Student research: Demystifying math research through problem-solving
In the summer of 2013, Jesse Williams left Chicago to spend a week in Normal. Those five days at Illinois State’s Math Research Camp transformed his life.
At the time, Williams was preparing to enter his senior year at Simeon High School on the city’s Southside. He was thinking of learning a trade after graduation. “Honestly, I hadn’t anticipated on going to go to college at that point.”
Williams had arrived at the camp with little confidence in his math skills. He left Normal realizing he had been limiting himself. Last May, Williams earned his degree in mathematics education from Illinois State. He is now pursuing a master’s degree in bioinformatics.
“The (camp) faculty showed us something that was attainable,” Williams said. “They guided us toward discovery.”
Williams is one of dozens of Chicago public school students who have participated in the math camp led by Distinguished Professor Saad El-Zanati. Each July, El-Zanati welcomes 12 to 18 of these teenagers to campus for a week dedicated to examining and finding solutions to original research problems in discrete mathematics. The students research under the tutelage of professors in the Department of Mathematics, and a group of current and aspiring secondary math teachers.
El-Zanati has shepherded the program since its inception in 2012. “This is my favorite week of the year, simply because you have these kids, a lot them have never been on a college campus, a lot of them have never been out of the city,” he said. “We can give them a college experience, and hopefully, they would consider ISU as a place to go, and if they are scientifically inclined, hopefully get them into a technical field where they could develop and use their math skills.”
The camp evolved out of another summer research program started by El-Zanati: the Research Experiences for Pre-Service and In-Service Secondary Mathematics Teachers. The programs share a symbiotic relationship, and both are largely funded by the National Science Foundation (NSF). Illinois State’s program is the only one out of about 50 NSF-funded Research Experiences for Undergraduates (REU) programs nationwide that focuses exclusively on future and practicing teachers.
The eight-week ISU REU program, begun in 2007, stretches from June through July and offers educators the opportunity to delve deeply into math research, many for the first time. El-Zanati built the REU program around the teacher-scholar concept: “The idea is you experience mathematics by doing the research, and then you are able to relay that in your teaching.”
The REU participants immediately apply what they have learned about math research by helping oversee the high school camp. For much of the rest of their program, the REU participants work in teams to develop solutions and prepare papers for publication in peer-reviewed research journals based on discrete math problems presented by the professor and his colleagues.
For the high school students, the REU participants take a few hours that first day of camp to explain the math research problem. By the end of the second day, the students are huddled around tables inside a classroom in Turner Hall, talking over different aspects of the problem, sketching graphs on dry-erase boards, and peering into computers as the REU educators circulate from group to group.
Discrete math deals with finite, countable quantities and covers graph theory, among other areas.
El-Zanati searches for difficult but attainable problems for the student researchers. “The beauty of the research project that the high schoolers are doing is that you can explain it to them. They don’t need to have a fancy mathematical background.”
Instructional Assistant Professor Ryan Bunge ’07, M.S. ’12, has worked with El-Zanati from the beginning of both programs: “What’s always interesting is working with fresh minds and finding new ways to think about things. It’s definitely very rewarding at the end when you have this product from these people who had no clue what they were doing, for the REU students eight weeks ago and for the high school students four days ago. They have no experience with this material, but they are still able to do something that is rewarding to them.”
Unsolved problems are an equalizer for students, said Teddy Schrishuhn ’09, who studied under El-Zanati at Illinois State. Schrishuhn has brought a group of his Pritzker College Prep students to the research camp the last three years.
“What I love about this camp is it’s almost like learning a new language, and no one comes here knowing anything of this language. It’s this level playing field,” Schrishuhn said. “No one has done discrete math, no one’s done graph labeling in high school, and so you have some students who think they are average or less than average, but they come here and sit with students who are generally highfliers and they are going through the same struggles, coming to the same conclusions, learning from each other, and sharing the same result.”
The programs promote collaboration and tear down preconceptions students may have about themselves. That was certainly the case for Cody Hatzer, a senior math education major at Illinois State. He received the Bonnie H. Litwiller Scholarship in Mathematics Education last summer to participate in the REU program.
Hatzer realized he didn’t need to be a “brainiac” to do math research. His biggest takeaway from the camp was that high school students can do this type of research as well.
Hatzer was one of 16 REU participants last year. Four of them were secondary math education majors at Illinois State, while the others were experienced high school teachers or teacher education majors from across the country. There were teachers from Detroit, Minnesota’s Twin cities, and San Francisco and students from as far afield as a tribal college in Montana. “We don’t cater to superstars,” El-Zanati said. “If you are in some little school where you don’t have the opportunity to do math research, we would love to take you, if you have a good attitude and are truly interested.”
Jesse Williams returned to the math camp during his time at Illinois State, serving first as a chaperone to high school students and later as an REU participant. One thing he learned is that if he planned on teaching math he would need to know the material three times better than his students. The camp also taught him the importance of working with others: “Discovery takes time and collaboration.”
That’s a lesson El-Zanati instills every summer in his aspiring math researchers.
Kevin Bersett can be reached at kdberse@IllinoisState.edu.