MAT226 Vector Calculus has a uniform syllabus. The course outcomes and the major outcomes incorporated into this course are assessed on a final exam designed by the professor.
MAT226 is a required course for all math majors and is also required for some other science majors.
MAT226 Course Outcomes:
1. Graph and determine the equations for lines and planes (as part of dept objectives in math a & b)
2. Compute sums, differences, dot products and cross products of vectors (a)
3. Determine velocities and accelerations of vector-valued position functions (a, b & c)
4. Find level sets, gradients and tangent planes to functions of several variables (a, b & e)
5. Apply the method of Lagrange Multipliers (a,b & c)
6. Apply Fubini's Theorem and Green's Theorem to integrate functions and fields (a, b & e)
Math Major Outcomes incorporated into MAT226:
A. Perform numeric and symbolic computations
B. Construct and apply symbolic and graphical representations of functions
C. Model real-life problems mathematically
E. State and apply mathematical definitions and theorems
MAT226 is a required course for all math majors.
Fall 2016 / Spring 2017 Assessment Report for MAT 226:
The data used for assessment may be found here (Fall 2016) and here (Spring 2017). The linked spreadsheets show which Course Outcomes and which Major Outcomes were tested on each problem of the final exam (the MAT 226 final exams are not uniform), as well as for each problem the number of students that solved that problem "correctly". The instructor of the Fall 2016 section interpreted "correctly" to mean that the student earned full credit, while the instructor of the Spring 2017 section interpreted "correctly" to mean that the student lost no more than 1 or 2 points on the problem.
The Course Outcome (CO) data shows that CO 6 had lowest success rates, 26% and 65% respectively, in the Fall and Spring sections. This is not surprising as Green's Theorem is an advanced topic taught at the very end of the course, though the Fall 2016 percentage seems abnormally low. Students taking MAT 226 in the spring often have taken MAT 176 the previous fall, and since the winter break is shorter than the summer break, it seems reasonable that they would have an advantage over the students that take MAT 226 in the fall, especially when it comes to integration. Another factor, as mentioned above, is that the Fall 2016 instructor's interpretation of "correct" was more stringent than that of the Spring 2017 instructor, so one would expect somewhat lower percentages. With this in mind, the data overall is encouraging: most of the percentages were near or over 70%.
The Math Major Outcome (MMO) percentages were all above 70% in the Spring, and were all just below 70% in the Fall.
The averages of the Fall and Spring data were about 70%, which is a reasonable target minimum.
The following suggestions will be brought to the attention of the Educational Policy Committee in the Math Department:
1. Prepare differentiation and integration review sheet, especially for students taking MAT 226 in the Fall.
2. Clarify the extent to which MMO C is an outcome of MAT 226.
3. Clarify Tally Sheet grading policy.
Fall 2012 Assessment Report for MAT 226:
MAT226 was assessed in Fall 2012 using the Fall 2012 MAT226 Final Exam designed by the professor teaching the course: final.
Data Analysis: Here we have a spreadsheet indicating how many students performed each question correctly,
which questions were used to compute scores for the course outcomes and which were used to compute scores for the major outcomes. If a course outcome is listed as computed using questions 1, 2, and 3, then that outcome's score is computed as the average of the numbers of students scoring each of these three questions correctly.
Conclusions:
The students performed the best on Course Outcome 3, the computation of velocities and accelerations. This is a fundamental topic needed for physics applications and demonstrates also that the students have mastered the prerequisite material from Calculus I. The students also performed very well on Course Outcomes 1 and 2. This indicates that they have mastered the fundamental geometric skills involving vectors that are essential background taught for the first time in this course and in Linear Algebra. The students had more difficulty with Course Outcome 4 and did especially poorly in Course Outcomes 5 and 6. It should be noted that Course Outcome 6 is a difficult topic, often skipped in Vector Calculus Courses and taught again in the more advanced Differential Geometry. Nevertheless 13 students mastered the topic. It should be kept in this course and repeated in Differential Geometry so that students who struggled the first time they saw the topic may learn it better the second time around. Course Outcome 5 is also a topic often not included in Vector Calculus courses however it is essential for students considering an MBA. So we keep this difficult topic in the course and are content that 11 students mastered it. Course Outcome 4 was assessed using two questions. The students performed fairly well on one of those questions but had difficulty with question 9, perhaps indicating a lack of understanding of the quotient rule from Calculus I.
The scores for the four major objectives of this course were all excellent with the students performing best on the applications objective.
This course will be assessed again in Fall 2014.