Assessment Report

Course: M 273Q, Multivariable Calculus 
Semester: Spring 2017
Instructors/supervisor: Christina Hayes and Jaroslaw Kwapisz
Submitted by: Christina Hayes and Jaroslaw Kwapisz 

 

Overview

Number of students in course: 769 (AY 2016-2017)
Number of students assessed: 34

Learning Outcomes

LO# Learning Outcomes
1. Interpret and draw inferences from mathematical or statistical models represented as formulas, graphs, or tables.
2. Represent mathematical or statistical information numerically and visually.
3. Employ quantitative methods such as arithmetic, algebra, geometry, or statistical inference to solve problems.

Assessment Questions

Aligned LO# Exam Questions
1. Two contour maps are shown. One is for a function whose graph is a cone. The other is for the function whose graph is a paraboloid. Identify which of the two is the contour map of the cone.
2. A solid object occupies a region inside a given cone, but between two given spheres. (One could imagine a “circular” chunk of rind only of a watermelon). Rewrite a triple integral over the described region in the spherical coordinate system. 
3. Use the Divergence Theorem to evaluate its surface integral over a region (from vector field). Identify the surface of the solid and then correctly apply the theorem.

Assessment

Criteria for Learning Outcomes LO 1 LO 2 LO 3
Total number assessed 34 34 34
Number of students demonstrated acceptable level 32 32 26
Proportion of students rated as acceptable 32/34 32/34 26/34
Does this meet minimum 2/3 threshold? yes - 94% yes - 94% yes - 77%

 

 

Comments/ideas for better alignment of course or assignment

 none The course is most definitely aligned with the Q-core rationale as almost all problems in multivariable calculus require relating visual and numerical representations of mathematical
problems. 		 Multivariable Calculus is a course very much aligned with the Q-core rationale. Students who did not perform at the “acceptable” level were generally able to calculate divergence, but confused or transposed the dimensions of the box with the correct axes, or were not able to relate the flux to a triple integral at all. The 77% acceptable performance score (lower than the other percentages in this report) is likely a reflection of the level of difficulty of the question. The Divergence Theorem belongs to the notoriously difficult part of the material covered at the tail end of the course. That 77% of students were able to use the theorem at an acceptable level is not only acceptable, but a result we are quite pleased with.

 

 

Comments/ideas for improving the assessment process

   Nearly all students were able to identify the contour map of the cone. This shows an ability to understand what shape in 3D corresponds to its 2D contour map. In terms of multivariable calculus assessment it is more interesting to see how many students are then able to take that knowledge and use it to critically problem solve. For future assessment of understanding of the method of Lagrange multipliers, for example, one could write a problem that ties contour maps to solving Euler-Lagrange equations, so that it is seen as less algorithmic by the students.       none     none

 

PDF of M273 Q-Core Assessment Report