“You Taught Me to Think, Professor Coughlin!”
Critical Reasoning in Gen Ed
—Lewis Gordon, College of Liberal Arts
Associate Professor of Mathematics, College of Science and Technology
What would make a group of Temple students give a mathematics professor a standing ovation?
A great course.
“It was the most fulfilling class I have ever taught,” said the professor, Raymond Coughlin (College of Science and Technology). He used the twenty-five most difficult questions on the LSAT (Law School Aptitude Test), as determined by the Law School Admission Council, to evaluate those students at the semester’s end. Very few of Coughlin’s students had more than three incorrect answers.
The course, “Critical Reasoning: Strategies for Analytical Judgment: Transcending the Limits of Incomplete Information,” is offered through the Mathematics Department by the Gen Ed program.
Omar Hijab, Chairperson of the Math Department, reports that the course has generated an “enormous buzz.”
When I heard about this course, I immediately thought about a similar one from my undergraduate years in the Lehman Scholars Program in the City University of New York. I had the good fortune of taking a class on critical reasoning taught by Raymond Smullyan, the famed mathematician and magician. In that course, lessons on logical reasoning were accompanied by heuristic magical tricks designed to make us think about thinking.
Photo by Paul Halmos
Thinking about thinking, to be critical of the presumptions of thought and how one thinks, is crucial for intellectual independence. Smullyan loved puzzles of self-reference. His books included the delightful, What Is the Name of this Book?: The Riddle of Dracula and Other Puzzles (Prentice-Hall, 1978).
Through a series of stimulating riddles and puzzles, that wonderful book introduced us, to of all things, the famous incompleteness theorem of Kurt Gödell. Any system that is sophisticated enough to refer to itself, the theorem and subsequent logicians such as Smullyan showed, is bound to produce paradoxes that would render it incomplete or inconsistent.
Nearly every student from that course of two decades ago subsequently did well in his or her academic career.
The Temple Gen Ed course is authored and taught by Coughlin, who, although not a magician, achieves his own kind of magic in the classroom as acknowledged by his receiving The Great Teacher Award in 1997, Temple’s highest teaching award. The Gen Ed Committee is thrilled that he is bringing such energy and dedication to the curriculum. In the words of David Watt (College of Liberal Arts and a member of the Gen Ed Committee):
“Ray Coughlin is an outstanding teacher, and a perfect fit for Gen Ed. Students are truly engaged in his classes. They see math in context. They understand the everyday significance of math, and how it relates to their lives.”
Coughlin came to Temple in 1970 after earning his PhD in mathematics from the Illinois Institute of Technology in 1969. He is the author or co-author of seventeen books and numerous articles on nonassociative algebras.
Coughlin loves teaching at Temple, where his pedagogical work includes his past directorship of the university’s Honors Program. It was while directing that program that he observed how students learn across a variety of disciplines. He noticed that many courses focused on information and often-mechanical research. Problem-solving skills were rarely on the agenda. The consequence was detrimental.
As Coughlin recounts, “When I was Honors Director and then Pre-Med advisor I was asked by the Provost to improve our students’ performance on national standardized exams, like the LSAT, MCAT and GRE. For almost a year I roamed the campus interviewing professors and administrators looking for direction, such as the right mix of courses for our students to take to improve their reasoning skills. I found none.
“Once I realized I had to do it on my own I was able to identify the significant lack in our students’ preparation for these exams. We don’t teach them how to reason critically. The exams are written at the fifth and sixth levels of Bloom’s taxonomy but few of our courses require them to reason beyond the third and fourth levels. Most of our courses are information-driven rather than problem-solving-driven. Even the law school itself assumes that their students either have these skills or don’t, and they either get it on the exams or they don’t.”
He continues, “With the support of Eli Goldblatt [in the College of Liberal Arts], I started suggesting that the new Core include a course that teaches our students critical reasoning. I was ridiculed. The lone voices of support came from Eli, my chair, Omar Hijab, and later Ben Rifkin [CLA] and Paul Crowe [CLA]. In the course, Coughlin teaches the students how to analyze an article critically. At first, the students are intrigued by how a math professor could help them with this task. “Students think mathematics is without creativity,” Coughlin explains. “We discuss the form and structure of creativity.” By this, he means he encourages them to think through many levels of reasoning at their disposal.
“Students make the error of thinking it’s their opinion that is asked for,” Coughlin explains. His course teaches them how to explore the author’s thought and its gaps, its contradictions and possibilities for its improvement.
Coughlin analyzing a news story with class
“He genuinely wants to demystify math,” observes Terry Halbert (Fox School of Business and Director of Gen Ed), “to make it comprehensible to students who are math-phobic. He’s convinced that students can succeed with the LSAT if they understand the underlying logic behind it. He helps students understand that logic, and gives them confidence that they can crack the code of standardized tests.”
Coughlin is on a mission to make these tests and forms of reasoning intelligible to his students. After several weeks of exploring these problems (among others) with him, the students are so at home in the world of such reasoning that the atmosphere during the in-class final examination is one of exuberance instead of a dreaded day of reckoning.
The students’ enthusiasm is from the joy of learning. Coughlin recounts a conversation with a student who had begun the course with much difficulty. “I helped my girlfriend with the GRE, Doc!” said the student, who completed the final examination with twenty-three correct answers out of the assigned twenty-five most difficult problems.
One of the techniques Coughlin uses to stimulate critical reflection among the students is to challenge their notions of common sense.
“I start the students with puzzles,” he says, “ones that are simply stated but whose solutions grow in complexity from one puzzle to the next. I also introduce them to sudoku puzzles that require a good bit of reasoning. Hopefully they’re having some fun at this point.
“Then we get to the twentieth puzzle, which has as straightforward a description as you can imagine, and whose solution seems obvious, so obvious that not one student even suggested we prove that the solution is, in fact, correct. I show them that the ‘obvious’ solution is incorrect, which puzzles them even further. They demand to know what the actual solution is, and when I show them it blows their mind it is so complex.”
From that point onward, the students are proverbially “hooked.”
Coughlin hopes that critical reasoning will become a feature of the entire Temple curriculum. It is not only analytical puzzles from the LSAT and the GRE that are explored in his course but also the construction of well-crafted arguments in student papers.
Many college students (and even graduate students) today do not know how to formulate a thesis. Learning to formulate their main argument could strengthen their work in the humanities and social sciences.
I would talk with Eli Goldblatt [Director of the First-Year Writing Program and 2007 Great Teacher Award winner] about the importance of getting students to see beyond the walls of their particular classroom. We agreed that we would like for students to see that there is more to what they are doing than simply their subjects of study. There is a higher-order understanding to develop to become a critical learner. We need to cultivate thinking.”
Coughlin’s message goes beyond his aspirations for his students. His daughter, Dr. Christina Coughlin, who was the first Alumna speaker for Temple’s College of Technology and Sciences, draws upon techniques she has learned from her father in her research in oncology. She takes a problems-solving approach to the study of tumors in the body. The admissions committee for the MD-PHD program at the University of Pennsylvania had recommended her admission in part because of her strong background in mathematics and the importance of bringing reasoning skills to the study of medicine.
“In forty years of teaching,” says Ray Coughlin, “I’ve never had so many students go out of their way to thank me for teaching them the material in the course. (Students don’t usually thank you for teaching them algebra or calculus.) So it wasn’t just an invigorating class that they enjoyed, they appreciated the subject matter and they believe it will be useful to them.”
In the students’ words, said to Coughlin repeatedly at the end of the semester’s end, “You taught me to think!”