Research yields prime conference spot, publication
John Paul Cook is not your typical mathematician.
Cook earned his Ph.D. in mathematics from the University of Oklahoma in 2012 but he describes himself as a “hybrid” because his research primarily has been aimed at undergraduate math education.
Now an assistant professor of mathematics at the University of Science and Arts of Oklahoma, Cook’s research, re-thinking the way certain higher-level mathematics courses are taught, is starting to turn heads nationally.
The International Journal in Mathematical Education in Science and Technology is set to publish Cook’s article “The Emergence of Algebraic Structure: Students Come to Understand Units and Zero-divisors” later this month.
The article is built off of Cook’s dissertation research, which takes a hard look at the way that students absorb concepts in a branch of mathematics known as abstract algebra.
His method for improving student outcomes, a process known as guided reinvention that has been applied successfully to other subject areas, has captured the attention of not only educators but pure mathematicians as well.
As a result, Cook has been offered a speaking slot to share his findings at the prestigious Joint Mathematics Meeting, a conference billed by its organizers as “the biggest mathematics meeting in the world.”
Cook’s interest in improving the way abstract algebra was taught stems from a wealth of research suggesting many students pass the course without having grasped the fundamental concepts that define it.
“Abstract algebra is different from something like calculus, which places a heavy focus on procedures,” Cook said. “Students get used to memorizing a set of strategies for solving problems and that serves them well for most of their undergraduate study.
“Abstract algebra is much more conceptual in nature. There is less focus on calculations and more on the big pictures. Instead of solutions, they are expected to produce proofs of theorems and, for many, the transition is tough.”
Cook’s solution to bridging the gap comes from starting instruction from a place that most math students find familiar – solving equations.
“The traditional approach is to start by saying, ‘These are the definitions of these structures,’ which is not meaningful to the student at that point,” Cook said. “While they may understand what it means, they won’t know why it’s important or how it is related to the other things you are asking them to know.
“The idea is to give them different concrete examples of these types of structures and have them solve equations, which is something they are comfortable doing,” Cook continued. “Once they’ve done that on five or six structures that behave differently, we can ask them to consider what they all have in common … Those are the axioms we’re trying to get them to understand.”
Cook’s paper deals with a small cross-section of the kinds of problems he researched in his dissertation and has been received warmly.
While putting the finishing touches on the paper, he submitted it in proposal form to the Conference on Research in Undergraduate Mathematics Education for consideration.
The submissions committee surprised him by offering to sponsor him as a featured speaker at next year’s Joint Mathematics Meeting.
This will be Cook’s second presentation at this conference on his guided reinvention technique.
He attended this year’s meeting sponsored by USAO and delivered a short, 15-minute version of his research, yielding some interesting results.
“A math professor from Augustana College in Illinois, another liberal arts school, who came to my talk at the Joint Meetings last year contacted me afterward asking if he could try out some of my methods,” Cook said. “I suggested we do a research project instead where he films his classes using the guided reinvention method to study the outcomes … so, we’re working on a grant for that now.”
Cook’s status as a featured presenter at the upcoming conference will afford him more time and visibility to share his ideas and, hopefully, more partners to apply and help him expand his research.
“My dissertation covered a very small section of this course, maybe two weeks’ worth,” Cook said. “What I’m looking to do is expand that, chip away bit by bit at the rest of the course.”
The 2014 Joint Mathematics Meeting is scheduled for January in Baltimore, Md.