# Problem Solving and the Random Number Generator

### by Justin Hollenback, Civil and Environmental Engineering

#### Teaching Effectiveness Award Essay, 2013

I am a graduate student in the Department of Civil and Environmental Engineering. In my experience teaching this subject matter, working through example problems during lecture and or discussion section can be a very powerful and useful teaching tool. However, its effectiveness is dependent on how engaged and active the students are during the presentation of example problems.

I recently was the GSI for a civil engineering risk analysis class (Fall 2012). During the first part of the term I observed lower than expected performance on the first two homework assignments and first quiz. The average homework grade in the class was 75% and the average on the quiz was 70%. The example problems worked out during lecture were prepared in parallel with the assignments and quiz. The students in my class didn’t seem to be benefitting from the example problems as much as I expected. Based on the mistakes the students were making, I felt that the example problems I presented weren’t conveying the material as well as I wanted. Students did not appear engaged or actively learning during lecture. In response, I developed a strategy to attempt to make the process of working out example problems in class more interactive. The strategy is as follows:

1. I set up the example problem on the blackboard. I clearly stated all assumptions and objectives of the problem.
2. I gave the students five to fifteen minutes, depending on the complexity of the problem, to work through it in small groups (one to three students).
3. I used a random number generator to select a student to direct me through part of the problem.

I repeated these three steps until the problem was completed.

Prior to my first time executing the plan, I made sure the students knew I was going to be calling on them.  The threat of speaking in front of their peers ensured that all the students were actively participating during small group work. The inspiration for this strategy came from my wife, who uses a similar technique in her elementary school classroom to get student participation. The main difference in my technique as compared to the classic “equity stick” approach used in elementary settings is the use of a random number generator. Civil engineering risk analysis is a class that is heavy in probability and statistics. We learn about random number generators in this course, so introducing them to the students in this way was an extra benefit. I was able to teach them about the math behind random number generators and then use one on a regular basis to help drive home the theory.

After introducing this technique I observed improvement in student performance. Homework scores increased from an average of 75% to an average of 80%. The average grade on the midterm exam was 81%. I also observed more engagement during other portions of my lecture, for example when introducing a new concept or when working through a derivation. Additionally, at the end of the term I got positive feedback on student evaluations specifically about the technique. The increase in student performance can be attributed to many things. It would be naïve to think that it was a direct result only of the strategy I employed. However, I do believe that it made a positive contribution to the students’ overall learning experience. I look forward to my next teaching opportunity to use this strategy again and learn about additional engaging and interactive teaching techniques.