## Harvey Segur and Mary Nelson

Applied Mathematics Department

APPM 1350 (Calculus 1 for Engineers) Course Description:

Applied Mathematicsâ€™ APPM 1350 course, Calculus I for Engineers, is a 4-credit course that offers students the opportunity to master the critical concepts of rate of change of functions, limits, derivatives, integration and their applications. Each week, students attend three lectures taught by a faculty member, plus one hour of recitation with a trained teaching assistant. Calculus I is a prerequisite for many courses in the Engineering curriculum, and about 500 students enroll in this class every fall semester. The department strives to be student-centered, particularly in their offer of oral assessments. Students can participate in oral reviews before each written unit exam. The orals are ungraded and voluntary. Facilitators ask groups of five students conceptual questions and give the students the opportunity to defend their thinking and negotiate meaning with their peers and the facilitator. Results suggest that students participating in orals deepen their understanding and pass Calculus I at higher rates.

Improving First-Semester Calculus:

Nationwide, 40 % of college students take some version of first-semester Calculus. But 40% of the students who take that course do not pass it: at CU/Boulder, that means that they get grades of D, F or W. (D is a failing grade in the sense that students who get D in Calculus I are not allowed to enter Calculus II, because history has shown that they will almost certainly fail Calculus II.) The numbers for the Department of Applied Math on the Boulder campus are slightly better, but not much: year after year, 30-35% of the students in our Calculus I class in the fall semester get grades of D, F or W. Most of them do not go on to take Calculus II, which means at least that they drop out of majors in Engineering, Science or Math, and often means that they drop out of CU altogether.

Over the years, Applied Math has tried several things to improve this dismal situation. The relevant one for your list began in 2006, when Mary Nelson and I decided to implement her voluntary, ungraded "Oral Assessments" before each of the three exams during the semester in APPM 1350 - Calculus I for Engineers. Each Oral typically consists of 5 students and a facilitator, and they are given in the two days before a written exam, so after the students have had a chance to study the material in question. Each Oral is given in a room with lots of blackboards, so the students all stand at a blackboard, and they answer questions from the facilitator. The questions are somewhat more conceptual than those that appear on the written exams - so the students are not asked to calculate X, but rather why one would want to calculate X, how to use X once it's been calculated, why X is the right quantity for that situation, and why X needs to be calculated this way instead of that way.

About 500 students take APPM 1350 each fall semester, so the logistics of such an operation are nontrivial: reserving enough suitable rooms, lining up enough good facilitators, and getting the right students to the right rooms at the right time all require some work. Mary Nelson had already invented and refined her concept of how Orals should work, so my biggest contribution to this large-scale experiment was to make sure that the logistics were handled properly each fall semester. I did this in fall semesters of 2006, 2007 and 2008. After that, I made a point of not teaching the class again, so that other people in our department would get involved in the project.

Aside from running the experiment, there is also an issue of measuring in some objective way the value of Orals for the students. Participation by students is voluntary, so it has been important to figure out how to separate the effect of the Orals on the students from the possibility that the more motivated students signed up for the Orals, and of course the more motivated students do better on exams.

I'll skip the grimy details of how we do that. After carefully taking data for the last 4 years, we now have objective measures of the effect of Orals. The NSF has agreed that we are getting somewhere on this project: in 2008, the NSF awarded a $450,000 grant to CU to continue this project. Mary Nelson is PI of the grant, James Curry, Anne Dougherty and I are co-PIs and Gene Abrams (at UCCS) has a smaller parallel grant to continue his version of Orals at UCCS. The grant is called CCLI, for Course, Curriculum and Laboratory Improvement.

The work on this grant spills over from APPM 1350 in several ways. (Mary Nelson, not me, has been responsible for most of this spillage. I take credit only for keeping the train on the tracks in APPM 1350 for the first 3 years of the experiment.) Spillage:

* Applied Math now uses Orals regularly in both first and second semester Calculus classes.

* Gene Abrams at UCCS is using his version of Orals in a class that he has organized there.

* Daria Kotys-Schwarz in Mech. Eng. and Penny Axelrad in Aerospace have begin using Orals in courses in their departments.

* Mary has been working with a teacher at Centaurus High School to use Orals in that teacher's Algebra class (for 15 year olds).

* Monica Geist at Front Range Community College has been using Orals in some of the Math classes at Front Range.