Additional Online Case Studies & Appendices

Developing a Departmental Assessment Program:

North Dakota State University Mathematics

### William O. Martin, Doğan Çömez

Sample report for Math 265 ( Calculus III), Spring 2002.

Preliminary Assessment Results

Mathematics 265: Calculus III

Spring 2000-02

Sixty-eight students took two versions of a eight-item free-response test in Mathematics 265 (Professor Sherman) during the second week of the Spring 2002 semester. The test was designed to see the extent to which students had quantitative skills required for success in the course. Students were not allowed to use calculators while completing the assessments. Graduate students from the Department of Mathematics graded the papers, recording information about steps students had taken when solving the problems. The graders also coded the degree of success achieved on each problem using the following rubric:

1. Completely correct
2. Essentially correct—student shows full understanding of solution and only makes a minor mistake (e.g., wrong sign when calculating a derivative or arithmetic error)
3. Flawed response, but quite close to a correct solution (appears they could do this type of problem with a little review or help)
4. Took some appropriate action, but far short of a solution
5. Blank, or nothing relevant to the problem

Corrected papers, along with suggested solutions to the problems, were returned to students the following week. Summaries of the grader’s coding are included on the attached copy of the test. A test score was computed by awarding one point for each A or B code and zero points for each C, D, or E code. This score reflects the number of problems that each student had essentially or completely correct. The distributions of test scores are shown in these

figures.

The second pair of charts gives the distribution of partial credit scores called scoresum (each

problem was awarded 0-4 points, E=0 to A=4).

It appears that many students will need to review some mathematics covered on the test, since a majority were successful on less than half the problems. Almost two-thirds of the students (44 of the 68) achieved overall success on four or fewer of the eight problems.

The problems are ranked according the degree of success students achieved on each problem in the following table.

 Degree of Success on Test Problems %AB %A %C No Problem description 85% 12% 3% V2#3 Integration using Fundamental Theorem of Calculus 73% 58% 3% V2#2 Solve using property of differences for logarithms (same as V1#2) 69% 66% 6% V1#2 Solve using property of difference for logarithms (same as V2#2) 66% 31% 20% V1#3 Set up a definite integral to compute the area enclosed by a parabola and line (same as V2#61% 55% 18% V2#1 Complete the square to find center and radius of an equation (same as V1#1) 60% 31% 11% V1#8 Use substitution to evaluate an indefinite integral 57% 51% 14% V1#1 Complete the square to find center and radius of an equation (same as V2#1) 52% 46% 18% V2#7 Use integration by parts to evaluate definite integral 52% 33% 46% V2#4 Set up a definite integral to compute the area enclosed by a parabola and line (same as V1#) 49% 29% 9% V1#7 Use substitution to evaluate an integral 42% 30% 21% V2#5 Use a sign table for a function and its derivative to sketch a graph of the function 40% 26% 23% V1#5 Estimate the derivative of a function at a point from its graph 23% 17% 11% V1#4 Solve using implicit differentiation 17% 11% 20% V1#6 Maximize area of a rectangle inscribed in a semicircle (same as V2#6) 15% 12% 21% V2#6 Maximize area of a rectangle inscribed in a semicircle (same as V1#6) 6% 3% 39% V2#8 Area enclosed by one-loop of four-leaved rose

The problems are primarily sorted in this table by proportion of students who received a code of A or B, indicating that at least essentially correct. For reference, the second and third columns report the proportion of students who had the completely correct (A, column 2) and the proportion who made good progress (C, column 3).

The problems have been divided into three groups. At least two-thirds of the students could integrate using the Fundamental Theorem of Calculus, and solve using properties of logarithms. About three-quarters of the students successfully set up a definite integral to compute the area enclosed by a parabola and line.

Fewer then three-fifths of the students completed the square to find the center and radius of an equation, or used substitution to evaluate an integral and/or indefinite integral. Similarly they successfully used a sign table of a function and its derivative to sketch a graph of the function and estimate the derivative of a function at a point from its graph. Under a quarter of the students could solve using implicit differentiation, or calculate the area enclosed by one-loop of a four-leaved rose.

Mathematics Backgrounds

University records provided information about the mathematics courses that had been taken by students in these classes. The following tables report up to the four most recent mathematics courses recorded on each student’s transcript. Every student with available records indicate exposure to at least one mathematics course. The median for Math 166 was a B, but one should notice that almost half of the students received and A in the course. Calculus III is a retake for seven students that were tested, of these seven, two have no record of taking the prerequisite.

These histograms help to illustrate possible connections between test score and grade in the most recently completed mathematics or statistics course. On version one students with higher grades (lighter shades in divided frequency bars) in most recent course generally scored somewhat higher on this assessment test, as one might expect.

Reactions

We asked the instructor five questions about the test results. Her responses are summarized below.

Instructor:

1. Are you surprised by students’ performance on particular test items?
1. Did you do anything different this semester because of your students’ performance on the test?
1. How well do you think the tests reflected the quantitative demands of your course? Is it accurate to say that the skills we testes were essential for survival in the course?
1. Would you suggest any changes in prerequisites, student preparation, or the nature of this course based on what you have learned from the preparation and administration of these tests?
1. If this or another course in your department was tested again in another semester, would you suggest any changes in the testing program?

Department:

Reactions to these results:

Suggested responses(action plans):