How to Solve a Hard Math Problem

January 27, 2021

Ever feel like you were in over your head during math class? Unfortunately, this seems to be a familiar sensation for incoming students at Berkeley, where most undergraduates take a course in mathematics. Beyond being unprepared to understand some core concepts, students who struggle through a gateway math course often stop studying a scientific or technical field. 

“For most STEM students, they need to be applying all of their math toolkit to very complicated problem sets, and if they do not have a full toolkit, it’s going to be really challenging to stay in STEM majors,” says UC Berkeley Foundation trustee Kathy Kwan ’87, M.B.A., M.P.H. ’93. She has spearheaded an ongoing effort with MPS and the Department of Mathematics to assess student aptitude and advise them about appropriate course choices. 

Dean Frances Hellman is concerned about a nationwide trend of undergraduates who intend to declare a STEM major but drop out after an unsuccessful encounter with a prerequisite class. In recent decades, the STEM dropout rate has been around two-thirds for underrepresented students — twice the rate for white males. Hellman says, “It seemed likely that this persistence gap could originate largely in math backgrounds, so we set out to study that.” 

After investigating available options, the team selected an online resource called ALEKS (for Assessment and LEarning in Knowledge Spaces), which combines a math preparation assessment with personalized opportunities to sharpen skills in any of 11 topics. “With ALEKS,” says Hellman, “students can identify specific areas of weakness and pursue independent study of these. It’s not just an assessment tool but also a teaching tool.” 

With support from the Eustace-Kwan Family Foundation, a pilot test of ALEKS with more than 600 students took place in Fall 2017, followed by a spring rollout for all students enrolled in four different calculus and pre-calculus courses. By now, some 5,000 students have participated in the study. Using a tool like ALEKS enables determining the math strengths and weaknesses for thousands of students at once. 

When those results came in, says Kwan, “I almost had a nervous breakdown, because a lot more students were not as good at math as we anticipated.” Across all student demographics, surprisingly wide knowledge gaps were revealed in five of the topical modules on ALEKS: relations and functions, quadratic and polynomial functions, rational expressions and functions, exponentials and logarithms, and trigonometry. A higher proportion of the unprepared students come from low-income families or underrepresented groups. 

To help bridge the gap, mathematics teaching professor Alex Paulin and lecturer Kelli Talaska created online modules to address the five problematic topics with content appropriate to Berkeley’s lower-division math classes. With only a week’s notice, more than 900 students signed up for the instructors’ intensive summer pilot for Pre-Calculus Essentials. About 200 of the students elected to participate in peer groups led by an undergraduate tutor recruited and trained by the Student Learning Center. For three weeks, these groups met daily to discuss lessons and work together on problems. The tutors successfully created communities and instilled confidence in their students that carried over into the fall semester’s classes. MPS will investigate how these interventions improve student success, while planning how to sustain efforts to assess and support so many undergraduates.