*Unit:*Mathematics

*Program:*Mathematics (BA)

*Degree:*Bachelor's

*Date:*Tue Nov 17, 2020 - 2:25:07 pm

### 1) Program Student Learning Outcomes (SLOs) and Institutional Learning Objectives (ILOs)

#### 1. Recipients of an undergraduate degree in mathematics are expected to learn, understand, and be able to apply: calculus in one and several variables.

(1b. Specialized study in an academic field)

#### 2. Recipients of an undergraduate degree in mathematics are expected to learn, understand, and be able to apply: linear algebra and the theory of vector spaces.

(1b. Specialized study in an academic field)

#### 3. Recipients of an undergraduate degree in mathematics are expected to learn, understand, and be able to apply: several mathematical topics at the junior and senior level.

(1b. Specialized study in an academic field)

#### 4. Recipients of an undergraduate degree in mathematics are expected to learn, understand, and be able to apply: in depth at least one advanced topic of mathematics.

(1b. Specialized study in an academic field)

#### 5. Students are expected to acquire the ability and skills to: develop and write direct proofs, proofs by contradiction, and proofs by induction.

(1b. Specialized study in an academic field, 2a. Think critically and creatively, 2c. Communicate and report)

#### 6. Students are expected to acquire the ability and skills to: formulate definitions and give examples and counterexamples.

(1b. Specialized study in an academic field, 2a. Think critically and creatively, 2c. Communicate and report)

#### 7. Students are expected to acquire the ability and skills to: read mathematics without supervision.

(1b. Specialized study in an academic field, 2b. Conduct research, 3a. Continuous learning and personal growth)

#### 8. Students are expected to acquire the ability and skills to: follow and explain algorithms.

(1b. Specialized study in an academic field, 2a. Think critically and creatively, 2c. Communicate and report)

#### 9. Students are expected to acquire the ability and skills to: apply mathematics to other fields.

(1a. General education, 1b. Specialized study in an academic field, 2a. Think critically and creatively, 2c. Communicate and report)

#### 10. Recipients of an undergraduate degree in mathematics are expected to have learned about research in mathematics.

(1b. Specialized study in an academic field, 2b. Conduct research, 3a. Continuous learning and personal growth)

### 2) Your program's SLOs are published as follows. Please update as needed.

Student Handbook. URL, if available online:

Information Sheet, Flyer, or Brochure URL, if available online:

UHM Catalog. Page Number:

Course Syllabi. URL, if available online: http://math.hawaii.edu/wordpress/syllabi/

Other:

### 3) Please review, add, replace, or delete the existing curriculum map.

- File (11/13/2020)

### 4) For your program, the percentage of __courses__ that have __course__ SLOs explicitly stated on the syllabus, a website, or other publicly available document is as follows. Please update as needed.

1-50%

51-80%

81-99%

100%

### 5) Does the program have learning achievement results for its program SLOs? (Example of achievement results: "80% of students met expectations on SLO 1.")(check one):

Yes, on some(1-50%) of the program SLOs

Yes, on most(51-99%) of the program SLOs

Yes, on all(100%) of the program SLOs

### 6) Did your program engage in any program learning assessment activities between November 1, 2018 and October 31, 2020?

No (skip to question 17)

### 7) What best describes the program-level learning assessment activities that took place for the period November 1, 2018 and October 31, 2020? (Check all that apply.)

Collect/evaluate student work/performance to determine SLO achievement

Collect/analyze student self-reports of SLO achievement via surveys, interviews, or focus groups

Use assessment results to make programmatic decisions (e.g., change course content or pedagogy, design new course, hiring)

Investigate other pressing issue related to student learning achievement for the program (explain in question 8)

Other:

### 8) Briefly explain the assessment activities that took place since November 2018.

All mathematics undergraduate majors are required to take a capstone seminar (Math 480), and as part of the seminar they take the assessment exam. The exam is written and it has three parts; Part I (Calculus and Linear Algebra), Part II (Differential Equations, Basic Proofs, and Examples) and Part III (Problems and Theorems from Senior Courses). Students do not receive credit for the course if they do not take the exam. In addition, the students prepare a research project, submit a 3-5 page paper written in LaTeX, and give oral presentations.

### 9) What types of evidence did the program use as part of the assessment activities checked in question 7? (Check all that apply.)

Assignment/exam/paper completed as part of regular coursework and used for program-level assessment

Capstone work product (e.g., written project or non-thesis paper)

Exam created by an external organization (e.g., professional association for licensure)

Exit exam created by the program

IRB approval of research

Oral performance (oral defense, oral presentation, conference presentation)

Portfolio of student work

Publication or grant proposal

Qualifying exam or comprehensive exam for program-level assessment in addition to individual student evaluation (graduate level only)

Supervisor or employer evaluation of student performance outside the classroom (internship, clinical, practicum)

Thesis or dissertation used for program-level assessment in addition to individual student evaluation

Alumni survey that contains self-reports of SLO achievement

Employer meetings/discussions/survey/interview of student SLO achievement

Interviews or focus groups that contain self-reports of SLO achievement

Student reflective writing assignment (essay, journal entry, self-assessment) on their SLO achievement.

Student surveys that contain self-reports of SLO achievement

Assessment-related such as assessment plan, SLOs, curriculum map, etc.

Program or course materials (syllabi, assignments, requirements, etc.)

Other 1:

Other 2:

### 10) State the number of students (or persons) who submitted evidence that was evaluated. If applicable, please include the sampling technique used.

24 students in 2019-2020 (both BA and BS)

20 students in 2018-2019 (both BA and BS); because of time conflict 2 students took it as a reading course.

### 11) Who interpreted or analyzed the evidence that was collected? (Check all that apply.)

Faculty committee

Ad hoc faculty group

Department chairperson

Persons or organization outside the university

Faculty advisor

Advisors (in student support services)

Students (graduate or undergraduate)

Dean/Director

Other:

### 12) How did they evaluate, analyze, or interpret the evidence? (Check all that apply.)

Scored exams/tests/quizzes

Used professional judgment (no rubric or scoring guide used)

Compiled survey results

Used qualitative methods on interview, focus group, open-ended response data

External organization/person analyzed data (e.g., external organization administered and scored the nursing licensing exam)

Other:

### 13) Summarize the results from the evaluation, analysis, interpretation of evidence (checked in question 12). For example, report the percentage of students who achieved each SLO.

The results of assessment activities as they relate to the SLOs are summarized below:

(1) Learn, understand and be able to apply: Calculus in one and several variables.

In Part I of the exam students demonstrated reasonable skill set developed in calculus classes. Most students made some progress on most problems. As is fairly typical, the weakest problem was one based on Taylor series. That is the only problem in Part I which requires a certain level of understanding beyond the skillset, and low scores on this problem have persisted for many years.

In Spring 2019 in addition to the assessment exam, class time was spent discussing several advanced calculus topics such as error estimates for numerical integration, and the non-existence of nowhere zero vector fields on the sphere. Students actively participated in these discussions and were generally able to offer substantive and considered comments, which was very encouraging.

(2) Learn, understand and be able to apply: Linear algebra and the theory of vector spaces.

Linear algebra questions from Parts I and II of the exam were answered well by the majority of students. Approximately half of students took more advanced linear algebra Math 411. In Spring 2020 some of those students gave reasonable answers to related questions from Part III of the exam. However, in Spring 2019 only two students made substantive attempts at questions based on the advanced 400-level linear algebra course.

In addition, a large portion of class time was spent discussing problems from the textbook on linear algebra used in the Math 480 course. The topics covered were typically applications of linear algebra to combinatorics, geometry, and some disciplines outside mathematics. The level of these presentations was variable (both in terms of communicating the ideas, and in terms of understanding the ideas), but was generally quite good. Students participated in each others’ talks, asking sensible questions, and seem to follow in the most part.

(3) Learn, understand and be able to apply: Several mathematical topics at the junior and senior level.

At the junior level, student responses to the questions about Math 311, 321, and 331 material were patchy. There were some very good responses, but a large number with fairly poor responses. Especially the performance on the questions related to Math 331 went down compared to previous years. Our assessment activities are not designed to judge student understanding in junior-level courses outside this core.

The number of 400 courses taken is in general far above our minimum requirements (two courses at the 400-level for both the BA and BS), which is encouraging. In Spring 2019 in terms of the assessment exam, the most popular areas for response were M 471/2 (10 students attempted questions), M 420 (10 students), M 412/3 (7 students), M 407 (5 students), and M 431 (4 students). However, there were no substantive responses to questions from some important areas of mathematics: notably, complex analysis, or any part of foundations, which is worrying. Having said that, one student did present on a topic from M 444, so it seems at least some students are taking and enjoying topics from that course. In Spring 2020 it was also noted that the questions related to Math 431 in Part III of the exam got no responses at all.

(4) Learn, understand and be able to apply: In depth at least one advanced topic of mathematics.

Although 400 level courses are more popular than required, which is certainly a good sign, the students have stopped taking two-course sequences since that requirement was removed a few years ago. Among the students taking the capstone course in Spring 2020 only one student took two-course sequences; this student actually took two of them: M 412 − 413 and M 471 − 472. Hence it is difficult to assess this SLO as we do not consistently offer as many two-course sequences as we used to.

(5) Students are expected to acquire the ability and skills to: Develop and write direct proofs, proofs by contradiction, and proofs by induction.

This SLO was primarily checked with Part II of the exam. The majority of students demonstrated their ability to create and reasonably neatly write down a simple mathematical argument. This was also confirmed in Math 480 class: during their presentations, many students demonstrated their ability to devise and explain a simple mathematical argument. However, the inclination towards taking mostly computational courses manifested itself: some students encounter conceptual difficulties with more sophisticated “non-constructive proof of existence” arguments. This is concerning, but consistent with results in the last 5 years.

(6) Students are expected to acquire the ability and skills to: Formulate definitions and give examples and counterexamples

As in (5) this was assessed using students answers to Part II of assessment exam as well as their presentations in Math 480. Both demonstrate satisfactory achievements towards this goal.

(7) Students are expected to acquire the ability and skills to: Read mathematics without supervision.

This was assessed in Math 480 class: every student had to read a topic from the textbook on their own and present the material in class. This exercise has worked out quite reasonably by the students demonstrating their satisfactory ability to read and understand mathematics without supervision.

In Spring 2019, all students also had to read mathematical texts by themselves for their final presentations based on a 400-level course. Some needed some help from the faculty teaching the course (in some cases because they chose quite ambitious topics), but in general the level of ability to read mathematics, and in some cases to search the relevant literature, seemed quite good.

(8) Students are expected to acquire the ability and skills to: Follow and explain algorithms.

This was not assessed uniformly for all students and was not assessed on the exam. However, many topics from the text covered algorithms of one sort or another, and the students were able to successfully present these. In addition, some students choose for their presentations topics in linear algebra which yield specific algorithms. Their explanations of the algorithms were very reasonable. In fact, some of them were double majoring in computer science; such students naturally demonstrated pretty good understanding of both algorithms and the ways to assess their efficiency. While the information is incomplete, there seems no cause for concern here.

(9) Students are expected to acquire the ability and skills to: Apply mathematics to other fields.

Again, this was not assessed uniformly for all students, and was not assessed on the exam. However, several topics from the text covered applications to other fields of one sort or another, and the students were able to successfully present these. In addition, several students talked about interesting applications in the topics they chose personally, including psychology, computer science, and game theory. This was generally done very well.

(10) Recipients of an undergraduate degree in mathematics are expected to have learned about research in Mathematics.

With regards to learning about research in mathematics, the senior seminar was successful in exposing students to the different areas of mathematical research particularly with the wide range of undergraduate seminars in Spring 2019. However, due to the pandemic in Spring 2020 there were no undergraduate seminars.

### 14) What best describes how the program used the results? (Check all that apply.)

Course changes (course content, pedagogy, courses offered, new course, pre-requisites, requirements)

Personnel or resource allocation changes

Program policy changes (e.g., admissions requirements, student probation policies, common course evaluation form)

Students' out-of-course experience changes (advising, co-curricular experiences, program website, program handbook, brown-bag lunches, workshops)

Celebration of student success!

Results indicated no action needed because students met expectations

Use is pending (typical reasons: insufficient number of students in population, evidence not evaluated or interpreted yet, faculty discussions continue)

Other:

### 15) Please briefly describe how the program used its findings/results.

The results were discussed at the faculty meeting, and the Curriculum Committee is considering changes that may be warranted. For example, we are evaluating the rotation of our 400 level courses and revising our abstract algebra courses. In Spring 2020 we introduced a new geometry course, Math 353, which combines topics from Math 351 and 352.

### 16) Beyond the results, were there additional conclusions or discoveries? This can include insights about assessment procedures, teaching and learning, and great achievements regarding program assessment in this reporting period.

Overall, the students’ performance, both on the assessment exam and in Math 480 class is satisfactory, and the program SLOs have been reached. We are satisfied that more students are taking more than required number of 400 level classes and will continue our advising efforts in that direction.

The main concern is that students seem to have difficulty writing correct logical arguments. This is a central skill in all of mathematics and seemed very uneven. Our curriculum is designed for students to pick up these skills in the required junior-level courses: 311, 321, and 331. It may be worth revisiting the effectiveness of these courses. It seemed students were better able to speak about, discuss, and read mathematics than they are able to write it. It might be particularly worth revisiting the effectiveness of the above courses (particularly 321 and 331, which are ‘Writing Intensive’) in teaching students how to write mathematics well.

A possible explanation for the disparity between students’ other abilities and their writing is simply that some of them do not take the assessment exams very seriously (they are not incentivized to do so in any way). It might be worth altering the course to better incentivize this.

In addition, for Spring 2020 assessment, very few students took more theoretical 400 level classes (Math 413, 421, 431, 444) which is of concern. The students’ knowledge of Analysis is especially worrisome: not only there were no attempts to solve problems related to Math 431 and 444, but also the responses to questions related to Math 331 looked weaker than they were in the previous years. This may be a result of low enrollment in Math 431: the knowledge acquired in Math 331 becomes isolated and gets lost by those students who discontinue their studies in Analysis.