**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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