Inquiry & CMP Research

Inquiry based instruction is supposedly student-centered (rather than teacher centered) and focuses less on learning the answer to a problem and more on learning various strategies for solving a problem. Proponents of the model suggest that traditional methods of instruction treat the teacher as the one and only source of knowledge in the classroom and that the teacher is supposedly only telling students about what has been learned (an abstract set of facts) rather than helping students learn (creating knowledge on their own). I believe that I detect a little bit of Vygotsky and in this supposition; if we learn through interactions with our peers and use cultural tools (language, books, and other resources) to build our pools of knowledge, then we must become adept at utilizing those tools (and persons) more than in simply memorizing facts (which in themselves are bits of knowledge, but which were not necessarily learned by the learner but given to them in the hopes that the knowledge would stick).

There are some problems with the approach, however, in as much as we can implement it in our current school systems. Students are taking tests in which they are being asked to show knowledge of a great deal of “facts”—instructors see that list of things the students “need” to know and realize that limited time means that memorization is the only way to get it all done. The other problem is that neither students nor teachers are accustomed to using this model. Students left to ponder how to solve problems might fail to generate any solutions (instead saying “but we’ve never done problems like this before!”) and teachers, who are accustomed to being the experts (and who themselves were taught that the teacher is the expert), are willing to present solutions to get the students moving forward. If too much time is spent on a single inquiry, then other time must be being wasted, perhaps?

The CMP model is designed to be a type of inquiry-based model of instruction. Believing that “math” is about strategies rather than facts, the creators have worked to make a program that presents students with engaging problems for which there are a number of “correct” solutions or a number of methods for reaching the solution. They suggest that their program moves students through a variety of inquiries that are interconnected, allowing students to build the skills necessary for solving more complex situations over time. Moreover, technology (computers and calculators, in particular) are recognized for the ways that they have changed our view of math and the usage of both is promoted rather than prohibited.

Personally, I think that while CMP has some excellent goals in mind, the actual implementation of their strategies in a classroom is not as easy as it sounds. Although I have not been an observer in many math classrooms outside my own education, I was able to observe one 8th grade classroom in the Salem-Keizer district which uses the CMP. In NO way did it strike me as being different from my own junior high experience (which occurred over ten years ago in a different state). CMP suggests that their questions are engaging, and yet, the probability question involving marbles, for example, still continues to be irrelevant to today’s middle school students. Do the 12-year old kids of today actually know what marbles are? Do they know how to play marbles? How on earth is a question about marbles engaging to students? The other problem with the approach, which I suggested somewhere in my first paragraph, is that sometimes students themselves are unable to see how to solve problems and will resort to whining. “But we’ve never done this kind of problem before!” was the one complaint I heard over and over (even though I had personally witnessed them doing similar problems previously—they apparently did not have the “self-help” skill of being able to look at previous work and to search their textbook for similar problems). This is a problem within itself—if you cannot see similarities between different problems, then you cannot possibly be expected to use the resources you have to solve the problem (i.e. transfer of skills or external tools). To me, this means that there needs to be a balance of memorization AND exploration (e.g. direct instruction and inquiry-based instruction).