# Outcomes and Assessment Plan

The Department of Mathematics has adopted the following Student Learning Outcomes for our programs, which are divided into two subsets. The first is applicable to all our classes and programs while the second applies only to our majors. Following our outcomes below, we detail our recently adopted Assessment Plan for Majors, as well as describe the main Assessment Tools we use to evaluate our program.

## Student Outcomes

#### We expect all students who complete math classes to demonstrate the ability to:

a) understand and utilize course contents at an appropriate level;

b) use problem solving skills by developing a strategic overview of a mathematical situation and using this overview to analyze that situation;

c) recognize that a problem can have different useful representations (graphical, numerical, or symbolic) and select the most appropriate methods and formats;

d) model real world problems mathematically and interpret the results appropriately;

e) use appropriate software and technological tools and judge when such use is helpful;

f) communicate mathematical results and arguments clearly, both orally and in writing;

g) appreciate the central role of mathematics in the sciences and the wider world.

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.

Degree/Major |
Core Math |
Rigor |
Breadth |
History |
Depth |
Certification |

BA Math | X | X | X | X | X | |

BA Econ/Math | X | X | X | X | ||

BAE Math Elem | X | X | X | X | X | |

BAE Math Sec | X | X | X | X | X | |

BAE Chem/Math | X | X | X | X | X | |

BAE Phys/Math | X | X | X | X | X | |

BS Math | X | X | X | X | X | |

BS Applied Math | X | X | X | X | X | |

BS Math/CS | X | X | X | X | X | |

BS Bio/Math | X | X | X | X |

## Assessment Plan for Majors

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.

2010-11 | 2011-12 | 2012-13 | 2013-14 | 2014-15 | 2015-16 | |

Core Math* |
Grades, ES | Grades, ES | Grades, ES | Grades, ES | Grades, ES | Grades, ES |

Rigor |
312, ES | ES | 302, ES | ES | 360, ES | ES |

Breadth |
Ct, ES | 331, Ct, ES | Ct, ES | 304, Ct, ES | Ct, ES | 341, Ct, ES |

History |
Ct, ES | Ct, ES | Ct, ES | Ct, ES | Ct, ES | Ct, ES |

Depth |
430/432, Ct, ES | Ct, ES | 475, Ct, ES | Ct, ES | 402, Ct, ES | Ct, ES |

Certification |
Count | Count | Count | Count | Count | Count |

**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. This person 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.

## Assessment Tools

Here we describe some of the tools which are used broadly to assess many aspects of our program.

### Student Exit Surveys

#### Undergraduates

Exit surveys are administered to all graduating students with majors in mathematics, including joint majors and math education majors.

The survey contains multiple choice questions as well as opportunities for more extensive open-ended responses.

These surveys are distributed and collected by our office staff, who compile the results and present them for review to the Department Chair and the Undergraduate Committee.

The survey seeks undergraduate student input in four areas:

(i) how well the department and the student's particular academic program are perceived to have satisfied each of the listed desired student learning outcomes for our programs;

(ii) an evaluation of other aspects of the student's experience in the department, such as the quality of advisement and teaching, the range and availability of courses offered, and the quality of computing facilities.;

(iii) identifying what the department does particularly well;

(iv) identifying areas in which the department might improve.

A copy of the Undergraduate Student Exit Survey may be found here.

#### Graduate Students

Exit surveys are administered to all graduate prior to completing their degree programs.

The survey contains multiple choice questions as well as opportunities for more extensive open-ended responses.

These surveys are distributed and collected by our office staff, who compile the results and present them for review to the Department Chair and the Graduate Committee.

The survey seeks graduate student input in six areas, with a number of specific topics in each area being addressed:

(i) how well the department and the student's particular academic program are perceived to have satisfied each of the listed desired student learning outcomes for our programs;

(ii) the quality of the academic program, such as the range and quality of the courses offered and required;

(iii) the admission process, academic advising and wider professional support;

(iv) their experience in their roles as graduate teaching assistants;

(v) the physical environment, such as office space and computing facilities;

(vi) the departmental human / social environment.

A copy of the Graduate Student Exit Survey may be found here.

### Individual Course Assessment

**Course Goals and Assessment**

Every class syllabus includes a detailed set of desired student learning outcomes, formulated specifically for the content and other goals of that course. Such outcomes are typically measured in the course of the usual student evaluation process, namely as particular items in examinations or components of student assignments. Data to assess the extent to which each desired outcome is met is accumulated by flagging the particular exam items or assignments that relate to that particular goal and then collecting data that documents the level of student success. Faculty maintain records on the particular course goals, related assessment items, and measured levels of student success on those items. The data is analyzed to determine whether the associated goal is being satisfactorily met or needs to be addressed further by curricular or instructional changes. Records of the relevant items, data and faculty responses are maintained by individual faculty.

Lists of the course objectives / student learning outcomes (both generic and specific) for each course taught are maintained in the department office and shared amongst faculty.

**Skills Tests **

To ensure that the goals of basic computational proficiency are met in the most fundamental courses, namely the pre-calculus and calculus sequences, we have established skills tests for students in those classes. This requires that students score at least 80% on a test focused entirely on one particular skill (such as differentiating 10 functions of specific types). Failure to pass the test (which may be taken, in different forms, several times) results in either lowering the course grade by one letter or course failure (depending on the course). This distinguishes such fundamental skills from the higher order goals of these courses, and is a very effective tool in forcing students to acquire the necessary basic computational skills.

### Feedback Loop

The primary conduit for curricular and programmatic review and change is the Math Curriculum Committee. This committee formulated the overall program objectives, coordinates the formulation of the particular course objectives, and is responsible for all aspects of the outcomes assessment process and data review. All the assessment data from individual faculty and the student surveys is available to that group. The Curriculum Committee meets regularly to discuss programmatic initiatives and course modifications.

While such changes have historically been at the instigation of particular faculty responding to perceived needs in specific areas, or sometimes at the behest of the Chair promoting more extensive programmatic changes in response to perceived weaknesses in the program or changes in the field, these discussions have not generally been driven by data on outcomes assessment. This has now changed, with the relevant assessment data being available to drive and direct the discussion. While this is unlikely to accelerate the on-going evolutionary changes in the nature and sequencing of most courses, it has facilitated more rapid and substantial changes to the structure and emphases of courses offered in multiple sections, enhancing the consistency of these offerings and the extent to which all students meet the desired learning outcomes.