Departmental Assessment Update - Natural Sciences Report

Department: Mathematics
Program: BA, BS
Level: Undergraduate

1. List in detail your undergraduate Student Learning Outcomes (SLOs) for each degree/certificate offered.

Recipients of an undergraduate degree in mathematics are expected to understand and apply: • basic real analysis of one variable; • calculus of several variables and vector analysis; • basic linear algebra and theory of vector spaces; • concerted study of at least one advanced topic of mathematics, chosen from: advanced calculus, abstract algebra, set theory and logic, probability and statistics, partial diﬀerential equations, and numerical analysis. In addition, they are expected to acquire the ability and skills to: • give direct proofs, proofs by contradiction, and proofs by induction; • formulate deﬁnitions and give examples and counterexamples; • read mathematics without supervision; • follow and explain algorithms; and • apply mathematics to other ﬁelds.

2. Where are these SLOs published (e.g., department web page)?

They are found on the Department web page: http://www.math.hawaii.edu/home/department_pr.html

3. Explain how your SLOs map onto your curriculum, i.e., how does your curriculum produce the specific SLOs in your students?

Degree Requirements. For the BA degree in mathematics, students must complete 21 credit hours in mathematics courses numbered above 300, including • Math 321 (an introduction to understanding and writing formal proofs), • 3 credit hours in a writing-intensive mathematics course, • 6 credit hours in a sustained two-course sequence approved by the department. For the BS degree in mathematics, students must complete 24 credit hours in mathematics courses numbered above 300, and 15 credit hours in additional upper division mathematics courses or appropriate non-introductory courses in the natural or information sciences, including • Math 321, • 6 credit hours in writing-intensive mathematics courses, • 6 credit hours in a sustained two-course sequence approved by the department. The upper division classes develop and reinforce the SLOs which are mostly based on logical reasoning strategies emphasized in Math 321. The two course sequence is designed to develop depth in one area of concentration.

4. What specific methodologies were used to collect data? In developing your response, consider the following questions:

Who carries out the assessment? We have an established departmental assessment structure, including both a curriculum committee that meets almost monthly to review and revise the departmental curriculum, and a separate assessment committee which monitors the eﬀectiveness of the program as a whole. The Associate Chair serves on both committees and supplements their work with his own immediate and longitudinal analysis of student performance. Departmental engagement is encouraged by bringing all proposed changes to general department meetings for discussion and debate. Departmental policy is to cycle teaching assignments so that all faculty regularly teach courses at all levels, from Math 100 through graduate oﬀerings. As a result, all faculty have a current knowledge of what is taught in the introductory classes and what is retained by students as they enter upper-division courses, as well as an immediate stake in any proposals to change standards or procedure. The UHM Foundations Board provides outside review for many of our courses; 11 of our courses are currently approved for general education ‘Foundations’ requirements, far more courses than any other department. How is assessment carried out? Performance evaluation at the course level is by instruments such as examinations which emphasize problem solving. Regular dialog with our client departments allows independent validation of the eﬀectiveness of service oﬀerings. A capstone course and exit examination are now required of all our graduating majors; these were created to help us evaluate the extent to which our students have mastered our program’s skills and content. The examination covers both basic mathematical reasoning at the 200 and 300 level, and content from speciﬁc upper-division level courses. It is graded by the Assessment Committee, which then reports on the results both orally to the Department and in a written report circulated to all tenurable faculty. The capstone course is not only an instrument of evaluation, but also an opportunity to ensure that all of our majors have met the requirements set by the Manoa General Education Program. It typically includes library search, oral research presentation and a written research paper. At the conclusion of this course, the instructor reports to the faculty at a department meeting as to what he covered, where the student strengths and weaknesses were, etc. Our majors are also invited to complete a post-graduation questionnaire to determine the extent to which their training with us was useful in their employment or further education. A baseline is established through the use of placement exams for students entering our introductory sequence; approximately 800 students take these exams every year. More recently, we have started a longitudinal statistical analysis using data from Banner to evaluate transfer policies and track student performance throughout the Calculus sequence.

5. How were the assessment data/results used to inform decisions concerning the curriculum and administration of the program?

The assessment activity has led to numerous reforms in recent years, including: • Diversiﬁcation of our Calculus oﬀerings, including the introduction of new Calculus tracks speciﬁcally geared to Business students (Math 203) and Life Science students (Math 215–216). • Substantial changes in the topic selection and order of presentation in the core Calculus sequences (Math 241–244 regular sequence, Math 251–253 accelerated and honors sequence). This has been accompanied by changes in the calculus text in consultation with client departments (particularly Engineering). • Introduction of a mathematical biology sequence Math 304-305 • Introduction of a new post-calculus service course for Engineers (Math 307). • Conversion of Math 321 from an elective course in advanced calculus to a required transition course on methods of mathematical reasoning and proof, and introduction of a new course (Math 331) as a bridge to 400-level Analysis. • Following recommendations of the Mathematical Association of America, a change in major requirements to require a linked 2-course sequence of upper-division courses. • Working with the College of Education, a reintroduction of Math 111-112, Mathematics for elementary education, with a new approach. • Introduction of a two step assessment for calculus readiness
General Education Assessment within Mathematics. As we have noted above, this has been a major factor in many of the changes we have implemented. We view assessment and reaction to it as an ongoing process of improvement, rather than something to be completed.

6. Has the program developed learning outcomes? Please indicate yes or no.

Yes

7. Has the program published learning outcomes? Please indicate yes or no.

Yes

8. If so, please indicate how the program has published learning outcomes.

On our website: http://www.math.hawaii.edu/home/department_pr.html

9. What evidence is used to determine achievement of student learning outcomes?

See #4.

10. Who interprets the evidence?

The professor in charge of the capstone course and a special assessment committee. See #4.

11. What is the process of interpreting the evidence?

See #4.

12. Indicate the date of last program review.

Spring 2007