The goal of the CMP Model of learning is very similar to the Inquiry Learning Model in that it aims to produce reasoning students. The classical sources of inquiry learning date back to Aristotle but more recently was introduced into modern education by John Dewey with the notion of constructivist education. The CMP model takes a functional approach to teaching mathematics as apposed to a structural approach. This aligns it more with the Inquiry Learning Model and centers it around the student. Rather than focusing on learning the procedures of solving equations it helps students to understand the function of the equations and to "uncover" equations as part of problem solving. This is directly apposed to the direct instruction model of education where the teacher is the primary source of information. Instead using CMP as an inquiry based learning model, students discover and put into contact mathematical principles and thus internalize the importance and properties of what is being studied. The traditional or Glencoe Mathematics system relies heavily on completely modeled examples with clear explanations that are accompanied by guided practice. Although this seems to be a good way to teach, it is the epitome of direct instruction and works very well for only students who thrive in this sort of environment. In order to reach a wider range of student, I feel inquiry based learning supported by a knowledgeable teacher with bits of direct instruction would do a better job of teaching higher order reasoning students. It would also make math more interesting to students who learning styles differ from the teachers teaching style.
Resources:
The Teaching of Equation Solving: Approaches in Standards-Based and Traditional Curricula in the United States, Pedagogies: An International Journal.
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