Daniel Zhou reflects on what his experience as a teaching assistant in an interdisciplinary course taught him about how mathematics anxiety affects students and what can help.
From October 2020 to March 2021 at the University of California Los Angeles (UCLA), I served as a teaching assistant (TA) in the general education course Public Health 200A-B: Foundations of Public Health. The course covered basic material between five departments: biostatistics, epidemiology, community health sciences, environmental sciences, and health policy and management and was a requirement for first-year Master of Public Health (MPH) students. As the course had only been offered once, the structure was largely experimental: its material from each subject was rudimentary both to acquaint students with the basics in each discipline and to facilitate the practice of integrating the quantitative and qualitative sciences in public health. This course took up to 8 hours per week and alternated between the five different modules in public health, each taught by a different professor from the relevant department: twice the time demand of a standard MPH course with the added complexity of the diversity in course structure and material.
After the first series of meetings my colleagues and I could see that the students were suffering from “math phobia”. Some worked full-time before beginning their Masters and had not touched the requisite math for basic statistics in years. Initially, I had little idea what being “math phobic” meant, but as the course proceeded, my students’ experiences gave me a clearer picture. Some students seemed unsure how they would handle the mathematics introduced in the material, which included elementary set theory. Several, when they turned in their first lab reports, reported the findings from running the programs, but did not report numbers to back up their claims. Few grasped the reasons or concepts behind an exercise involving weighted percentages. While many students were otherwise able to handle their assignments competently, they were genuinely afraid of working with the numbers. It seemed as if the thought of getting a question wrong would make the student uneasy to answer it, especially when faced with the prospect of missing every mark for that question.
To tackle this problem of “math phobia”, I used as a base UCLA’s TA preparation and coursework, which emphasizes two key concepts: having a “growth mindset”, and engaging students in “active learning”. Having a growth mindset focuses not on what the student could achieve in taking the course, but whether they will grasp what they have learned in the course. Fundamentally, applying a “growth mindset” to every student is an exercise in patience, especially for struggling students. Encouragement must not be demeaning, since as instructors, we have to meet students where they are and help them to grow and see them for the knowledgeable professionals they can grow into.
“Active learning” emphasized getting the students actively involved in the task at hand, be it through demonstrations or discussions. In the case of the biostatistics segment, it was given in the professor’s labs, which took the form of scripts written in the R programming language, structured so that the students would not need to write code from scratch. Owning the tools and allowing the students to play around with them involved them directly with an industry tool and with visualizing and computing the statistical tools involved. This was helpful for getting them acclimated to quantitative figures and reasoning, especially if they did not trust themselves to do the math by hand.
Growing as a TA enabled me to reflect on some ways students may be able to overcome math phobia. The short answer is that to not fear math one must be exposed to more math; the longer answer depends on how to do this intelligently, and more importantly, relevantly to the students’ experiences.
The first and most significant conclusion was a difference in mindset between approaching the social sciences and the physical sciences modules in the course. Switching between different tasks, especially when they consist of different materials requiring distinct skillsets, requires significant overhead effort, more than we generally give students credit for. (I used to fear essay writing in English classes for much the same reason). As the first quarter progressed into the second, our professors were able to integrate their assignments with one another better, both to demonstrate the practices from each departmental discipline in selected case studies and to demonstrate ways in which these diverse subjects interacted with one another in practice. Not only did this provide a motivating context in which mathematical theory might be used (in various public health settings), but it helped students understand the details that the bigger picture encompasses.
The second conclusion relied more on the students’ involvement and hinged on two strategies: 1) be personal in interacting with students, and 2) do not be afraid to refer students to additional practice if they need help understanding what they are learning, however fundamental the content may be. Effective teaching depends strongly on personal interaction (1), especially with students who fear math but must work with it regardless. (Not to mention the COVID-19 pandemic consigned the students to their computers with otherwise limited means of personal engagement). My co-TA Richard was an experienced teacher and tutor who was willing to help his students to review for their midterms and final exams; consequently, his students loved him and feared math less by his tutelage. Strategy 2) provides students with some means of gauging and/or improving their math abilities, not unlike setting up a sandbag for beginning boxers or targets for archery students. A student who doesn’t know to follow 2) can at least be pointed there by a teacher who knows how to practice 1), although I’ve found that students who want to (or at least realize their need to) learn math but are afraid to touch it are generally motivated to practice. Any additional effort spent doing practice problems to reach these concepts is worth the trouble, not to mention that having a guide ready to help would significantly help students overcome their fear of math. (Whether or not these additional problems should be graded in general depends on the teaching style of the instructor; they were not for this course).
A third conclusion involved exposing students to the numbers and their meanings in the context of the problems they need to solve. For instance, encouraging students to report numbers that they have obtained from their statistical tests helped them engage with the numbers that they seemed to fear would cause them to be marked wrong. Superficial as this may seem, consider the difference between answering “we reject the null hypothesis” and “the p-value was 0.00053, thus we reject the null hypothesis”: the second answer provides a value to back up the conclusion being made by involving numbers. And if the student fears that the reported numbers will definitely be wrong, encourage them to simply report what they see: Doing so would help the to student trace their error (which is more descriptive than simply being told they are “wrong”) and will help them to make improvements for the future. Furthermore, since programming in a math setting often involves formulas, having students modify values in their code to visualize different results (e.g. epidemiological growth models) would also help them associate certain numbers or sets of numbers with a visual aid, not unlike how mnemonics work in verbal settings. (Curiously, one student testified that something as simple as punching numbers into a calculator made the math in the course more approachable). “Word problems” are often used in a math course to train students to calculate figures, but in the context of this course, it was less for the sake of having word problems written to spur quantitative thinking (e.g. “a bug travels in this path”) and more a case of a real problem with assumptions and constraints to involve quantitative analysis (e.g. “The coronavirus grew at this rate in March 2020. Based on the model, how many people would it infect in 2 months?”).
I realize these points seem like common sense for people who have prolonged experience studying, and especially teaching, mathematics, but they bear repeating if only to emphasize their importance for students who are afraid of mathematics and expect some trick or strategy to work and help them make progress. Having utilized some mnemonics and key concepts that helped me better understand more complicated mathematical concepts (such as the product rule to understand tabular integration), I believed that there were certain tricks some teachers could share to help their students excel at math. But outside of standard or basic techniques taught in class, the strategies that worked for me may not necessarily work for others. I came to see that the basis for my students’ mathematical knowledge should be in practicing what they know and developing their own conceptions or mnemonics for handling mathematics. Little things add up, and the more a student piles on, the better their ability to tackle mathematical problems that they were previously too afraid of dealing with.
I must close with some qualifying remarks: the course was being run for the second time and so was not far from its prototype iteration or beta release. Understandably, there were students who didn’t do as well, in part due to a course cramming five modules into the allotted time for two modules. Finally, this course was my first attempt in math instruction (though as a TA), and so even accounting for my improvements over the quarters, my teaching abilities have room for improvement. Nonetheless, the course, an introduction to five interplaying public health subjects, also gave me an introduction to math anxiety and math phobia, which will help me to better address it in the future.
Finally, I would like to thank Dr. Hilary Aralis for her leadership and direction of the Biostatistics portion of the course and her engaging lab design; and my co-TA Richard Williams, who gave me valuable advice and also reviewed this essay prior to its submission.
Second-year PhD student in Biostatistics
University of California, Los Angeles.
Prior to his PhD, Daniel obtained a BA and MSc in Mathematics and worked as a computer scientist at the National Institute of Standards and Technology. Daniel’s current research interests concern longitudinal biomarkers and their models.