Discrete Math Primer Levels Educational Playing Field

A program built from Carnegie Mellon University’s OpenSimon Toolkit aims to prepare students for their first college-level math course before they even step on campus.

In the summer before computer science students start their courses at Carnegie Mellon, they must complete the Discrete Math Primer, a tool that uses self-paced interactive modules to provide students a baseline of math competency necessary for their future classwork.

“Here are CMU, we have amazing computer science applicants. While our students are really strong, there is still variability in their math background,” said Marsha Lovett, associate vice provost for Educational Innovation and Learning Analytics and co-coordinator of The Simon Initiative. “The computer science department found that some students struggled year after year in the discrete math course. The Discrete Math Primer provides a way to level the playing field before students take that first course.”

The creators of the Discrete Math Primer built it using the OpenSimon Toolkit, said Lovett, who’s also director of the Eberly Center for Teaching Excellence & Educational Innovation. They specifically designed the modules to target prerequisite skills that struggling students sometimes lack. Eberly Center learning engineers then used pre- and post-module quizzes to see how students improved, or didn’t, in the modules' main topic areas. Data from those quizzes reveals where to revise the course with the aim of raising student outcomes, Lovett said.

“You can see that by the end of the modules, students were doing quite well in logic and sets, but not so well in functions,” Lovett said. “Knowing this, the faculty worked with the Eberly Center to revise and refine the piece of the modules focused on functions to improve them.”

Over time, the learning engineers and designers added a cognitive tutor to the module that prompts students as they’re going through the problem, asking them to reconsider their answer if they’re using the wrong approach. CMU's Vice Provost for Education Amy Burkert said the tutor adds to the module’s overall goal of providing students with a more personalized and adaptive learning experience.

Thanks to the successes seen with computer science students, Mellon College of Science students majoring in math-focused areas also have begun using the modules in recent years. Other programs are also considering adding the Discrete Math Primer to their curriculum.

CMU faculty interested in this program or creating a similar module with the OpenSimon Toolkit can work with the Eberly Center to find the best solution. While the work requires faculty investment upfront, the rewards can extend to both students and faculty.

“The investment not only improves students' learning, it provides efficiencies that help faculty better support their class,” Burkert said. “For instance, instead of responding to questions on basic concepts, faculty can use that time to delve deeper into theory and concepts that will enhance students’ learning in future courses.”

Carnegie Mellon University is committed to educating, empowering and aligning its community around the world to address the Sustainable Development Goals, also known as the Global Goals, which aim to create a more peaceful, prosperous planet with just and inclusive societies. Recognizing the critical contributions that universities are making through education, research and practice, CMU publicly committed to undertaking a Voluntary University Review of the Global Goals. The 17 Global Goals cover wide-ranging issues, including reducing violence, ending extreme poverty, promoting equitable education, fighting inequality and injustice, advancing economic growth and decent work, and preventing the harmful effects of climate change by 2030.

The preceding story demonstrates CMU's work toward attaining Global Goals 4 and 10.