Project Goals Sandefur wants to understand what type of support students need to solve problems successfully in order to redesign the course Foundations of Mathematics. The problem-solving process he wants students to internalize is: Interpret what is to be shown in the problem. Reframe the problem in a usable form using standard approaches. Experiment with the problem. Think informally about possible paths to a solution. Write the solution in a clear and concise manner.

Evolving Course Design The new course structure incorporates individual and group work during class so that students receive maximum support from the professor and the TAs. To improve the writing process, a draft system has been established so that students can receive feedback about their written solution before the final work is submitted. Another change to the course design is that Sandefur now provides students with the opportunity to explain their thinking about a problem and its solution through individual or group presentations in front of the entire class. This forces students to reflect on the strengths and weaknesses of their approaches.

Individual Think-Aloud Please click on link to play video file of individual think-aloud

Reflection While the course has improved over the two years that Sandefur has worked with CNDLS on this project, he still wants to learn more about student-centered teaching approaches. One of the most difficult aspects of teaching this course is finding the appropriate balance between letting students struggle versus leading them through a process. Too much struggling is counterproductive, but if the students do not struggle enough, they do not develop ownership of the ideas.

Investigation of Student Learning To understand more about how students learn in his course, Sandefur uses the think-aloud technique in which students are videotaped working on a difficult disciplinary problem while being prompted to talk out loud about their process. The purpose of this technique is to document the process of solving the problem rather than emphasizing the final solution. Process: Groups of three or four students volunteer to participate in the think-alouds. First, the students perform individual think-alouds with a difficult problem. Next, the students attempt to solve the same problem together in a group think-aloud. Ideally, this process is followed at the beginning, the middle, and the end of the semester.

Group Think-Aloud Please click on link to play video file of group think-aloud

Think-Aloud Observations By analyzing the videotapes, Sandefur has witnessed where students had mental blocks and has determined what types of support students need both in class and out of class for them to become independent problem solvers. He has found that: Students' difficulties arise early in the problem-solving process. When they can't see the solution immediately, they often get stuck right in the beginning, without exploring possible approaches. There seems to be an unwillingness to try different approaches, even when it is clear that the student's current approach isn't working. Students are persistent. They will continue to work on a problem even when they are making little or no progress.