This paper describes the philosophy, structure and content of M316K,
a mathematics course for pre-service elementary teachers offered at the
University of Texas, Austin.
M316K is an innovative course which incorporates the use of manipulatives,
technology, extensive (and challenging) problem solving activities, and
writing within a cooperative, constructivist environment. The objectives
of the M316K course include:
1. Challenging the students' beliefs about mathematics:

There are two equally important elements to mathematics. One is the content:
knowing how to use algorithms to find correct answers; and the other is the
practice: knowing how to explore, create, describe, refine and justify
mathematical ideas. Most students know only about the former element,
content. This course focuses on the latter element, practice.

2. Increasing the students' explicit understanding of selected mathematics ideas:

Most students enter college with a knowledge of how to manipulate mathematical
symbols in order to get a correct answer. Our more successful students
have an intuitive understanding of a given concept, but find it difficult to articulate why a given concept makes sense. All teachers need to reach an even deeper level of understanding --- the ``explicit" level. Students at the explicit level of knowledge are able to clearly articulate why mathematical ideas make sense and convincingly justify their assertions.

3. Increasing the students' ability to independently increase their own
explicit understanding of elementary topics

4. Introducing students to common manipulative and technological
tools

5. Developing skills for effectively communicating mathematical ideas

Tracy L. Rusch, University of Texas, Austin