MAT320 Analysis is an advanced math course required for the math major. The syllabus and final are designed by the professor teaching the course.
MAT320 is a required course for all math majors.
MAT320 Course Outcomes:
1. find limits, sups and infs by applying theorems
2. prove that a sequence converges and a function is continuous at a point
3. write a proof by contradiction
4. state, apply and prove theorems related to Calculus including Riemann sums
5. write a proof by induction involving series
6. find Taylor series, prove convergence theorems and find radii of convergence
Math Major Outcomes incorporated into MAT320:
A. Perform numeric and symbolic computations
B. Construct and apply symbolic and graphical representations of functions
E. State and apply mathematical definitions and theorems
F. Prove fundamental theorems
G. Construct and present a rigorous mathematical argument
Fall 2018 Assessment Report for MAT320:
Assessment was based on the final exam, which consisted of 7 problems. The data collected from the exam may be found here.
For each problem on the exam, the number of students that received full credit for that problem was recorded. Out of a total of 36 students, the percentages of students receiving full credit were as follows:
Problem #1: 58.3%
Problem #2: 69.4%
Problem #3: 50%
Problem #4: 55.5%
Problem #5: 38.8%
Problem #6: 36.1%
Problem #7: 16.6%
Here are the Math Major Outcomes (MMOs, see above) connected with each problem:
Problem #1: E
Problem #2: E, G
Problem #3: B, E, G
Problem #4: B, E, F, G
Problem #5: A, B, E
Problem #6: A, B, E
Problem #7: B, E
The percentages in Problems #5-7 are certainly unsatisfactory, though it should be mentioned that Problem #7 consisted of 4 separate true-false questions and 63.8% of the students got 3 of the 4 correct. Also, the material covered by Problems #5-7 was taught over the last 2 weeks of the course, so the students had less time to master it. Another possible factor, which may have affected all the percentages, is that only just over half (55.5%) of the students in the course were math majors. It is tough enough getting math majors to practice proof-writing and to appreciate the need for rigorous proofs; with non-math majors it is an even greater challenge.
Action: the next time I teach MAT320 I will spend more class time on the material covered by Problems #5-7.
Spring 2018 Assessment Report for MAT320:
Assessment was based on the final exam for MAT320, which consisted of 3 parts: Part I (problems #1-6), Part II (problems 7-18), and Part III (problems 19a-19j). In Part I students were asked to solve 5 of the 6 given problems, in Part II they were asked to solve 7 of the 12 given problems, and in Part III they were asked to solve all 10 of the given True/False problems. The data used for assessment may be found here.
MAT320 is one of the most difficult courses in the math major. For some students at Lehman it is the first course in which they are routinely required to read and to write proofs. The art of proof-writing takes years to master, so it is to be expected that scores and averages in MAT320 are lower than what a non-mathematician might expect.
On the final exam, each of problems #3, #4, #5, #6a-6e, #8, #9, #11, #13, #14, and #19a-19j was attempted by 17 or more of the 26 students that took the final exam, so to simplify the analysis we will focus on the results of those problems. The average percent correct for the selected problems was about 65.4%. However, if problem #12 were included, that average would jump up to about 70%. Since arguably every problem on the exam could be used to assess Math Major Outcome (MMO) A, these averages give some indication that MMO A was achieved to an acceptable degree. Among the selected problems, those that measure MMO B are arguably #6b, #8, #9, #11, #13, #14, and #19a-j. The average percent correct on those problems was about 68.4%. If the "state" portion of MMO E is emphasized, then the selected problems measuring MMO E are arguably #3, #5, #6a-e, #13, #14, and #19a-j. The average percent correct for those problems was about 66.2%. The selected problems measuring MMO F are arguably #5, #8, #9, #11, and #14. The average percent correct for those problems was about 66.3%. Finally, the selected problems measuring MMO G are arguably #3, #4, #5, #8, #9, #11, #13, and #14. The average percent correct for those problems was about 61%.
Each average given in the previous paragraph is the average percentage of students receiving full credit on certain problems, and therefore it indicates the percentage that fully achieved the relevant MMO. Also included in the data (but not in the analysis above), for most problems, is the number of students that got the problem half correct. If those numbers were added to the number of correct solutions, the averages in the previous paragraph would all be increased, in some cases substantially (see problem #3).
It would be interesting to track how each of these students performs in the next upper level math class they take. Mastery of MMO's, especially MMO E, F, and G, usually occur over the course of the entire major as the student develops "mathematical maturity".
The assessment reports below may use the following map between final exam problems, course outcomes, and major outcomes.
MAT320 Course Outcomes [assessed using the problems in the brackets]:
1. find limits, sups and infs by applying theorems [4]
2. prove that a sequence converges and a function is continuous at a point [1,2]
3. write a proof by contradiction [3]
4. state, apply and prove theorems related to Calculus including Riemann sums [7]
5. write a proof by induction involving series [5]
6. find Taylor series, prove convergence theorems and find radii of convergence [6]
Math Major Outcomes incorporated into MAT320 [assessed using problems in the brackets]:
A. Perform numeric and symbolic computations [1,2,4,6]
B. Construct and apply symbolic and graphical representations of functions [1,4,6,7]
E. State and apply mathematical definitions and theorems [partial credit on 1,2,7]
F. Prove fundamental theorems [1,7]
G. Construct and present a rigorous mathematical argument [1,2,3,5,7]
Spring 2014 Assessment:
In Spring 2014, this course was assessed using the Spring 2014 MAT320 Final Exam designed by the professor teaching the course following the
Spring 2014 MAT320 Syllabus. The analysis is not yet complete.
Fall 2013 Assessment: (posponed due to lack of enrollment)
Fall 2010 Assessment Plan and Report for MAT320:
In Fall 2010, this course was assessed using the Fall 2010 MAT320 Final Exam designed by the professor teaching the course following the Fall 2010 MAT320 Syllabus.
Observations before Data Analysis:
Incoming data was collected by passing around the Fall 2009 MAT320 Final and asking students to sign problems they knew how to complete already. One student signed problem 6. No other problems were signed by any students
At the end of the course, 12 students passed. The performance of all 12 students was used to assess the course. 11 students passed with a grade above D. As a D does not count towards the math major, only the performance of the 11 students was used to assess the major.
Data Analysis (12/16/2010):
The spreadsheet with the scores of each passing student on each problem of the final, their course grades, identification numbers and performance on the course outcomes and the major outcomes.
Over half the students passing the class achieved perfection on Course Outcomes 1,3,5. Performance on other course outcomes were reasonable with only 1-2 students failing to meet each particular outcome. The D student was failing on all but one outcome (and failed the final but had done significant extra credit work and was not a math major). Another student failed on four outcomes but perfected others (and was also not a math major). Overall the class did very well on outcomes which required less prerequisite knowledge.
Over half the class had good or excellent performance on the Major Outcomes. All students met Major Outcome G: constructing and presenting a rigorous mathematical argument. This was the great challenge and primary focus of the course. There was a math ed major in the class who earned a C- in the course who failed to meet Major Objectives A, B and F. This student had difficulty with basic precalculus but had actually achieved perfection on proof by induction and contradiction, otherwise this student should have failed the course. Other than this student, only one other student failed to meet a major objective and this student was a straight A student who achieved nearly perfect scores on the final in all problems except the one integration. The professor will discuss this situation with both students ensuring that they spend extra time over the January break to improve their major outcomes.
Conclusions (12/16/2010):
Overall we are very happy with the students proving and performance on Major Objectives E, F and G, especially G which is only introduced in 300 level courses. We would like to see better performance on the easier Major Objectives A and B. The students' lack of expertise in precalculus is a concern at this level. In fact, quite a few students dropped the course due to weak precalculus skills. While Lehman is introducing a new uniform precalculus final, there is the problem that many of our 300 level majors took precalculus in high school or at a community college.
The course outcomes also reveal difficulties students have with Calculus II topics of Riemann sums and Taylor series. We will be introducing a uniform final in Calculus II in Fall 2011 and will be sure to test these topics on that final.
This analysis took 4 hours of instructor time.