SAUM Additional Online Case Studies & Appendices


 

Developing a Departmental Assessment Program:

North Dakota State University Mathematics

William O. Martin, Doğan Çömez

0. Abstract.

This article describes the process used to develop assessment in the mathematics programs at the North Dakota State University (NDSU). The Mathematics Department has developed a comprehensive assessment process that examines student learning in (a) services courses, (b) the major, and (c) the masters and Ph.D. program. The most ambitious component, established with external funding, examines the introductory mathematics courses in conjunction with the NDSU general education program. Assessment of the undergraduate and graduate programs involves many of the Department’s faculty. All components of the project are designed to minimize extra demands on participants, to provide useful information for participants as well as the Mathematics Department and University, and to focus on assessment as an integrated part of departmental activities rather than an “add-on” activity done primarily for external purposes.

 

1. Context and Setting.

North Dakota State University is a land grant, Doctoral I research university, and is the top institution in the state for graduating agriculture, engineering, mathematics and science students with baccalaureate through doctorate degrees. The number of undergraduate students (Fall 2002) is 9,874; and the number of graduate students is 1272. The average ACT composite score of all entering students (Fall1 997) is 23.1 (the national average is 2 1.0). The student to teacher average ratio is 19 to 1. Most of the classes specifically relating to the majors typically have fewer than 25 students, and mostly research faculty with terminal degrees teach those courses. The normal teaching load for research faculty is four courses per year.

The Department of Mathematics at NDSU offers BS (mathematics and secondary mathematics education), MA, and PhD degrees. The Department also has a major service role for other science and mathematics-intensive programs in the institution, particularly in the Colleges of Science and Mathematics, Engineering, Business Administration, and Pharmacy. The Department offers a broad and balanced curriculum of courses with 15 tenure-track faculty and about 10 lecturers (Computer Science and Statistics are separate departments). In Fall 2002 there were 38 mathematics majors in sophomore-senior standing among 83 undergraduate majors. Many talented students participate in the EPSCoR-AURA program; mathematics faculty members frequently supervise the undergraduate research projects of talented mathematics students. The undergraduate mathematics major’s degree program culminates with a capstone course, usually completed during the senior year. The Department, as the largest service department on the campus, enrolls 300-400 students each in calculus I and calculus II every semester (taught in a large lecture and recitation format) and 150-300 students per semester in each of calculus III and differential equations (taught in classes of about 35 students). The Department provides free tutoring services for all 100-300 level mathematics courses, staffed mostly by graduate students and talented undergraduate mathematics and mathematics education majors.

 

2. Assessment Project Goals.

Our goal is to develop and conduct a comprehensive assessment program to monitor the impact of all of our instruction on student learning of mathematics. We focus on three components of our instructional role: (a) Service courses through the first two undergraduate years, (b) the undergraduate program for mathematics majors, and (c) the graduate program. The assessment program is designed to involve many departmental faculty in our activities and to coordinate our departmental efforts with the work of the University Assessment Committee.

 

3. Assessment Program Description.

3.1. Development of the program.

Two components of our departmental assessment activities have been developed separately: (a) a campus-wide quantitative assessment project focusing on first- and second-year service courses through multi-variable calculus and differential equations and (b) departmental assessment of our undergraduate major and graduate programs. The campus-wide quantitative assessment project uses a model first developed by Martin and Bauman at the University of Wisconsin-Madison (Bauman and Martin, 1995; Martin, 1996) that originally was funded at NDSU by the Office of Assessment and Institutional Research. A recent, more extensive implementation occurred with support from the Bush Foundation of Minneapolis.

The departmental degree program assessment activities were developed to make use of existing instructional activities, reducing financial costs and time demands on faculty. Data is obtained from specific courses required of all undergraduate students, graduate program written and oral examinations, and advisor reports. Additionally, the Department has developed and begun to implement a peer review of teaching program, which will provide additional information about instruction and student learning.

 

3.2. Departmental service role assessment.

The most ambitious component of our assessment activities is the quantitative assessment project. Briefly, the purpose of the project is to gather information about (a) quantitative skills used in specific beginning upper-division courses and (b) the extent to which students can show these important skills at the start of the semester. Instructors play a key role in helping to design free-response tests reflecting capabilities expected of students from the first week and essential for success in the course. Two important characteristics of this form of assessment are (a) direct faculty involvement and (b) close ties to student goals and backgrounds. We have found that the reflection, contacts and dialogs promoted by this form of assessment are at least as important as the test results.

The process begins with the selection of beginning upper-division courses across the campus. These courses are selected either (a) by the Department Assessment Committee or (b) by the instructors themselves. Course instructors, selected from a range of departments, identify the specific quantitative skills their students need. The students are then given a test at the start of the semester designed to determine whether they have these skills. The tests, given early in the term, assess the extent to which students possess those quantitative skills that their instructors (a) identify as essential for survival in the course, (b) expect students to have from the first day of class, and (c) will not cover during the course. The tests are intended to be neither “wish lists” nor comprehensive examinations of the content of prerequisite mathematics courses.

A sample report for Mathematics 265 (University Calculus III, Spring 2002) is attached as Appendix A. This report was provided to the course instructors, the Department of Mathematics, and the University Assessment Committee. The report includes a copy of the two test versions that were used. In each test we have reported success rates for the students who took the test (proportions who successfully answered each question), reported by problem (Report, pages 6 ff.). The report also provides (a) information about the performance of students on each test version (Report, page 1), (b) a ranking of problems by their success rates (Report, page 2), and (c) information about the grades students earned in previous mathematics and statistics courses (Report, pages 3 and 4).

Corrected test papers are returned to students, along with solutions and specific references for remediation, within one week. Instructors receive information about the students’ test performance a few days later. Thus, early in the semester both students and instructors possess useful information about instructor expectations, student capabilities, and the need for any corrective action. We do not prescribe any specific action in relation to the test results, leaving those interpretations and decisions to the course instructor and students. We do indicate here each type of problem is covered in textbooks used in NDSU mathematics courses so that instructors and students can review the material, if necessary.

We have developed a reliable grading system that allows mathematics graduate students, with limited training, quickly to record information about the students’ work and their degree of success on each problem. The coding system provides detailed data for later analysis while allowing the quick return of corrected papers to the students. The sample report in Appendix A includes summary comments about students’ performance on the tests (for example, on the first and second pages of the report).

Information of two kinds is generated by this assessment process: (a) a detailed picture of those quantitative skills needed for upper-division course work in other departments and (b) an assessment of the quantitative capabilities of emerging juniors outside the context of specific mathematics courses. The first comes from personal contacts with faculty members as we design the test and interpret the results; the second is provided by analysis of students’ performance on the assessment project tests and their quantitative backgrounds as shown by university records.

 

3.3. Mathematics degree programs assessment.

We have also developed a process for assessing learning in the Department’s three degree

programs: Bachelors, Masters, and Doctoral. Because we have extensive contact with our majors and graduate students over more extended periods than students in service courses, a priority was to make better use of existing data rather than developing new, specialized assessment instruments. Faculty members reviewed the Department’s instructional objectives, which had been prepared as part of early assessment activities for the university, and identified existing opportunities to assess learning in relation to these stated objectives. We were able to locate evidence related to all objectives. The evidence was obtained from three main sources: (a) The undergraduate introductory proof course (Math 270, sophomore level) and our capstone course (Math 490, senior level); (b) Graduate qualifying and final examinations; and (c) Graduate student advisors. We developed forms to be completed by faculty members (a) teaching targeted courses, (b) preparing and grading departmental examinations, and (c) advising graduate students. Sample rating forms from each of the three programs are attached to this report in Appendix D.

 

3.4. Department Instructional Objectives.

The Department had previously adopted a list of objectives for student learning in its three degree programs (see Appendix B). We designed rating forms that list objectives that might be assessed through observations in a particular context (for example, the masters comprehensive exam or the capstone course–see Appendix D). Faculty are asked to rate students as fail, pass, or high pass on each outcome. They are then asked to provide descriptive comments about student performance as shown by this assessment or activity to provide evidence that supports their evaluations and to expand on the ratings. These forms are available for faculty members to complete while they conduct the targeted activities. Faculty ratings and comments are based on the standard tools of measurement used to assess and evaluate the student performance in a class, such as classroom tests, quizzes, written assignments, and group work reports. The Department has course descriptions (called TACOs for Time Autonomous Course Outlines) for instructors in all undergraduate courses and uses common exams and grading in most introductory courses. These are designed to help ensure a degree of uniformity for sections taught by different instructors and from semester to semester.

Completed forms are returned to the Department Assessment Committee, which analyzes results and prepares a summary report to the Chair, Graduate and Undergraduate Program Directors, and the Department. This process has ensured that a large majority of our Department’s faculty are involved in assessment activities each year. At the same time, the extra demands made on individuals by assessment is minimized-most faculty are only asked to provide information they obtained for other reasons and to review and react to the summary assessment report. This is a welcome change for the Chair, in particular, who formerly took responsibility mostly alone for preparing the annual assessment report for the University Assessment Committee and university administration.

 

4. Implementation.

The assessment program implementation is being done in an ongoing fashion while focusing in one or more courses each year, and continuing the data gathering in the courses whose assessment has begun earlier. To illustrate our implementation process we provide the assessment activities for the academic year 2002-2003.

 

4.1. Aspect of Program to be Assessed.

We chose to focus this year on the three-semester engineering-calculus sequence, introductory linear algebra, and differential equations. The guiding question for our work was “Do students develop the quantitative skills they need for success in later studies in their chosen field?” To respond to this question we investigated three things:

 

1.      What are the existing goals for our introductory service courses?

2.      What are the quantitative expectations of our clients (for example, later math courses, engineering programs, physical science programs)?

3.      To what extent do students meet the expectations of our clients?

 

4.2. Status of learning goals for this subprogram.

We have two kinds of goals for this program. The Department has an explicit objectives

statement that covers the undergraduate program, including these courses. These objectives are described in Appendix B as:

1.      Students will be able to analyze problems and formulate appropriate mathematical models

2.      Students will understand mathematical techniques and how they apply.

3.      Students will recognize phenomena and be able to abstract, generalize, and specialize these patterns in order to analyze them mathematically.

4.      Students will be able to express themselves in writing and orally in an articulate, sound and well-organized fashion.

 

This project additionally identifies implicit objectives for the introductory sequence of service courses. Part of the data analysis includes a review of the items that appear on tests. This analysis identifies implicit goals and objectives for the service program.

An important part of the project is for the Mathematics Department to review and respond to the findings, including these implicit goals. This took place at assessment committee and departmental meetings during April and May.

 

4.3. Activities during 2002-03.

Following the guidelines we set for this years assessment program, we completed the following activities:

 

4.3.1. Quantitative Assessment of general education and service courses. This is the continuation of the assessment process we started seven years earlier and is an ongoing process for the regular calculus sequence; and initiation of the assessment process for focus courses for this year (the three-semester engineering-calculus sequence, introductory linear algebra and differential equations). This part of the program implementation involved more assessment and reporting than analysis and response, particularly for the new courses.

4.3.2. Undergraduate majors. We had faculty members rate student performance in the introductory proof course and in the senior seminar capstone course.

4.3.3. Graduate students. Faculty members and advisors rated student performance on exams and progress toward their degree (see forms in Appendix D).

4.3.4. Increased involvement of faculty. We have wanted to increase faculty involvement in the assessment program for many years. It seemed that having the same small group of faculty conducting the assessment activities did not promote wider faculty involvement, since most assumed the people who had done it before would continue to take care of the work. Working with the Department administration, we adopted a new strategy to increase faculty involvement:

Each year a new group of 4-5 faculty (which includes at most two faculty from the previous year) would conduct assessment activities. This strategy worked well. The new members of this year’s assessment committee took ownership of the program, carrying the bulk of the activities, but they were not intimidated by the task since they had a good model to use as a template for their activities and reports and experienced faculty members to provide guidance. Formation of the committee for the next year’s assessment activities has been significantly easier since more faculty were willing to participate, recognizing that the task did not impose onerous expectations for additional work.

4.3.5. Peer review of teaching. Several faculty developed a proposal for a departmental peer review of teaching program to complement the limited information provided by student course evaluations. The committee that developed this program began their planning in Fall 2001. The program was adopted by the Department in Fall 2002 and has been piloted by four pairs of faculty or lecturers during 2002-3. (Appendix E)

4.3.6. Connections to University Assessment Committee (UAC) activities. One Department member, Bill Martin, has been actively involved in NDSU assessment activities as a member of the UAC steering committee, the University Senate Executive Committee, and the Senate Peer Review of Teaching Board. This institutional involvement has contributed to the integration of Department assessment activities with the assessment work being conducted at NDSU. Consequently, activities conducted in the Mathematics Department have helped to shape the assessment strategies adopted at the university level.

 

5. Insights and Lessons Learned.

5.1. Findings and success factors.

The process we have developed takes an ongoing, integrated approach that seeks to embed assessment activities in our instruction. We believe the process provides useful insights to the learning that takes place in our programs. To illustrate the sort of information we obtain, a recent summary report described findings of the annual quantitative assessment project, that focuses on service courses, in this way:

 

The tests of greatest interest to the Department of Mathematics were given in [Calculus III] (235 students, four instructors), [Calculus III with vector analysis] (47 students, one instructor), and [Differential Equations] (264 students, five instructors). These courses include many students who are majoring in technical programs across the campus, including physical sciences, mathematics, and engineering. All require students to have successfully completed the first year regular calculus sequence. A sample course report, giving detailed information about the outcomes, is attached as Appendix A. Faculty members discussed reports of the Fall 2001 tests during a December faculty meeting. The discussions ranged over the nature of the assessment program (for example, whether the tests were appropriate) and the success rates. While there was a range of opinions expressed at

the meeting, it was agreed that the program was potentially very useful and should continue. These initial results did not lead to specific proposals for course changes this year.

 

Individual faculty who taught the courses in which assessments were given were asked for their reactions to the test results. T he tests revealed areas of strength in student performance along with weaknesses that concern faculty. These patterns were reflected both in the comments at the meeting and in written responses to the reports. There was agreement by many that the information was useful as an indicator of program strengths and weaknesses. More specific information about success rate patterns and their perceived significance is provided in the reports themselves.

 

So far, our assessment findings have not led to major changes in courses or programs at NDSU. A current focus of our work is on making better use of the information obtained from assessment activities. We plan to have a more extensive review and discussion of findings by departmental faculty, now that we have data from several years. The purpose of the discussion is to address several questions:

1.      What do the findings show about student learning and retention from our courses?

2.      What might account for these patterns? In particular, why do students seem to have specific difficulties?

3.      What could and should the Department do to address areas of weakness?

4.      Are we satisfied with the Department’s stated goals and our assessment procedures, having attempted to assess student achievement in relation to the stated goals for several years?

While the focus of each test is on a particular course, we are able to gain a broader perspective on faculty expectations and student achievement by pooling results from different assessments and over several years. The table below illustrates the patterns that can be discerned in the results. The table also summarizes some generalizations we can make based on tests administered by the project. We have found three levels of mathematics requirements or expectations in courses across the campus. Within each level, patterns of students’ success rates have become apparent over the years.

The course level is based on mathematics prerequisites. For example, Level 2 courses require just one semester of calculus (examples include Finance and Agricultural Economics courses). The success rates range from High (where more than two-thirds of the tested students in a class are successful) down to Low (when under one-third of the students are able to solve a problem correctly). Each cell reports a general trend we have observed. For example, typically any calculus problem administered to students in a Level 2 course will have a low success rate. The cell also mentions a specific problem to illustrate the trend. The example problem for typically low success rates in a Level 2 course is asking students to estimate the value of a derivative at a point given a graph of the function. The most important characteristic of this table is that it illustrates how the use of tests that are custom-designed for particular courses can still provide detailed and useful information about mathematics achievement on a much broader scale at the institution.

 

Appendix C contains a more complex table that illustrates how even more detailed information can be extracted from a large number of tests administered across many departments and years. The table illustrates that not only success rates on particular problem types, but even the distribution of types of problems can be analyzed to help identify how mathematics is used across the campus in different programs. This table compares the nature of tests and patterns of success rates in mathematics, engineering, and physical science courses, all of which require the full three-semester normal introductory calculus sequence.

The table is based on 240 individual problem success rates (PSR-success rates for each time a problem was used on a test). The three groups of courses were: (a) Mathematics (four distinct courses, including a differential equations course that was tested in successive semesters; with 58 PSR); (b) Physical Sciences (five distinct courses, including a two-course atmospheric science sequence with retested students in successive semesters; 68 PSR); and (c) Engineering (six distinct courses, two of which-electrical and mechanical engineering-were tested in successive semesters; 114 PSR). The table has been included not so much for detailed analysis of its content in this paper, but to illustrate the detailed information that can be provided by this assessment process.

For example, the table illustrates quite different patterns of mathematics usage across the three disciplinary areas: Mathematics courses emphasized non calculus material (60% of the problems that appeared on tests in those courses), Science courses drew most heavily on differential calculus material (56% of problems), while Engineering courses had a more balanced use of problems from across all the introductory areas (22% non calculus, 31% differential calculus, 16% integral calculus, 26% differential equations, and 5% probability and statistics). Much more detailed information is included about specific types of problems and typical success rates. For example, the first entry for Mathematics is Graph Interpretation problems which appeared on two different tests in one math course (2-1). These problems represented 3% of all problems that appeared on math course tests, and the median success rate across all problems of this type that were administered in a math course fell in the second quartile (2) representing 25-50% for students taking those tests.

 

5.2. Dissemination of Findings.

Our assessment findings have been shared with four distinct groups: (a) Mathematics faculty at NDSU, (b) NDSU departments who depend on mathematics, (c) other NDSU faculty interested in departmental assessment, and (d) mathematics faculty from other institutions involved in the MAA Assessment Project SAUM. The first two groups are most interested in student performance and its implications for their courses and programs. The second pair are interested in the assessment methods employed by our project.

A goal of our work, both in the design of assessment activities and the strategies used to involve faculty and disseminate results, has been to only do things that have value for participants. For example, when we ask students to take tests, we want it to have personal value for them at that time rather than just appealing for their participation for the good of the department or institution. Similarly, when we ask faculty to conduct an assessment in their class or to review reports, they should feel they have gained valuable insights as a result of their work rather than submitting a report because it is required for some external purpose.

 

6. Next steps and recommendations

Some of our work requires the assistance of a graduate student to help with test administration and data analysis and some financial support for duplication and test scoring. We have found support for this work through external grants and are working to institutionalize this support as a part of the University’s institutional assessment and accreditation activities. The work is valued at the institutional level because the extensive service role played by mathematics is well recognized. Consequently, we expect to receive some level of institutional support for our general education assessment activities, the ones that require the most extra work to conduct and analyze.

We recognize that we have to date had more success gathering and disseminating assessment data than getting faculty to study and respond to the findings. This partly reflects the natural inclination of faculty to focus on their own courses than on the broader picture of how programs are working to develop student learning. We plan to concentrate our efforts now on ensuring that assessment findings are regularly reported and discussed by faculty, both in participating departments and in the Mathematics Department. We believe that regular conversations about the patterns of results will lead to the formulation and implementation of responses to shortcomings revealed by assessment activities. Our approach reflects the belief that faculty are in the best position to respond to findings and that our most important role is in providing accurate information about student achievement. Consequently, our reports focus on providing descriptive statements about student performance, rather than making detailed recommendations for changes in courses and instruction.

We also believe that widespread faculty involvement in assessment activities is a necessary condition for an effective assessment program. Our strategy has been to adopt a non judgmental approach that seeks to minimize special effort required of participants and to ensure that participants clearly see that they stand to benefit from the activities in which they are involved. Our efforts to increase departmental and university faculty involvement and impact will continue. The strategies initiated during the last academic year seem to work. The Department’s assessment committee will continue to work with UAC and General Education Committee to increase the impact of the departmental assessment activities to a broader audience.

 

References

Bauman, S. F., & Martin, W. O. (May 1995). Assessing the Quantitative Skills of College Juniors. The College Mathematics Journal, 26(3), 214-220.

Martin, W. O. (1996). Assessment of students’ quantitative needs and proficiencies. In T. W. Banta, J. P. Lund, K. E. Black, & F. W. Oblander (Eds.), Assessment in Practice: Putting Principles to Work on College Campuses. San Francisco: Jossey-Bass.




Appendix A. Sample report for Math 265 ( Calculus III), Spring 2002.


Preliminary Assessment Results

 

Mathematics 265: Calculus III

 

Spring 2000-02

 

Sixty-eight students took two versions of a eight-item free-response test in Mathematics 265 (Professor Sherman) during the second week of the Spring 2002 semester. The test was designed to see the extent to which students had quantitative skills required for success in the course. Students were not allowed to use calculators while completing the assessments. Graduate students from the Department of Mathematics graded the papers, recording information about steps students had taken when solving the problems. The graders also coded the degree of success achieved on each problem using the following rubric:

  1. Completely correct
  2. Essentially correct—student shows full understanding of solution and only makes a minor mistake (e.g., wrong sign when calculating a derivative or arithmetic error)
  3. Flawed response, but quite close to a correct solution (appears they could do this type of problem with a little review or help)
  4. Took some appropriate action, but far short of a solution
  5. Blank, or nothing relevant to the problem

Corrected papers, along with suggested solutions to the problems, were returned to students the following week. Summaries of the grader’s coding are included on the attached copy of the test. A test score was computed by awarding one point for each A or B code and zero points for each C, D, or E code. This score reflects the number of problems that each student had essentially or completely correct. The distributions of test scores are shown in these

figures.

 

The second pair of charts gives the distribution of partial credit scores called scoresum (each

problem was awarded 0-4 points, E=0 to A=4).

 

It appears that many students will need to review some mathematics covered on the test, since a majority were successful on less than half the problems. Almost two-thirds of the students (44 of the 68) achieved overall success on four or fewer of the eight problems.

 

The problems are ranked according the degree of success students achieved on each problem in the following table.

Degree of Success on Test Problems

%AB

%A

%C

No Problem description

85%

12%

3%

V2#3 Integration using Fundamental Theorem of Calculus

73%

58%

3%

V2#2 Solve using property of differences for logarithms (same as V1#2)

69%

66%

6%

V1#2 Solve using property of difference for logarithms (same as V2#2)

66%

31%

20%

V1#3 Set up a definite integral to compute the area enclosed by a parabola and line (same as V2#61% 55% 18% V2#1 Complete the square to find center and radius of an equation (same as V1#1)

60%

31%

11%

V1#8 Use substitution to evaluate an indefinite integral

57%

51%

14%

V1#1 Complete the square to find center and radius of an equation (same as V2#1)

52%

46%

18%

V2#7 Use integration by parts to evaluate definite integral

52%

33%

46%

V2#4 Set up a definite integral to compute the area enclosed by a parabola and line (same as V1#)

49%

29%

9%

V1#7 Use substitution to evaluate an integral

42%

30%

21%

V2#5 Use a sign table for a function and its derivative to sketch a graph of the function

40%

26%

23%

V1#5 Estimate the derivative of a function at a point from its graph

23%

17%

11%

V1#4 Solve using implicit differentiation

17%

11%

20%

V1#6 Maximize area of a rectangle inscribed in a semicircle (same as V2#6)

15%

12%

21%

V2#6 Maximize area of a rectangle inscribed in a semicircle (same as V1#6)

6%

3%

39%

V2#8 Area enclosed by one-loop of four-leaved rose

The problems are primarily sorted in this table by proportion of students who received a code of A or B, indicating that at least essentially correct. For reference, the second and third columns report the proportion of students who had the completely correct (A, column 2) and the proportion who made good progress (C, column 3).

 

The problems have been divided into three groups. At least two-thirds of the students could integrate using the Fundamental Theorem of Calculus, and solve using properties of logarithms. About three-quarters of the students successfully set up a definite integral to compute the area enclosed by a parabola and line.

 

Fewer then three-fifths of the students completed the square to find the center and radius of an equation, or used substitution to evaluate an integral and/or indefinite integral. Similarly they successfully used a sign table of a function and its derivative to sketch a graph of the function and estimate the derivative of a function at a point from its graph. Under a quarter of the students could solve using implicit differentiation, or calculate the area enclosed by one-loop of a four-leaved rose.

 

Mathematics Backgrounds

University records provided information about the mathematics courses that had been taken by students in these classes. The following tables report up to the four most recent mathematics courses recorded on each student’s transcript. Every student with available records indicate exposure to at least one mathematics course. The median for Math 166 was a B, but one should notice that almost half of the students received and A in the course. Calculus III is a retake for seven students that were tested, of these seven, two have no record of taking the prerequisite.

 


These histograms help to illustrate possible connections between test score and grade in the most recently completed mathematics or statistics course. On version one students with higher grades (lighter shades in divided frequency bars) in most recent course generally scored somewhat higher on this assessment test, as one might expect.

 

 

 

Reactions

We asked the instructor five questions about the test results. Her responses are summarized below.

Instructor:

  1. Are you surprised by students’ performance on particular test items?

 

 

 

 

 

  1. Did you do anything different this semester because of your students’ performance on the test?

 

 

 

 

 

  1. How well do you think the tests reflected the quantitative demands of your course? Is it accurate to say that the skills we testes were essential for survival in the course?

 

 

 

 

 

  1. Would you suggest any changes in prerequisites, student preparation, or the nature of this course based on what you have learned from the preparation and administration of these tests?

 

 

 

 

 

  1. If this or another course in your department was tested again in another semester, would you suggest any changes in the testing program?

 

 

 

 

 

Department:

Reactions to these results:

Suggested responses(action plans):

 

 

 



Appendix B. Department mission statement and program objectives.

 

Mission Statement.

The mission of the Department of Mathematics is teaching, research and other scholarly activities in the discipline; providing quality education to our B.S., M.S. and Ph.D. students and post-doctoral associates; and influencing the mathematical climate of the region positively. The Department strives for excellence in teaching its majors and service courses, while providing stimulating and informative courses. The Department’s research activities include pure and applied mathematics.

 

Program Objectives.

A. Bachelors program

  1. Students will be able to analyze problems and formulate appropriate mathematical models.
  2. Students will understand mathematical techniques and how they apply.
  3. Students will recognize phenomena and be able to abstract, generalize, and specialize these patterns in order to analyze them mathematically.
  4. Students will be able to express themselves in writing and orally in an articulate, sound and well-organized fashion.

 

B. Masters program

  1. Students will have experienced both breadth and depth in the study of advanced mathematics so that they: (a) can recognize and create good mathematical arguments, (b) have knowledge of fundamental topics in both classical and modern mathematics, (c) can create and pursue new ideas and application in and of mathematics.
  2. Students will have experience as a teaching assistant with classroom experience or as a research assistant.

 

C. Doctoral program

  1. Students will have experienced both breadth and depth in the study of advanced mathematics so that they: (a) can recognize and create good mathematical arguments, (b) have knowledge of fundamental topics in both classical and modern mathematics, (c) can create and pursue new ideas and application in and of mathematics.
  2. Students will have exposure to and experience with current research.
  3. Students will develop ability to understand and create new mathematical ideas and applications.
  4. Students will have experience as a teaching assistant with classroom experience or as a research assistant.

Appendix C. Patterns of Test Results in Mathematics, Science, and Engineering

 


Appendix D: Sample Rating Forms

 


 

Appendix E: Mathematics Department Peer Review of Teaching Program

Peer Evaluation of Teaching Proposal

NDSU Department of Mathematics

 

The Department of Mathematics believes that the purpose of peer evaluation is to help faculty recognize and document both strengths and weaknesses in their teaching. The word “peer” means that this activity should involve reciprocal observation and discussion of teaching and learning by small groups of 2-3 faculty who exchange visits in each other's classes. The committee believes that the members of the department have all the qualifications necessary to make this process reach its intended goal. The committee proposes that:

 

1.   Tenure-track faculty be reviewed at least once each year; Tenured associate professors be reviewed at least once every other year; Tenured full professors be reviewed at least once every three years.

 

2.   The process begin with the identification of the faculty to be evaluated by the chair. Then the faculty member identifies his/her teaching goals and strategies (in writing). These objectives are discussed with a peer colleague or colleagues, with a view to developing evidence that supports the individual's claims. This evidence could come from classroom observations, student evaluations, and review of written course materials, such as tests and assignments. It should include multiple sources (i.e., not a single classroom observation). After reviewing this evidence, the group prepares a report that describes the activities and the extent to which the evidence supports the original claims. The report should include plans for future teaching strategies, including possible changes or enhancements that the faculty member plans to try.

 

 3.  A team of 2-3 faculty members will complete the work described in (2) for each member of the team. This helps to ensure that peer evaluation does not become a one-way process that involves one person observing and evaluating another primarily for external purposes. Instead, the process is designed primarily to increase collegiality and reflective practice within the department, while providing documentary evidence of the regular review of teaching that can be used for external purposes (such as annual reviews, PT&E).

 

4.   Observers of a faculty member should include at least one member of the department PT&E committee.

 

5.   The observation process should always include a Pre-Observation Conference between the observee and observer to discuss the objectives of the class to be observed and other relevant issues (see Peer Review Observation Instrument). Following the in-class observation, a Post-Observation Conference must also be held to discuss the observations as documented by the Peer Review Observation Instrument.

 

Attachments: Peer Review Observation Instrument (sample), Characteristics of Effective

Observers/Things to Avoid (sample guide), Tips for Observers and Observees (sample)