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“I’m not trying to train robots,” Prof. Dawn Berk says of her
approach to teaching calculus. “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.”
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. In this story, Associate
Professor Dawn Berk explains how she teaches an introductory calculus
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
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
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
“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
“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
“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
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
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.”
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.
Biology: In the first story in the How I Teach series, Associate Professor Oyenike (Nike) Olabisi explains how she teaches an introductory course in biology.
Writing: In the second story in the How I Teach
series, Délice Williams, associate director of composition and
assistant professor of English, explains how she teaches an introductory
writing class called, "English 110 - Seminar in Composition," which is
the only course required for every UD undergraduate.
Business: In the third story in the How I Teach
series, Associate Professor Julia Belyavsky Bayuk explains how she
teaches Basics of Business, an introductory course designed to help
first-year students choose their path.
Article by Diane Stopyra; photos courtesy of Dawn Berk; illustration by Jeffrey C. Chase
Published April 2, 2021
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