Imagine a math classroom, and for most people a specific scene springs to mind: rows of desks, with students bent silently over calculators and paper. The smell of pencil. A professor at the front of the room, lecturing, the blackboard filled with calculations.
Step into Karen Marrongelle’s classroom and it is something very different.
Students sit at tables in groups of three and four, talking and working together on problems. A professor and a couple of graduate students roam the aisles, observing the groups and lending help as needed. The room is anything but silent.
“There’s little lecturing,” explained Marrongelle, an assistant professor of mathematics at Portland State. “I ask questions that push the students. I want to engage them in situations that are problematic in some way. It acts as a hook, and allows them to dig deeper into math ideas.”
According to Marrongelle, math education at its best is a collaborative process, embraced by students and teachers working together. The teacher guides the process, but the process is interactive and students retain a great deal of input.
“I may have the course all mapped out, but in class, I’m picking up and running with the students’ ideas,” Marrongelle said. “They’re actually discovering ways to reinvent math as they go.”
Marrongelle’s use of collaborative strategies comes from watching and working with experienced teachers and then putting her observations into play.
“We have lots of classroom discussions,” she said. “I want to foster a sense of autonomy in my students. They learn to listen to another’s argument and then judge whether or not they buy it.”
Marrongelle, who received her Ph.D. from the University of New Hampshire in 2001, joined the PSU mathematics faculty that same year. Her interest in mathematics started in elementary school.
“I was never a stellar student, but something about math made sense to me,” Marrongelle said. “I liked solving things and I viewed algorithms and processes as a puzzle.”
Marrongelle’s love of math continued into college. Once she began studying above the calculus level, she got a sense of how mathematicians think about logical argumentation and unified theory. She also indulged her passion for philosophy.
“Math and philosophy are inextricably connected for me,” she said. “So much of what we do in math goes to the structure of how we prove things. It’s very social in a sense – in math, the peer community decides whether your arguments and proofs are acceptable. It’s fundamentally philosophical and logical.”
Marrongelle entered graduate school in mathematics, winning a TA position and beginning to teach. Although she hadn’t previously considered teaching as a career, she became fascinated with the learning processes in math education. The interest developed into key research interests, including the learning and teaching processes of undergraduate math students, mathematics teacher professional development and integrated math and science education.
Research funding supports Marrongelle’s work. She is co-principle investigator for a $5 million National Science Foundation grant, the Oregon Mathematics Leadership Institute Partnership.
The five-year project, now in year two, involves 10 Oregon school districts and some 200 K-12 mathematics teachers. Thomas Dick and Karen Higgins, both from Oregon State University, and Linda Foreman, from the Portland-based nonprofit Teacher’s Development Group, share the work as co-investigators.
The grant, aimed at increasing the capacity for generative and sustainable math leadership in all 10 districts, includes a summer institute in Corvallis.
“We take over Linus Pauling Middle School,” Marrongelle said. “The teachers refer to it as “math camp.” The math teachers involved in the project return to math camp each summer for training, and then are charged with going back to their schools to involve other teachers in improving math instruction.
“The thing that we hang our hat on is discourse in the classroom,” Marrongelle said. “If we can improve the quality and quantity of K-12 math discourse in the classroom, we’ll see the effects of that in the students’ achievement scores.”
So far the program has been extremely successful. Marrongelle said that some of the elementary teachers – who teach multiple subjects within the same classroom – are extending the collaborative techniques into their other subjects, not just math.
Marrongelle recently received a second NSF grant as part of the Interagency Education Research Initiative. Her co-investigators are Tom Dick (OSU) and Edith Gummer (Northwest Regional Educational Laboratory, Portland).
The five-year $1.8 million IERI grant focuses on models of middle-school mathematics problem solving and decision-making. The grant is in its first year.
Marrongelle has also received several smaller awards, including a $7,000 Faculty Enhancement Grant from PSU and a grant from the Korean Research Foundation, both supporting her work in differential equations, another research interest.
Besides teaching at PSU and conducting research, Marrongelle’s vitae includes a long list of journal articles and book chapters as well as frequent presentations at professional meetings. One of her most recent publications, “Making Mathematics more Meaningful: Drawing on what Students Know about the Physical World,” will soon appear in Mathematics Teacher, an education journal.
“The article has interviews with students, finding out how they were using ideas from physics to reason through calculus problems,” Marrongelle said.
Calculus is the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions. The word “calculus” originated in the mid-1600s and comes from a Latin term meaning “small pebble,” an early reference to the abacus.
Even though she likes math subjects of all kinds, Marrongelle does have a favorite.
“I’d have to say differential equations,” she said. “I have a fairly active research program around differential equations, investigating how each student’s thinking affects how I teach the class. It’s really fun to teach where the curriculum is already more or less there and I can just go to class and get really excited about what the students will accomplish that day.”
As for her next big project? “I’d like to go back and think some more about how physical models promote student thinking and reasoning in calculus courses. That’s my next endeavor,” she said.