*Unit:*Mathematics

*Program:*Mathematics (BA, BS)

*Degree:*Bachelor's

*Date:*Sun Oct 11, 2009 - 10:05:36 am

### 1) List your program's student learning outcomes (SLOs).

Recipients of an undergraduate degree in mathematics are expected to learn, understand, and be able to apply:

- calculus in one and several variables,
- linear algebra and the theory of vector spaces,
- several mathematical topics at the junior and senior level,
- in depth at least one advanced topic of mathematics, an approved two-course sequence.

In addition, students are expected to acquire the ability and skills to:

- develop and write direct proofs, proofs by contradiction, and proofs by induction,
- formulate definitions and give examples and counterexamples,
- read mathematics without supervision,
- follow and explain algorithms,
- apply mathematics to other fields.

Finally, recipients of an undergraduate degree in mathematics are expected to have learned about research in mathematics

### 2) Where are your program's SLOs published?

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:

Other:

Other:

### 3) Upload your program's current curriculum map(s) as a PDF.

- File (03/16/2020)

### 4) What percentage of courses have the course SLOs explicitly stated on the course syllabus, department website, or other publicly available document? (Check one)

1-50%

51-80%

81-99%

100%

### 5) State the SLO(s) that was Assessed, Targeted, or Studied

All of the ones listed in the Program Goals, see 1).

### 6) State the Assessment Question(s) and/or Goal(s) of Assessment Activity

We give an assessment exam, about 15 pages long, that is taken by the students in our capstone course (Math 480), graded by the assessment committee. The results are discussed and written up in an assessment report.

Based on last years' assessment results, the program had modified the capstone course from a 1-credit course to a 2-credit course. The program wanted to find out whether that change had the desired results of increasing attendance at the undergraduate colloquium and increasing student effort on the assessment exam.

### 7) State the Type(s) of Evidence Gathered

In accordance with the plan, the Mathematics Department offered a two-credit capstone seminar, Math 480, in the Spring semester of 2009. The course was taught by Professor Thomas Hoover. The fourteen students enrolled **completed and presented a report and lectured in class**. Each of the topics allowed the students to synthesize and expand on previously learned material.

The students in Math 480 also took a faculty-devised **assessment exam** covering the entire mathematics major. The exam had questions from the elementary courses as well as the advanced ones. In general, each question had several parts, of increasing difficulty. The students indicated which advanced courses each had taken, and were expected only to answer questions from those courses (and the elementary ones).

The Mathematics Department normally sends questionnaires to all mathematics majors upon graduation. The department is behind schedule on sending the questionnaires. So we have nothing to report about the results of this survey this year.

We also made a **table of what courses the Math 480 students had taken**.

### 8) State How the Evidence was Interpreted, Evaluated, or Analyzed

Exam is graded and results are evaluated by the assessment committee.

### 9) State How Many Pieces of Evidence Were Collected

All students in Math 480 must take the exam to receive credit for the course, and the course is required for graduation.

In Spring 2009, 14 students enrolled.

### 10) Summarize the Actual Results

__EFFECT OF THE 2-CREDIT CAPSTONE__. The 2008 Assessment Report included the suggestion that Math 480 be changed to a 2 credit course (from 1 credit). One purpose was to require attendance at the undergraduate colloquium to increase students’ exposure to research. This change had the desired effect.

In 2008 the students appeared to not take the assessment exam seriously, which made it hard to evaluate the results. Changing Math 480 to two credits allowed some class time to be devoted to giving the assessment exam, although the students were allowed to take it home to finish. This change had the desired effect. The students seemed to take the 2009 assessment exam seriously.

__ASSESSMENT EXAM__. The results on the elementary parts of the exam were fair although the students exhibited some weakness in a few specific topics. The results on the advanced part of the assessment exam were sparse and uninformative because of scheduling difficulties: students had not yet taken many 400 level courses.

Exam results indicate that students are meeting expectations in the following areas:

- calculus in one and several variables
- basic linear algebra and the theory of vector spaces
- develop and write direct proofs, proofs by contradiction, and proofs by induction
- formulate definitions and give examples and counterexamples

__CAPSTONE COURSE__. Capstone seminar evidence indicates students are meeting expectations in the following areas:

- develop and write direct proofs, proofs by contradiction, and proofs by induction
- formulate definitions and give examples and counterexamples
- read mathematics without supervision

Instructor of the spring 2009 capstone course noted that students had difficulties with the oral presentation.

No attempt was made to assess the success of the program in preparing majors to follow and explain algorithms and to apply mathematics to other fields.

__TABLE OF COURSES TAKEN__. Years of data showed few majors taking core courses such as 412–413 and 431–432. So the 2008 Assessment Report included a request that the Curriculum Committee consider requiring that all majors take at least one core course. They did, and the department added this requirement for majors this fall (2009).

### 11) Briefly Describe the Distribution and Discussion of Results

The report (results) is given in a faculty meeting (first Friday in September), and posted on the insiders page on the department website (password protected).

### 12) Describe Conclusions and Discoveries

The 2-credit capstone course has had the desired effect.

Due to scheduling difficulties, at the time the assessment exam was given, students had not yet taken many 400 level courses. So the results on the advanced part of the assessment exam were sparse and uninformative.

Students are not taking core courses (e.g., 412-413).

Based on the observations of the Math 480 instructor, we recommend that students be required to make presentations to the class in more upper division courses. Perhaps the Curriculum Committee could add such a requirement to some syllabi.

### 13) Use of Results/Program Modifications: State How the Program Used the Results --or-- Explain Planned Use of Results

We proposed a change to the degree requirements, as outlined and justified in our report. The change was discussed by the curriculum committee, brought to the faculty meeting, was approved by a vote, and has been submitted to the administration (VCAA via Dean).

__ASSESSMENT EXAM__: More emphasis needs to be placed on Taylor approximation, error bounds, equivalence relations, and inverse images. Next year’s Assessment Committee should rethink and rewrite the assessment exam.

__ORAL PRESENTATIONS.__ We recommend that students be required to make presentations to the class in more upper division courses. Perhaps the Curriculum Committee could add such a requirement to some syllabi.

### 14) Reflect on the Assessment Process

Ensure students have taken appropriate courses before enrolling in capstone.

Rethink and rewrite the assessment exam.

### 15) Other Important Information

Assessment is a futile exercise if there are no resources to implement changes.