Connected Mathematics Program: What 3 'supportive' studies say

June 19, 2004

Last time we wrote how one Milwaukee school board is trying to increase math achievement by using the Connected Mathematics Program (CMP). This is yet another fuzzy-math program based on an unfortunate set of standards that places problem solving and the discovery approach on such high pedestals that little real teaching and learning can take place.

We think the CMP logo (right) is fitting: sending groups of children in circles, with no end in sight.

What is especially interesting about CMP is the evidence they cite on their own website.

One page called Curriculum Reviews examines three different evaluations. Two of the reviews had glowing praise for CMP, but when we examined their evaluation criteria, we found little more than gobbledygook. Only the third review seemed to be interested in any kind of mathematical rigor, and their conclusions were very interesting, as we'll see.

Math and Science Expert Panel
The 1999 Mathematics and Science Expert Panel for the U.S. Department of Education named CMP an "exemplary" program. However, upon examining their criteria we found seven categories (with a total of thirty-three sub-indicators) focused on all sorts of high-sounding rhetoric including goals, alignment, engagement, and even societal needs.

Only the eighth criterion ("Makes a difference in student learning") was interested in whether the program actually works, and in this criterion the evidence required was weak: publishers could turn in just about any evidence of gains for validation. For example, if students improved only one-half grade level in an entire year of instruction, but their gains were not only in their understanding of math but their problem-solving skills, then that program would become eligible to be named "exemplary."

With "makes a difference" listed last among the eight criteria, it is clear just how highly the Expert Panel regarded it.

While it is true that the Expert Panel named CMP "exemplary," we think it is mainly because of a rigged definition. (Read how a similar group redefined the word effective.)

Project 2061
In 1999, Project 2061 of the American Association for the Advancement of Science examined several middle school math programs, giving CMP "the highest ranking by quality instruction in student and teacher editions, and most or partial content ranking on selected content benchmarks." (Whatever that means.)

However when we examined their methodology, we found more rhetoric.

Project 2061 breaks down their criteria into seven categories and a total of 24 sub-criteria. They have a lot to say about "connecting benchmark ideas" and "promoting student thinking" and "guiding interpretation" and "the mathematics environment." They have little to say about practice, as in students actually doing math problems. Only two of their twenty-four criteria mentions this incredibly important aspect of learning math.

Given their focus on all things wishy-washy, we have little faith in their recommendation of CMP.

On a side note, one math program which we know first-hand to be extremely effective (partly because their problem sets seem engineered, they're so well written) is the Saxon series. One look at Saxon, and the Project 2061 folks punted:

Although we analyzed [Saxon] Math 65, Math 76, Math 87 (Saxon Publishers, Inc., 1997, 1995), this series' philosophy, organization, and format . . . were not well suited to our evaluation.

University of Washington
A group of math professors from the University of Washington examined three middle school math programs, including CMP, Math in Context, and Singapore Math, and they have some rather damning statements about CMP.

What we find delicious is that the CMP folks cite the study anyway, quoting the following section without a hint of irony:

They (Connected Mathematics Program and Mathematics in Context) represent the new thrust in American mathematical education of inquiry-based, discovery-based and student-centered learning.

They mean this as an insult. Math instruction has been going down the drain in the U.S. because of these "new thrusts." The reason? "Inquiry-based, discovery-based and student-centered learning" are replacing direct instruction and problem sets where students actually practice doing math.

The American curricula strive to produce independent thinkers who can analyze problems, select appropriate tools to solve them and achieve conceptual understanding of the mathematics behind the algorithms, usually through a real-world context.

The key word here is "strive." Sure, Americans strive to have all these wonderful things happen, but the approach is all wrong. In the end, rigorous analysis, problem solving, and conceptual understanding happen best in traditional, teacher-based classrooms.

Singapore mathematics, on the other hand, is more traditional in orientation and emphasizes the acquisition of proficiency in mathematical skills and teacher-directed learning. . .

The CMP folks didn't notice the authors meant this as a compliment to the Singapore program. They also fail to note that no nation's children perform as well as Singapore youngsters in math. None.

When compared with the 2000 NCTM Principles and Standards, the Singapore curriculum scores lower than the two American texts.

Exactly! The NCTM standards have removed a great deal of math from the study of mathematics, and CMP was designed with precisely these NCTM standards in mind. Of course they'll do well on any evaluation that ranks them according to how well they follow the party line!

'Supportive' indeed
If this is part of the evidence that the Connected Mathematics Program staff cite in support of their program, we'd like to know why people (such as the good folks in Germantown) continue to regard it, and programs like it, as being part of the solution to their math woes.

Stay tuned, and next time we'll pull some actual quotes from the University of Washington study to help show just how bad CMP really is (and by proxy, how low the NCTM standards are).