue, it was never necessary to know how to read. This was an astonishing claim and I wondered if there was some exaggeration about his lack of skill. Some brief questions revealed that he was totally illiterate. He couldn't read at all.

How did he manage to pass tests, I asked. He said that he was just able to do it.

Why didn't any of his teachers have special classes for him or anything? The answer was that in 13 years of schooling, none of his teachers had noticed he was illiterate. He certainly would have been glad to get some help in this, but the topic never came up in school and he didn't even think such extra help was possible in any case. This was a top rated school in a very well regarded district.

I found the situation very interesting for two points.

First, it appeared that reading was not a necessary skill in schools, and perhaps in life.

Secondly, I found it very enlightening to know that a student could make it through 13 grades, which is 1+6+6*6 = 43 separate teachers, and none of them had noticed in any fashion that he was completely illiterate, and all passed him. He never repeated a grade or a class.

A few years later, I worked as a math and physics tutor at a community college. I was the only one in the program able to teach calculus. This worked out fine because most of the demand in the program was not for calculus, but for very basic skills. How basic? I had access to placement statistics. Around like 70% of students needed remedial math. About 50% of students placed only for the bottom most class for math. This class, which was called Concepts of Numbers or some such, how to count to 100, which number is bigger than the other, and what is an integer. The second class after that got into addition and subtraction, fractions and powers of ten. I would say these classes corresponded to kindergarten and first or second grade respectively. I was not able to teach these classes because I would not know where to start with this when dealing with an adult college student, but I did observe and interact with those that did, as well as hundreds of students in the student body and most students genuinely did not know how to divide numbers or what fractions were. Most could actually count and do addition and subtraction given paper and time, but they made mistakes. This was a pretty good community college in a good area.

A few years later, when I was at the state university, I observed similar levels of math competency, though the numbers that were at this level were smaller, more like 20% of admitted students did not know fractions or how to divide. But that was an exclusive school that only took the 5% of top high school graduates, and required high SAT scores for admission.

Years after that, I tutored in a program for homeless people and saw similar levels of competence, which led me to realize that lack of education was not a problem for homeless people since their skills level was average for the population.

From these and other experiences over the years, I realized that the normal situation in the US for the majority of graduates is that they know how to add and subtract and count, and can do multiplication. But they do not understand fractions at all, and can not do long division at all. Algebra is completely beyond most high school graduates, even though they took two years of it and passed.

I could see that people probably had abilities only that were necessary, and knowing how to divide is simply not something people do. Fractions are only understood to the extent that if you need 1/2 cup of flour, you fill the cup up to the mark that says 1/2. Dividing a recipe in two or doubling it is not possible, except to measure that 1/2 cup out twice.

I was not sure how students could pass algebra though and not have any ability or understanding of it a couple years later. Had they simply forgotten?

The answer came when I worked teaching high school math and computers. My math students had completed "advanced algebra" and were prepared for a challenging textbook in geometry. The results were disasterous. It took me a half semester before I figured that the reason most of the students could not solve the problems or understand things is they knew no algebra at all, but believed that they did since they had passed, often with high grades. In asking them in detail about how things worked, I discovered that algebra was taught by the teacher assigning problems, then giving the answers, then guaranteeing that only the homework questions would be on the test and only as multiple choice questions.

Students were shown:
y + 2 = 6, y = ?
The next day, they were told:
y + 2 = 6, y = 4
was the answer. They memorized it and picked c from a list with their #2 pencils:
a) y=0
b) y=2
c) y=4
d) y=6

If you asked them instead to solve this problem:
y + 2 = 5, y = ?
... they could not solve it. They were completely stumped. They complained the question was unfair to have on a test because that was not one that they were 'taught' in class.

This was the only way for the students to 'learn', other teachers told me. In this case, 'learn' meant to pass the multiple choice test. And how they did that was not by learning concepts of algebra, but by memorizing the correct answers, and then being able to recognize them from a list of multiple choice. Students had developed excellent abilities to memorize useless and arbitrary data in order to succeed, and their teachers were happy with these results.

So at last I understood how my buddy Pete had managed to pass all those tests.