2003-2004 MIL Fellows: Mark Burtch's Project

2003-2004 MIL Fellows: Mark Burtch's Project
the maricopa institute for learning

Mathematics education at the undergraduate level has traditionally been marked by a teacher-centered approach. Recently however, there have been calls for this type of instruction to give way to instruction that is marked by teachers who facilitate opportunities for understanding and sense making to emerge from students' reasoning (Rasmussen, 2001). One way to accomplish this is to utilize a curriculum development approach called Realistic Mathematics Education (RME) (Gravemaiejer, 1998). One basic principle of RME is that as the teacher facilitates opportunities for sense-making, students should be given the opportunity to (re)invent much of the mathematics that they learn. This will at times require students to make, test, refine and communicate conjectures. The purpose of this project is to begin to answer two questions. First, "Does curriculum developed from an RME perspective provide richer opportunities for students to learn?" Second, "What role(s) does conjecturing play in student's attempts to learn differential equations?" I will be utilizing curriculum developed using RME principles and will teach the class from an emergent perspective of learning (Cobb & Yackel, 1996). The students and I will develop the classroom norm of making, communicating, critiquing, and refining conjectures. In addition to opportunities in the classroom, students will be given opportunities to make, test and refine conjectures in interviews, homework assignments, and a course portfolio. All the data will be analyzed to determine how conjecturing was used by the students to learn differential equations.

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