Assessment of GUR Outcomes
The GUR outcomes most relevant to our department's GUR courses are:
- Use quantitative and scientific reasoning to frame and solve problems.
- Apply tools of technology, with an understanding of their uses and limitations.
During years when CUE assesses either of the above outcomes, we will assess student performance in much the same way student achievement is assessed for the Breadth and Depth outcomes for our majors. For the first GUR outcome above, student performance in relevant aspects of MATH 114 would be assessed. For the second, student achievement in relevant aspects of MATH 114 and/or MATH 240 would be assessed. With the department's Assessment Coordinator, instructors of the relevant course(s) during that year would agree on one or more course objectives that match the relevant outcome and discuss how student achievement would be measured by performance on test or quiz questions or other activities that reflect that outcome.
Assessment Plan for Majors
The Mathematics Department offers a total of 10 major options, including combined majors with other departments. These can be grouped into three degree categories: Bachelor of Arts, Bachelor of Arts in Education and Bachelor of Science.
Below is a list of student learning outcomes that are relevant to one or more of our major options. None of our majors require the achievement of all of them. A table below summarizes which of these outcomes we expect for each of our major options.
In completing a major in the Mathematics Department, for each of the following items relevant to that major we expect a student to demonstrate:
1) Mastery of the essentials of core lower division mathematics courses: calculus and linear algebra (Core Math);
2) Understanding of the importance of abstraction and rigor in mathematics, ability to construct complete proofs and to critically examine the correctness of mathematical work and logical arguments (Rigor);
3) Knowledge of concepts and techniques from a variety of mathematical areas, by demonstrating understanding of material in upper division courses in at least two of the following disciplines: abstract algebra, differential equations, geometry, linear algebra, mathematical analysis, number theory, optimization, numerical analysis and probability and statistics (Breadth);
4) Awareness of the historical context of areas of mathematics studied and familiarity with major contributions of some prominent mathematicians of the past and present (History);
5) In-depth understanding of at least two mathematical subjects at an advanced level, by showing understanding of material in a second course of a sequence in these subjects (Depth);
6) Completion of the appropriate professional preparation program, including the earning of the appropriate professional certification (Certification).
The table below summarizes which student learning outcomes we expect for each of our major options. The combined majors combine in-depth study of another discipline with the mathematics most relevant for that subject.
|BAE Math Elem||X||X||X||X||X|
|BAE Math Sec||X||X||X||X||X|
|BS Applied Math||X||X||X||X||X|
The following table indicates when and how we will assess each of the outcomes for majors over the next six years, realizing that the results of and experience with assessment in the beginning of this schedule may suggest changes to this schedule and the way in which the outcomes themselves are assessed. ES stands for Exit Survey, given to each of our graduating students, and Ct stands for Count. More specific comments about the assessment of each of them follow.
|Core Math*||Grades, ES||Grades, ES||Grades, ES||Grades, ES||Grades, ES||Grades, ES|
|Rigor||ES||312, ES||ES||302, ES||ES||360, ES|
|Breadth||341, Ct, ES||Ct, ES||331, Ct, ES||Ct, ES||304, Ct, ES||Ct, ES|
|History||Ct, ES||Ct, ES||Ct, ES||Ct, ES||Ct, ES||Ct, ES|
|Depth||Ct, ES||430/432, Ct, ES||Ct, ES||475, Ct, ES||Ct, ES||402, Ct, ES|
Core Math: Assessed every year. Since success in Math 224 depends heavily on success in Math 124 and 125, we will record the grades of graduating seniors in Math 224 and 204. Since calculus and Math 204 classes are made up largely of non-majors, assessment of learning in those courses does not tell us how our majors are achieving this outcome. Exit Survey. *In later courses that do require the mastery of this material, instructors who are teaching courses that are used for assessment of other outcomes (say Math 331 or 341) could be encouraged to collect data to measure how well students understand the core material.
Rigor: Assessed by in-class performance every other year, using a three-course cycle (Math 312, 302, 360). Instructor of each section of that course could count students who "met/exceeded/did not meet expectations" concerning, for example, the ability to independently construct a complete and correct proof of a theorem not seen before. How this will be measured would be up to the individual instructor, but there should be agreement among instructors about what the expectations are. Data collected and used to improve course, if warranted. Exit Survey.
Breadth: Assessed by in-class performance every other year, using a three-course cycle (Math 331, 304, 341). These courses are taken by a large number of students from all of our major options. At the beginning of the year, instructors of course used for assessment agree on which course objectives to measure that year. Instructors choose how to assess the achievement of those objectives in their classes. Data compiled and used to improve course, if warranted. Count of number of different areas studied (successfully) at upper division level by graduating seniors (every year). Exit Survey (New question needed).
History: Assessed every year. Since many instructors incorporate history into their classes as time permits and when appropriate, this is maybe best measured by the question on the exit survey. It seems that most of our majors take Math 419, although it is required only of our BA and BAE students. Count the number of graduating students who take Math 419. Maintain a list of topics of term papers completed by students in Math 419 to document what students actually study outside of class, and maintain an archive of completed term papers.
Depth: Assessed by in-class performance every other year, using the following courses: Math 402, Math 475, and Math 430 and/or 432. Most of these courses, with the possible exception of 475, are taken by a large number of students. Math 475 is required for the BS Applied Math major, and 435 is required for the Operations Research concentration for the BS Applied. Similar to assessment in the breadth category (except that there will typically only be one section of each course used for assessment of this outcome): instructor of the course could choose some combination of homework and exam questions clearly connected to course objectives to measure student understanding of course material. Data collected and analyzed to improve course, if warranted. Count the number of sequences successfully completed by graduating seniors. Exit survey (new question needed).
Certification: Assessed every year. Count the number of students who get certification.
Review of Assessment Data and Activities
The department's Assessment Coordinator will collect data from the instructors of the courses used for assessment, and assist those instructors in their assessment activities. He will also analyze the data from the exit survey and from the analysis of transcripts of graduating majors. The results of all of these activities will be reviewed and discussed in the department's curriculum committee. This committee will also decide what action and additional assessment activities, if any, should be taken as a result of the collected information.