A Video Solution for Classroom Math Problem
Teaching math can be challenging. Besides the challenge of reaching students who automatically tune out their math professors, math professors also typically have students who try very hard yet still "don't get it"— students who have the right idea yet can't quite translate it to mathematical language. That language barrier also makes it difficult to know where a student has gone wrong.
One solution to this common classroom problem appears to be showing short videos. For the last two years, Professor Kay Somers, chair of mathematics, has been using video cases to understand and promote student critical thinking about the proof process. The edited videos show real students working through proofs—with varying degrees of success. Professor Somers pauses the 5- to 10-minute videos several times to allow classroom discussion.
The technique is part of a design experiment aimed at improving the teaching of proof at the college level. A team of three mathematicians and two mathematics education specialists from Moravian College, Georgetown University, and Millsaps College are participating in the research, which is funded by a National Science Foundation grant. A mathematics educator from Umea University in Sweden is involved with assessment of the program.
"The videos make the invisible visible," explained Professor Somers. "Student feedback has been very positive. The majority of students seem to benefit greatly by observing the process and seeing other students articulate their struggles, which are normal."
"The case videos have helped me better understand certain methods of solving problems," noted Mark Hop '12, a math education major. "It's sometimes difficult to know what steps to take to find a solution. Having a visual guide through the problem, as performed by another student, can be a great aid."
Other students report that they relate better to other students, who "speak in the same language;" and they feel encouraged, "knowing that these are smart kids … and they struggled too." Students also like the videos simply because they are different—they make it "impossible to nap," said one.
Professor Somers and her colleagues have reported their research in several published papers, including "'Is that a Proof?': an Emerging Explanation of Why Students Don't Know They (Just about) Have One" (2009), presented at the Sixth Conference of European Research in Mathematics Education in Lyon, France, and at other international and national conferences. The researchers are writing a new grant to allow additional research in other problem-solving math classes (such as calculus) and more video recording, as well as sharing the method with other faculty members.