#### Dr. Christine von Renesse uses unconventional examples, such as maypole dances, to show students the beauty of mathematics.

#### Educator

### Christine von Renesse, PhD

Associate Professor of Mathematics, Westfield State University in Westfield, Massachusetts

PhD in Algebraic Geometry, MA in Mathematics, BA in Elementary Education, minor in Music

Having failed some of her math courses in high school, Christine von Renesse may not have been voted “Most Likely to Teach Math.” But it is *exactly* her early struggles with the subject that make her the perfect professor for nonmajors taking mathematics at Westfield State University in Massachusetts.

She is also a cofounder of “Discovering the Art of Mathematics,” an educator-led project that focuses on creating active learning environments with the goal of teaching students to appreciate and understand the humanistic role mathematics has played in shaping history, culture, logic, and philosophy. Among the goals of this group—and her personally, in the classroom—is to use inquiry-based learning (IBL)—a form of active learning that poses questions and challenges for students to explore and solve.

“I see myself as a facilitator, not a lecturer,” she tells students. “My job is not to tell you what’s right or wrong but to give you opportunities to find out yourself. Is this easy? Nope. Is it fun? Yes—especially after you find an answer and you feel the excitement and accomplishment of a mathematician at work. I find mathematics beautiful, just like art.”

IBL, she explains, can inspire this sort of passion—even in students who fear math—because it creates mathematical explorations that introduce new ideas to students, so they can make connections that they otherwise would miss. Students also gain a greater appreciation for mathematics and its applications. “People believe you either have the brain for language or the brain for math, but that’s not true,” von Renesse says. “People are not separated into these two groups. If you decide that you can’t [do math], it’s because *you* decided that.”

Here, she shares some IBL-based exercises that she uses to foster a sense of curiosity in students so they can connect to mathematics in a personal, meaningful way—and realize that they have a mind for math after all.

## Context

“Mathematicians do math because it’s beautiful. I do math because I can, and because it’s fun. I try to give students that perspective.”

— Christine von Renesse, PhD

**Course: **Math 0110 Mathematical Exploration

**Description:** An introductory course designed to provide the liberal arts major with an opportunity to develop a broader appreciation of mathematics by exploring ways in which the artistic, aesthetic, intellectual, and humanistic aspects of mathematics are as important as its utility. Topics may include: mathematical reasoning, the infinite, topology, chaos and fractals, symmetry, elementary number theory, modern geometry, and the history of mathematics.

## See resources shared by Christine von Renesse, PhD

See materials## Fostering curiosity with inquiry-based learning

Some of von Renesse’s research is published on inquiry-based learning in the 2017 *Primus *journal article Teaching Inquiry with a Lens Toward Curiosity, with coauthor Volker Ecke.

Below, she shares some practical exercises she uses to help students ask the right questions—and answer them.

##### Get them comfortable with quizzing their peers

To foster curiosity and create a connection between math and her students’ personal interests, she requires one student each class to spend five minutes presenting a favorite subject and explaining how it relates to mathematics. Subjects can be as diverse as dance, theater, or even football. The rest of the class asks questions, although many students at first find it challenging to quiz their peers. “Being curious is quite difficult to learn,” von Renesse says. “They need to practice being curious, and I make it very explicit that this is what we’re working on.”

##### Spark inquiries with odd activities

Unconventional classroom activities (for example, maypole dances), which may not at first appear to have a mathematical tie, appear on von Renesse’s schedule. She wants students to open their minds and ask probing questions about the activity, questions that ultimately—and unexpectedly—lead to a math-based answer. “Everything I do is based on something that’s very active,” she says. “I try to help them change their belief system and work in groups, which is the core of inquiry-based learning.”

During the maypole project, for example, students often ask questions like these: What happens if one dancer messes up? Can they get back into the pattern? Which kind of ribbon would create which pattern? As she guides them in a discussion of the answers, students begin to realize that all of these inquiries can be answered by mathematical patterns.

##### Add in some confusion and frustration

Many students view math as cut and dried: There is a right answer and a right way to reach it. To challenge that notion and spark creative thought, von Renesse gives students challenging activities, such as straight-line origami (folding paper so that one straight cut will render a shape when the paper is unfolded), which often leads to frustration. And that’s on purpose. “If I give them an activity that they can immediately do, then that’s not a good activity,” she says. “We read a lot about mindset and growth mindset, how our brain works, and that we need to be persistent and keep working to learn. If you’re confused, that’s great—it means you’re learning and trying.”

##### Mix up the seating chart

To spur more interesting group discussions, von Renesse says she decides where students sit for every class. Sometimes she groups them based on speed or prior knowledge—for example, if a few students are afraid of math, she may put them in the same group so they can lean on each other. “I group them for different reasons, and every time I have new thoughts,” she says.

##### Recommended Resources

Traditional educators may find it difficult to use inquiry-based learning, von Renesse says, and it may help to talk with a professor who knows the ropes. “You switch everything. Your assessments will change. Interactions with students change, and your curriculum is changing. I’ve seen people try it and get discouraged because they haven’t had support. So team up with someone who has done this, or have someone come in and give you feedback. It takes some time before you fine-tune this new way of teaching.”

She also recommends the following online resources:

* Journal of Inquiry-Based Learning in Mathematics

* Discovering the Art of Mathematics (von Renesse’s site)

##### Have them work out their own answers

Though von Renesse sees the beauty in math, students will not find her waxing poetic on the subject for an entire class period. That is because she believes that a key part of inquiry-based learning is requiring students to do the mathematical work themselves. This means less chalk-and-talk on her part—and more pencil-and-paper on theirs. “If you want to learn it, you have to do it,” she says. “You can’t learn doing math by watching someone give a lecture about math.”

##### Get them talking about math

The professor has learned how to stir an inclusive class discussion, which has its roots in elementary school teaching. “It sounds easy, but it’s tricky to make people talk about math,” von Renesse says. She does not evaluate student answers for correctness, or even participate in the conversation as a mathematician—after all, her goal is for the students to be the mathematicians—but she keeps the conversation moving by using prompts such as, “This is what I heard Joe say. Who agrees or disagrees?”

##### Help them connect math to their passions

A love for math will grow organically when students can connect math to something else that they love. One former student, who had yet to declare a major, enjoyed photographing her family while they were on vacation and turning the pictures into what are known as tiny planets. The challenge was for the student to use mathematics to explain how an app could transform a flat panoramic picture into what looks like a sphere. “That connected with her and was mathematically meaningful,” von Renesse says.

##### Grade on participation as well as mathematics

In her math for liberal arts classes, von Renesse does not require exams: All assignments are pass/fail. Students have six writing assignments tied to the biggest topics the class will tackle, plus three journal entries, as well as a paper and presentation about a subject they like, along with the math that relates to it.

##### Question them about the journey

Weekly journals give von Renesse’s students a chance to reflect on what they are learning. “By the second or third journal [entry], they’ll say, ‘Wow! Math is actually fun! I have to admit I’m kind of liking this,’” she says. “That is a big learning goal—these mathematical aha! moments. Do I get all of [the students interested]? No. But I do have one or two every year that are interested in looking deeper into math. I can tell that their brains are loving it.”