In introductory courses in mathematics at the University of Michigan, an instructional consultant visits the class one-third of the way into the semester. This observer holds a discussion with the class, in the absence of the instructor, about how the course is going, and provides feedback to the instructor.
Background and Purpose
Each fall at the University of Michigan, most of the incoming students who take mathematics enroll in one of the Department's three large introductory courses. These three courses, Data, Functions, and Graphs, Calculus I, and Calculus II, enroll a total of 3600 students each fall. Not only must the department design and run these courses effectively, but it is clearly crucial that we find out whether the courses are succeeding. Each course is systematically monitored by all the conventional methods such as uniform examinations, classroom visits, and student evaluations, but one assessment technique has proved especially helpful. This procedure, which we call Early Student Feedback, has the advantage of simultaneously giving both students and instructors an opportunity to review the goals of the course and providing a simple mechanism for improving instruction.
The courses have been planned around a set of specific educational objectives which extend beyond the topics we list in our syllabi. We are interested in encouraging the transfer of knowledge across the boundaries between disciplines, so our course goals reflect the needs of the many other disciplines whose students we teach. For example,
Course Goals for Introductory Calculus
1) Establish constructive student attitudes about the value of mathematics by highlighting its link to the real world.
2) Persuade more students to continue in subsequent mathematics and science courses.
3) Increase faculty commitment to the course by increasing the amount of student-faculty contact during each class period and having faculty grade students' homework themselves.
4) Develop a wide base of calculus knowledge including: basic skills, understanding of concepts, geometric visualization, and the thought processes of problem-solving, predicting, and generalizing.
5) Strengthen students' general academic skills such as: critical thinking, writing, giving clear verbal explanations, understanding and using technology, and working collaboratively.
6) Improve students' ability to give reasonable descriptions and to form valid judgments based on quantitative information.
All three of our large first-year courses are run in the same multi-section framework, a framework which makes achieving these objectives possible. Classes of 28-30 are taught by a mix of senior faculty, junior faculty who come to Michigan for a 3-year period, mathematics graduate students, and a few visitors to the department. Here is the general format.
Key Features of Introductory Courses
1) Course content: The course emphasizes the underlying concepts and incorporate challenging real-world problems.
2) Textbook: The textbook emphasizes the need to under-stand problems numerically, graphically, and through English descriptions as well as by the traditional algebraic approach.
3) Classroom atmosphere: The classroom environment uses cooperative learning and promotes experimentation by students.
4) Team homework assignments: A significant portion of each student's grade is based on solutions to interesting problems submitted jointly with a team of three other students and graded by the instructors.
5) Technology: Graphing calculators are used throughout the introductory courses.
6) Student responsibility: Students are required to read the textbook, discuss the problems with other students, and write full essay answers to most exercises.
Early Student Feedback was originally introduced to the Mathematics Department by Beverly Black of the Center for Research on Learning and Teaching (CRLT) at the University of Michigan. The procedure we currently use evolved from the Small Group Instructional Diagnosis (SGID), described by Redmond and Clark .
A) Overview: Approximately one-third of the way into the term, each class is visited by an instructional consultant. The consultant observes the class until there are about 20 minutes left in the period. Then the instructor leaves the room and the consultant takes over to run a feedback session with the class. Soon afterward, the consultant and the instructor have a follow-up meeting to discuss the results and plan teaching adjustments. The results of each Early Student Feedback procedure are confidential.
B) Consultants: The consultants we use are the instructors who run our professional development program. They are upper-level mathematics graduate students and faculty members. Consultants are trained according to CRLT guidelines for observing classes. These guidelines stress the importance of having instructors reflect on their plans and goals for each class session in light of the overall course goals.
C) Observing the class: During the observation period, the consultant objectively records everything as it happens; the classroom setup, what the instructor says and does, student interactions with the instructor and with each other, etc.
D) Running the feedback session: First, the consultant explains to the class that the Mathematics Department routinely conducts these sessions at this point in the term and briefly explains the procedure.Then the class is divided into groups (of four or five students each) and the groups are given 7 minutes to discuss, reach a consensus, and record their responses on the Early Feedback Form:
In your small group, please discuss the following categories and come to a consensus on what should be recorded for the instructor. Using detailed examples and specific suggestions will make your comments more useful to the instructor. Please have a recorder write down the comments that you all agree on.
List the major strengths in this course. What is helping you learn in the course? (Space is provided for five responses)
List changes that could be made in the course to assist your learning. (Space is provided for five responses.)
While the students are talking, the consultant writes two headings on the board:
After getting a volunteer to copy what will be written on the board, the consultant calls on the groups in turn to read aloud one "strength." One by one, the consultant records the comments on the board in essentially the students' own words while continually checking for clarity and consensus. When all the "strengths" have been read, the consultant uses the same procedure to generate a list of "changes."
E) Debriefing the instructor: Before the meeting to debrief the instructor, the consultant makes a two page list of the comments from the board (strengths on one page and changes on the other). The beginning of this meeting is an opportunity for the consultant to get instructors to talk about how the class is going, what goals they had for the class, and what they see as their own possible strengths and weaknesses. The consultant then gives the instructor the list of students' comments (strengths first) and goes over it one point at a time. The consultant's own observation of the beginning of the class period provides valuable detail and backup for the students' interpretation of their experience. The final step is to plan with the instructor how to respond to the students and what adjustments should be made. For instance, if students suggest that the instructor spend more time going over homework problems, the answer may well be "OK." But, if they want to do less writing ("after all, this is a mathematics class, not an English class"), the instructor will need to spend more time explaining the connection between writing clear explanations and understanding the ideas.
During the feedback process, we find that everyone involved in the course, from the individual student, to the instructor, to the course director benefits from reflecting on the goals of the course. For example, students often complain (during the feedback session) that their instructor is not teaching them; that they have to teach themselves. They think that a "good" teacher should lead them through each problem step by step. In response, the consultant gets a chance to talk with the instructor about students' perception of mathematics as simply performing procedures, whereas what we want them to learn is how to become problem solvers. Commonly, both the students and their instructors respond well to the Early Student Feedback process. The students are pleased that the Mathematics Department cares what they think. We find that they will discuss the course freely in this setting. Similarly, there has been a uniformly positive response from instructors at all levels, from first-time graduate students to senior faculty. All instructors feel more confident about their teaching after hearing such comments as "he's always helpful and available" or "she knows when we're having trouble." In fact, since these feedback sessions have proved so useful in the introductory courses, the Department has begun to use them occasionally in more advanced courses.
Use of Findings
Each Early Student Feedback session is confidential and the results are never recorded on an individual instructor's record. However, the consultants talk over the results in general looking for patterns of responses. We ask questions about how the courses are going. Do students see the value of the homework teams? Is there lots of interaction in the classrooms? Do the students seem to be involved with the material? Are the instructors spending too much time on their teaching? The answers give a clear profile of each course. The timing of the procedure allows us to reinforce the course's educational objectives while the course is still in progress. Furthermore, it gives us the opportunity to improve the instruction in each individual classroom and make any necessary adjustments to the courses themselves.
Early Student Feedback has been used successfully in many courses throughout the University at the request of individual instructors. But in the Mathematics Department, we require it every term in every section. Making the process mandatory had the effect of making it seem like a routine (and hence less threatening) part of each term. Since almost everyone has had a consultation, there are always many experienced instructors who spontaneously tell newcomers that the sessions are very beneficial. It is easy to calculate the "cost" of using Early Student Feedback as an assessment technique.
Students - 20 minutes of class time
Instructors - 1/2 to 1 hour for debriefing
Consultants - (1 hour class visit) + (1 hour preparation time) + (1/2 to 1 hour debriefing)
The method is certainly cheap in comparison to the amount of information it generates about teaching and learning.
 Redmond, M.V. and Clark, D.J. "A practical
approach to improving teaching," AAHE Bulletin