## Student Learning in Linear Algebra:

The Gateways to Advance Mathematical Thinking Project

**Michelle Manes**

Education Development Center, Inc.

E-mail: michelle@edc.org

http://www.edc.org/LTT/GAMT
**ABSTRACT**

The GAMT project is funded by the National Science Foundation. Our work is
divided into three categories:

- Empirical research in student learning in Linear Algebra
- Curriculum development in precalculus
- Theoretical research on mathematical ways of thinking

The empirical research working group is looking at students' ways of reasoning
about calculations and their use of "linear thinking." There are, we believe,
ways of thinking in mathematics that are inherently algebraic, for example one
can realize, without doing any calculations, that if one has two linear
equations in two unknowns with integer coefficients, then the intersection must
be at a rational point. We wanted to see what types of reasoning students who
have recently completed a linear algebra course would apply to these types of
problems.

Paper is available in the following formats: