In 2000 the Connected Mathematics Project used the Curriculum and Evaluation Standards for School Mathematics developed and issued by the NCTM. It appears as though the CMP has been designed in alignment with the Content Standards set forth by the NCTM, from Number and Operations all the way to Data analysis and probability. Another striking similarity that can be seen as a philosophical alignment are the Six Principles set forth by the NCTM, striking because the language used seems to almost mandate a teaching style that the CMP has been designed to facilitate. Principles such as Equity, which the NCTM says should encourage the provision of extra help to students in need and advocates that teachers not shy away from having high expectations for all of their students; Teaching, where the NCTM suggests teachers not adopt a 'one size fits all' methodology. The NCTM standards and guiding principles go on to basically say that students should not merely be able to perform calculations in vacuum. And that they recognize that helping students improve their problem solving skills is something that all students have the capacity to accomplish.
2. 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?
Judging on the literature concerning the CMP model it appears as though many students are behind when the begin being instructed in the CMP way, and that the CMP method does not initially raise those students' apparent skill level, based on standardized tests, until they reach their 3rd year of CMP instruction according to a study titled Standards-based Mathematics Curricula and Middle-Grades Students' Performance on Standardized Achievement Tests, published by the Journal for Research in Mathematics Education, 2008, Vol. 39, No. 2, 184-212. Basically they are saying that while the CMP model did not provide immediately measurable positive gains in learning, the learning gains over time were significant when compared to the standard methods of teaching math. "In related investigations, the authors concluded that there is no immediate short-term advantage to CMP, but that the longer view is promising, with CMP students making large gains on a broad range of curriculum topics and processes when compared to non-CMP students."
That being said, CMP model is designed so that overtime those students who need extra attention, are afforded it. With CMP it is imperative that a teacher be instrumental in care-taking each student's needs with regard to their current skill level. Given the instructional material that has been devised to accompany the CMP classroom, students will find that even though they may lack certain mathematical skills initially, they will still be able to contribute to the overall understanding of whatever math concept is being taught, and will come to realize that understanding the concept is more powerful than merely knowing how to do the calculations, which overtime they will gain the skill to perform regardless. So, the CMP student with sub-par skill sets will overtime gain those missing skills by the very nature of learning in the CMP way; that is, through a realistic and relevant problems based curriculum.
3. What is the role of homework (and accountability) in the CMP?
While the role of homework in the CMP is still very much tied to an individual teachers philosophy some of the most common reasons for giving homework in the CMP are:
- To provide additional explanation and practice of the key mathematical ideas in the lesson.
- To grade students' work .
- To assess what students do and do not know in order to plan instruction.
- To connect learning experiences on two consecutive days.
- To instill good study habits.
- To accomplish more mathematical study outside the time limits of the classroom.
4. CMP Investigations are often composed of small-groups (pair-share, teamwork, cooperative learning).
Notebooks and journaling can be on great method for assessing students, while also helping to ensure that all the students are participating. When students are in these small groups some of the ways that teachers can ensure maximum engagement from every students are:
- Have students assign numbers to each student in their group. Then, have them roll a number cube or draw to determine who will present the group's findings.
- Write each student's name on a craft stick, store the sticks in a cup at the front of the room, and choose one stick at random to determine who will present.
- Have the students choose the presenter for their group, but ask each of the other students a question related to the work.
