MAT237 Applications of Discrete Mathematics is an advanced mathematics course. Individual professors will design their own syllabi and final exam. The course and major outcomes will be assessed on the final exam.
MAT237 is a required course for math majors who intend to teach mathematics.
MAT237 Course Outcomes [assessed using the problems in the brackets]:
1. Perform numeric and symbolic computations (as part of departmental math objective A) [1-12]
2 State and apply mathematical definitions and theorems (E) [1,4,7,8, 9, 10, 11, 12]
3. Count by using combinatorial arguments (A,B,C) [3,4,6,7,8,9]
4. Analyze and prove identities and inequalities for discrete functions (B, G) [2,9]
5. Apply discrete mathematics to real-life problems (C) [3,9,12]
Math Major Outcomes incorporated into MAT237 [assessed using problems in the brackets]:
A. Perform numeric and symbolic computations [1-12]
B. Construct and apply symbolic and graphical representations of functions [1,4,6]
C. Model real-life problems mathematically [3,9,12]
E. State and apply mathematical definitions and theorems [1,3,6,7,8,9,10,11,12]
G. Construct and present a rigorous mathematical argument [2,9,10,11]
Fall 2013 Assessment Plan and Report for MAT237:
In Fall 2013 this course was assessed using the professor's final exam following the professor's syllabus. The final exam will be similar to the one from Fall 2010 and a sample final is linked here. The syllabus is linked here. The actual final used for assessment is here. A spreadsheet with data and analysis is here. This spreadsheet records each student's performance on each problem in the final in columns A-T.
Each student is given a score corresponding to each of the outcomes in the course, based upon the corresponding exam problems as described in the first row. 100% of students passed course outcomes 1-4, and 90% passed course outcome 5. 90% of students performed well on course outcome 3 (counting by using combinatorial arguments) which is the key new subject for this course. Only 20% of the students performed well on course outcome 5 (real life problems), so more applications should be included in the homework in future courses.
MAT237 is an elective in the math major required for high school teachers. It should cover Major Outcomes A,B,C,E and G. Each student was given a score on each of these major outcomes as well (based upon corresponding problems on the final as described in the first row). An impressive 100% of students performed well on Major Outcome B (graphical representations). This is an especially crucial project for future teachers and the professor should be commended. All other Major Outcomes had 90-100% of students passing. Again modelling real life problems had only 20% of students performing well.
Overall the students did not perform nearly as well as students did in Fall 2010 despite the fact that the same textbook and similar syllabi were used. One key difference is that in Fall 2010 the students were taught by a full professor with an active research program and in Fall 2013 they were taught by a lecturer. It should also be noted that the 2010 class had two exceptionally highly performing students while no students in the Fall 2013 class scored above a 90% on the final. Nevertheless the assessment ambassador cautions against the reduction in full professors in the Lehman College Mathematics Department.
Fall 2010 Assessment Plan and Report for MAT237:
In Fall 2010, this course was assessed using the Fall 2010 MAT237 Final Exam designed by the professor teaching the course following his Fall 2010 MAT237 Syllabus.
Observations before Data Analysis:
The students were allowed to skip a problem on the final. Almost all students chose to skip problem 8 so this problem should not be used for assessment. One student chose to skip 7 so this should not used for assessment purposes either. Both problems were assessing only outcomes that were also assessed on many other problems.
Data Analysis:
A spreadsheet with data and analysis is here. The upper left corner lists scores (0 to 1) on each problems by each student.
The upper right corner computes scores (0 to 1) for each course and major outcome. The lower right corner computes percents of passing students who perform well and pass each outcome.
100% of students passed Course Outcomes 1,2, and 3. This exceeds expectations. Two students had difficulty with Course Outcome 4, these students earned a C overall on the final. One of these two students also failed to achieve Course Outcome 5. Usually more students have difficulty with this. At least 37% of students performed well on all the outcomes. This is unexpected as 20-30% is more likely. Two of the students in this class were exceptionally high performers.
100% of students passed Major Outcomes A, B & E. Such high performance on Major Outcome E is exceptional. 75% of students passed Major Outcomes C and G, the most difficult outcomes of the major. While one might only expect 20-30% of students to perform well on any outcome, all outcomes had 37% or more students performing well. Two of the students in this class were exceptionally high performers. One is continuing on for a PhD at Indiana University.
Conclusions:
This was an exceptionally strong class and reflects the quality of the students who are now arriving at Lehman College. The final exam was truly challenging and the students met that challenge. Professor Karp should be commended for the level of the course he has taught. Other faculty may wish to imitate his syllabus and final.
Time:
4 hours by the professor teaching the course and 3 hours by the assessment ambassador.