Why Quantitative Reasoning Skills are Necessary In and Out of the Classroom
Most college students recognize the importance of mathematics to understanding the world around them, yet they also grumble that their math courses lack relevance in their lives. Even for students majoring in one of the sciences, it is often difficult to see how lofty mathematical theorems connect to their lives.
For Dr. Bill Wolesensky, a professor at UT Austin, teaching Calculus is about showing his students quantitative reasoning’s relevance as well as teaching them how to apply it to problems in the real world. These two goals reflect the Quantitative Reasoning Flag’s mission to help UT students “build skills necessary for understanding quantitative arguments in [their] adult and professional lives and engaging critically with our data-rich world.”
Professor Wolesensky knows the value of quantitative reasoning in his career, which has ranged from co-owning a beef jerky company to teaching math at UT, and wants students to understand it’s importance personally as well. “Quantitative reasoning will make every part of their lives better. It made my life better. It made me better as a mechanic, and in working with my horses.” Throughout the course, one of his primary goals is to show the students the relevance of quantitative reasoning to their lives.
His second goal builds on the first goal by teaching the students to go beyond memorized equations and apply their mathematical skills to problems beyond the textbook. Professor Wolesensky wants his students to understand that Differential Calculus is about more than just solving for the correct number; it is about knowing how to analyze a problem and interpret results. The students have to go beyond just finding the correct answer, instead learning to think through what that number means and how they used the tools to find it.
However, meeting these two goals required rethinking the way quantitative reasoning is taught in calculus. To do this, Professor Wolesensky teamed up with his colleague Professor Pedro Morales and Dr. Lin Winton, with the Center for Skills and Experience Flags, to thinking of new ways they could strengthen quantitative reasoning in their courses. Together, they began quietly changing the way quantitative reasoning skills are taught in Calculous courses at UT.
One of the most noticeable changes they made was to the discussion sections of the class. Out of a large lecture class, often only 40–50 students would attend the biweekly discussion sections. They made the decision to make these discussion sections mandatory and use them to work on quantitative reasoning questions in groups. Benefitting from the chance to work on problems with their peers, students discuss the reasoning behind how they found their answers, and what their answers mean.
In their discussion questions, the students apply calculus to everyday issues like speeding tickets. For example, they are given information about a car’s speed on a highway with construction to justify why or why not a police officer should give a ticket. Then, Professor Wolesensky takes a vote on which is the best answer. After seeing the classes’ results, the students share with their peers their solutions and argue why or why not the driver should get the ticket. Some days all the students quickly agree, other days there are heated discussions. These questions require the students to not only apply calculus to everyday problems, they force the students to explain their reasoning and interpret their results.
Professor Wolesensky and Professor Morales also rewrote many of the exam and discussion questions to incorporate more quantitative reasoning. The previous questions had not required students to interpret or show how they arrived at their results. In describing his goal in writing the new questions, Professor Wolesensky noted that “one of the challenges was to make them relevant to the students. That was challenging as we wanted the questions also to be locally relevant (when possible).” With the new questions, students have to answer questions about sharing the cost of a ride across town, for example, or how income inequality is calculated in Austin.
A second major challenge in rewriting the questions was limited teaching resources. One of Professor Wolesensky’s goals was that other instructors could adopt his modifications without adding to their workload. With that in mind, he kept all the graded questions multiple choice. “With good quantitative reasoning questions, interpretation is essential. Thus, writing the choices in a way that included interpretation was also a challenge.” The changes to these questions is also an ongoing process, as he continues to think of ways to strengthen quantitative skills in the course. “I now want to go through and rewrite the choices on many of the questions as I’ve become more acquainted with quantitative reasoning since I started the process and believe I can do better on many of the questions that we created.”
As Dr. Wolesensky continues to think of ways to further quantitative reasoning skills in his courses, other professors are taking cues from him. Several instructors from other first-year Calculus courses noticed the difference in his methods and the students’ successes and have begun integrating his questions into their courses as well.
If you would like to know more about the Flags program at UT Austin, you can find this information here.
By Abby Attia, Graduate Assistant for CSEF