kitchen table math, the sequel: Engelmann teaches fractions to disadvantaged 5 year olds

Wednesday, March 14, 2007

Engelmann teaches fractions to disadvantaged 5 year olds

from 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.
pages 1-3

I tear up every time I read this.

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

They need knowledge.


Unknown said...

Wow, what a touching story!

You're right. They don't need lessons in character from a school - parents, caregivers, relatives, clergy should have this responsibility.

Anonymous said...

Does anyone know where these kids are now? Is there a follow-up?

And can we stop with the name calling. This blog used to be informative and increased my knowledge. I miss the old days. Sigh...

palisadesk said...

There was no official follow-up -- that would have required funding, etc. However, Engelmann kept in touch with those students over the years.

One day I phoned Engelmann-Becker offices in Eugene about something different and was privileged to speak with Engelmann himself. I immediately asked about those children. He told me they had had one or more reunions and these kids had continued to do well in school, despite attending rather poor inner-city elementary schools. They finished high school, some, maybe most, went to college and have "middle class" occupations. One (a girl) became an engineer (electrical engineer, I think); another is a loans manager for a major Chicago bank, another became an officer in the Marines. They did well for themselves and their promising beginning did not "wash out" the way many other early interventions seemed to do.

I suspect a major reason is the affective benefit of the preschool program -- the children saw themselves as smart and capable and were not discouraged by having to work hard to "get" something. They were confident they could succeed. If our ideas of self-efficacy are shaped early, as many psychological studies suggest, this (along with their skills advantage) goes a long way towards explaining their further success in life.

I have the peer-reviewed article about the success of the program.

I'll see if I can post some of the conclusion.

palisadesk said...

Here's more on the preschool program:

Engelmann, S. (1970). The effectiveness of Direct Instruction on IQ performance and achievement in reading and arithmetic. In J. Hellmuth (Ed), Disadvantaged child: Vol 3, Compensatory education: A national debate. New York: Brunner/Mazel

"Perhaps the most noticeable characteristic of the experimental children after two years of instruction was their confidence...The children exhibited confidence because they had received many demonstrations that they were competent and could succeed in challenging situations. They had surprised -- even crushed -- the teacher with their smartness. This is not to say that the children would be confident in all situations or even in all instructional situations. But they had firm and realistically based expectations about their capacity to perform in new learning situations of the type presented in the B[ereiter]-E[ngelmann] program"

The summary is also worth noting:

"The major hypothesis tested by the program was that children are taught at different rates; if the effective rate at which disadvantaged and middle class children are taught is increased substantially, these children will perform at an above-normal level, which means that the disadvantaged subjects may become "superior" in specific areas of achievement.

This hypothesis was confirmed...The disadvantaged children in the comparison group showed no particular advantage over children in similar compensatory programs, such as Head Start. The [control] program failed to bring half the children up to an IQ of 100. The mean for the group was 99.6. The experimental program, however, brought the IQ of every child to above 100. The mean IQ after two years of instruction was 121, with a range from 103 to 139. The mean achievements of the experimental group were what one would expect of 8-10 year old disadvantaged children; the experimental subjects, however, were six years old at the end of the program ....

The present experiments seem to indicate, rather strongly, that the reason disadvantaged children fail in public schools is not necessarily that they are genetically inferior or developmentally impaired, but that they receive poor instruction. If younger children with initially lower mental ages can achieve at an above-normal rate, school-age disadvantaged children (who usually learn more rapidly) should have little trouble achieving at the rate of normal children in specific achievement areas if instruction is adequate. The results of the experiment cast rather serious doubt on the validity of IQ measures as indicators of genetic endowment. The children in the experimental group were changed rather dramatically during the two years of instruction..."

The ratio of positive to negative feedback provided the children (if later DI instructional protocols are anything to go by, at least 5:1 or more) was likely a major component of the children's confidence and ongoing success, as it was in Hart and Risley's observations. Also, as I have read elsewhere, the intensity of early reinforcement seems to be key . Although the B-E experimental children were not officially followed up, they were tracked down as adults and proved to have vastly outperformed what would have been expected given their initial tenement origins, low IQ's and family background -- many had successfully completed post-secondary education, and were in professional or middle-class occupations. This outcome would have been extremely unlikely even given other interventions such as Head Start. Clearly more than simply teaching the academic skills (at the time) was involved.