Connected Mathematics is standards based and problem centered. Adopting and implementing a standards-based mathematics curriculum can be a major step for school districts.
To replace a curriculum often described as "a mile wide and an inch deep," standards- based mathematics curricula focus attention on a core agenda of important and broadly useful mathematical ideas. To replace instruction that asks students to watch passively and imitate teacher demonstrations of routine computational techniques, these curricula engage students in challenging mathematical investigations that help them construct solid understanding of key ideas and confident ability to solve tough mathematical problems.
(James Fey, Montgomery Gazette, Montgomery County, September 10, 1999)
Standards-based curricula such as CMP are organized differently than traditional mathematics textbooks. Parents and teachers are accustomed to textbooks that have examples followed by pages of skill exercises. Many teachers are accustomed to instruction characterized by working a few examples for the whole class, then assigning a set of practice problems to be done independently by the students. Although most teachers supplement this pattern by occasionally having students solve non- routine problems, such activity is not at the core of their curriculum or central to their teaching.
Not only do the standards-based textbooks look different but they also ask teachers, students, and parents to play different roles. In the traditional curriculum, teachers actively demonstrate solutions, students somewhat passively observe, parents and guardians support and supervise practice, and the textbook provides examples. In CMP classrooms, students actively investigate problems and develop solutions, and teachers question, challenge, and orchestrate explicit summaries of the mathematics being learned. Teachers, parents and guardians will benefit from information about the rationale for the organization and sequencing of the problems, the role of ACE questions and Looking Back/Looking Ahead activity in each unit, and the way that student notebooks are designed to capture a student's evolving knowledge of a topic. Standards-based curricula like CMP look different and make different demands on all members of the community.
Connected Mathematics teaches mathematics through a sequence of connected problems in an inquiry-based classroom. This is a major shift away from a focus on developing skills and procedures to a focus on mathematics as a set of relationships between a specialized symbolic language, concepts, facts, ways of thinking, and procedures.
School districts can make this shift and smooth the implementation of CMP by following guidelines for orchestrating the process. Bay et al. (1999) list ten important factors related to successful selection and implementation of standards-based mathematics curricula. These include: administrative support; opportunities to study and pilot the curricula; time for daily planning and interaction with colleagues; knowledge of appropriate assessment techniques and tools; ongoing communication with parents; and articulation with colleagues at the elementary and secondary level.
Before adopting Connected Mathematics, school personnel should take time to:
Seek reviews of research that might answer the questions, "Why do we want to change? What more do we want for our students that the current texts do not provide?"
Seek reviews of research that might guide evaluation of textbooks, rather than rely solely on the data provided by the publisher. "What are we seeking in a new text, and how can we find helpful and reliable information?"
Know how middle school students in your district are performing on state or local assessments. Ask teachers to provide input into where they see strengths and/or weaknesses in the current curriculum materials. Involve a parent group in reviewing the evidence and establishing goals. "Are there particular areas of strength or weakness?"
Seek, or request from the publisher, data describing the effectiveness of CMP or any other curricula under consideration. "Was the curriculum used in a district like ours?"
Create an evaluation plan for measuring student achievement. Plan to collect baseline data the year before implementation. "What is our goal for student achievement? What realistically can we expect? How will we evaluate student's achievement over the long run?"
Seek information about the preparation and confidence level of teachers in the district. "What support is there for teachers either in the textbook itself or from other sources?"
Garner Administrative and Community Support
Superintendents, principals, and other administrators as well as school boards and parents must have access to clear information about the CMP materials. The administration and staff need a well-developed strategy for providing the mechanisms through which such information is made available to the school board and to parents and kept updated.
Familiarize principals and other administrators with CMP. They should know the rationale for the change in curricular emphasis and how CMP will better meet the needs of students.
Work with parents to gain support. Some districts have found that a parent/community advisory group is helpful. Involving parents during the conceptualization of the implementation can avoid misunderstandings later.
Work with teachers to gain support. Request and respect input from all teachers.
Address Important Issues and Questions
How does CMP "fit" with district and state frameworks? Correlate curriculum goals with local/state requirements and assessment instruments.
How does CMP handle basic skills? The answer to this question, as well as the evidence of the impact of the curriculum on students' basic skills, is readily available. The results consistently show that CMP students do as well as, or better than, non-CMP students on tests of basic skills. And CMP students outperform non-CMP students on tests of problem solving ability, conceptual understanding, and proportional reasoning.
Will CMP be used in all grades (6-8), with all levels of students? Will students with learning difficulties or reading difficulties find it too difficult? (See Differentiated Instruction)
If algebra is offered as a separate course in middle school, will CMP be used in this course? If so, how does CMP support the development of algebra concepts and skills? (See Algebra in CMP2 under Mathematics Content) Experiences of other schools that are successfully using CMP in 6-8, including for an 8th grade algebra class, can be a powerful resource.
How will students make the transition from CMP to high school? Who should be involved in making a transition plan?
Are students coming out of our K-5 ready for CMP? Should we involve elementary teachers in making a transition plan from upper elementary to CMP?
Enable Teacher Buy-In
The size, composition of staff, and past experiences of the school district and staff will determine how the following actions are handled.
Consider piloting units before adopting the entire curriculum (if feasible).
Develop an implementation plan. Will all students (and teachers) begin using the materials at the same time? Will they be phased in over the course of two to three years?
Establish plans for long-term professional development that coincides with the implementation schedule (more on this in the next section).
Designate teacher or building leaders responsible for scheduling/planning professional development.
Districts need to take early action on the preceding items. The best professional development plans have gone astray because schools did not take the time to share with the key players in their districts the rationale for a new curriculum focus and to develop a wide base of support. If a district committee, representing all the key players, has collected evidence about CMP as suggested above, then any questions from parents or teachers can be honestly and rationally answered. If the adoption process has been transparent, then the community will have had an opportunity to ask questions and seek reassurance.
The successful principal of a school has many roles to play as he/she interacts with all members of the school's community. Broadly speaking, with district level administrators the interaction is about the business of managing a school, with teachers the interaction is about the teaching and learning of a curriculum, and with parents the interaction is about the success of individual children. When CMP is adopted, the principal who takes the time to become knowledgeable about the curriculum will be better able to support teachers and answer parent questions. Becoming knowledgeable is the first step.
Becoming Knowledgeable About the Curriculum
In the initial stages of selection and adoption, the district committee will have sought out evidence of reasons for adopting CMP, of current achievement levels of students, of the success of CMP in other districts and of the preparation of teachers to implement CMP. The district committee will also have sought answers to questions about how students with disabilities or gifted and talented students succeed in CMP, about the place of Algebra in CMP, and about the issues to be considered in helping students make successful transitions from elementary school to middle school, and from middle school to high school. This evidence and current thinking about these issues should be shared with principals so that they feel confident that a thoughtful decision has been made, and so that they can relate achievement goals and teacher preparation to their own buildings. The building principal needs to be knowledgeable so that he/she can speak confidently and supportively about the curriculum and related issues to teachers and to parents.
Since CMP is standards based and problem centered the principal will need to find time to understand what these two terms mean, and how this kind of curriculum looks in a classroom when it is being successfully implemented. In this role the principal is acting like the principal teacher in the building, asking questions such as, "What research backs this kind of approach? What does this kind of curriculum mean for student groupings? What role does the teacher have? What help will the teacher need in organizing this kind of classroom? What can I do to help with classroom issues?" If the principal is knowledgeable about the curriculum and teacher needs, then more teachers are apt to "buy-in" to the curriculum.
After becoming knowledgeable about the curriculum, the principal will also have to consider his/her role in professional development activities. There is only so much a principal can do to learn about a curriculum by reading about it. The principal who actively participates in professional development will be much more knowledgeable, and will be perceived as much more supportive by teachers.
Being Supportive of Teachers
When teachers attend professional development activities to help themselves successfully implement CMP, they learn first hand about the mathematics in the units, about the connections among units, and about how problems are sequenced to develop mathematical ideas. They also learn about pedagogical aspects of the curriculum: why the curriculum is organized the way it is, what the teacher role is in the launch phase of a lesson, in the student exploration of a problem, and in the crucial summary phase. The principal who is present at professional development activities with teachers is likely to be attending less to the actual mathematics under study than to the perceived needs of teachers. Just as teachers learn to ask questions about what their students have learned and how they can be more supportive of student learning, so the principal can ask, "Do some of my building's teachers seem to need more help with the mathematics than others? How can I get them this help? Who seems fearful or resistant? Why is that? What can I do to increase the confidence of the teachers in my building that they can implement CMP? Do they need more information? More encouragement?"
As the building leader, the principal is the point person when questions come from district administrators and from parents/guardians. And as such the principal can be an advocate for teachers. When professional support for teachers needs district approval, the principal can make a case for what is needed; or when concerned parents/guardians have questions about a teacher's unfamiliar classroom practices, the principal can knowledgeably reassure the parent and support the teacher. It is important to be supportive of teachers in the evaluation process. When both teachers and principals understand the goals of CMP and how these goals are achieved, then the process of evaluating teachers has integrity and validity that would be lacking if the principal had one picture in mind and the teacher had another. Principals may find it helpful to see what a successful CMP classroom looks like. Evaluation based on mutually valued goals and practices fosters professionalism. The opportunity for a principal to observe and evaluate how CMP is being enacted in a particular classroom can be an opportunity to reinforce the common goals and aspirations of the building's personnel.
Communicating with Parents/Guardians
The building principal knows better than any other district administrator what his part of the district looks like, which parents he/she can expect to be involved in building activities, and which he/she can expect to have questions or concerns. The district can make general plans and suggestions to involve parents/ guardians, but the principal is uniquely placed to know best which plans are good fits for his/her school. From the list of suggestions below, or from others, each principal must make a wise selection so that parents and guardians feel included, and can be more supportive of their students' success in learning mathematics.
Some parents and guardians may have been involved in the initial stages described above. But most will only become aware that a new curriculum has been adopted after the fact. They may have questions about why CMP was adopted, why it looks different from traditional textbooks, and what evidence there is of student success. As mentioned above, the unfamiliarity of the problem- centered approach may be an obstacle that parents need help in overcoming. These are questions that a district committee that has done its work well in the initial stages can answer, or can arrange to have answered in a variety of ways.
Conscientious parents have always been concerned about their children's middle school education. Their concerns usually have two distinct foci:
What is my role in helping my child be successful now?
How well does this class prepare my child for high school mathematics and for post-secondary education?
Keeping Parents and Guardians Informed
Parents/guardians need to understand the goals of the program. Administrators and teachers can help them do this by keeping them informed, early and often, about both long-term and unit goals. Parents and guardians should know that the primary goal of CMP is to have students make sense of mathematical concepts, become proficient with basic skills, and communicate their reasoning and understanding clearly. The concepts and topics that students study should be familiar to parents/guardians, but the problem-centered textbooks may not make the particular topic or skill as explicit as the associated student work and reflections will. Parents and guardians need advice and help in making good use of their students' classwork as a resource.
The emphasis in reasoning and communication may be less familiar. Curriculum leaders and teachers can help parent/guardians understand why reasoning and communication are valued and that the program provides many opportunities to demonstrate students' progress in these areas. There are many specific ways that a district can gain the support of parents and guardians, and keep them informed:
Form a Community Advisory Group The group should be composed of knowledgeable and strong advocates for the program. The committee should consist of parents and guardians, teachers, university people (if there is a university in the area), business people (particularly those who appreciate the need for critical thinking) and administrators. This group will play a crucial role in the early stages of implementation, and less of a role as the success of CMP speaks for itself.
Present Information to the Community As implementation matures, a district might create a pamphlet for parents and guardians, including the results of district evaluation studies showing how well CMP students did on state tests.
Conduct Parent Workshops These can be helpful at the beginning of the school year, and at different stages of the implementation during the year. Topics to be discussed might include: overarching goals, evidence of effectiveness of CMP, specific mathematical information, the instructional model, mathematical expectations for students by the end of the year and the end of the program, the use of calculators, and transition to high school. An effective strategy for conducting these workshops is to engage parents/guardians in a problem from one of the student units, so they can experience first hand how understanding and skill are developed in CMP. These workshops might be tailored to fit specific concerns such as use of calculators and other technology, and how this affects learning or the particular mathematical goals of a unit that is about to start.
Send an Introductory Letter An introductory letter complements the Parent Workshops outlined above. A sample letter is included in the Parent Guide for CMP2.
Send a Parent/Guardian Letter As students begin a new unit, the teacher can send a letter to parents/guardians stating the goals of the unit and suggesting questions that parents/ guardians can ask their children. The Parent Guide for CMP2 contains a sample parent/guardian letter for each unit. These letters are available on the publisher's website and on the TeacherExpress CD-ROM, also available from the publisher.
Send Home Parent/Guardian Handbooks A district can create and send home handbooks addressing the mathematics in units and suggesting ways that parents/guardians can help their children.
Send Home Newsletters A newsletter is an excellent way to highlight the mathematics students are studying. A newsletter might include student work, stories about student insights, summaries of rich class discussions, or other evidence of achievement. If your district already has a community newsletter, then it may be possible to include news from the mathematics classroom in the newsletter.
Inform Parents/Guardians of Resources CMP provides a Parent Web site offering both background information and specific mathematical help to parents seeking to assist their students with homework.
Tutoring Labs Conduct a tutoring lab after school to reassure parents that additional help is available to students for homework. In one CMP district, a mathematics lab is held two days a week after school. Students sign up with their mathematics teacher to attend, and must bring with them work to do, such as homework, redoing a past assignment, organizing their notebooks, working on vocabulary lists or projects, or studying for a test or quiz. Copies of student units and Teacher's Guides and other materials and tools typically found in the classroom are available in the lab.
Teachers' Guides Make a copy of the Teacher's Guides, with answers removed, available in the school library for checking out.
Parent and Guardian Role:
A Supportive Parent CMP Web site Parents/guardians are an invaluable resource to the district if their knowledge, good intentions, and caring can be channeled to be compatible with the problem-centered approach of CMP.
"The first teachers are the parents, both by example and conversation."
In helping children learn, a parent/guardian's first goal should be to assist children in figuring out as much as they can for themselves. They can help by asking questions that guide, without telling what to do. Good questions and good listening will help children make sense of mathematics, build self-confidence, and encourage mathematical thinking and communication. A good question opens up a problem and supports different ways of thinking about it. A list of such questions is available at the CMP Parent Web site, along with background information about the curriculum. In addition to general information and advice, the Web site also offers specific mathematical information. A vocabulary list, with examples to illuminate meaning and use of new vocabulary, and examples of solutions of homework exercises are just two of the aids that parents/guardians will find at this site. This site can help parents/guardians to have meaningful mathematical conversations with their children.
Parents/guardians are some of the knowledgeable experts in their child's universe. Their expertise may be in the mathematical ideas, or in the learning process itself. They can help with homework by learning how to scaffold a problem for a child, without taking away all the gains to be made from the student's individual struggle.