Our fundamental goal is
to gain access to and analyze teachers’ and students’ understandings
of shared classroom interactions, and the teaching and learning that results.
In particular, the project coordinates analyses of taken-as-shared classroom
problem-solving practices with individual teachers' and students' understandings
of those practices. Our strategy is to videotape classroom interactions and
to pursue the sense that teachers and students make of those interactions during
subsequent videotaped interviews. Thus, the project examines the sense that
students make of their opportunities to learn and teachers’ sensitivity
to the core learning issues for their students. The scope of the proposed research
requires a team in which each researcher takes primary responsibility for a
different piece of the project, and all members of the team collaborate on data
collection and analysis.
The mathematical content
at the center of proposed research lies at the intersection of algebra, problem
solving, and representations. New, expanded forms of algebra that are making
their way into middle schools emphasize not only operating on and transforming
algebraic symbols but also ways of representing and reasoning about problem
situations. Problem situations can have many different features, and we focus
on multiplicative comparisons, including ratio and rate, in problem situations
that contain unknown quantities, patterns, or covariation. The proposed research
will examine students’ knowledge for generating and using representations
to solve problems before they have established strategies and ways that teachers
gain access to students’ sense making through the use of representations.
The research will consider both standard and non-standard representations that
teachers and students use.
The project will gather
and analyze videotaped lesson and interview data in three classrooms in a nearby
middle school that has recently adopted the standards-based Connected Mathematics
Project materials, whose development was funded by the National Science Foundation
(NSF). The school has 10 mathematics teachers and 685 students from diverse
racial and socioeconomic backgrounds. The project will focus on three teachers
(one 6th-, one 7th-, and one 8th-grade teacher) and on three cohorts of six
students (one cohort in each of the three teacher's classrooms). As part of
the negotiated relationship between the research team and the school, the project
will also include a program of teacher professional development that, among
other things, will enhance the implementation of CMP, will make teachers' and
students' learning more visible to the researchers, and will allow the research
team to develop a broader understanding of the teaching and learning context
at the school.
Important products of the CoSTAR project will include (1) methods that coordinate research on the cognition and learning of teachers and their students, (2) integrated studies of teaching and learning middle-school algebra through solving rich problems (problems for which there are multiple solution paths), and (3) contextualized professional development focused on resolving instructional problems that arise when teaching mathematics through such problems.
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 Funded by the National Science Foundation - Research on Learning and Education Program |
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Last updated March 7, 2005 by Chandra Orrill.