# For new professors, teaching Mathematics 32A creates learning experiences

A large lecture hall with students is pictured. Professors teaching Mathematics 32A, a lower-division course with hundreds of students, discussed some of the challenges they have faced and rewards they have found through teaching the class. (Daily Bruin file photo)

### By Shaun Thomas

#### Jan. 10, 2024 6:01 p.m.

The first time Richard Wong stood in front of a lecture hall of hundreds of students, it felt like a performance.

“It was kind of scary to be like, ‘Here’s a class of 210 students. Teach them multivariable calculus,’” said Wong, an assistant adjunct professor of mathematics.

Wong is one of several professors who teach Mathematics 32A: “Calculus of Several Variables,” a prerequisite course for many STEM students at UCLA. Some of these professors, such as Wong, only recently received their doctoral degrees, making this class one of the first large lectures they have ever taught – which has led to some challenges, but also learning experiences, they said.

José Ignacio Yáñez, an assistant adjunct professor of mathematics who taught Mathematics 32A in fall quarter, said he completed his undergraduate and master’s studies in mathematics back in his home country of Chile, knowing even before undergrad that he wanted to pursue the field. Yáñez, who earned his doctoral degree at the University of Utah, said he had some experience teaching classes of about 40 to 50 students there, which prepared him in some ways for when he arrived at UCLA.

However, he added that there were some significant differences, such as having to respond to more questions. He said when he arrived as a postdoctoral student at UCLA, he had weekly faculty meetings to address questions and problems that he may have had in class.

“This is my sixth class that I’ve taught so far. So there is some background that I’m carrying from those classes, and in particular, for 32A, as I said, after teaching it once, then you learn what topics students struggle with more,” Yáñez said. “Then, essentially, you prepare for a next version of the class with those questions in mind and try to answer them ahead of time before they happen.”

He also added that as professors are expected to follow a tight schedule, time management and preparation have been important to try to keep the number of students’ questions to a minimum.

Other professors found their way to teaching via different paths. Wong, who also taught Mathematics 32A in fall quarter, said he realized math was something he wanted to do after getting inspired by an honors multivariable calculus class in his undergraduate years.

He added that he is passionate about both teaching and mathematical research, and UCLA offered both.

But after teaching small classes in graduate school, Wong said it was initially daunting to teach his Mathematics 32A class – which had over 200 students – in an effective way. To deal with that, he tries to explain topics in a more general way rather than trying to tailor them to a specific student, he said, adding that he also reached out to institutions such as the Center for the Advancement of Teaching and the Center for Education Innovation and Learning in the Sciences for help developing a syllabus and structuring the course.

“In my lectures, I’ll ask questions or I’ll have students turn to their neighbor (and) talk to each other about the stuff because I think that’s … the best way to learn,” Wong said. “I want to also create an environment where that is encouraged – an inclusive environment where you feel like you can ask questions and make mistakes.”

Wong added that he has also learned from his students and that student feedback is important for his class. Last quarter, his students gave informal names to mathematical curves, calling them “cocktail shakers” or “bowls,” he said, adding that it was nice to see a fresh approach to understanding the material.

The logistical aspects of the course have also produced some challenges. For example, Yáñez said preparing for midterms required a variety of different steps such as making sure that everything was written correctly, that there were several types of problems and that there would be no cheating.

However, despite professors’ efforts, not all students have had positive experiences in the course.

First-year chemistry/materials science student Asta Li said she took Mathematics 32A in fall quarter with Professor Mark Ebert because she needed it for her major. She added that she made her decision based on the time slots for the classes because most of the professors were new, so there was no information about them on Bruinwalk.

Li said she felt that her experience was not as interesting, as it felt like her professor taught in a very textbook manner. She added that she thinks more could be done to help students succeed in the class.

“Some of the textbook questions don’t have answers, so we don’t know if we’re doing them right,” she said. “It just kind of felt like we’re on our own.”

As part of addressing this, professors could adapt more to student feedback than just by implementing a curve, and they could also provide practice tests with more detailed solutions, Li said.

In the process of teaching classes and listening to student feedback, both Yáñez and Wong said they have formed their own teaching philosophies. Yáñez said he believes that every student should be able to learn at their own pace.

He said he hopes students understand that math doesn’t need to be complicated, adding that he enjoys teaching and the interactions that have come out of it.

“I am generally happy when I teach, so I think that students also respond positively to that,” Yáñez said. “When you see someone that actually cares about teaching, you learn from them.”