Annual Report Overviews

Annual Overview and Findings Sections from the Annual Report

Implementing Investigations in Mathematics (InMath) is a partnership between Western Michigan University (Kalamazoo, MI) and 6 school districts in west Michigan - Battle Creek Public Schools, Holland Christian Schools, Lakeshore Public Schools, Portland Public Schools, Traverse City Public Schools, and Vicksburg Community Schools. The twenty-six participating schools across these districts have approximately 400 teachers and 10,000 K-5 students. These school districts are committed to district-wide reform of their elementary mathematics program through their adoption of the NSF-funded elementary mathematics curriculum, Investigations in Number, Data, and Space. Investigations is a K-5 mathematics program aligned with national and state standards in mathematics teaching and learning. Organized around four major strands--number, geometry and measurement, data, and change--there are six to eleven modules for each grade level. The focus of the program is on reasoning and problem solving where students are required to explain their thinking orally and in writing. Successful implementation of Investigations requires that teachers understand the mathematical content, use questioning to probe students' reasoning, and promote discussion and sharing of ideas to encourage construction of knowledge by students rather than dispensing of knowledge by the teacher. The InMath collaborative is designed to help participating schools implement Investigations.

Specific project objectives are: improving teachers' mathematical content knowledge, including knowledge of the technology employed by the curriculum; extending elementary school teachers' understanding of the pedagogical underpinnings of the Investigations program; facilitating elementary school teachers' abilities to critically analyze the process of teaching and student learning; fostering the development of teacher leaders and communities of learners within and across schools; and supporting schools' efforts to communicate positively with the community about issues pertaining to reforming mathematics teaching and learning.

To accomplish these goals we have held: week-long summer workshops, Reflecting on Teaching sessions, one-day conferences, Coordinating Council meetings, and district-specific workshops. Week-long summer workshops (discussed below) are held each summer of the project and focus on a particular content strand. Reflecting on Teaching sessions (discussed below) have served as the major school-year follow-up to summer workshops and have provided teachers with opportunities to deal with issues and concerns at their particular grade level and share ideas and experiences with colleagues from different districts. The Coordinating Council (made up of representation from each district) met bi-monthly in year 1 to assess project activities, plan professional development, and discuss plans for school/district meetings. An all-day annual conference (discussed below) was held in March of year 1 to provide teachers with opportunities to interact with colleagues and discuss issues around implementing a reform curricula in the classroom (e.g., student thinking , teacher questioning) and outside the classroom (e.g. State-wide testing, dealing with parents). Finally, a cadre of teacher leaders was recruited in the Spring of 2000. This group was established to increase our abilities to meet the professional development needs of the InMath participants, as well as providing a vehicle for sustainability of our efforts after the grant ends.

One of our main accomplishments this year has been the continued growth of our cadre of teacher leaders and their ability to take on more responsibility for the professional development offerings in their districts and provide for each district's unique needs. Leaders from several districts met with the project directors to plan professional development for their districts based on district needs. For example, leaders from the Portland district perceived a need to focus on the number strand, to consider what research has to say about student learning in this area, and to consider reasonable goals for number at each grade level. The Portland leaders implemented the first in a series of workshops around these goals in August 2001, and shared the results with the rest of the teacher leader group during our planning meeting in September 2001. This set the stage for the leaders to think about how to support their districts in continuing to think hard about teaching and learning mathematics.

Another major accomplishment continues to be our ability to provide a range of professional development opportunities to meet the needs of our participants, and push their thinking about teaching and learning mathematics. As mentioned above, many of the leaders have begun to consider ways to support their district after the grant ends. In addition to these district level professional development activities, InMath cross-district offerings focused mainly on the grade-level specific Reflecting on Teaching workshops and the additional summer conference on Numerical and Algebraic Thinking.

The "Reflecting on Teaching" workshops continued to be a success in encouraging teachers to think more deeply about the main components of a lesson: launching or introducing the lesson, supporting students as they work on mathematics task(s), and closing the lesson. The teachers continued to grapple with some major issues about teaching and learning so that they could weigh the advantages and disadvantages of certain approaches and the effects these approaches have on student learning. A total of 186 teachers and administrators attended these sessions. Another indication of the success of this professional development format is the fact that some of the districts chose to offer additional Reflecting on Teaching sessions for the teachers in their district during the 2001-2002 school year.

Although we had not planned to have a fourth summer workshop, one was added based on the interest expressed on the evaluation forms from the previous summer. This final two-day summer workshop was viewed as a kind of "capstone" where we revisited ideas involved in numerical reasoning while extending it to algebraic reasoning as well. Although this workshop was not part of the original plan, there was enough demand to offer the workshop twice during the third week of June. The workshop was attended by 145 teachers and administrators. As can be seen in the evaluation report, the workshops were considered a success by the participants. Participants spent the first day working on what distinguishes algebraic reasoning from numerical reasoning; how these ideas are developed K-5; and how algebraic reasoning can be developed during whole number computation work. On the second day the participants analyzed the embedded assessments in the computation units in order to determine the big mathematical ideas for the whole number computation strand and expectations for student performance on these assessments. Discussions began in grade-level groups, and then expanded to cross-grade discussion in order to consider the development of big ideas and expectations across grade levels. The workshop concluded with a panel discussion in which the teacher leaders who had allowed their videotapes to be the focus of the Reflecting on Teaching workshops shared how their experiences had influenced their practice. This final session was a fitting end to the whole collaborative professional development in that it left the participants with powerful incentive to open up their classroom to others as a way to continue to think hard about their own teaching. One measure of the success of this message is the fact that at the end of the conference 54 participants completed a form volunteering to be observed teaching mathematics during the upcoming year.

The strong attendance at our professional development sessions is one indicator of our success. Three hundred and fifty eight teachers and teacher-leaders are currently participating in the InMath project, and an additional 152 teachers have, at some point, been participating members of the InMath project. This additional group includes teachers who currently do not teach mathematics (including special education teachers) and teachers who have left participating schools. Thus far the 358 targeted teachers have received a total of 31,227 hours of professional development, an average of 87 hours. The implementation of well designed professional development at the individual districts is another indicator of the influence we have had on individual teachers, and districts as a whole.

In addition to the professional development offerings designed for all the InMath participants, the Project Directors designed and implemented professional development for the cadre of teacher leaders that had been recruited during the Spring of 2000. These leaders attended the third, and final, Leadership Institute in April 2002, in which we worked on problems to enhance their algebraic reasoning abilities, discussed ties to numerical reasoning, and discussed issues around facilitating professional development that supports teacher thinking. In addition they attended follow-up meetings during the year designed to provide them with support as they planned and implemented professional development offerings.

During the 2001-2002 school year we continued to offer grade-level specific Reflecting on Teaching (RT) sessions. As designers of these sessions we continue to be amazed at the variety and complexity of the issues that arise during these sessions, and the effect that experiencing multiple sessions of this type has had on the participants' abilities to thoughtfully challenge ideas about teaching and learning mathematics. Therefore we have begun two related research projects around analyzing this phenomena. One study is focused on analyzing the issues that arise during the RT sessions. For the past two years we have been videotaping the RT sessions, and writing post-session reflections on the issues that were successfully pursued during the session, as well as those issues that were not pursued. Although we have not begun formal analysis of this data, the themes noticed during the data collection itself greatly impacted our decisions about what types of lessons to focus on for the RT sessions that were held this year and helped us determine which issues to tackle during our final summer workshop (discussed below).

The second study focuses on tracking the shifts in thinking and practice made by teachers as a result of participating in the Reflecting on Teaching (RT) sessions. All teachers who attended the sessions completed post-session questionnaires, while a subset of the participating teachers and facilitators were interviewed and observed teaching after attending the sessions. In most cases, we were able to observe the teachers doing the same lesson which was the focus of the RT session they attended in order to garner information on what alterations they may have made to that specific lesson. We also interviewed them about the impact of the RT sessions on their teaching in general to obtain information on what aspects of their teaching they were working on as a result of the discussion from the RT session. Initial analysis of this data suggests that the RT format has a positive impact on teachers, both at allowing teachers to think hard about teaching mathematics for understanding and implement changes in their classroom. In particular, this format was useful at dealing with both content and pedagogy as well as both general and lesson-specific issues. Although the level of impact varied according to the amount of experience teachers had using the curriculum and the amount of RT sessions attended, the positive results overall suggest the potential for these sessions to impact a diverse range of teachers.

We feel it important to acknowledge that these results occurred in a particular context. For the most part, the teachers in this study had been involved in InMath for three years and had the opportunity to attend several RT sessions during that time. Although the teachers attending each session changed over time, the learning community that had been established among the teachers as part of their participation in the grant clearly laid the groundwork for this kind of work. The participants learned to think more deeply about issues of teaching and learning, to value the in-depth analysis of lessons, and to appreciate the teachers who were willing to open up their classrooms and instruction to such scrutiny. Rather than looking for easy solutions or quick fixes, this community of teachers was bonded together by the common goal of tackling the complexity of teaching and learning through analysis, reflection, and implementation. Without this common goal and common participation in the project, it is probably less likely for impactful learning to occur in RT sessions.

As a result of our preliminary research on the RT sessions (described above) and our observations and videotaping of teachers in the project, we have begun to formulate some ideas about the particular challenges of teaching for understanding. One line of thinking that has developed as a result of this work has been the importance of determining what makes a reasonable explanation of one's mathematical work. We have noticed that when students share their solutions, they are more often than not, simple descriptions of what they did. Teachers seem to be challenged to push for explanations of why solutions work and why various procedures work. It is in this work of pushing for explanation that one can make better ties between numerical reasoning and foundational ideas for algebraic reasoning. Therefore, for the summer 2002 workshop, we designed a session specifically to address this issue in the context of whole number computation and facilitating discussions in the classroom around the procedures students invent. The post-workshop evaluations from the summer were very positive and many teachers described the impact this session in particular had on their thinking. One participant response on the evaluation form that was indicative of most of the responses was, "I can see that asking students to explain their work can help them better develop algebraic reasoning."

In terms of what the teacher leaders have learned as a result of participating as leaders in this project, they have grown in their ability to facilitate professional development sessions where the participants are encouraged to think and develop a more grounded and well-articulated philosophy on teaching and learning. At the last Leadership Institute, the teacher leaders were asked to write about issues around facilitation and what has helped them overcome some of the challenges of facilitating well. One teacher leader wrote: "Prior to the sessions, I find if I think deeply about specific issues and critically think about these issues (trying to think how participants would think), I'm prepared to respond in a manner that does not condescend, criticize, threaten, but does challenge thinking as a whole group as well as individually." The panel that we held during the summer 2002 workshop where some of the teacher leaders were asked to share their thoughts about what they learned from RT sessions, being the teacher on the tape for at least one RT session, was also very enlightening in terms of how these leaders' thinking and practice have been impacted positively as a result of the InMath project. One teacher even described how she altered a lesson the next time it was taught as a result of discussion during an RT session, but then felt it did not improve the lesson whatsoever-it was an alteration with a negative result. However, she explained that this was a valuable experience for her, because reflecting on teaching and making alterations may not always result in positive outcomes. Yet it is through this process of sometimes making moves that are successful and sometimes making others that you decide you can eliminate for the future that improve teaching and allow one to develop more grounded notions of teaching and learning in general.