Encouraging Mathematical Thinking


 Abstract
 Introduction

 Discourse
 Interventions
 Decisions

 Cylinder Problem
 Lesson Reflections
 Student Predictions

 Project Reflections
 Conclusion

 References
 Acknowledgments
 Teacher Resources



Authors'
Biographies

Table of Contents


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Reflections

Roya Salehi       [Biography]



Throughout this year, as part of my involvement in the BRAP project, I have had to wrestle with my perception of the roles of "researcher" and "teacher." To begin with, I have always been bothered by the unspoken dichotomy that exists in education in America today: the overwhelming separation of teachers and researchers. I feel these two communities have much to talk about, to share, to collaborate on, and to learn from each other, yet a hidden wall separates them.

I have noticed that some teachers who are interested in dialogue and interaction with researchers do not know where to go to find researchers who are interested in collaborative work and reciprocal communication. I know teachers who use the excuse that they are already overwhelmed and don't have the time. I have talked with teachers who say researchers' contributions are not relevant to them, not accessible or applicable to their work in the classroom. Still other teachers have told me that they lack the language and the vocabulary used in the research communities to be able to have meaningful conversation and exchanges of ideas.

Researchers know where the teachers are, but some do not want to make the effort to start a dialogue. One would think that education researchers would benefit from either having had some prior teaching experience that they could draw from in their work, or from being involved in teaching at the time of their research. I've heard researchers say that they don't have the proper training to teach, and hence they stay away from real classroom settings and leave teaching in the hands of teachers. Still other researchers do not think that the practical aspect that comes from being in the trenches benefits them. Schoenfeld, Ball, Renninger, Schifter, Bowers, Lampert and Chazan are among the few researchers who have tried to lessen this gap, but it seems as if the overwhelming majority of researchers in education today, do not see the value in discourse or hands-on collaborative work with practioners. Then there are those in the research community who look down on the "first person research" or "action research" initiated by some teachers.

I was excited about participating in BRAP, since I saw this project as an opportunity to discuss and explore some of the issues surrounding this dichotomy. As someone who has always been interested and involved in research, and as a former teacher, I felt I had a lot to share and learn from both communities.

At some point in the project, we realized that the distance between research and practice was greater than one would imagine, and that any temporary bridge built might not span the distance. It became obvious that before any bridge can be built, one must first help to narrow the gap. We needed to create a common language and a vocabulary that we could all draw from and have a common understanding of. We also learned that integrating the two communities, where each one keeps its own identity yet has a closer understanding of the other, was a better solution -- weaving research and practice rather than building a bridge between the two. From that point on, we decided to call our local version of the BRAP project WRAP: Weaving Research and Practice.

Through the readings that I have done this year, I have learned that this separation between practice and research is a norm that has been established in the United States, and that it does not necessarily reflect the beliefs of educators in other countries, researchers or teachers alike. One model of weaving research and practice is the Japanese version of research and professional development. Teachers in Japan contribute to the collective knowledge of the field of education in that country more than do the educators we would traditionally call "researchers" in this country. The research done by teachers in Japan is looked upon as one important form of research, and the process of producing such research is considered an important form of professional development. In Japan, teachers believe that it is their job to get involved in research as part of their professional growth. They see themselves as authorities in the field, and others consider their contributions valuable additions to the broader knowledge.

Through creating "research lessons," these Japanese teachers work with groups of colleagues and choose a common lesson involving a rich topic that they all like to teach. They videotape the lessons, allocate time to watch and reflect on what they see on the tapes of their own teaching, and comment on each other's teaching. They implement the improved lesson, go back and focus on moments of the lesson and the questions that the kids asked, use this knowledge to role-play different scenarios that might arise in the course of the lesson and come up with open-ended or leading questions that they might want to ask in those situations. Finally, after several rounds of testing and reflecting, they publish their results. Each teacher is usually involved in at least one of these year-long research lessons, if not more. In Japan, the teacher's scholarly work in the form of "research lessons" is appreciated as much as the work of other researchers in the field.

It has been interesting to watch the WRAP project evolve to resemble the Japanese research model -- by default, not by design. The project has been flexible, to allow participants' input at all times. Active participant involvement has been and will continue to be an important part of WRAP, and is considered to be one of its great strengths. It will be interesting to see the reaction of the research community to our effort and to the unique genre of research found in our videopaper.

In the course of this project, we have learned that communication, collaboration, risk-taking, having a safe circle in which to share ideas, and creating time for ourselves for reflection are important to us, that they help build our confidence in what we are doing. We've learned that we have a lot to say, and are ready to talk about our ideas.

As I continue my participation in the WRAP project, and as we embark on inviting other teachers and researchers who are interested in the message of our paper to participate in our dialogue, I will carry and challenge my colleagues in the research and the teaching communities with these questions:

What is the value of educational research if it does not have a practical aspect that can immediately be applied to the classroom? Who are educational researchers? How do we define researchers? Does one have to have specific degrees, or a certain number of publications before being accepted into the research community? Or is it a matter of mastering the vocabulary used in the community? What are the challenges involved in weaving research and practice? What is its impact on our teaching and on our research?

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