*Unit:*Mathematics

*Program:*Mathematics (BA, BS)

*Degree:*Bachelor's

*Date:*Thu Oct 09, 2014 - 10:15:00 am

### 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) Select one option:

- File (03/16/2020)

### 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) Did your program engage in any program assessment activities between June 1, 2013 and September 30, 2014? (e.g., establishing/revising outcomes, aligning the curriculum to outcomes, collecting evidence, interpreting evidence, using results, revising the assessment plan, creating surveys or tests, etc.)

No (skip to question 14)

### 6) For the period between June 1, 2013 and September 30, 2014: State the assessment question(s) and/or assessment goals. Include the SLOs that were targeted, if applicable.

According to the Department Assessment Plan, we are committed to assess to what extent our graduating majors meet our program goals, except Skill 4 and Skill 5.

### 7) State the type(s) of evidence gathered to answer the assessment question and/or meet the assessment goals that were given in Question #6.

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) State how many __persons__ 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 25 students. We offered two sections of the capston course; 13 students were enrolled in Section 1 and 12 students in Section 2.

### 9) 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:

### 10) 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:

### 11) For the assessment question(s) and/or assessment goal(s) stated in Question #6:

Summarize the actual results.

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 set-theoretical language and notations. Part III of the assessment exam tests knowledge of material taken in 400 level courses. Most students did not put much effort into Part III of the exam, but the general conclusion is that they do well with questions that require formula manipulations, but lack in mathematical creativity. One of the reasons students did not devote adequate time to the assessment exam may be due to the fact that it was given during the finals week. 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 TeX. Many of these presentations were outstanding.

### 12) State how the program used the results or plans to use the results. Please be specific.

Results were discussed in the September faculty meeting, and the curriculum committee is considering changes that may be warranted. For example, the curriculum committee is working on a proposal to standardize the content of Math 321, Introduction to Advanced Mathematics, to include topics that are crucial in a number of courses that follow. This should help in furthering the retention and understanding of basic concepts. Also, the Mathematics Department has decided to make Math 331, Introduction to Real Analysis, a required course for the major. This course covers a rigorous axiomatic development of one variable calculus and builds a solid foundation for further study. In addition, the instructors of Calculus II have been asked to emphasize and spend more time on Taylor series and its applications. We will also discuss the most appropriate time to administer the assessment exam.

### 13) Beyond the results, were there additional conclusions or discoveries?

This can include insights about assessment procedures, teaching and learning, program aspects and so on.

In order to accomodate the increase in number of majors in recent years we have added an additional section of the capstone course. This has had some positive impact since the students were able to get more individual attention. However, the structure and "traditional way" the course is being taught has been questioned and the curriculum committee will consider possible changes and updates.