You've probably never heard of the Madison Project or of its founder in 1956, Robert B. Davis. But you've certianly heard of new math. I was asked, in connection with the 25th anniversary of the Madison Project to, "Write something about how the Madison Project activities touched you personally. What do you remember about your involvement? what effect has it had on you?"
I'll have to admit that the first effect was a big yawn.
I'd driven to Syracuse to attend a workshop on the fledgling Madison Project in 1957 because a course I'd taken that winter at Harvard University in finite mathematics taught me to conceptualize the math I had previously learned by rote.
I got excited about translating what I was learning at the college level down to the elementary grades where I felt considerably more comfortable, and I'd leraned that the Madison Project was doing this for junior-high-level students.
Since this is to be a reminiscence about Bob Davis, and since I long ago told him this story, I can repeat it here:
I couldn't have been more disappointed the first morning of the workshop. So much so that I went out at a break and called my hostess to tell her I would be available early that afternoon for a picnic.
But after the lunch break Dr. Davis stopped "defining the parameters of why he had gotten involved" and began recounting lessons in higher mathematics he had been able to get across to "slow" junior high students who were failing traditional algebra.
His low-key enthusiasm was enormously effective, and the roomful of teachers from throughout the Northeast came alive with excitement.
I had to go to the picnic, but spent the entire evening engaging one youngster after another in mathematical ideas.
The next two days were thrilling, and as quickly as I grasped a math concept, I thought of how I might teach that concept to 8-to 12-year-olds.
Then the letdown.
I asked Dr. Davis if he wasn't interested in trying some of the material in the elementary grades, and he, more comfortable then with graduate students, looked askance at my suggestion.
But would he let me take some of his materials (stacks and stacks of mimeographed sheets) and try them with fourth graders? Too gentle and kind to refuse, he nodded his head.
I first asked the Greenwich, Conn., school superintendent if he wouldn't let me practice on a fourth grade class, and he agreed somewhat hesitantly. The regular classroom teacher was bored by the class sessions and generally took refuge behind her Ner York Times.
But the children were excited, and on the first parents' night, the teacher was amazed to find that all her parents had come -- and all had come to find out what this "Madison Project" was all about.
I thought I was doing famously, and kept writing Dr. Davis and Syracuse University to say so. He replied cautiously -- after all, most of those involved then with the "new math" movement were mathematicians of note, not classroom teachers who had no college math.
I next asked the superintendent of schools in Tarrytown, N.Y., if I might try Madison Project math with one of his fourth grades.
He was amused, found a cooperative principal, and I once more the youngsters willing and able to tackle exciting and mature math problems through a conceptual approach.
The Tarrytown superintendent, alerted by the principal, came and sat in on an early lesson and at the close said: "I can't let you do this for just one of the district's fourth grade classes, and I don't know how i'll do it, but I'll find the money somehow to pay you for teaching them all."
Now, I've explained how Madison Project activities touched me personally -- although there's lots more i've not spoken of. My involvement took me not only to those two schools, but eventually throughout the US, and to Asia and Europe giving demonstration classes of Madison Project math.
One time, in particular, I remember with great joy. About 1960, I went to a small town in central Georgia and offered to teach a demonstration class in the all-white elementary school, and next day to teach a similar-aged class in the all-black K-12 school.
Some 300 black teachers from throughout the county school district watched me work with 25 fourth graders on the stage in the auditorium. I told the children that they were free to disagree with me when they though they had a case.
But their teachers and particularly the principal had read them the riot act before they took their places on the stages, telling them at all costs to be polite to the "white lady" who would be teaching them. The first white lady who had ever been in their school to teach.
They kept "Yes, Ma'aming" me until I made a ridiculous statement. One of the boys was tall, much taller than I, so I said to the class: "I am taller than he is. Can you guess how much taller I am than he?"
I repeated myself in a sharp voice and said, "Is there no one here who can tell me how much taller I am than he?"
I glared at a girl who had not been ale to extinguish the sparkle in her eyes. She looked nervously around at the principal, then raised her hand.
"If you want to be taller than Roscoe, you gonna have to ge a whole lot taller . . . ma'am."
We were off then, they flew through some equations and began figuring ways to express numerical relationships in geometric terms. They became enormously excited, and when I gave permission for them to talk things through with their fellow students, my girl with the sparkle was the one they all turned to.
After 30 minutes, the children were excused and I began a discussion with the teachers. That is, I was supposed to have a discussion, but they sat absolutely still. As the principal hastily explained. "We're been struck dumb."
And what they were most curious to hear, and almost unable to believe, is that their children had done as well as the "other" children across town. In fact, as I kept assuring them, "I taught a group of city slickers in Chicago last week and they did no better than your children."
Yet the principal knew already what would happen to new math as its exponents tried to engage a whole nation in not only a new way of teaching, but a whole new mass of curriculum material. He shook his head and said:
"Our teachers can't do what you did; they don't have the math. And they don't think in concepts. They just try to follow the book rules."
I look back on those Madison Project days and feel a certain sadness about the demise of new math -- about the absence of conceptual thinking in those colleges and universities charged with preparing teachers for US classrooms.
A sadness that teachers were so weak in their own math skills that they weren't free to improvise and innovate, but were rigidly dependent on the texts provided them to know what to teach, in what order, and with what intensity.
A sadness that so many of those interested in new math, skilled in teaching it to children, able even to inspire classroom teachers have, like myself, left full-time classroom teaching. We didn't leave classrooms to those who were cleverer than we; to those whose love of new math exceeded our beginning enthusiasm.
No, sadly, we left our classrooms to those who had gone through some very poor and sporadic teaching themselves. Some tried to teach something they thought was "new math." But as nationwide test scores indicate, arithmetic and math skills have suffered from inept teaching.
Yet, I don't feel the answer is to return to rote teaching. It isn't. It is to bring to teaching the most conceptual methods possible, and to inspire a discipline of thought and action which will manifest itself in well-trained young mathematicians.
Of course, calculators and computers --machines which can do all the rote mathematics necessary -- are forcing a rethinking of math and arithmetic curriculums around the world.
New Madison Projects are needed, ones which will train youngsters to use calculators and computers to do routine figuring, while the youngsters do the exciting, imaginative, and worthwhile programming.
When the "old" Madison Project friends meet in St. Louis, honoring 25 years of Bob Davis' contribution to improving math ed, sadness can give way to expectation.
No one in charge of our schools is satisfied with our poor performance as mathematicians, and steps are well under way to bring about improvements.
And I don't feel one bit foolish in saying: Look what another 25 years may bring!
When we meet again in the year 2006, we'll be astounded that we were ever discouraged about the state of conceptual math. It will be so commonplace that we'll need to pinch ourselves to remember "the old days" of algorithms and solving for X.