The author discusses constructivist learning techniques in a program for 
secondary mathematics teacher preparation at a large state university. 

Fifteen students were selected for participation in the program. 
The selection was based on GPA and whether students expressed interest in 
secondary teaching. Students were required to take Discrete Mathematics, 
Modern Geometry, and a third course, a practicum. The faculty were encouraged 
to use constructivist techniques. 

This report focuses  on the practicum course in which students met twice 
weekly in a discussion section and in a Macintosh-based computer lab. 
The stated objectives of the practicum were as follows. 

(a) To introduce students to appropriate technology. In this case, geometry, 
logic and fractal modeling software were made available. 

(b) To encourage ``active learning'', students were required to participate 
in problem solving, group discussions, and the presentation of a semester 
project. 

(c) To encourage awareness of learning styles and teaching styles, students 
were required to discuss and critique the teaching of faculty associated with 
the program. They were also required to write three papers on their own 
learning styles. 

(d) To encourage use of constructivist techniques, students were required 
to demonstrate their knowledge of a mathematical concept by researching 
its historical roots, experimenting with various problem solving techniques 
from an historical to modern perspective, and then presenting their findings 
to the class. 
Students were also required to apply the use of constructivist techniques 
in an actual classroom environment. 

(e) To develop professional contacts for the future, the program adopted a 
``cohort'' model, suggested by Professor Uri Treisman, in which students 
take the mathematics courses required for certification as a group. 
They also had the opportunity to meet with outstanding high school teachers 
from the area. 

The success of the program is evaluated based upon faculty response, a 
Likert scale student survey, and student exit interviews. 

Carol Jean Bell, University of Texas, Austin