CU-Boulder freshman engineering students at risk of failing calculus don't have to struggle alone. When these students are encouraged to talk about the subject's concepts in small discussion groups, they are more likely to pass the class.
When voluntary pre-test discussions, called oral assessments, were introduced into a special two-semester-long Calculus I class in 2003, 95 percent of the students passed the course. The national failure rate for Calculus I is about 40 percent. By participating in the oral assessments, at-risk students not only earned better grades in Calculus I, but they took and passed Calculus II at higher rates, and a higher percentage of them stayed in engineering.
Based on the success of these oral assessments, the National Science Foundation awarded a $450,000 grant to the Department of Applied Mathematics to introduce assessments into other engineering classes on the CU-Boulder campus and in math classes at CU-Colorado Springs and a local high school. Mary Nelson, PhD, is an applied math instructor and the principal investigator for the grant.
Groups of five students meet with a facilitator a day or two before a written exam to talk about the fundamental concepts being covered on the upcoming exam. Facilitators ask students to explain how and why specific mathematical procedures are used and to draw graphs that illustrate the concepts.
The orals are optional and are not graded. Last semester approximately 60 percent of engineering freshmen participated in at least one oral. Talking through mathematical processes and negotiating meaning with fellow students and the facilitator clarify the concepts of the course and let facilitators see where there are gaps in students' understanding.
Q: Why did you introduce the oral assessments?
A: Students were coming to us who didn't have enough math preparation in high school for various reasons. They may have come from a rural or urban school that didn't offer higher math classes or their teacher didn't explain it to them well enough or they just didn't fully grasp the concepts.
Q: Why are the math assessments important in a college of engineering?
A: Calculus is what we call a gatekeeper to engineering. If aspiring engineering students can't pass Calculus I, then they're not going to be engineers. We think these orals help retain students in engineering majors.
Q: How have you found that oral calculus assessments improve students' conceptual understanding and retention rates?
A: The awareness of the process of learning is a critical ingredient to successful learning. Once they understand the underlying concepts, it's much easier for students to use the information in novel situations. They see that there can be a different application of the same concept outside of the examples given in class.
Q: What are the benefits of the assessments for students and for the college?
A: We find that by getting students to talk about basic concepts, two things happen. One is that by sharing solution strategies and by explaining their mathematical thinking to the facilitator and to others in the group, conceptual understanding is developed and enhanced. The other thing that happens is when the facilitators hear the students talk through problems, they find out why a student might be getting an answer wrong.
Q: What other changes have you seen in students who complete these oral assessments?
A: Students who participate in the orals tend to form study groups in their other courses. They see that it helps them to talk about the concepts because when they can put the mathematical information into their own words, they take ownership of their learning.
Q: What changes, if any, do you anticipate in the oral assessment program as a result of your NSF grant?
A: In addition to oral assessments in calculus classes, assessments will be offered in classes for introductory mechanical engineering this spring and an aerospace engineering class in the fall. Also, assessments are being introduced in algebra classes at Fairview High School in Boulder to help prepare students for college.