Check, Please
Math professor Nathan Carter may not have all the answers, but he has a pretty good idea how to get them. Students can learn to do the same through software that Carter is developing with the help of a grant from the National Science Foundation (NSF).
The program, which is called Lurch, enables students to check their work on math problems and adjust direction as needed to arrive at the correct solution. But don’t think for a second that Carter is offering an easy out for math haters. Instead, he aims to boost learning by helping students solve math problems in the right way from the start.
Fast and frequent feedback is the gold standard for learning, notes Carter, who is pictured above with directed-study student Jeff Smith '10.
“You might do 10 problems wrong, in the same way – and it would have been better to find the mistake when you were doing the first one. That can happen if you hire a tutor. Or, we can develop software like this.”
Lurching Forward
Carter hatched the idea for Lurch more than 10 years ago, as an undergraduate at the University of Scranton in Pennsylvania. In learning to do proofs, he identified the step-by-step process as one that a computer could probably check. He discussed the concept with Ken Monks, his professor at the time and now his partner on the project. They developed a prototype before Carter had even finished his bachelor’s degree.
Though rough around the edges, the prototype “showed us that, yes, this software could be built,” he says. “We were just getting the ideas out there.”
The name “Lurch” reflected their initial halting but forward movement – and it stuck.
The pair continued to discuss Lurch through the years, as Carter earned a PhD in logic at Indiana University and started teaching at Bentley. Then came the $130,000 NSF grant, awarded in 2007, which allowed research time for fine-tuning and bringing the concept to life.
Customized Solutions
Lurch is planned to function like a word processor’s spelling and grammar checker tool. But instead of flagging errant vowels and faulty sentence structure, the program will indicate when a student has violated a math rule or left out a significant step in problem solving. Carter and Monks intend the software to be robust enough to handle multiple branches of math and serve different educational levels.
“We want it to be very flexible and customizable for whatever the instructor wants,” Carter explains, noting that the target users are students in upper-level college mathematics courses. “It will come with a couple branches of math built in, and if it doesn’t have the one you want, you can add it.”
Having started work in earnest during summer 2008, Carter and Monks are about halfway through Lurch’s three-year development phase. Last fall, Carter tested an early version of the program with honors students in his mathematical logic course at Bentley; their feedback inspired some revisions.
Development continues in the current semester, with help from a handful of Bentley students: directed-study participants Jenna Bergevin ’10, Derek Breen ’10, Ryan Colwell ’10 and Jeff Wright ’10, and research assistant Timothy Delaney ’10. The work is sure to be an education on many fronts.
“The students are learning about the math related to this program, and learning how you go about working on a team, in different geographic locations, to build open-source software,” says Carter. “Their contributions will further the project – and I hope they enjoy it, too.”