How I Teach — Calculus
Photos of courtesy of Dawn Berk | Illustration by Jeffrey C. Chase April 02, 2021
Don’t believe you are a math person? Prof. Dawn Berk believes otherwise
Editor’s note: First-year students, prospective students (and some of their parents) wonder and worry how they will handle the academic transition from high school to college. In a series of stories, UDaily speaks with University of Delaware professors who teach courses commonly taken by students during their first year on campus. The series includes professors who teach biology, writing, business, calculus, political science and sociology, and those stories can be read on the How I Teach website. In this story, Associate Professor Dawn Berk explains how she teaches an introductory calculus course.
Professor Dawn Berk will not move on from a concept until her students understand it to the point of, she said, “feeling it in their heart.”
No, really — she even equips these students with a hand signal (a balled-up fist beating against the chest) to communicate that moment when the material becomes more than just abstract curriculum. That moment when it becomes part of who they are.
This probably would not sound all that unusual if Berk were an instructor of, say, romantic poetry or expressionistic art or some other subject for which emotionality is generally considered a prerequisite. But the University of Delaware associate professor teaches calculus — not typically your most touchy-feely course of study.
“I’m not trying to train robots,” she said. “We already have computers that can crank out a procedure. But the human element? The conceptual understanding? That is going to serve you in whatever major you choose.”
Berk is the founding director of the Mathematical Sciences Learning Laboratory at UD. Known as MSLL (affectionately pronounced “missile”), this unit strives to improve teaching and learning in some of the University’s most foundational math classes. One course that has been successfully MSLL-ized? Integrated Calculus.
Typically taken by first-year students, this two-semester experience is geared toward Blue Hens who need calculus for their intended major but who may not be excited or ready for that level of math, as determined by a placement test. Rather than have these students retake the pre-calculus they had in high school — a discouraging way to begin a college career — the integrated course incorporates just those key pre-calculus concepts that need review while introducing important calculus concepts at the same time… a research-backed strategy for success.
“At first, even the title of the class was nerve-wracking,” said Sarah Dente, a sophomore environmental science major who completed the course in the spring of 2020. “I was like: ‘Woah, what does Integrated Calculus even mean?’ But as long as you pay attention and do your work, this is a rewarding experience. I actually had fun taking it, and I never thought I’d be able to say that about a college math class.”
This type of testimonial is common from Berk’s students, and it stems partially from the professor’s commitment to a strategy known as active learning.
“One big problem with the way these courses are typically taught is that they are very intimidating,” she said. “Imagine what you see in the movies: A large, impersonal hall in which a professor who feels 12 miles away is giving a dry and boring lecture and students are simply watching this person do mathematics at a board, furiously taking notes and hoping to figure it out on their own later. My MSLL colleagues and I strive for a much more interactive, engaging experience than that.”
To begin with, the Integrated Calculus course is small — typically between 45 and 65 students, as opposed to the several hundred you might see at other universities. And these students are seated not in a tiered, every-person-for-himself-style lecture hall, but in small groups that allow for discussion, collaboration and — yes — fumbling.
“In math courses, it is a common misconception you should only raise your hand if you have exactly the right answer,” Berk said. “But I want students to talk through their ideas, even if they’re not fully formed, because the research shows this supports learning.”
When relaying material, Berk focuses on the big picture. Want to figure out how fast something in the real-world is growing or changing? Like, say, a wolf population or a company’s profit? You will need to find something called the derivative of a function, a fundamental tool in calculus. But it is not enough for Berk to teach her students how to determine this derivative — she also explains why.
“In the past, the mentality of professors in this type of course has often been: Just believe me. Do it this way, flip it upside down, put a four there, then memorize it,” Berk said. “We are really pushing against that. Everything we teach, we explain. It’s not about memorizing an equation. It’s about understanding why this makes sense.”
To support this understanding, MSLL faculty strive to create a community of math learners. All Integrated Calculus professors require not just the same textbook or exams, for instance, but the same workbook assigned at the same pace, so that students across course sections can collaborate with one another: “It is coordination to the extreme,” Berk said. Free tutoring in MSLL is also offered for anyone who wants a little extra help.
When it comes to assessment, no one’s grade comes down solely to one giant, stress-inducing midterm or final. Instead, plenty of smaller, lower-stake assignments are built into the course as well, meaning there are multiple chances for feedback. And on these smaller quizzes, should they underperform the first time around, students are given a second attempt.
“Sometimes, you just mess up,” Berk said. “And that’s okay, because these are meant to be learning opportunities. I don’t really care if you understand this material by noon today or 2 p.m. — I just want you to understand it. We still have high standards, and you need to grasp these concepts, but we will do everything we can to help you get there, because we believe and know everyone can be successful in these courses.”
Or, as sophomore economics major and Integrated Calculus veteran Ellen Dubs put it: “The focus is on learning, not perfection.”
This idea that calculus can be for anyone — not just a naturally inclined, left-brained set — is a core tenet of Berk’s teaching philosophy.
You could even say she feels it in her heart.
“I love to hear a student say: ‘I’ve changed my mind — I actually can do math’,” Berk said. “Every time I can make that difference… that is the most rewarding part.”
Support for Academic Success
The University of Delaware empowers all Blue Hens with the skills and strategies they need to succeed.
UD students in any major are encouraged to take advantage of a range of peer tutoring services, as well as comprehensive skill-building resources offered by the Office of Academic Enrichment (OAE). Most services are available free of charge. To learn more, visit the OAE website. Students may also utilize the Blue Hen SUCCESS platform to connect with their academic advisor or access additional resources on Advising Central.
For UD’s community of educators, the Center for Teaching and Assessment of Learning (CTAL) offers programs, workshops and confidential consultations to support faculty as they develop and achieve their pedagogical goals. UD instructors at every stage of their career are invited to explore online and contact firstname.lastname@example.org.
How I Teach — Series
The How I Teach website provides a collection of the stories in this series.