M 383 Introduction to Analysis I 

Assessment Coordinator: not listed

According to the below description of Mathematics Program Learning Outcomes and Assessment, 14 Mathematics Option students were assessed for Outcomes 1, 2 and 6 in M 383. The Class had a total of 24 students. 

Outcome 1

Effectively communicate mathematical ideas by precisely formulating them in proper mathematical language.

Outcome 2

Produce rigorous proofs of results that arise in the context of real analysis.

Outcome 6

Write solutions to problems and proofs of results that meet rigorous standards based on content, organization, coherence, logical arguments, and style. 

Evaluation

Outcomes 1 and 6 were assessed on the overall writeup and formatting of a take home midterm exam. The students were required to turn in a LaTeX document with their solutions/proofs. 

Results

For outcomes 1 and 6, this course required the students to LaTeX at least one problem in each problem sets that was turned in throughout the semester in addition to the take home midterms and final. It is felt that this requirement is very beneficial to obtain good results on these outcomes. 

Assessment 1 Exceptional Acceptable Marginal Unacceptable
LO 1 0-12 0-12 2 0
LO 6 0-12 0-12 2 0

For outcome 2, the prerequisite for this course was M-242 method of proof or equivalent. One of the two students that was deemed unacceptable did not take this class here.

Assessment 2 Exceptional Acceptable Marginal Unacceptable
LO 2 1-8 1-8 4 2

Recommendations

A prerequisite diagnostic assessment might be beneficial in this course. 

M 384 Introduction to Analysis II

Assessment Coordinator: not listed

According to the below description of Mathematics Program Learning Outcomes and Assessment, 12 Mathematics Option students were assessed for outcomes 2 and 5 in M 384.

Outcome 2

Produce rigorous proofs of results that arise in the context of real analysis.

Outcome 5

Construct direct, indirect, and proofs by induction and determine the appropriateness of each type in a particular setting. Analyze and critique proofs with respect to logic and correctness.

Results

There were 16 students enrolled in the beginning of the semester. Two of these students withdrew with a W before the end of the semester. Of the remaining 14 students, 12 were majoring in Mathematics – Mathematics (non-applied option.) Problems 1-6 on the final exam were used to assess the learning outcomes. Results were as follows:

Assessed Exceptional Acceptable Marginal Unacceptable
LO 2 1-8 1-8 3 1
LO 5 1-7 1-7 2 3

Recommendations

The question chosen to assess this outcome may have been too difficult to obtain a valid conclusion. Four different methods of proof were used throughout the course by all of the students successfully. This problem was chosen because everyone had to typeset the solution in LaTeX and that may it very easy to assess the content of the student's work.

However this was the only problem on the final were a clear choice of proof technique made a difference. A better choice of problem should be made in the future or we should assess this learning outcome only in M- 242.

A comment on learning outcome 5. By checking the prerequisite for M-383, M-242 method of proof, it is apparent that learning outcome 5 listed below is being more then adequately covered in M-242. It could be the case that there is no need to assess learning outcome 5 in M-383 and M-384. 

Program Learning Outcomes

LO# Students should demonstrate the ability to:
1. Effectively communicate mathematical ideas by precisely formulating them in proper mathematical language (M 333, M 383, M 384, M 431).
2. Produce rigorous proofs of results that arise in the context of real analysis (M 383, M 384).
3. Produce rigorous proofs of results that arise in the context of abstract algebra (M 431).
4. Produce rigorous proofs of results that arise in the context of linear algebra (M 333).
5. Construct direct, indirect, and proofs by induction and determine the appropriateness of each type in a particular setting. Analyze and critique proofs with respect to logic and correctness. (M 333, M 383, M 384)
6. Write solutions to problems and proofs of results that meet rigorous standards based on content, organization, coherence, logical arguments, and style. (M333, M 383, M 384, M 431) 

Rubric

LO  Unacceptable Marginal Acceptable Excellent
1-6 Needs major revision. Score of 1. Needs minor revision. Score of 2. Meets expectations. Score of 3. Considered proficient. Being excellent. Score of 4. Considered proficient.

Threshold

At least half of the majors in each of the courses are assessed as "excellent" or "acceptable" for all the learning outcomes. 

 

PDF of M383 and M384 Assessment Report