Note: To avoid a long header list, I am sending this to myself, and Bcc'ing it to the people on my list. Thank you for your understanding.]
From Jerry Uhl -- This came in from George Reese , a Math Ed Ph.D student at Illinois . With his permission, I am posting it.
Hi Jerry (Uhl):
I have to chime in here. "Stand and Deliver" came out at the end of my first year teaching mathematics to a diverse poplulation of kids in the public schools in Santa Fe, NM. When they showed the numbers at the end of the movie on how many kids had passed the AP, I practically cried. Most of the kids I saw were signed up for bluff courses: business math, general math, Algebra I part I, Algebra I part II. All four of these courses had the same content: nothing. But were able to give kids mathematics credit in 4 separate "math" courses.
At the time, I thought Escalante was really on to an important point, namely that schools were lying about mathematics and they should stop. I still believe that is true.
I left the public schools and went to teach at the Indian School in Santa Fe. As I continued to teach, I realized that there was another issue. Namely that the tests that are used to measure progress in mathematics may not really measure anything important. I had moved down the Escalante-idolization pathway, and I realized that the best way to get to high test scores was to have a textbook that emphasized the skills that were on tests. Enter John Saxon.
The Saxon texts are the best "math test" preparation books out there. Scores go up at places that use them. They are intensely drill oriented and totally teacher proof. John Saxon told me in a phone call that "any secretary down the hall" can teach out of these books. I pretty powerful put-down of teachers, but if it was true, hey, better to face it than continue the deceptions implicit in watered-down courses.
However, the issue is more complex. Students can learn drill and practice and love it, and Saxon is the best at it. But when they get an honest to goodness problem without a textbook answer they are helpless or worse, namely angry that they don't have what it takes to deal with the situation. A real problem is then a trick that the teacher has pulled on them. Also, these drill and practice books and tests are very effective at discouraging those who don't get it right away, and are very good for the handy rankings that we parents seem to care about but that damage so many kids who start with disadvantages. Escanlante did great things to empower the kids he had, but it was his personality not his textbook that made it happen.
Well, this sermon has gone on a bit. But I want to say that I believe that Escalante, Frank Allen,Charles Sykes, E. D. Hirsch and others with similar viewpoints have maybe two valid premises: first that watered down stuff is no good, and second, that getting some cultural capital in the form of computational skills will help students with the ubiquitous tests. Their conclusions however, tracking, drill and kill curricula, and more standardized tests are simple-minded and wrong.
George ****************************************************** A comment and question, by Ken Koedinger [firstname.lastname@example.org]:
1. The Pittsburgh public schools once did a study comparing three math textbooks one of which was Saxon. They found no end-of-course difference between student test courses in the three conditions. For what it's worth, this study seems to suggest that the Saxon books are not totally teacher proof.
2. My intuition is drawn by the claim above that the drill and practice approach of Saxon does not transfer well to more novel, non-routine problem solving. However, it reminds me of the defense of the poor performance of US math students relative to Asian students: "Yes, but US students are more creative". As I recall, Stigler and Stevenson reported in their book that a number of efforts were made to test for this creative edge and no such differences were ever found. Of course, the situation with Saxon may be quite different, but it raises the question in my mind: Has any one done any experimental studies to test whether or not students using Saxon are better at routine math, but worse at non-routine problem solving? ******************************************************** A response by Jerry Uhl:
The only esponse that comes to my mind is this: Most math tests are defective. They tend to concentrate on the part of the course Saxon is good at. As one teacher put it to me: "I teach a very conceptual course, but I don't dare ask conceptual questions on tests."