January 1998, Vol. 29, Issue 1
Open and Closed Mathematics: Student Experiences and Understandings
Jo Boaler
This paper reports
on three-year case studies of two schools with alternative mathematical teaching
approaches. One school used a traditional, textbook approach; the other used
open-ended activities at all times. Using various forms of case study data,
including observations, questionnaires, interviews, and quantitative
assessments, I will show the ways in which the 2 approaches encouraged
different forms of knowledge. Students who followed a traditional approach
developed a procedural knowledge that was of limited use to them in
unfamiliar situations. Students who learned mathematics in an open,
project-based environment developed a conceptual understanding that provided
them with advantages in a range of assessments and situations. The project
students had been "apprenticed" into a system of thinking and using
mathematics that helped them in both school and nonschool settings.
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