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Private Universe Project in Mathematics

Synopses
Structure
Contributors
Brochure (PDF)

 

Series Overview

Children using manipulativesThis workshop series provides an interactive context for teachers, administrators, and other interested adults to explore issues about learning and teaching mathematics. Central to each session is a 60-minute videotape that offers a sequence of episodes showing children and/or teachers engaged in authentic mathematical activity and discussion, consistent with state and national standards for teaching and evaluating mathematics. These episodes come from a variety of sources in diverse school communities and across grade levels from pre-kindergarten to 12th grade. The episodes and accompanying narratives in each videotape focus on:

  1. students and teachers actively engaged in doing mathematics;
  2. conditions that encourage meaningful mathematical activity; and
  3. implications for learning, teaching, and assessment.

The materials and activities presented in the sessions have been developed in long-term research programs about mathematical thinking that share certain presuppositions about learning and teaching. Key to this perspective is that knowledge and competence develop most effectively in situations where students, frequently working with others, work on challenging problems, discuss various strategies, argue about conflicting ideas, and regularly present justifications for their solutions to each other and to the entire class. The role of the teacher includes selecting and posing the problems, then questioning, listening, and facilitating classroom discourse, usually without direct procedural instruction.

Each videotape contains episodes from a 12-year research study carried out in the Kenilworth, New Jersey public schools within a partnership with the Robert B. Davis Institute for Learning at Rutgers University that began in 1984. This partnership included an intensive, classroom-based staff development program in mathematics for teachers and administrators at the K-8 Harding Elementary School. Classroom sessions in which students frequently worked together in small groups on meaningful problem activities. One classroom of children was followed from first through third grades by regularly videotaping small-group problem-solving sessions, whole class discussions, and individual task-based interviews. From 1991 to the present, with periodic support from two National Science Foundation grants, the research team has continued documenting and studying the thinking of a focus group of these children through grade 12. The videotapes from these later years document the students as they participated in problem-based activities developed by the university researchers in classroom lessons, after-school sessions, a two-week summer institute, and individual and small-group task-based interviews.

In the workshop videotapes, participants will see some of the same children solving mathematical problems at various grade levels over the years. In addition, the activities they engage in have been used in other communities and at other grade levels. In June 2000, the focus group of students in this study graduated from Kenilworth's David Brearley Middle/High School.

Workshop participants will explore particular questions about learning and teaching mathematics based on the shared experience of watching the videotapes. Key questions are:

  1. How do children (and adults) learn mathematics?
  2. How do children (and adults) learn to communicate about mathematics and to explain and justify solutions to problems?
  3. What conditions (environments, activities, interactions) are most helpful in facilitating this development?
  4. What does it mean to be a teacher of mathematics?
  5. What is the connection between learning and teaching?
Each videotape includes episodes of children engaged in mathematical problem activities. The goal is for participants to become able to recognize what is mathematical in students' activity by attending very closely to what they do and say. As they observe, study and discuss what they see on the tape from the perspective of the questions listed above, participants will gain insights about learning and teaching. As preparation, participants need to build their own solutions to the central problems in each tape with assignments given between sessions and during the first hour of each workshop. They are encouraged to select and use appropriate problems with their own students and to read further about the learning and teaching of these ideas.

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