Give a student an answer and he will pass the class. Teach the student how to find the answer and he will pass every class.
This is the adage adopted by the mathematics department as it implements inquiry-based learning methods to traditional, lecture-taught classes.
In inquiry-based learning (IBL), professors help students in the process of discovery rather than telling them what they need to know, said Stan Yoshinobu, director of the Academy of Inquiry-Based Learning and an associate professor of mathematics.
“When students are engaged in learning, they tend to have better attitudes about it,” Yoshinobu said.
Mathematics professors are exploring inquiry-based learning with the primary goal of improving students’ experiences with math, said Dylan Retsek, an associate professor of mathematics.
Students lose many fundamental aspects of theoretical proof-based mathematics by the time they reach a higher math level, Retsek said.
A proof is a convincing demonstration that proves a mathematical statement is true.
As a result of students not retaining information, professors spend time re-teaching basic concepts rather than focusing on presenting new material, Retsek said.
Lecture, Yoshinobu said, is a passive way of learning, whereas inquiry-based learning is much more active and forces students to invest more in their education process.
Though the Academy of Inquiry-Based Learning has existed for about a year, the movement has been around for decades, Yoshinobu said.
In an inquiry-based learning classroom, the instructor acts as a mentor to students, guiding them in a general direction and providing advice and encouragement.
A professor gives students detailed problems, which students discuss and develop methods for solving in groups. They then present and explain their solutions to the class.
Yoshinobu asks the students why they believe a solution is correct or why they believe it is incorrect. Yoshinobu does not say whether a solution is right or wrong, but a smile or certain look are good indicators of progress or if a student needs more information, said Kevin Lamb, a mathematics senior and facilitator of Yoshinobu’s Math 248: Methods of Proof class.
An inquiry-based learning classroom is like an open forum, where students bounce ideas off one another. Inquiry-based learning helps a student develop public speaking skills and intuition, overcome shyness and work with peers in a collaborative effort, Lamb said.
While teaching a math education class in inquiry-based learning for aspiring elementary school teachers at Cal Poly, Yoshinobu noticed transformative changes in the students, he said. The students’ doubts about their math competence diminished after learning with inquiry-based methods. The class led many students to pursue higher math forms in order to teach at the middle school level.
“Math talent is often buried deep,” Yoshinobu said.
Inquiry-based learning helps students harness and improve that talent, Yoshinobu said.
Retsek will conduct an experiment in the spring where he will teach two sections of Math 248 in IBL. He will use his book called “Mathematical Inquiry,” which he wrote for the purpose of the experiment. The experiment will study the results of the IBL classes versus past lecture classes. Retsek will also report on students’ progress in future classes.
Retsek said he hopes to discover whether students will learn more or less under inquiry-based learning and whether they will like inquiry-based learning more, the same or less than standard lecture methods.
Retsek’s experiment, as well as the sabbatical needed to write the book for the experiment, had to be approved by Don Rawlings, the mathematics department chair, a committee of department heads from each college and the dean of the College of Science and Mathematics.
Retsek also needed consent from students to be involved with the experiment.
Class time will be spent presenting and discussing proofs, Retsek said. The number of chapters covered in the book is not important, as long as students gain the ability to understand a new definition and apply it to prove a concept.
Assessment in the courses will be similar to a normal Math 248 class with a couple of midterms and a final, Retsek said. Students will also be graded on how they defend and justify points about their proofs, as well as the mathematical language they use in their discussions.
Retsek said he plans to share the results with his colleagues and possibly publish his findings in a science and math education journal. If there is a significant difference in the depth of his students’ understanding, he will incorporate inquiry-based learning into his other classes.
“Inquiry-based learning is much more in line with Cal Poly’s idea of ‘learn by doing,’” Retsek said.