The University of Colorado at Boulder applied mathematics department has been awarded a $450,000 grant by the National Science Foundation to introduce pre-examination "oral assessments" in a number of courses to improve student understanding.
Led by principal investigator and applied math department instructor Mary Nelson, the oral assessments effort will be increased on the CU-Boulder campus and implemented at several other sites, said Anne Dougherty, associate chair of the department and a co-investigator on the grant with applied math Professors Jim Curry and Harvey Segur. Faculty from CU-Boulder's aerospace engineering sciences department, UC-Colorado Springs mathematics Professor Gene Abrams and teachers at Fairview High School also will be involved.
In recent years the applied math department has tried to teach math more effectively to university students, said Nelson. Since 2003, oral assessments have been offered in a number of courses and appear to strengthen students' understanding of important math concepts and their capacity to apply knowledge in new and novel situations, she said.
Before each written exam, groups of five students meet for an hour with a facilitator, who helps the students to talk about the basic concepts of the course. "The process includes asking students to explain how and why specific mathematical procedures can be used and to draw graphs that clarify the meaning of important concepts of the course," Nelson said.
In 2003, the applied math department introduced oral assessments into a two-semester Calculus I course designed for students at risk of failing calculus. Analyses showed that students in the two-semester course earned higher grades, took and passed Calculus II at a higher rate and were more likely to be retained at the university than their counterparts, said Dougherty.
According to the data, a combination of oral assessments and the two-semester Calculus I class for at-risk students cut the calculus failure rate at the university from more than 30 percent to under 22 percent. The national failure rate for Calculus I is about 40 percent. "We are excited about the gains we have seen to date and are hopeful that with the NSF grant, we will see continued improvement among our students," Nelson said.
Such research is important, the researchers say, because calculus is a gateway course for science, technology, engineering and math majors.
The NSF grant will make it possible to collect and analyze data and to introduce oral assessments into a wider range of courses both at CU-Boulder and local schools. Oral assessments are now in use in calculus classes at CU-Boulder and UC-Colorado Springs and are being introduced in two algebra classes at Fairview High School. In fall 2009, oral assessments will be offered in CU-Boulder introductory mechanical engineering and aerospace engineering classes, said Dougherty.
Nelson received her doctorate from the CU-Boulder School of Education on research and evaluation methods and math education. She has taught at the college level since 1973 and at CU-Boulder since 1997.