Closing the loop 2007

Desired Outcome:

Students will demonstrate mastery of the fundamental principles of 2D Calculus by generalizing and extending these principles to 3D.

Data Collection:

• Pretest administered early (week one or two) in semester in MTH 27, Multivariable Calculus 1 compared to a post test at the end of the semester.
• Used assessment instrument consisting of ten question to complete in 30 minutes without calculators: four questions from MTH 171 (Calculus I); four questions from MTH 172 (Calculus II); and the remaining two questions required material from both courses
• Fourteen students (first time enrollees who were sophomore to senior math and engineering majors who had been away from calculus a semester) participated in the assessment.

Interpretation of the Data:

• Students demonstrated a solid foundation with respect to MTH 171 skills. Reinforcing the derivative of the tangent function may be of help to most students.
• Results suggest that the students need to have the skills acquired in MTH 172 sharpened as well as have better-developed problem solving strategies for attacking integrals.
• Students were aware of the underlying concept of integration (i.e., it is anti-differentiation), even though they did not remember the specifics.

Changes to implement:

• Strengthening of simplifying exponents may be necessary. Derivative should be emphasized more in MTH 171. Differentiating the logarithmic function, in concert with the Chain Rule, needs to be stressed more in MTH 172.
• Integration by substitution and integration by parts needs to be emphasized more.
• Basic algebra/Pre-Calculus skills may need attention but these skills allow students to convert “hard” problems into easy problems. The math department suspects that the students could simplify the expression, but that they didn’t see that that is the move to make. Is this algebra skill or is it something larger, like problem solving strategies? It seems that students don’t get the strategy of changing something that we don’t recognize how to solve into something that we could recognize.