Here’s what James Milgram, Professor of Mathematics, Stanford University

Here’s what James Milgram, Professor of Mathematics, Stanford University, said about the Connected Mathematics program we have in our middle schools. Apparently the math decisions makers in Ridgewood see no need to ask a mathematician about mathematics.

“Overall, the program seems to be very incomplete, and I would judge that it is aimed at underachieving students rather than normal or higher achieving students. In itself this is not a problem unless, as is the case, the program is advertised as being designed for all students. In fact, as indicated, there is no reputable research at all which supports this.

The philosophy used throughout the program is that the students should entirely construct their own knowledge and that calculators are to always be available for calculation. This means that

1. standard algorithms are never introduced, not even for adding, subtracting, multiplying and dividing fractions

2. precise definitions are never given

2. repetitive practice for developing skills, such as basic manipulative skills is never given. Consequently, in the seventh and eighth grade booklets on algebra, there is no development of the standard skills needed to solve linear equations, no practice with simplifying polynomials or quotients of polynomials, no discussion of things as basic as the standard exponent rules.

4. throughout the booklets, topics are introduced, usually in a single problem and almost always indirectly — topics which, in traditional texts are basic and will have an entire chapter devoted to them — and then are dropped, never to be mentioned again.

5. in the booklets on probability and data analysis a huge amount of time is spent learning rather esoteric methods for representing data, such as stem and leaf plots, and very little attention is paid to topics like the use and misuse of statistics. Statistics, in and of itself, is not that important in terms of mathematical development. The main reason it is in the curriculum is to provide students with the means to understand common uses of statistics and to be able to understand when statistical arguments are being used correctly. “