Inquiry and CMP Research

Guiding principles:

•     Both the big idea of the curriculum or unit are identified for the student as well as the underlying skills and concepts, so the student will know what they are learning and how it connects to what they have learned. 
•      It is made clear how the concepts the student is currently learning are connected to what the student has learned in the particular lesson, unit, grade, and how the concepts are connected to what the students have learned in previous grades.
•       The most effective way of learning math includes a process of investigation for the student, where they are actively exploring and solving an idea or problem
•       The explorations are purposefully in depth to support deeper understanding and memory by the students.
•       Part of making problems in depth is having students read and write problems in multiple representations—graphic, numeric, symbolic, and verbal, and to fluently move between these representations.
•       Calculators and computers have changed the way people think about and solve mathematical problems, and the curriculum reflects this transition.

   Comparison of CMP and direct instruction:

In direct instruction, the initial phase is a set, or hook, where the teacher’s goal is to introduce and interest the student in the material. In contrast, the initial phase of CMP is Launch, where the teacher helps the students understand the problem setting, the mathematical challenge, and the concept. In both methods, the teacher is introducing the lesson.

The main difference between the two methods is evident in the next sections. Typically in the direct instruction method, the teacher moves on to the instruction step of the lesson while the CMP method moves to the Explore step. In instruction, the teacher is instructing the class how to accomplish the goals of the lesson, and providing examples of the concept that is being covered while the students are listening to the instruction, answering questions that the teacher asks, and taking notes or following along either in groups or individually. In the Explore step of CMP, the students are presented with a problem and they gather data, share ideas, and look for patterns, while the teacher roams the class and helps individuals and groups.

The final stage of the CMP method more closely resembles the instruction phase of its counterpart. This is where the teacher helps guide the students to the goals of the lesson, clearing up areas of frustration along the way. In case some groups did not make it to the final product of the lesson, the teacher must also find a way to get everybody caught up. In direct instruction, the final activity also wraps up the lesson, and makes sure everybody is on the same page about what should have been learned.