RMTC is a collaborative of eighteen high schools and middle schools from ten districts in West Michigan focused on helping teachers effectively implement the Core-Plus Mathematics Project (CPMP) and Connected Mathematics Project (CMP) curricula. These districts have adopted these curricula for some or all of their students as part of their efforts to improve mathematics teaching and learning in their schools. The evaluation results reported below include only the high schools, as the middle schools were added after the end of Year 2.
An external evaluation is being conducted by Science and Mathematics Program Improvement (SAMPI) at Western Michigan University, the purpose of which is to provide information to help improve programs and assess project accomplishments. Data are collected through annual surveys of principals and teachers, interviews with teachers, classroom observations of mathematics lessons, observation of professional development sessions, pre/post-content tests for teachers, end-of-session questionnaires, and documentation of activities. What follows are summaries of selected evaluation findings at the end of Year 2.
Classroom observations of mathematics lessons, using a nationally developed rating system framed around investigative-oriented mathematics instruction, shows substantial differences between teaching practices of those using Core-Plus and those using other materials. Core-Plus teachers are clearly using more investigative strategies in their mathematics teaching. Most Core-Plus teachers tend to closely follow the curriculum, although all make at least minor modifications as to how many of the investigations and problems they assign. Those with the most Core-Plus experience tend to substitute or supplement text materials with their own investigations.
An Example of an Investigative Strategy. Lesson observations show effective questioning strategies among those teachers who are successfully implementing Core-Plus. The vignette below is illustrative.
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Effective Questioning: The teacher, as she circulates among the small groups and when the groups are presenting, challenges students with probing questions that require them to make a case for their thinking. Questions are not designed to solicit facts, but to stimulate thinking. As students presented their solutions to the problem, the teacher asked such questions as "Why did you use that procedure?" and "How else could you have done it?" She also asked, "Does everyone agree with this solution?" and follows up with (for those agreeing), "Why do you agree?" For those not agreeing, she asks, "What's wrong with this solution?" and "How would you do it differently?" This teacher doesn't let a solution or answer go unchallenged. She expects students to be able to support their answers. She expects them to reflect on what they are learning and how. She asks such questions as "What have we learned from this problem?" and "What are the different ways that you came to a proposed solution?" and "Where would you encounter this idea in the real world?" The initial exercises on probability were followed up with a problem called "Fantasy Baseball Game" using real-life statistics and requiring students to determine probabilities given different scenarios. They were expected to show the mathematics computations they used to determine the probabilities. |
RMTC professional development is extensive and varied and designed to build the content, pedagogical, and leadership knowledge and skills of participating teachers so they can successfully implement the Core-Plus Mathematics Project curriculum in their classrooms and schools. The RMTC PD programming is also intended to build learning communities within participating schools and across schools in the collaborative.
Summer workshops, which often serve as the entry point into the program for teachers, are intensive 5-day sessions in which teachers, collaborating in small groups with the guidance and coaching from workshop facilitators, actually do the activities and problems their students will be doing. These same teachers gather for follow-up sessions in the fall. All teachers are also invited to participate in a one-day whole collaborative conference that provides opportunities for networking and discussion. Staff and school representatives facilitate school-site and regional meetings periodically throughout the school year. The Coordinating Council, made up of teachers representing each of the participating districts, provides another forum for dialogue and learning.
RMTC professional development is sustained, in-depth, and curriculum-focused. It encourages and facilitates interaction and substantive conversation among participants, models the kind of pedagogy teachers should use with their own students, builds leadership skills, and supports teachers as they implement mathematics curriculum in their classrooms. Teacher feedback about their PD experiences is positive. One teacher said, in relating her summer workshop experience, "Makes me realize the validity of having students discover mathematics with me as a guide, rather than me as a lecturer and 'teller' of information."
In an annual survey, teachers are asked to rate their preparation in knowledge of mathematics topics, pedagogical content, and instructional strategies. Data were disaggregated on the basis of how much professional development teachers had received. In general those with the least exposure to the RMTC PD programming tend to rate themselves higher on preparation than those in groups who have received PD. This phenomenon has been seen by the evaluator in other projects. It is apparent that as teachers become more familiar with the topics and issues that are the focus of the PD, they seem to realize they are not as well prepared in those areas as they may have though before becoming involved in RMTC. As teachers receive more PD and have opportunities to implement what they are learning in the classroom, they become fore confident of their preparation. The survey results from the RMTC teachers clearly show that pattern.
Although interviews revealed that teachers were generally enthused about the investigative nature of the Core-Plus curriculum, several were cautious about it because it represents a significant departure from the traditional mathematics programs. A few are opposed to implementation of the Core-Plus curriculum. Some of the resistance comes from philosophical differences, while other teachers are unwilling to invest their time in substantive professional development. Those actually using the Core-Plus curriculum generally said that the more experience they have with the materials, the more comfortable they are in using them. When they have colleagues in their schools also using the program, they do consult with them regularly. Some teachers who have Core-Plus classes and traditional classes indicate their strategies in traditional classes have been affected by their Core-Plus work.