Inquiry & CMP Research

CMP is a student-centered, inquiry-based teaching model. First the teacher sets the stage, states the objective and provides real-world context and any necessary background information (Launch). Then the students work together to solve the problem or complete the project with the teacher acting as facilitator and offering open-ended questions as answers to students' inquiries (Explore). After students work independently in groups, the class is brought together to share what they've learned and share problem-solving strategies. The teacher summarizes what the students learned (Summarize).
Compared with the traditional model of instruction, guided practice and independent practice, there is less modeling by the teacher and instead students are more left to their own devices to discover how to complete tasks, and they share their strategies with the class. The CMP also emphasizes more group collaboration as a given.
As the Connected Math Project website states:

• Classroom instruction focuses on inquiry and investigation of mathematical ideas embedded in rich problem situations.
• Mathematical tasks for students in class and in homework are the primary vehicle for student engagement with the mathematical concepts to be learned. The key mathematical goals are elaborated, exemplified, and connected through the problems in an investigation.
• Ideas are explored through these tasks in the depth necessary to allow students to make sense of them. Superficial treatment of an idea produces shallow and short-lived understanding and does not support making connections among ideas.
• The curriculum helps students grow in their ability to reason effectively with information represented in graphic, numeric, symbolic, and verbal forms and to move flexibly among these representations.
• The curriculum reflects the information- processing capabilities of calculators and computers and the fundamental changes such tools are making in the way people learn mathematics and apply their knowledge of problem-solving tasks.

CMP-Inquiry Middle School Interview

Interview with Perrydale math teacher Bryan Toller, who teaches high-school-level algebra to middle-school students.

* How does the CMP curriculum align with the national Common Core and NCTM standards? 1. The CMP curriculum aligns well with the national standards. Each curriculum is unique and must be aligned to match the standards. It is the teachers responsibility to go through and ensure that the standards are met.

*Numerous students are a year or more behind in the basics. How does one address the needs of these students on a daily basis so they can get up to grade level and also experience success in the inquiry to investigation philosophy of the CMP? 2. Inquiry based curriculums such as CMP present problems for struggling students because the problems are very contextual and if a student is missing pieces sometimes dealing with the context in addition to the mathematics can be overwhelming. On the other hand because of the context the problems tend to be less abstract and a struggling student can "put themselves into" the problem and then they are able to figure it out. The context also leads to a deeper contextual understanding that helps bridge the gaps between lessons and ideas.

* What is the role of homework (and accountability) in the CMP?
CMP Investigations compose of small-groups (pair-share, teamwork, cooperative learning). Describe several classroom management techniques that ensure all students are actively engaged. Eg, how are individual roles established? Accountability (Group, individual)? Ongoing assessment(s) and checking for understanding?

3. It is the teacher's job to ensure individual and group accountability. On an individual basis the teacher must collect and assess classwork, homework and provide on demand assessments. On a group level classwork can be assessed on a participatory level, with some group projects, but ultimately grades are individual and should represent and individuals work and effort.

 Homework is critical in any math class, it is the daily practice that supports the lessons and learning that happens in the classroom. Homework needs to be assessed on an individual level but, homework in my opinion should be graded on completion rather than accuracy.

 When students are engaged and working on problem solving in small groups most classroom management issues dissolve. Most management issues stem from students being bored and finding alternative ways to entertain themselves by acting out or disrupting others.