Apprenticeship in Teaching

You Do the Math

Jim Sandefur, Ph.D

When he saw his "Foundations of Mathematics" students struggling to apply formulas, Jim Sandefur wanted to know how they were using the problem-solving methods discussed in class. Ultimately, he wanted to help them think and communicate like mathematicians. CNDLS helped him implement innovative assessment techniques that involved student collaboration.

At a College Curriculum Renewal Program (CCRP)-sponsored retreat, Prof. Sandefur learned about CNDLS' assessment technique in which students verbalize their thinking process as they tackle a problem during a video-taped session. Groups of three or four students volunteer to participate in which they perform individual think-alouds with a difficult math problem. Next, they 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. The purpose is to document the student process of solving the problem rather than solely looking at whether they completed the problem correctly.

By analyzing the 'think-alouds,' Sandefur was able to identify where students experience mental blocks and what type of support they need in and out of class. He adjusted class time and lectures to emphasize the problem-solving process and to focus on problem areas. The analysis of the tapes combined with minor course adjustments led to a course redesign where students are asked to work through complex problems as they communicate their struggles and discoveries to peers and the professor. The success of the think-alouds helped Prof. Sandefur refine his course each successive semester with new strategies including: structured group work, weekly presentations, and student teaching opportunities.

He has presented his findings and the think-aloud technique at the 2005 Korea Advanced Institute of Science and Technology conference and continues his work through the Visible Knowledge Project (VKP). His course serves as a model at Georgetown and at other institutions, such as Loyola Marymount University in Los Angeles.

For more information and strategies regarding think-alouds, visit our Think-Aloud Teaching Commons page.