Inquiry-based learning (IBL) is a powerful force for positive change, mathematician Michael Starbird (University of Texas) argued on the opening night of the Fourteenth Annual Legacy of R.L. Moore Conference. Throughout the meeting, in Washington, D.C., June 2-4, one participant after another echoed this sentiment and provided vivid examples of the impact this teaching method has had in the mathematics classroom and beyond.
On the first day, program co-organizer Stan Yoshinobu (California Polytechnic State University) told more than 200 conference attendees that teaching mathematics via Moore-inspired methods "changes people’s lives." As part of the afternoon’s New Users Panel, Robert Vallin (Slippery Rock University) made the same assertion, phrased more poetically. Watching a student grow over the course of an IBL class, Vallin said, is like "watching a cygnet turn into a swan."
Such a metamorphosis from awkward youngster to poised adult has effects beyond the mathematics classroom, presenters reiterated throughout the day. "If you can prove theorems, you can do anything," William "Ted" Mahavier (Lamar University) said in a talk entitled "The Moore Method: Transformative Experiences."
So when Starbird took the floor to deliver an after-dinner address titled "Transforming Lives: Teaching Thinking and Creativity," his audience was primed for a pep talk. And Starbird did not disappoint, treating listeners to what master of ceremonies Lee May (Salisbury University) afterward described as "a wonderful combination of a standup routine and a sermon."
In the standup portion of the talk, Starbird regaled the crowd with tales of Moore’s distinguished student—and Starbird’s own onetime adviser—R.H. Bing, who served as president of the Mathematical Association of America (1963-64). Starbird recounted with obvious relish how Bing, talking math as he drove a warm car speeding through a cold "dark and stormy night," traced mathematical figures in the fog condensed on the windshield instead of wiping it off to give a clear view of the road ahead. Bing’s passengers were "interested in the topology" under discussion, Starbird reported, but they were "more interested in survival."
The tenor of Starbird’s talk changed from amusing to motivational, though, when he posed a question to his audience of mostly mathematics professors, and then answered it. "What business are we really in in our profession?" he asked. "We are in the business of transforming lives."
Starbird hinted that the transformation effected by inquiry-based learning is at once dramatic and unsurprising. Yes, over the course of a mere semester spent truly engaging in mathematics for themselves, students sometimes become "more than they imagined they could be," but the gains are not serendipitous. There is a cause-and-effect relationship, Starbird stressed, between what IBL teachers do in the classroom and the observed improvement in student skill and confidence. "It’s not just randomness," he said. "It’s not just luck."
"Systematically encourage people to face the unknown and learn the strategies of thinking," Starbird said, and you equip tomorrow’s workforce with the intellectual wherewithal to tackle the many unforeseen—and unforeseeable—problems that will arise in the decades to come.
A lofty claim, perhaps, but one Starbird supported by enumerating specific benefits of Moore method instruction.
Inquiry-based learning encourages the development of deep understanding, Starbird said, forcing students to cement basics and dwell longer on issues than they might otherwise. An IBL classroom fosters skills that can’t be outsourced to machines; thinking and creativity is prized over memorization or mastery of algorithmic processes. Students taught by any of the many modified Moore methods learn, first and foremost, to think for themselves.
They also learn to appreciate mistakes. "I don’t think anybody has ever done anything creative except building it on a pile of failed attempts," Starbird said, adding that IBL aims to "have every student experience the arc from mistakes to success, and to understand what role the mistakes . . . play in actually coming to a resolution and understanding."
IBL encourages students to view not just errors differently. Questions, too, take on a new significance. As the name inquiry-based learning suggests, the method of instruction Starbird advocates has questioning at its core. Students exposed to the method realize, he said, that questioning is not something you do only "when you’re confused or lost or if there’s a test." It’s what you do "when you’re just living life, when you’re looking for new ideas."
Starbird doesn’t ask students if they have questions; he tells them to write down questions in consultation with their neighbors. Having questions, he suggests, is what you’re supposed to do in both mathematics and life.
Although Starbird cited the ability of IBL classes to give students a feel for the flow of mathematical ideas, to leave them with the knowledge that there is more mathematics beyond what any one course or sequence of courses can cover, it was the nonmathematical reach of Moore-inspired instruction that he wanted to impress upon his audience as the first day of the Legacy Conference drew to a close.
"Never for a minute think that what we’re doing is teaching a narrow collection of mathematical facts and skills," Starbird said, emphasizing that the habits of mind developed in IBL classrooms make students better artists, better writers, and better citizens. He encouraged attendees to think big: "We are absolutely central to what needs to be done to improve the world for the future." —Katharine Merow