At long last, E.D. Hirsch, Jr., answers this question and more in his new book, The Schools We Need & Why We Don't Have Them (Doubleday, 1996). Finally we have a clear, well-supported statement that identifies the forces that have brought about the reform movement in mathematics, as well as other reforms like Whole Language. Hirsch makes it painfully clear how extensive these changes are and how entrenched American education is in this movement, along with the great losses these changes bring to our society and our children.
Hirsch identifies the enemy behind this movement -- it is not the teachers or even the educationists, it is the ideas promoting the movement that must be attacked. Here are two samples:
E.D. Hirsch has a new book, The Schools We Need & Why We Don't Have Them, which is very interesting. In addition to being dedicated to teachers and principals of Core Knowledge Schools, it is in memory of William C. Bagley and Antonio Gramsci who explained in the 1930's why the new educational ideas would lead to greater social injustice.
As someone whose reading in education is far too spotty, I had not come across either of these. In 1932, when in prison in Italy, the Communist intellectual Antonio Gramsci wrote the following:
"The new concept of schools is in its romantic phase, in which the replacement of 'mechanical' by 'natural' methods has become unhealthily exaggerated ... Previously pupils at least acquired a certain baggage of concrete facts. Now there will no longer be any baggage to put in order.... The most paradoxical aspect of it all is that this new type of school is advocated as being democratic, while in fact it is destined not merely to perpetuate social differences but crystallize them in Chinese complexities.
Bagley was a professor at Teacher's College, and one of his colleagues thought enough of his ideas to write a biography of him after he died.
Hirsch lists one of the many "more" and "less" lists. This includes:
Here is Hirsch's next paragraph, on page 173:
The authors praise the current consensus on these 'child-centered' principles for being 'progressive, developmentally appropriate, research based, and eminently teachable.' These claims are not, however 'research based' in the way the authors imply. Quite the contrary. No studies of children's learning in mainstream science support these generalizations. With respect to effective learning, the consensus in research is that their recommendations are worst practice, not 'best practice'.
I have been asking for citations to the research which shows that the practices listed under MORE are effective and only a few have been given to me, none of which is more than experimental work with a small number of teachers and students. The best that has been cited is the summary in "Schools For Thought" by John T. Bruer, MIT 1994. What is there is not very impressive by world standards, and that is what we need to compare to, not the system in math education which we have that does not work very well.
Hirsch gives data on how variable the grading on written papers can be. There was a 1961 study where 300 student papers were graded by 53 graders. More than one third of the papers received every possible passing grade, A, A-, B+, B, B-, C+, C, C-, and D. He quotes 94 percent [of the papers] received either seven, eight or nine different grades; and no essay received less than five different grades from fifty-three readers. Even when the raters were experienced teachers, the grades given to the papers by the different raters never attained a correlation greater than .40.
Hirsch's book is full of detailed comments like this. The last chapter is especially valuable for someone just starting to read the education literature. It contains a 30-page glossary of terms with a long paragraph to describe each. I wish I had had such a guide five years ago.
Richard Askey