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MERN Abstract id=23
Source : MERN Forum 5, Concurrent Session 2A
Date: 3/4/2005
Author: Evan Janzen Roth, Dr. Ralph Mason
Title : Thinking Like Archimedes: An Instructional Design Experiment
Text : This presentation will report on a design experiment (Cobb et al., 2003) aiming to develop curriculum that incorporates the thinking of Archimedes about the geometry of the circle into high school mathematics. Students graphed relationships among radius, diameter, circumference, and area of circles. They circumscribed and inscribed regular polygons to approximate pi. They constructed a geometric representation of the calculus-like thinking of Archimedes involving progressively subdividing a circle into more and more sectors. Readings from historians’ accounts of the life of Archimedes were interwoven throughout the unit. Overall, the curriculum design reflects principles of inquiry-oriented learning to make students’ engagement with content more thoughtful and rewarding. Design experiments operate on at least two levels, both dependent on ongoing interpretation of data on student learning. On one level, this project is developing a unit of instruction for use in Manitoba schools. Data includes the students’ products from each lesson, and the interactive writing between the students and the teacher/researchers. On a second level, this research is investigating the nature of students’ orientations toward learning in senior years. For this element, along with the data for the curriculum development aspect, a narrative-inquiry process will elucidate students’ beliefs about their purposes and role in schools and in mathematics. In the presentation we will outline only briefly the theoretical framework of the study and the instructional elements of the unit. Instead, we will focus on the data interpretation procedures to illustrate a design-experiment methodology. Cobb, Paul & Confrey, Jere & diSessa, Andrea & Lehrer, Richard & Schauble, Leona (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13.
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