Close shot of student doing calculus equations on a digital tablet.
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Duke University

Calculus Classes Dismantle Barriers to STEM Success

Rann Bar-On has been teaching Duke’s introductory first-year calculus courses for more than a decade. During that time, his classroom has become a lab for developing new teaching models that show success in helping all Duke math students excel in STEM pathways.

On the morning I visited Bar-On’s Math 106 class, the first thing that struck me was the layout of the room. The desks were arranged in squares, with two to five students clustered around each. The students faced inwards, an arrangement that encouraged them to engage with each other, rather than watch their professor.

Bar-On, a senior lecturer in the Department of Mathematics specializing in early undergraduate math education, wouldn’t have it any other way.

“We have a number of different entryways into math classes at Duke,” said Bar-On. “Some students arrive on campus highly prepared and go straight into Multivariable Calculus. Then we have students who took some calculus in high school and either want to review the more advanced topics or aren't quite ready to go into Multivariable. They start in our calculus 2 classes, Math 112 and Math 122.

“Finally, there are incoming students who either didn't take the Calculus AP exams or didn't have access to resources for various reasons.” These students go into Math 105 and 106, the two-semester sequence Bar-On teaches, which incorporates a lot of precalculus.

“These students didn't get into Duke on the strength of their math background,” Bar-On observed. “They got to Duke on the strength of many, many other amazing qualities. The goal is to give them the necessary mathematical preparation to be competitive in the sciences, pre-med, economics or any other careers they want to pursue.”

About 70 students each year pass through Math 105 and 106. Bar-On noted that the majority of them are pre-med. “The students who come to me are often those who, at some point earlier in their academic careers, found that math was a barrier for them.”

Bar-On’s voice took on a passionate tone. “There are a lot of systemic issues here. My classes have a higher percentage of people of color, of female students, of students from lower socioeconomic backgrounds, of public school students, than your average STEM Duke class. In all those populations, it is far more likely that someone has communicated to them, either directly or indirectly, that math is not theirs.”

This is the narrative Bar-On works to dismantle every day in his classes. On the morning I visited, the students were working on a take-home assessment. Bar-On wove around the room, perching on desks or squatting beside his students’ chairs, offering individual help to anyone who requested it. Hands that were raised stayed in the air for no more than 15 seconds before Bar-On or the TAs assisting him appeared at the student’s side.

One of the biggest innovations of Bar-On's classes grew out of the COVID-19 pandemic. “We had to make a lot of adjustments to our teaching very quickly,” Bar-On said. In the summer of 2020, I was having conversations with a number of my colleagues in the Math department, especially Shira Viel, about implementing mastery grading.”

Mastery grading is the idea of grading students less on what they know at a particular time through traditional testing in favor of assessing how their knowledge of a subject evolves over time. In the case of Math 105 and 106, this meant making the classes Satisfactory/Unsatisfactory rather than graded, having no timed assessments and giving students the opportunity to have their work evaluated and returned with comments from Bar-On or one of his team of 14 undergraduate graders and TAs to be resubmitted, if necessary, with corrections. It's a time- and labor-intensive method of teaching, but its results are unmistakable.

“Even before COVID, I had been developing a set of worksheets for my classes,” he said. “I turned those worksheets into assessments, which I put online at the beginning of the semester. The students have access to all the materials from the very beginning. Nothing is a surprise.”

Despite not receiving a letter grade and having up-front access to all the assessments, the classes are challenging and academic expectations are very high. The topics tackled are far more complex than would be expected in a class at this level, often dealing with real-world issues.

“We have a lab in Math 105 on human development,” Bar-On said, “about how the height of children changes over time. In looking at it very superficially, it seems like the difference between male- and female-born children only pops out in puberty. When we dig a little more deeply, using some calculus-adjacent tools, the picture becomes a lot more complex. We see multiple growth spurts and come to understand that the actual development of children involves more complex behavior than it seems at first.

“We also have a lab at the end of Math 106 on sustainable fishing that examines conflict between the fishing community and environmentalists. How do we design a fishing regime that’s environmentally sustainable? As a group, the students develop a mathematical argumentation in the design of a fishing scheme, which is a pretty advanced idea. The point is to gather all these graphs, all these numbers, all these ideas, and then interpret them to address an actual problem.”

Bar-On credits the labs with helping students see the practical value of what is often viewed as an esoteric subject. “I’m hearing a lot less of ‘what on earth is this useful for?’,” he said, laughing.

He also feels strongly that making Math 105 and 106 ungraded (simply recorded as Satisfactory/Unsatisfactory on the students’ transcripts) encourages undergraduates to enter a different intellectual space, focusing on learning rather than just points. “It's really reduced some of the ‘Did I get these two points here? Is this taking me up from a B-minus to a B, or a B-plus to an A-minus?’,” he said.

Although the changes in Math 105 and 106 curriculums are recent, Bar-On is already seeing positive results. “The problem with the old system was that I was only able to notice a student really needed support when I got the first midterm back, around week 5 or 6 — honestly, too late. Now, with constant assessments and feedback, I can identify students who need support in the first week and a half of class. I can then refer them to support and spend more time with them. It’s the difference between those students withdrawing from or not passing the class and staying in a classroom and learning.”

Unsatisfactory grades and withdrawals in Math 105 and 106 have dropped from 15% to 3% in the last two years. Although this is a significant change, Bar-On said another measure of student success involves what happens when students from Math 105 and 106 enter higher level courses in their sophomore year. “What we’re seeing in Math 112 is that the grades of the students coming from Math 105 and 106 are just as high as those of students who entered Duke at a higher level (Math 111) and had better high school preparation,” Bar-On said. “That’s a big change.”

He admitted there are challenges to implementing the time-intensive mastery grading structure more widely, but advocates for Duke doing just that. “If the university is committing to admitting students whose preparation is not the same as our wealthiest students receive, then for them to succeed we need to invest in them. You can’t overcome systemic issues, systemic disadvantages, without an investment of resources. It's not throwing money at the problem. It's using the resources we have available — because we're at a place like Duke — in a very targeted way.”

“It's not just giving students a little extra support,” he stressed. “It's structurally changing the entire class, the entire structure of assessment, in a way that enables students who previously felt like this cannot be theirs to have a sense of belonging and a sense of ownership over their work. Yes, it requires money and resources, but also a great degree of intentionality about design. It’s not ‘we're gonna get rid of grades because we don't like grades.’ It's restructuring in a way that redefines what it means to be successful. I'd love for this to spread. I think it works.”

After Bar-On dismissed the class, I approached two women who were zipping up their backpacks. I asked them what they are considering majoring in.

“Bio or Chem, probably,” said Pauline Jonglerthan.

“Maybe Bio or Psych,” said Angela Sapu. “Something in STEM.”

Both agreed that Bar-On has hit on a structure that works. “Not having a letter grade emphasizes learning,” Sapu said. “It’s comfortable being here.”