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Illinois Geometry Lab: Changing the Shape of Math Research...and Outreach

Assortment of shapes created at Illinois Geometry Lab
Assortment of geographic shapes created in the IGL. The outreach team uses shapes like these to explain complex mathematical principles.

April 10, 2013

Armed with handfuls of brightly colored geometric shapes, three ambassadors from the Illinois Geometry Lab (IGL) have been dropping by Centennial High School's Tap-In after-school program on Thursdays to share their love of mathematics—specifically geometry—with the students.

According to IGL Outreach Manager Noel DeJarnette, it is this emphasis on outreach that sets the IGL apart from other geometry labs. While the lab's main focus is to create a community that enables researchers at all levels—professors, graduate students, and even undergraduate students—to perform novel research in mathematics, a growing mandate of the lab is to share this research in language everyone, including non-mathematicians, can understand.

This process whereby complex research projects are broken down so researchers at every level can understand and participate, DeJarnette alludes to as "a chain."

"Professors take a difficult problem and explain it to a graduate student, and the graduate student breaks it into parts that the undergraduate can get access to. So at every level, everyone is doing the most difficult and interesting task that is also accessible to them."

Tap-In student and Noel DeJarnette
IGL Outreach Manager Noel DeJarnett (right) discusses mathematics with a student.

Noel DeJarnette indicates that the lab fosters networking and collaboration regardless of position or educational level. "It's not always obvious to undergraduates and even graduate students that it's ok to talk to professors; its ok to talk to graduate students. But this sort of breaks down those barriers that are created by titles and really allows this sense of community."

And out of this sense of community flows outreach to the community. As an extension of what occurs in the lab every day, the lab's grad and undergrad students will continue breaking the research down into concepts that high school students—and even middle school students—can grasp.

Why expose high schoolers to the complex projects researchers at the lab grapple with day-in, day-out?

Local high school student uses geometric shapes to conceptualize a math principle during a Tap-In afterschool program at Centennial.
A high school student uses geometric shapes to conceptualize a math principle during the Tap-In after-school program at Centennial.

Says DeJarnette: "We do activities that take things that are outside of the curriculum that they might not have ever seen before and won't see unless they become mathematicians, but are still very accessible to them. We want to let them see that math exists outside of their textbooks; it's not the algebra, it's not just the number manipulations, its' a way of thinking and a way of processing."

The main instructional tool they use during their outreach is hands-on activities that bring math down to a level that students can not only see, but hold in their own two hands. "So we do these activities where they can have a physical connection with mathematics," explains DeJarnette. "And we really want them to touch stuff and see that mathematics can be physically felt." He also hopes to impart to students that math isn't always boring: " It's okay to work on things that are fun and interesting."

Originally created as a research laboratory, the IGL has a two-pronged purpose: to provide professors a network of graduate students and undergraduates which allows them to work on projects they normally wouldn't have time to work on by themselves. The lab currently has around 40 IGL scholars: usually ten professors doing twelve projects, twelve graduate students who are team leaders for the projects, and three to four undergraduates on each team. For the undergraduates, it's a way to get research experience "not just working on problems we know how to do," qualifies DeJarnette, "but novel, new research that normally they wouldn't have access to."

In addition, most Thursdays, the lab holds career preparedness workshops on topics like how to make a poster to present at a conference, how to apply for scholarships, and what to expect in grad school, etc.: "We really want to give them meaningful experiences and let them know what math graduate school is like, because I went without even knowing really what it was."

One thing DeJarnette finds particularly rewarding are opportunities the lab gives to students to experience things earlier in their careers—something he himself would have appreciated.

"When I was an undergrad, I never talked to a graduate student. Ever. When I was a graduate student, I didn't work on research until my second year or my third year. So that means really I was selected for graduate school based on skills that don't necessarily relate to what my career is going to be…We are really trying to move all of that much lower on the chain."

Maggie Witkowski and Allison Rogala
IGL math undergrads Maggie Witkowski and Allison Rogala, who are part of DeJarnette's outreach team.

Although as an undergrad, DeJarnette never spoke to a graduate student, this is not the case for two undergraduate members of the IGL, Maggie Witkowski and Allison Rogala. Math majors who intend to teach high school math, they are heavily involved with IGL's outreach program, and have found the relationships developed with graduate students like DeJarnette to be one of the perks of working with IGL.

"I think just getting to work with Noel, also, that's kind of unique," indicates Rogala, "because he's been through the program…and now he's a grad student. So it's cool to talk to him and get his advice on things. He helps us out with our lessons and gets us to think about new things that we can talk about and expand on what we think we should do. If we weren't part of the geometry lab, we wouldn't get to work with him and other grad students and everyone else in the math department as well."

Maggie Witkowski
Illinois math undergrad Maggie Witkowski works with a Tap-In participant at Centennial.

They have also enjoyed working with the lab because it gives them opportunity to implement some of the instructional techniques they've studied. "We always hear about, in our education classes, teaching in a fun and interactive way," acknowledges Witkowski. "And it's nice to be able to implement that in the classroom and take things from the curriculum that these kids wouldn't necessarily see in the classroom and do that with them in a fun and interactive way."

Witkowski also reports that as future teachers, the opportunity to "try new things and kind of experiment" and then learn from their successes and failures is a principle that they expect to put into practice in their classrooms. "Noel has told us many times that 'This is your chance to try things out. If it works, it works; if not, then you learn from it.' I think that's a huge part of being a teacher as well. You try things out, and you know that nobody's going to teach the perfect class, and then you go back and reflect on it, on the things that went well, and didn't go well, so you can change and improve next time."

Witkowski believes the time she has spent as a member of IGL has been extremely valuable. "The lab has been a really great experience for us, and I'm really grateful to have had the opportunity to be a part of it and my college career, because I definitely think it's going to be something that's going to benefit me later on as a teacher."

Allison Rogala helps a student during a hands-on activity at Tap-In.
Allison Rogala helps a student during a hands-on activity at Tap-In.

Rogala, who in high school, "had a great geometry teacher, so he was the person who inspired me to be a teacher," doesn't necessarily "want all the non-math people to love math." But she does hope that the students she works with learn something. "Maybe they won't take everything away from your lessons but if they take away one thing…something unique. Giving them new opportunities and new experiences and fun lessons…just getting them to think a little bit is the biggest thing, and not just memorization."

And in addition to experiencing fun new things, local high-schoolers are getting exposed to possible career opportunities—which DeJarnette believes to be important: "We're asking them to make an incredibly expensive guess when they start choosing careers and come to college. And so we really want to expose them to all of the opportunities that are available to them."

And that includes the University itself: "We don't want any student to be limited to their personal network. We have an incredible network and an incredible amount of resources. There are students in our community that are literally in our shadow who don't even know that the University of Illinois exists. And that's something that we're really trying to fix."

DeJarnette also hopes to provide resources for local teachers. "My ultimate goal is that the community and high school teachers, middle schools teachers, will all come to our workshops and get trained in our resources…We want to dream for them and let them know what's out there that they may be too busy to explore on their own—to let them know that it exists. And if it's something they can't do in their classroom, send their kids to us."

Story and photographs by Elizabeth Innes, Communications Specialist, I-STEM Education Initiative.
More: 8-12 Outreach, Centennial High School, Illinois Geometry Lab, Math, 2013

Noel DeJarnette uses geometric figures to explain a math principal to a Tap-In student at Centennial High.
Noel DeJarnette explains a math principle to a high school student at Centennial.