from 2007: Siegfried Engelmann teaches fractions to disadvantaged 5-year olds

Excerpt from Siegfried Engelmann's War Against the Schools' Academic Child Abuse:

In the summer of 1966, the Anti-Defamation League expressed interest in making a film showing the achievements of the disadvantaged black preschoolers we had been working with at the University of Illinois. Two years earlier, these kids had been selected for the project as four-year olds on the basis that they came from homes that were judged particularly disadvantaged and nearly all of them had older siblings in classes for the mentally retarded. These kids came to our school half-days as four-year-olds and as five-year-olds.

The school, The Bereiter-Engelmann preschool, received a lot of bad press. It was called a pressure cooker. Sociolinguists took shots at it on the grounds that we ostensibly did not understand "black English," or even know the difference between "thinking and speaking."

Despite our alleged mental deficiencies, we managed to teach these kids more and make them smarter than anyboy else had done before or after. That was our goal, particularly with this first flight of kids--to set the limits to show what could be done. We felt that this demonstration was particularly important because Headstart was looming in the wings, and it was clearly moving in a direction of being nothing more than a front for public health, not a serious educational project. We saw this as a great contradiction because disadvantaged kids were behind their middle class peers in skills and knowledge.

We taught reading, language, and math to our preschoolers. And they learned these subjects. They also learned to learn well and therefore how to be smart. A film showing what these kids could do might moderate what seemed to be the inevitable mandate of the Office of Economic Opportunity to designate Headstart as a "social experience" based on the model of the middcle-class nursery school. It seemed obvious that the model would not work.

We rounded up seven of the kids who were in our top group. (We grouped kids for instruction according to their performance.) They were in the middle of summer vacation, and we didn't have an opportunity to work with them before the film to "refresh" or rehearse them. A professor at the University of Illinois found out about the filming and asked if she could bring her class to view it. Why not?

So seven little black kids came into the classroom, sat in their chairs in front of the chalkboard with big bright lights shining on them, with two big cameras on tripods staring at them, and with a class of university students in the background. And these kids did it. There were no out takes, no cut sequences, nothing but the kids responding to problems that I presented, the types of problems I had taught them to work. These were not necessarily the problem types that one would present preschoolers as part of a 12 grade sequence, but they were good problems to show that these kids could learn at a greatly accelerated rate.

On the film, the kids worked problems of addition, subtrction, multiplication, and fractions. They worked problems in which they found the area of rectangles and problems in which they found the length of an unknown side of the rectangle (given the number of squares in the rectangle and the length of one side). They worked column-addition problems that required carrying and problems that did not require carrying. They even worked problems involving factoring expressions like 6A + 3B + 9C. And they used the appropriate wording: "Three times the quantity, 2A, plus 1B, plus 3C."

The kids told me how to work a simple algebra problem: "The man at the store tells you that 1/4 of a pie costs 5 cents. You want to buy the whole pie. How much is the whole pie?"

After telling me how to work the problem by multiplying the reciprocal of 1/4, I wrote the answer as $20. The kids jumped up to correct my sign error, one boy observed, "Wow, you have to pay that much for a pie?"

And the kids did dimensional analysis involving the equation: A + B = C. They told me how to rewrite the equation so it told what A equals (A = C - B), what B equals (B = C - A), and what C equals (C = A + B).

The last problem type I presented on the film was the simultaneous-equation problem:

A + B = 14
A - B = 0

They had worked on similar problems in which A and B were the same size (inferred from A - B = 0) and they quickly told me that the numbers were 7 and 7. There was still time left so I presented them with a brand new problem type:

A + B = 14
A - B = 2

I pointed out that when you start with A and minus B, you end up with 2. So A is bigger than B. They frowned, they thought; and finally the little girl sitting on the end of the group -- who is now an engineer -- said in a wee voice, "8 and 6." These were kids who had not yet entered first grade.

The film made no difference in deterring Headstart from becoming a program that produced no real gains. Nor did it give notice that failure with disadvantaged kids was a failure in instructional practices. We had shown , however, that all the disadvantaged black kids we worked with could learn to read and perform basic arithmetic operations in the preschool and that the average IQ gain of these kids was 24 points.
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I tear up every time I read this.

The children of the poor don't need lessons in good character.

They need knowledge.  Head Start

Film of Engelmann teaching preschoolers 
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