Two additional and related resources (besides your own time) may be needed to implement CPS effectively:
Adequate assistance (personnel); and
Adequate rooms.
There are many tradeoffs between these resources, which are both in short supply at many institutions. Some of the tradeoffs are outlined in the sections below.
Adequate Assistance
The limiting factor in implementing CPS is the number of students per instructor. It is difficult for any instructor to teach 9 or more groups without assistance. Experienced instructors can teach comfortably 7 - 8 groups per class section.
Inexperienced (first-year) graduate or undergraduate TAs, however, can handle only 5 groups per section.
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Part 2: Using Cooperative Problem SobvingIf you are the only instructor of small classes, then no additional assistance is needed to implement CPS. If you are in this fortunate situation, you could skip the rest of this section. But if you do not have one experienced instructor per 20-28 students (or one first-year TA for every 15 – 18 students), people have found creative ways to find free assistance for CPS.
"Free" Undergraduate Assistance. We know one instructor who teaches an introductory physics course with 40 students at a small, liberal-arts college. He negotiated with the Education Department to offer course credit to physics undergraduate students in their secondary teacher-education program. These selected students assist the instructor during the course time set aside for CPS.
Change Responsibilities of Paid Assistants. If you have undergraduate or graduate students who spend all or part of their time grading homework problems and/or lab reports, consider reassigning all or some of this time for assistance with CPS. For example, we cut down slightly on the number of required lab reports, and devised a rubric for grading that allows TAs to do some lab evaluation during lab time. We also eliminated or sharply curtailed the grading of homework and redirected this effort to coaching in CPS sections.
Other colleges and universities have instituted computerized homework “grading”, or give short multiple-choice tests on the computer each week. Both options allow you to check whether students can use appropriate mathematics in simple one-or two-step exercises. Of course, you can continue to assign some of the more difficult, end-of-chapter problems for homework, even when they are not graded.
To get students to do homework, it is useful to make one problem on your quiz very close to a homework problem and tell students you will do so. After the quiz, point out which problem was very close to the homework problem. Because subtlety is lost on most students, it is useful to use similar objects and situations as the homework problem simply solving for a different variable. The most useful homework procedure that we have found is to post a sample quiz on your web site about 2 weeks before your next quiz. Do not post the answers or solutions until a few days before the quiz. Many more students will seriously work on problems and get help from the TAs in the tutorial room if you call something a sample quiz rather than homework.
What Kind of Room is Needed?
The ideal room for CPS (in most disciplines, not just physics) is a carpeted room with two walls of boards and small, round cocktail-style tables with moveable chairs that accommodate 3 to 4 students (see Chapter 8, page // for optimal group size).
The room has adequate space between groups for the instructor to circulate easily among the groups. However, such rooms are rarely available. The minimum room requirements for CPS are:
1. The room must have sufficient wall space for one person from each group to write or post simultaneously parts of their group’s problem solution.
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Figure 9.2. Top diagram view of movable chairs (black circles) in room arranged for a CPS session. Dashed arrows indicate spaces for instructor to circulate to each group.
2. Students must be able to sit facing each other. In other words, for effective group interactions, students need to be able to look directly at each other, knee-to-knee (see Chapter 7, page //).
3. The room must be large enough so there is space between groups to allow groups to function independently and the instructor to circulate to each group.
No Boards (or not enough boards). The problem of enough board space can be solved in many ways. If you have storage space in the room, you can make “white boards” on which groups can write their diagrams and equations with dry-erase pens. White boards are actually preferable to writing on the blackboard because each group can decide what they want to put on the board together, rather than sending one person to write on the blackboard. Large sheets of whiteboard can be purchased at hardware/lumber yards and cut into 2 ft. x 3 ft. pieces.
If you have neither storage space for white boards nor sufficient board space, you can use sheets of white butcher paper for groups to write on. The disadvantage of butcher paper is the need for a large flat surface to write on (our students sometimes use the floor), and the necessity to tape the sheet to the wall and remove them at the end of class.
The minimum requirements for CPS eliminate rooms with stadium seating and strip tables with fixed seats. However, the following rooms meet the criteria.
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Part 2: Using Cooperative Problem SobvingFigure 9.3. Top diagram view of room with strip tables (rectangles) and movable chairs (black circles). Dashed arrows indicate spaces for instructor to circulate to each group.
Figure 9.4. Diagram of studio format room at Massachusetts Institute of Technology (MIT)2
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No Tables, Moveable Chairs. Minimally you need a room with moveable chairs that is large enough to accommodate your class size. The room does not have to be in the science or physics building. We schedule CPS discussion sections in small
classrooms all over campus. The map in Figure 9.2 is an example how chairs can be arranged so the groups can function independently and the instructor can circulate to each group.
Strip Tables with Moveable Chairs. We do not recommend that you implement CPS in a room with rows of long, narrow tables fixed to the floor. But it can be done if the room is large enough and the chairs are moveable (or at least swivel). For example, the map on Figure 9.3 shows how 8 groups could be arranged in a room with eight strip tables. The groups are far enough apart, and the instructor can get to each group.
Lab Room. Lab rooms are not ideal, but if you have a small class, you can do cooperative problem solving in most lab rooms. You must, however, be able to arrange the groups so students can be sitting facing each other, for example at the end of tables. Of course, all the apparatus must be cleared out of the way.
Room with Large Tables. Some universities have replaced stadium seating in large lecture rooms with the studio format – large rooms with tables that seat 6 to 10 students, as illustrated in Figure 9.4. There is usually sufficient space for the group recorder, in the middle chair, to move his/her chair back away from the table. The other two group members on either side of the recorder can turn their chairs around to face the recorder.