Teaching skills
On the teaching of slow students
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On the teaching of slow students
First of all, let us acknowledge that every human will find some subjects difficult to learn. Therefore, in some situations, we are all slow students. Indeed, it is only by visualizing yourself learning a subject you find difficult, in a classroom where you feel inferior, that you can begin to understand how to teach slow students.
Then, all you have to do is answer this question: How would I myself like to be taught this subject?
Invariably, the answer will be the same for everybody, from the beginning of history to now. You want to be taught patiently and courteously, small step by small step. You want to feel confident, you want to feel youre making progress, you want to feel that everything is unfolding the way it should. You feel relaxed. You think, hey, this might be fun.
Conversely, you never want to feel that you are falling behind, that you are too dumb to understand the subject, that the other people understand it better than you, and that the whole effort is a waste of time.Such negative feelings, can be inspired in the first minutes of the class if the teacher says something that is too abstract, vague, convoluted, technical, or ahead of where you actually are.

Instead of starting with the easy detail, many courses start with difficult information, mysterious details, or big generalizations that make sense only if someone already knows the subject. Soon the students are shaking their heads and worrying that nothing good will come of this course.
Keep in mind, the moment a student feels 10% behind the others, this student will shut up. He will not be comfortable asking questions, or answering questions, because whatever he says is sure to reveal just how slow he is. He does not want to embarrass himself.
One of the ways we all knew that New Math was completely fraudulent is that it wanted to teach elementary kids about Boolean algebra, matrices, base-8 and other advanced topics. This guaranteed confusion for everyone except future math professors. Reform Math continues to use the same nutty idea. New Math and Reform Math show exactly the wrong way to do things.

Here is how it should be done. Whatever a teacher says, the students should react: Yeah, I get that. No problemo. Theres the golden gate to all pedagogical success.
Now suppose a teacher could put together 50 assertions that inspired exactly that response. 50 assertions add up to a lot of progress. Now students are deeply into the subject. Clearly, its the teachers job to find the 50 assertions that even the slower students will quickly grasp.
By all accounts, schools of education waste a lot of time on trivial material. Instead, they should be teaching how to identify the simple bits and arrange them in an ideal sequence. The students could take turns trying to solve the problem of how to teach chemistry, biology or American History. There’s room for a lot of creativity in these areas.
As a college student I had to take calculus and found it very difficult. I was a slow, slow student. My failure in this subject has given me a personal frame of reference for how things should and shouldn’t be taught. What is your own worst subject? You might find it very edifying to search that term on Google or in encyclopedias, and find out how various experts believe that subject should be explained. Quite often, unless you already know a subject, you wont understand what theyre talking about. So you can explore the question: how should these people be teaching this subject to me?
Lets consider how Stephen Wolffram, a famous mathematician, starts his lesson on calculus: In general, a [sic] calculus is an abstract theory developed in a purely formal way.
I have no idea why he thinks that is going to draw students into his presentation. His next sentence is: "The" calculus, more properly called analysis (or real analysis or, in older literature, infinitesimal analysis), is the branch of mathematics studying the rate of change of quantities (which can be interpreted as slopes of curves) and the length, area, and volume of objects.
Wolfram doesnt know how to teach calculus to people who don’t already know the subject. He might consider putting his huge intellect to work on this question: how then should we teach complex subjects to simple minds?
In 1953 a young schoolteacher named Joan Dunn wrote a book about her experiences in Brooklyns public school system. I think this is one of the most profound passages ever written about education, especially the last sentence: The time that should have been devoted to school work in reading, writing, thinking, and speaking is given over to chatter. Nobody knows this better than the children. They want to be taught step by step, so that they can see their progress. The duller they are, the more important and immediate is this need.
The slower they are, the more carefully they need to be taught. Meanwhile, bright kids will figure things out and survive. It’s the not-bright kids that desperately need to be carried along. But everything in our public schools does the opposite. Reading is taught in a way that will destroy the slower kids. Ditto arithmetic. Everything is taught in ways that will destroy the slower kids. Someone seeing a pattern here?
Whatever you want to teach, make a list of the 100 most interesting facts covered by that field. Arrange them in a sequence from easiest to less easy. So the first minute of the first day, you will tell students the single most interesting/easy tidbit in your field.