*Unit:*Mathematics

*Program:*Mathematics (BA, BS)

*Degree:*Bachelor's

*Date:*Thu Nov 19, 2015 - 1:54:59 pm

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

#### 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, 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, 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 (11/19/2015)

### 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) Did your program engage in any program learning assessment activities between June 1, 2014 and September 30, 2015?

No (skip to question 16)

### 6) What best describes the program-level learning assessment activities that took place for the period June 1, 2014 to September 30, 2015? (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 curriculum coherence. This includes investigating how well courses address the SLOs, course sequencing and adequacy, the effect of pre-requisites on learning achievement.

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

Other:

### 7) Briefly explain the assessment activities that took place in the last 18 months.

All mathematics undergraduate majors are required to take a capstone seminar (Math 480), and as part of it they take the assessment exam. The exam is written, it has three parts, and students are expected to spend in excess of one hour on each part. Students will not receive credit for the course if they do not take the exam. In addition the Math 480 instructor evaluates oral presentations that each student is required to give in the seminar.

### 8) What types of evidence did the program use as part of the assessment activities checked in question 6? (Check all that apply.)

### Direct evidence of student learning (student work products)

Artistic exhibition/performance

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

Other 1:

Other 2:

**Indirect** evidence of student learning

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

Other 1:

Other 2:

### Program evidence related to learning and assessment

(more applicable when the program focused on the use of results or assessment procedure/tools in this reporting period instead of data collection)

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

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

Other 1:

Other 2:

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

All of our graduating majors must take the assessment exam, and last year the enrollment for the capstone course was 27 students. We offered two sections of the capston course; 16 students were enrolled in Section 1 and 11 students in Section 2. 25 of those students took the assessment exam.

### 10) 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:

### 11) 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:

### 12) Summarize the results of the assessment activities checked in question 6. For example, report the percent 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. Students mostly did well on Part I of the assessment exam (Calculus, Linear Algebra and Differential Equations) although some students exhibited weakness in a few specific topics, in particular the material related to Taylor series and Taylor approximation. On Part II (Basic Proofs and Examples) students demonstrated good understanding of standard inductive proofs. However many students had problems with equivalence relations and with proofs involving more difficult logical structures. Part III of the assessment exam tests knowledge of material taken in 400 level courses. Student results were varied in this part. For example, students attempted many of the Math 420 and Math 412-413 questions and were largely successful with these. On the other hand students did not attempt many of the Math 444, Math 454-455 questions, and were not successful on those attempted. However, it was noted by the Assessment Committee that the questions in this part of the exam were not of equal difficulty. Also, it was noted that students that took several 400 level courses did better on all parts of the exam. The evidence from the capstone seminar shows that the program succeeded in establishing Program Skills 1, 2 and 3. Students were required to do a research project, give an oral presentation on that project and submit a writeup done in LaTeX. Many of these presentations were outstanding.

### 13) 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:

### 14) Please briefly describe how the program used the results.

Results were discussed in the September faculty meeting, and the curriculum committee is considering changes that may be warranted. Last year the curriculum committee worked on standardizing the content of Math 321, Introduction to Advanced Mathematics, to include topics that are crucial in a number of courses that follow. We are in the process of finalizing this effort. This should help in furthering the retention and understanding of basic concepts, especially concepts covered in Part II of the assessment exam. Also, Math 331, Introduction to Real Analysis, has become a required course for the major starting Fall 2015. This course covers a rigorous axiomatic development of one variable calculus and builds a solid foundation for further study. We plan to pay special attention to how Math 480 students do on problems in the assessment exam related to the Math 331 material. We expect more students will take 400 level classes after successful completion of Math 331. In addition, the Mathematics Department has introduced a common final exam for Calculus II starting Fall 2015. This should standardize the content covered, and emphasize Taylor series and its applications. We also plan to look into making assessment exam questions in Part III similar in difficulty.

### 15) 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.

This year Math 480 students attended a number of lectures in the Undergraduate Seminar, which was evaluated as very successful. One of the sections of Math 480 incorporated the undergraduate seminar into the course by giving lectures or in-class exercises related to the seminar topics. The other section recommended the student's projects be related to the material presented in the undergraduate seminar. The students also had two sessions in the library. The first meeting was about typesetting using LaTeX. During the second meeting students learned about finding appropriate mathematical research materials. We plan to repeat the Undergraduate Seminar and Library sessions in the future.