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Integrating Mathematics and Pedagogy (IMAP):

An Investigation of the Effects on Elementary Preservice Teachers' Beliefs and Learning of Mathematics

Grant funded to San Diego State University Foundation by the National Science Foundation and Department of Education, 1999 - 2002

In all disciplines but education, students enter as novices in need of learning the culture and terrain of the discipline. But in education, students enter as insiders with many years of experience during which they have developed deep-seated beliefs. Their beliefs about mathematics and their beliefs about how people learn mathematics interfere with their reconceptualizing mathematics in ways that will help them teach mathematics effectively. Their expectations of what they should learn in mathematics content courses constrain what they do learn.

The research team for this project will undertake a series of experimental and qualitative studies that will lead us to better understand the effect of carefully designed early field experiences, coupled with mathematics content courses, on the beliefs and the mathematical growth of prospective elementary teachers of mathematics.

Might integrating content with pedagogy change initial beliefs that are in conflict with the present consensus on how mathematics is learned and how it should be taught?

How do beliefs affect what is learned in content courses?

Do these effects depend on whether the integration of content and pedagogy occurs early in the prospective teachers' program or late in the program?

How do variables such as age and experience with children affect the findings?

Is the use of software programs developed for children and aimed at developing conceptual understanding, then used in both content courses and in early field experiences, effective in helping prospective teachers focus on conceptual learning and understanding?

Because San Diego State University has a large teacher preparation program in which prospective elementary teachers take four content courses in mathematics and one course in methods of teaching mathematics, we have opportunities to experimentally investigate these questions with large groups of students.

Studying these questions will require instruments more sensitive to change than those that now exist. Thus we will first need to develop instruments that will
  • (a) provide accurate measures of beliefs prospective teachers hold and of how these beliefs change over time,
  • (b) measure prospective teachers' depth of understanding of the school mathematics they will be expected to teach, and
  • (c) determine the similarities and differences between what novices and experts attend to when observing teaching situations.

These findings will help guide development of both the belief assessment and the field-based course. Initially a library of videoclips will be collected. Then cutting-edge eye-scanning technology will be used to determine what those in different groups (preservice teachers, inservice teachers, and university mathematics educators) attend to while viewing teaching and learning episodes.

Furthermore, estimates of observers' cognitive processing as they view the videotapes of teaching situations will be made. The results will be used in designing the content course and the beliefs assessment. The beliefs assessment will consist of videoclips with an accompanying questionnaire that can be used not only in this project but also in other studies of teacher change. The research results will offer other universities a knowledge base for planning effective teacher preparation programs. The model used here can be extended to secondary preparation and to other disciplines.

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