Frequently Asked Questions
About the Core-Plus Mathematics Project

Last Updated: 23 October 2012

 

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Local Implementation

Local Implementation
Q What are some tips for effectively implementing the Core-Plus Mathematics Project curriculum?
A Based on our experiences working with schools to implement the CPMP curriculum, Contemporary Mathematics in Context, we recommend that careful consideration be given to the form of implementation in a district and to the groundwork needed to build support for school mathematics reform. In addition, a professional development plan to support teachers is crucial to effective implementation of the curriculum. Some things to consider prior to implementation are the following:
 
  • As a department, spend time studying the CPMP curriculum and instructional model.

  • Build understanding of, and a consensus for, mathematics education reform among administrators, counselors, parents, board members, business/community leaders, other departments within your high school, and middle school faculty.

  • Assess district technology needs. A graphing calculator with at least the capabilities of a TI-82/83 is required for each student.

  • Develop an extended professional development plan for ongoing support for teachers (see the third question in this section).

  • Begin adoption with Course 1 and add a course level each year, allowing teachers to grow with the curriculum.

  • Formulate a plan to evaluate your mathematics program and the results of changes made. Plan to collect data over the long term, not just the year or two before and the year or two after the changes.


Q How can students be accelerated in the Core-Plus Mathematics Project curriculum?
A
  • If your district has a history of enrolling strong eighth-grade students in an algebra course, you may wish to maintain an accelerated program using CPMP Course 1 for select eighth-graders. These students could then enroll in AP Calculus as seniors upon completing Course 4 as juniors. Students can enroll in AP Statistics anytime after completion of Course 3. (Advanced Placement Calculus topics covered in the Core-Plus Mathematics curriculum)

  • For students who don't start Course 1 until ninth grade, consider ways to schedule classes to allow students to move through the curriculum more quickly. The following is a list of options that some districts implementing the CPMP curriculum have successfully used.

    1. A student could double up on classes as a senior by enrolling in both Course 4 and AP Statistics.

    2. In schools with semester block scheduling, a student could enroll in two courses in a given year.

    3. In schools with alternate-day academic-year block schedules, the schedule could be adjusted for one or more classes of a course to meet each day for the first semester and classes of the next course similarly scheduled the second semester.

    4. In schools with traditional academic-year schedules, two mathematics classes may be scheduled back-to-back to allow study of one course in the first semester and the next course the second semester.

    5. Strong students who have completed one of the NSF-funded middle school mathematics programs, or an algebra course, could enroll in Course 2 in ninth grade. (Some supplemental material on Course 1 topics may be needed.)


Q What is the role of professional development in implementing the Core-Plus Mathematics Project curriculum?
A

Because much of the content in statistics, probability, and discrete mathematics is new for many teachers, and because some of the familiar material is developed more fully than in traditional mathematics, teachers need advice and support from other teachers and administrative support in order to implement the curriculum effectively. (Professional Development Opportunities)

Active involvement of students also requires a different type of planning by teachers. The Teacher Resource materials encourage teachers to be listening, observing, questioning, facilitating student work, and orchestrating class discussions in new ways. Professional development programs organized around reflecting on practice enable teachers to hone their skills in these areas.

At the very least, teachers should attend a professional development workshop led by an experienced CPMP teacher. In addition, schools should strongly consider providing the following supports:

  • Arrange cooperative learning, technology, and alternative assessment workshops for mathematics teachers before they attend CPMP workshops or begin teaching the curriculum.

  • Schedule teaching assignments so that teachers can progress from teaching Course 1 to teaching Course 4 in stages, and thereby develop an understanding of the growth of mathematical ideas across the curriculum.

  • Schedule classes to allow for common planning periods for teachers teaching the same course, especially if one or both of them are teaching it for the first time.


Q What behaviors and characteristics of Core-Plus Mathematics teachers are associated with students' growth in mathematics achievement?
A

We examined the classroom practices of 20 teachers during the field test of CPMP Course 1. Ten of these teachers comprised the top quartile of field-test teachers and the other 10 the bottom quartile with respect to their students' growth in mathematical achievement over the one-year course. Achievement was measured by a nationally standardized test called the Ability to Do Quantitative Thinking which is the mathematics subtest of the Iowa Tests of Educational Development. The primary data sources were: trained observer's holistic rating of the alignment of the instructional practice and classroom climate with CPMP's teaching for understanding model, self-perceptions of practice by the teachers, and expressed concerns of the teachers about the new curriculum.

The research results from this study, summarized below, are reported in a peer-reviewed article published in the Journal for Research in Mathematics Education:
Schoen, H. L., Finn, K. F., Cebulla, K. J., & Fi, C. (2003). Teacher variables that relate to student achievement when using a standards-based curriculum. Journal for Research in Mathematics Education, 34(3) 228-259.

The description of the "effective" (i.e., first-quartile) teacher that emerged from analyzing the data from these sources follows. This teacher may be of either gender, but we will use female pronouns for convenience.

  • She would either have strong preparation in reform curriculum and teaching before her first CPMP class, or she would have completed a workshop to specifically prepare her to teach the curriculum. That preparation appears to be very important. A year of teaching a pilot version of the same CPMP course does not appear to be a good substitute for a focused professional development experience.

  • She may teach in a wide variety of urban, suburban, or rural school settings. The beginning achievement level of her students may also vary widely. She would most likely be teaching classes of students who have a wide range of mathematical interests and aptitudes, although that is equally true of teachers in the fourth quartile in this study.

  • She would use the various parts of the CPMP lessons in ways that align well with the developers' expectations. For example, she would use mainly whole class discussion during the launch, spend about two-thirds of her class time on student investigations in which students were mainly working in small groups or pairs, and only spend about 10% of class time working on or reviewing homework.

  • She would use the CPMP recommendations for homework for the most part, keeping in mind that in each lesson the recommendations involve several choices for teachers and students.

  • She would assign "Extending" problems regularly - about one for homework and one in class per lesson.

  • She would use a variety of assessment techniques including group observations, written and oral reports, and take-home exams. She would also use student journals but typically not for grading purposes.

  • About 50% of her students' grades would be based on in-class exams and quizzes, another 20% on homework, about 10% on group work, and the remainder spread among written and oral reports, notebooks, and attendance/class participation. Each semester, or at least each year, she would assign a group project entailing several days of student work selected from those provided in the Assessment Resources.

  • She would not be likely to supplement the curriculum materials, and if she did it would probably be to add more discovery material. She would also be unlikely to supplement or revise the assessment materials except possibly to combine similar questions or mix forms of a test or quiz. In particular, she would not be inclined to make either the materials or the assessments more structured or skill-oriented.

  • A trained classroom observer would be likely to rate her class as "Excellent" or "Good" in terms of its alignment with CPMP's teaching for understanding model.

  • By year's end, this teacher would have few concerns about the CPMP curriculum. She would feel well informed about the curriculum, its goals and the resources it provides. She would feel confident of her ability to manage her class in group and pair investigations and comfortable with the changes required, including changes in her role as a teacher. Most likely, she would have little concern about the impact that the curriculum has on her students' levels of understanding, algebraic skills, and excitement about mathematics. After one year of using CPMP, she would have little concern about trying to improve upon the curriculum.

 

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