### by Jonathan Schellenberg, Economics

#### Teaching Effectiveness Award Essay, 2018

In the social sciences, we seek to understand all types of human behaviors. Economics, my sub- discipline, formalizes these actions with mathematical models, both to reduce the complexity of the world and to highlight the rules that we believe govern human nature. Due to this added structure, economics classes often resemble applied math courses, in which math is used as a tool to develop deeper insight. Unfortunately, when we use more complicated models, students can become immersed in the underlying math, and subsequently overlook the models’ societal implications. Instead of applying the models to reality, the math problems are solved in a vacuum and, as a result, the social relevance of the model is left undiscovered. This “math trap” was particularly problematic in my microeconomics course. Although the instruction heavily stressed interpretation of results, many students still had trouble taking that final analytical step; every major mistake on the first exam resulted from the failure to connect math to economic intuition.

In order to combat the above tendency, I reversed the typical order of analysis; rather than start with the math and then ask my students to interpret the findings, I had them summarize their economic observations and then formalize them with math. I accomplished this task by adding a short, small-group exercise at the beginning of section. The students were given a simple, real-world scenario and were asked to logically deduce how they would expect people to act in the given situation. They were then asked to express their conclusion with a mathematical statement. For example, I began our discussion on uncertainty by asking if they would prefer $10 or a 50% chance to win $20; after a brief deliberation, we concluded that in general, people enjoy random payoffs less than the average value of those payoffs. As we analyzed more complicated models later in the section, I made sure to revisit the insights we made from these exercises.

By providing real-life motivation for the equations we would later use, the students could see why we were writing these models down instead of reducing them to algebra problems that needed to be solved. Moreover, by having students develop the initial motivation for our theoretical assumptions before formally modeling the situation, they would better understand the origin of our equations, which could make it easier to relate the model back to the underlying economics following additional mathematical derivations. And finally, by repeatedly highlighting where we saw our initial insights embedded in our models, we frequently made direct connections between math and intuition, ensuring that the economics portion of the class was not lost amongst the math.

I administered an anonymous mid-semester evaluation five weeks after including these exercises in my sections to assess their impact and reception. The responses were quite positive—75% of the class both believed that these practice problems were helpful at connecting economic intuition to math and wished to continue them, and only 15% wanted them to be discontinued. Additionally, after implementing these introductory problems, I noticed two positive changes in students’ approach to the course. First, in their graded assessments, their problem set responses more frequently discussed the real-life implications of their calculations. Rather than simply solving an equation, students developed their reasoning further and gave economic meaning to their derivations. Second, in the classroom I started receiving many more questions about the interpretation of our models. While there were still numerous questions about the math, many students were no longer satisfied with just the symbolic expression of the answer—they wanted to know what the results meant, and often asked for real-world applications to gain a deeper understanding. Instead of focusing on the exact mathematical solution, the students started concentrating on why we were trying to get the answer and what we could learn from it. If these exercises helped highlight the social science insights of the course, I would call that a success!