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The Thinking Mathematics project was begun with seed money from OERI; the St. Agnes School project has been substantially supported with OERI funds throughout its application and dissemination efforts. Both projects are based largely on earlier research conducted under OERI auspices in NRCSL, and both represent a true partnership among government, research, and education practitioners to further a substantive understanding of learning processes and an application of that understanding to improvements in education.
For most of my colleagues, researchers are viewed as ivory tower people not connected with reality. When they would come to the schools, teachers would turn up their noses. [Yet] I've found teachers eager to receive valid, real-class research that we ourselves have tried out. I think that there is a great hunger on the part of teachers for ways to solve the problems they see every day.
--Alice Gill, elementary mathematics teacherDuring the 1987-88 school year, NRCSL mounted a dissemination effort that was meant, at first, to be accomplished through the translation of research findings, by teachers, for teachers. The model upon which it was based was that of the American Federation of Teachers (AFT) successful Educational Research and Development (ER&D) program, in which teachers called Local Site Coordinators (LSCs) synthesized and disseminated research for colleagues in their school districts on such topics as classroom management and cooperative learning.
The new collaboration, however, was the first ER&D attempt to synthesize cognitive research on the content of a given discipline. NRCSL's interest in working with the AFT to convey research on mathematics learning to the union's membership was motivated first, as NRCSL's William Bickel explains, "because practitioner groups such as the AFT are skilled at communicating to their own communities, but we're not. To the extent that we could establish a relationship and dialog with the AFT, we could reach the larger constituency that they represent." AFT responded well to the idea, says Bickel, because of an equal concern about "the conditions of mathematics instruction in the schools. . . . We believed, and the AFT agreed, that there was new math research knowledge that could help."
Most of the research to which Bickel refers had to do with children's intuitive, preschool knowledge of mathematics and with ways in which instruction could build upon this knowledge, promote discovery instead of leaning heavily on repetitive drill and practice, and foster reasoning and problem-solving skills. The joint AFT/NRCSL goal was to help teachers apply the research findings in the classroom. The plan for reaching the goal was to commission cognitive science experts to write articles synthesizing recent math research and then to recruit expert math teachers from the AFT to translate those articles for other practitioners. The translators--called Visiting Practitioners--would come to NRCSL for a summer workshop at which they would read, discuss, and prepare to disseminate the research synthesis.
The plan hit a snag when its initial one-sidedness became apparent. The researchers, in designing the project and the workshops, focused primarily on research findings that might improve practice, but they attended little to the world of practice itself. The readings they gave to the Visiting Practitioners had much to say about concepts and principles that could affect instruction; but they did not prescribe actual reforms or methods, nor did researchers always interpret findings in the same way. The Visiting Practitioners, though they had decades of practical and intuitive knowledge about instruction, were unfamiliar with the standards, language, and procedures of the "ivory tower people." As a consequence, what was meant to be a collaboration came to resemble a tutorial, with expert mathematics teachers placed unwittingly in the role of the researchers' students. These "students," in carrying our their reading and translation assignments, were not urged to question research findings, interpret them in the light of their clinical expertise, or suggest refinements.
Thus, the first AFT/NRCSL attempt to launch a productive, extended dialog became, almost literally, a monolog. Gaea Leinhardt videotaped the sessions that took place in that first workshop and coded them, as she recalls, "with respect to issues like who was speaking, who initiated it, whether we were talking about math, whether we were telling anecdotes or talking about the politics of schools." She was looking for lively discussion, she explains. "What I was hoping to see over time was an increase in the amount of talk that was being controlled and actually spoken by teachers and an increase in the amount of mathematical discussion." What Leinhardt found instead was that most substantive discussion that summer was initiated and led by researchers. The teachers said little.
The results of that workshop led the researchers to realize that they needed to say less and listen more, which meant they had to create conditions under which the Visiting Practitioners would be motivated to speak. As Leinhardt says, "to get teachers to talk about how to actually teach a substantive topic in math is quite difficult. You must give them time to talk, and you must make sure that it's a very supportive environment in which to bring those topics up. Their assumption may be that researchers know exactly how to teach this, which is not true. We often haven't the foggiest idea."
By the next summer's workshop, for which a second group of Visiting Practitioners was recruited, the new plan, Leinhardt says, "was not to understand research articles and see how they could be applied to the classroom, but to understand the nature of a classroom lesson and see how research might support the goals of that lesson."
Calling upon the Visiting Practitioners clinical expertise added the key element to the collaboration. The project already was the only content-based ER&D effort and the only one to attempt an extended dialog between practitioners and researchers. But the dialog could succeed only if it were conducted as a conversation among equals, with the researchers as willing to learn from the teachers as to instruct them. By degrees, the shift in focus from the researchers' world to the teachers' world made way for the Visiting Practitioners to become the researchers' colleagues and coauthors, eventually taking the lead in preparing the Thinking Mathematics series, volumes of teacher training materials that combine the best insights of both research and practice, while adhering to the standards of the National Council of Teachers of Mathematics. The volumes that have been issued so far cover counting, addition, subtraction, multiplication, division, and problem solving.
Alice Gill, a 22-year veteran of the Cleveland Public Schools, was one of the teachers recruited for the 1989 summer workshop where the new clinical emphasis took hold. Gill, a generalist who taught all subjects in second and third grades, says, "I plodded along with traditional teachings, but I was always searching for better ways. I wasn't happy with what was happening in my classroom." Gill was not the only one in her school who was discouraged. The year before she joined the collaboration with NRCSL, she recalls, "A staff-led team began to work on revitalizing the school. More than 50 percent of the kids in kindergarten through third grade were getting D's and F's in math. That was startling. Everybody thinks elementary math is easy."
When Gill learned that NRCSL was looking for collaborators, she was both excited and apprehensive. She already had been a Local Site Coordinator for AFT for 3 years, but this time, she says, "the call for applications said that they wanted teachers with a math background, which I didn't have. I called to ask about that and was encouraged to apply." Today, Gill feels "the project is probably better for having someone like me, without the deep math background. What we produce has to be disseminated to people like me. We have to ask, what's daily life like for the teacher who does more than teach only math? There's a different way of looking at things when you have a math background than when you teach eight subjects a week."
That second summer, the project began to produce the first volume of Thinking Mathematics, on counting, addition, and subtraction. Teachers who applied to the project were asked to review some of the research and to design lesson strategies as part of the application process. The five who were chosen to be Visiting Practitioners--including Gill--continued reading research and devising applications so that they would be prepared, by summer, to enter a dialog with the researchers. As William Bickel and Rosemary Hattrup write in their account of the project, a paper entitled "Paths to Professionalism," this early emphasis on lessons "placed the conversation on the teachers' home turf and provided the opportunity for the teachers to examine the research through the lens of their own classroom experience. It was the collaborative's hope that the dialog, rooted to classroom expertise at the outset, would begin more quickly . . . and that the teachers' clinical knowledge would be . . . reflected substantively in the conversations as well."
The new Visiting Practitioners did engage earlier and more substantively in dialog with the researchers, but they still were tentative in their linking of research to practice. According to Bickel and Hattrup, "Notions such as building on the students' own knowledge and the acceptance of multiple correct solutions (and sometimes answers) represented fundamental departures for many of the teachers. . . . The sense of unease was aggravated by the press of the schedule." These teachers were therefore entering with some apprehension into the very process that research suggested they should lead their students through. The teachers' credibility--which eventually came to illuminate the Thinking Mathematics materials, the teachers' own classrooms, and their relations with colleagues at pilot sites--came directly out of their firsthand experience with bridge-building between the clinical and scholarly worlds. They were able to link the practical, intuitive knowledge that is based in experience with the formal, theoretical knowledge that derives from close, disciplined studies of cognitive phenomena. This bridge-building experience is called "sense-making" by researchers. Things do not make sense until they are put into practice, refined, and adapted--until one can walk freely back and forth between the two worlds and their related but differently based concepts. The same is true for students, who must learn to relate the formal knowledge they gain through instruction to their lives beyond school walls.
True sense-making began for the Visiting Practitioners when they started pilot testing the Thinking Mathematics materials in their own schools and school districts. They put new methods into practice, based on instructional principles derived from their knowledge of research. These principles, which they identified in collaboration with the researchers, included the following means of linking abstract concepts to concrete referents: building on students intuitive knowledge; presenting students with situational story problems; making considerable use of manipulatives; stressing the acceptability of multiple solutions to problems; requiring students to explain and justify their procedures and answers. Other principles that the Visiting Practitioners applied had a somewhat different focus--instructional flexibility. For example, the Visiting Practitioners worked on developing the metacognitive skills Leinhardt had observed in expert teachers; that is, the ability to monitor their students' comprehension constantly and to adjust their instruction as needed. They also relaxed their notions of the traditional curricular hierarchy that assigned math topics grade by grade and began to cover some topics earlier than before. Finally, they shifted their priority from quantity to depth of material covered, often extending by a matter of weeks the time they spent on important material.
In addition, the Visiting Practitioners conducted in-service sessions and discussions aimed at sharing new principles and methods with colleagues. Thus, their goal was not only to improve their own instruction but to build a culture of professionalism among their peers.
For Alice Gill--one of the overly busy generalists for whom Thinking Mathematics has been developed--both processes were dramatic. "I came back to my school, and the first thing I had to do was to bury my textbook. My goals were so different from what the text was after--getting kids just to learn basic facts and perform computations. My new goals were to produce kids who could think about math, solve problems--who really had confidence. And I saw all of this happen in my classroom. . . . Kids came up with so many ways of reaching right answers. Kids who had done nothing became contributors. What I saw was so much more than I would ever have thought these children could do."
When Gill began disseminating results of her summer work to teachers in her school district, she found that task, too, very different from her past ER&D work. "You can do a unit on effective teaching of rules and procedures," she explains, "and then the teachers can try it. But when you're developing radically different math instruction, it is necessary to do some modeling in the classroom and to have teachers interact with each other about what's happening."
Both Gill and the other Visiting Practitioners thus discovered the importance of a culture of professionalism. "Before," says Gill, "I would make independent efforts at reform, but even the things I thought were great were not so great. I didn't have the math knowledge to see that. I think teachers need more math knowledge, and I think they need to understand the NCTM standards; but it is going to take quite a dissemination effort to get them to buy in. What happens is, teachers who might decide to experiment might run up against district requirements that slap them down. They have to teach to standard, traditional tests. They revert back to the conventional ways of teaching." Gill and others in the AFT/NRCSL collaboration hope that leaders and role models who can demonstrate the success of new approaches to math instruction will appear increasingly among the ranks of teachers and gradually gain the backing of administrators and district management.
The role of the teacher, as the Visiting Practitioners' experience shows, is crucial to any system-wide changes in instruction. Through developing, piloting, and reflecting on the Thinking Mathematics materials, the teachers have been able to appreciate the appropriate and powerful ways in which their clinical insights can shape reforms in the collaboration itself, in their schools, and among their colleagues. Almost no researchers are likely ever to be in as good a position to gain such well-rounded an expertise--a professionalism that comes both through close familiarity with researchers as colleagues and through years of classroom experience. The teacher is the link between the intuitive and the formal, between the students and the research that can benefit them. Yet, in the past, as one Visiting Practitioner told Bickel and Hattrup, "attempts at professionalizing teachers [too often] have focused on giving them 'teacher proof' programs that were supposed to succeed in spite of the teachers. This collaboration, on the other hand," said the teacher, "has truly professionalized teachers by trusting them to build the design necessary to influence classrooms." The same might be said for NRCSL's other major teacher-researcher collaboration, the St. Agnes school project.
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[St. Agnes School Project]