To set the tone of a course at the beginning, develop with the class a "class mission statement," which can be revisited as the course progresses to assess progress toward meeting course goals.
Background and Purpose
Several semesters of teaching expression manipulation-type courses tired me out. In order to re-establish my enthusiasm for mathematics in the classroom I remembered that mathematics is a science in which we look for patterns, generalize these patterns and then use them to better understand the world around us. Yet when I introduced these ideas into a traditional atmosphere, the students revolted because it wasn't what they expected or were accustomed to. It was difficult to acquire the new skills being asked of them: attacking a problem they had never seen before, experimenting with a few examples, choosing from the assortment of mathematical tools previously learned, sticking with a problem that had more than one answer, communicating their answers, and even asking the next question. During the transition period, frustration levels were high for everyone. I was disappointed with their work which showed little or no improvement throughout the semester. The students were angry and I found myself on the defensive. From their point of view, it was a desperate semester-long struggle to bring their grades up with very little idea of how to accomplish that. This led to the introduction of the Mission Statement into my classes during the first week of each semester. When I began to use Mission Statements I was at a small liberal arts college in upstate New York. I am currently at a state college in New Jersey. Although the atmospheres of the colleges are quite different, mathematics education at the K-12 level is fairly consistent. Students come out of the secondary system in the expression manipulation mode. For this reason I believe that Mission Statements can be useful at any institution and in every classroom. To date, I have used them successfully in service courses, general education or core distribution courses, and program courses. While the process takes a full class period, from the first day of class, students begin to take an active role in their own learning. Learning becomes a process over which students have control, something they can improve, not something to simply submit to. Once they have some control, once they see a purpose, their motivation to learn carries the class, rather than the more typical scenario where the professor carries the course dragging the students with her.
I begin the first day with a preliminary process to determine students' expectations for the class. I read each of the following statements aloud and have the students complete them.
Each day I come to class I expect to (be doing) ...
Each night for homework I expect to (be doing) ...
Each day I come to class I expect the professor to (be doing) ...
I expect to do ____ hours of homework between each class (even on weekends??).
I expect my grades to be based on ...
If I could get anything out of this class I wanted to, I would make sure that I (got) ...
After each statement is completed, I pick up the responses, usually written on index cards, and react to them. This allows me to express my expectations for the class. It brings us a little closer together on what the course is all about and it opens up a dialogue between the students and me. Once this preliminary exercise is complete, I facilitate the creation of individual Mission Statements. Each student is handed 20 to 30 post-it notes or index cards and a large sheet of paper. Then I read through the following process.
1. To establish a PURPOSE for the course, ask yourself why you are taking this course. What's your purpose? What do you hope to achieve? You must write until I tell you to stop. Brainstorm everything that comes to your mind. Write each thought on a different card. (Have students write for five minutes.) Now organize your thoughts by prioritizing them, grouping them, or whatever works best for you. (Allow up to 2 minutes.) Then set these ideas aside for now.
2. To establish a PROCESS for the course, ask yourself how you expect to fulfill those purposes. What means and methods will you use? What skills and behaviors will you use, both inside and outside of the classroom? (Have students write for five minutes.) Organize in the same way. Then set these aside.
3. To establish your ACCOMPLISHMENTS, ask yourself, what results do I plan to achieve? What specific outcomes will be evidence that I've succeeded? What topics do I want to have learned? (Have students write for five minutes.) Organize in the same way.
4. Arrange your individual thoughts from the cards onto the large sheet of paper using the following format:
I AM TAKING "COLLEGE ALGEBRA"
At this point you may switch any statements between categories if you find they fit better elsewhere. The grammar necessary to make each statement follow the category headings will help you decide which statements go under which categories.
5. Take these home and type them up. (This ensures that they at least read them one more time and in the best case ponder over them again.) Also write a paragraph or so reacting to the entire process.
During the semester, we reflect on our Mission Statements several times, to make sure that those goals, processes, and accomplishments which we chose to the best of our ability at that time still work for us. For example, after returning a project I ask them to decide if the assignment pertained to any of their goals, if they actually used the processes on their Mission Statement. If so, did they work; if not are they willing to try them now? If the processes didn't work, I ask them either to think of other processes that might work, or to come to see me, because I have experiences which might be beneficial to them.
By the time the process is complete, I have assessed students' goals for the course, students' expectations of themselves, students' expectations of me, and students' definitions of success. Maybe even more importantly, students have taken the time to ponder these questions for themselves, many for the very first time.
Use of Findings
If the Mission Statements appear to be too diverse to work with, you can combine common elements from the individual Mission Statements, plus anything that was in at least one statement that you feel is essential, into a common Mission Statement for the course. Presenting this gives you another opportunity to get those students who chose to avoid the process, by writing shallow statements, to buy into it. If, during this process, you have had to eliminate goals that would lead to learning, you can have students create individual projects, related to the course material, which help them realize their individual goals. Keep in mind that each discussion about goals and how to achieve them, offers opportunities for students to learn about themselves, their learning styles, and their defense mechanisms.
This method of assessment has enabled me to make many changes in my classroom. One major change that I have incorporated into several of my general education courses is that I no longer use the textbook as the course syllabus. Our goal is no longer to complete sections 2.1-6.5 skipping as few sections as possible. Now we set our goals based on my own and my students' Mission Statements and use the textbook when and as needed. As an example, in my College Algebra class, students wanted to see the usefulness of mathematics. Therefore, we began the semester with a linear programming problem. As we solved it we found ourselves graphing lines and linear inequalities, finding points of intersection, and invoking major theorems. We turned to the textbook in order to remember how to accomplish some of these tasks. We began in the index and the table of contents, and often found ourselves in several different chapters in a single day. Many students are finally seeing that much of the mathematics they have previously learned is useful and that they can return to a textbook as a reference when necessary.
Another substantial change that I have incorporated into my classes is that of allowing revision on projects. Many of my students are being asked to make decisions based on quantitative data, and to communicate these decisions for the first times in their academic careers. This can be an onerous task for them. It is my experience that once a grade is assigned, learning stops. So instead of reading, commenting, and assigning grades to projects, I glance through them to find what is lacking and/or most misunderstood. Then I either make anonymous copies of the misconceptions or lackings on transparencies for the next class period or I create a peer review form in which students are asked to look for these particular misconceptions/lackings in their peers' work. Using transparencies on an overhead projector takes less time - the students look through their own paper for each suggestion I present. The peer review takes more time but better prepares them for critically looking at their own papers in the future. Peer review works better if each student is working with different data. In either case I offer the class the opportunity to work on projects one more time before I put a grade on them. Students are very grateful. This change took place as a result of our discussion of whether we were meeting our goals or not. Again the usefulness of the subject came up. We realized that in order for work to be useful, we need to be able to communicate it to others and the students had absolutely no training in this area. On a personal note, revision has been a life-saving device as far as time goes. Rather than write the same comments over and over, assignment after assignment, I can glance through a set of projects and decide if I should grade them or build in a revision. The second time around I have the same choice, request a second revision or grade. When I do decide to make individual comments and assign a grade, it takes very little time because I am reading the assignment for the second or third time and the comments are more often about how to extend the project, include deeper mathematics or simply suggest that next time the student take advantage of the revision process. A more impromptu change in the course took place when several of my students made statements about integrating mathematical ideas into their own lives. It developed rather like a challenge: I apparently claimed that mathematics is everywhere and as a result their Mission Statements challenged me to integrate any subject of their choice into the class. From that conversation the following project developed during a class session. Each of my thirty-two students had to think of a situation that could be modeled linearly. That night's assignment was to call two companies which provided the service they suggested in class. These ranged from mechanics' shops to pizza parlors to long-distance phone carriers. Students had to write a narrative description comparing and contrasting the two services to decide how one would choose between the two. The narrative had to be supported by appendices which included graphical, numerical and analytical representations of the data. Each representation had to point out all pertinent information used in their narrative argument. Both the creation of and reflection on our Mission Statements have us continually rethinking our intention for the course. For the first time I am treating general education students differently from mathematics majors. We spend significant time and effort thinking about how to communicate the mathematics we learn (as otherwise it is useless to us) and how to create assignments and processes that enhance this learning. One of the most exciting aspects of the new journey we are on is that for the first time we have student input at a time when students have a stake in the course rather than relying on student evaluations when often they are commenting on their success in the course not on improving or increasing the learning that takes place.
The more responsibility I give to the students, the more success we all have. However, you must be willing to relinquish the feeling of control! This has been difficult for me. Originally I asked the students to write their Mission Statements during week three or four so that they would have an idea of what the course was all about. Now I ask them to create them on the first day or two, before they feel that they are stuck with my choices. Then after three or four weeks we review the Mission Statements to decide whether they are working for us or not.
A second transition I have had to make to ensure
success is accepting that this process takes time. You can't rush it!
It takes an entire class period at the beginning of the
course, and a few minutes of class time on occasion for
reflection and discussion. I now know that the time is well worth
it because when students and professor are working
towards the same goal, progress is hastened dramatically. The
time spent on the Mission Statement is made up in the first
few weeks of class. I have had several students, reflecting
on their Mission Statements, admit that they are not
doing anything they claimed they would and this is affecting
their grades. That is taking responsibility for one's own
actions. If you feel as though your job is to educate students
beyond covering content, you will have given them a useful,