*Unit:*Mathematics

*Program:*Mathematics (BA)

*Degree:*Bachelor's

*Date:*Fri Nov 16, 2018 - 10:53:16 am

### 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:

Other:

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

- File (11/04/2018)

### 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 June 1, 2015 and October 31, 2018?

No (skip to question 17)

### 7) What best describes the program-level learning assessment activities that took place for the period June 1, 2015 to October 31, 2018? (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)

No (skip to question 17)

Investigate other pressing issue related to student learning achievement for the program (explain in question 7)

Other:

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

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. During the academic year 2017-18 one of the sections of Math 480 also completed a GRE-based assessment. 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.

21 students in 2017-18

26 students in 2016-17

32 students in 2015-16

### 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 of the assessment activities checked in question 7. For example, report the percentage of students who achieved each SLO.

The evidence from the assessment exam shows that the program succeeded in Program Goals 1 and 2, and Program Skills 1 and 2.

The results of the first part of the exam indicate that most of our majors have a reasonable knowledge of calculus, many of them also have a basic understanding of the real number line and can prove theorems using its properties. The students had a hard time with multi-variable calculus, certain topics in linear algebra and Taylor series. Similarly, the GRE-based assessment indicated that students knew real analysis rather well but multivariable calculus rather poorly.

For the Program Goal 3, the required courses Math 307 or 311, Math 321 and Math 331 seem successful in teaching students basic notions about proofs, and concepts from linear algebra and analysis. However, the students struggled when they were asked to write proofs on their own. These results are encouraging since they show progress in comparison with the previous years. However, for the topics courses at the 400 level, student results were varied. Of those who tried Math 431 questions on the third exam, many were successful. Few students attempted the 400 level linear algebra questions, although 13 students had taken Math 411. However, from the course lists, it seems that more students are taking upper division courses.

It was difficult to assess our success with the Program Goal 4 since the students are no longer required to complete the two-course sequence requirement at the 400 level.

Regarding the Program Skills category, the students displayed a firm grasp of the proof by induction and did a good job with the vector space problem. The results were more varied on the real analysis problems but those who answered the problems did a relatively good job. There were significant difficulties on the problems concerning equivalence relations and with proofs involving more difficult logical structures, such as dealing with an “or” condition in statements about relations and the quantifiers.

The objective "Read mathematics without supervision" was best assessed through the material in the Math 480 course itself. The students were asked to read new material and present on it. The students often found this difficult as Math 480 is probably the first and only chance they get to practice this. In the end students were mostly successful in working through the material on their own, sometimes with help from their professor. The students did spend time and effort on this, and showed enjoyment in doing their presentations. The presentations were well done, and students really tried to convey their new knowledge to their classmates.

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.

### 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 the 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 syllabi for some of the courses. In Fall 2017 we introduced a new course, Math 372, which covers both probability and statistics, taking topics from Math 371 and Math 373. We are considering a similar consodilation of our geometry courses, Math 351 and Math 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.

From the results of the assessment, we see that students are taking more 400 level courses and some are enrolling in 600 level ones. This has been a point of emphasis in advising in recent years and it seems to be yielding results.

Preparation for Graduate School: There was a feeling that more students were applying and being admitted to graduate schools than in previous years. The rise in student interest in graduate school is a positive development in the department but there needs to be more advising so that students have adequate preparation in analysis.

PLOs and Assessment: One of recommendations was to make some of the SLOs more specific; for example, listing which essential topics in linear algebra should be grasped instead of stating generally about learning linear algebra. Also several of the PLOs were difficult to assess or seemed lacking in the current structure of the degree: these include the ability to read mathematics independently, follow and explain algorithms and apply mathematics to other fields. In the first case, the difficulty is of course in assessment but also it is unclear where the students would be exposed to this skill before entering Math 480. The latter two topics are not addressed in the assessment exam and are not clearly part of the degree requirements. The objective of ``In depth (study of) at least one advanced topic of mathematics" is also difficult to assess and implement with the loss of the two course sequence.