To adopt CPS, it is helpful to be in the frame of mind of an experimenter -- cut yourself some slack and take thelong-term view. Implementing a new teaching technique is similar to implementing a completely new measurement technique in a laboratory. When you start, it naturally takes more time and effort than the old, comfortable technique.
More frustrating still, the first time you "turn it on," it either doesn't work at all, or you don't get the
expected results. You have to tinker with it, make adjustments, and fine-tune the technique until you get the optimal results.
If you and your students have no experience with active learning techniques, we recommend that you start with informal groups in the lecture before you implement CPS. Informal groups involve asking a short question during a lecture, having your students turn to their neighbor(s) to discuss the answer and come to consensus.
This time-honored technique for improving lectures has been given many names, such as the “one-minute paper,” “peer instruction,” as well as “informal”
cooperative grouping.” Some example questions for two-dimensional motion are shown on the following pages. After students discuss the answer for a few minutes, the instructor asks for a call of hands for each answer (or use an electronic system of clickers).
There are many times during a lecture you can stop and ask a short question of informal groups. For example, you can ask a question before you start a lecture to find out what students already know, and focus their thoughts on the lecture to come (see Figure 9.7a). You can ask a question after lecturing for some time to see if students have understood the main ideas of your lecture (see Figure 9.7b). When you are demonstrating how to solve a problem, you can ask students about the next step in the problem solution (see Figure 9.7c).
Chapter 9: Course Structure for Cooperative Problem Solving
121
Figure 9.7. Examples of group questions to use in lecture.
Figure 9.7a. Example of group question to use before a new topic is introduced.
1. A ball is thrown into the air and follows the path shown at left.
Which arrow best represents the direction of the ball’s acceleration at point B?
At point C? At point D?
Which arrow best represents the direction of the ball’s velocity at point B?
At point C? At point D?
Figure 9.7b. Example of a group question to check for understanding after the topic is introduced.
Three identical balls are simultaneously thrown with the three velocities shown by the vectors in the diagram at right.
Ignoring air resistance, which of the following statements is true?
A. They all move through the air with the same speed.
B. They hit the ground at the same place.
C. They remain in flight for the same length of time.
D. While all three balls are in flight, they are always at the same vertical distance above the ground.
E. While all three balls are in flight, they are always the same horizontal distance from the starting point.
Figure 9.7c. Example of group question to use for moving on to the next step..
A ball rolls off a flat roof that is 5 meters high. One second later, the ball lands 15 meters from the house at an angle from the ground. When the ball lands, the horizontal
component of its velocity (vx) is 15 meters/second and the vertical component of its velocity (vy) is 10 meters/second.
122
Part 2: Using Cooperative Problem SobvingFigure 9.8. Examples of informal group questions for before and after a demonstration.
Figure 9.8a. Example prediction question before a demonstration
Two balls will be released from the same height at the same time. Ball A is dropped straight down, while B is given a horizontal kick. Which ball do you think will hit the floor first?
A. Ball A will hit the floor first.
B. Ball B will hit the floor first.
C. Both balls will hit the floor at the same time.
D. There is not enough information is given.
E. I don’t have any idea.
Figure 9.8b. Example confirmation question after a demonstration.
Two balls were released from the same height at the same time. Ball A was dropped straight down while ball B was given a horizontal kick. Which ball hit the floor first?
A. Ball A hit the floor first.
B. Ball B hit the floor first.
C. Both balls will hit the floor at the same time.
D. I didn’t hear when the balls hit the floor.
Finally, it is very helpful to ask questions before and after a demonstration. A prediction of what students think will happen in the demonstration (and why) helps focus student’s attention on the purpose of the demonstration and provides you with information about your students’ alternative conceptions (misconceptions). An example prediction question before a demonstration is shown in Figure 9.8a.
Because some students’ alternative conceptions are so strong that they “see” what they expect to see, also ask students what they observed right after the
demonstration (see Figure 9.8b).
Several resources are available for conceptual questions that can be used for informal groups during lectures. In his book Peer Instruction: A User’s Manual, Eric Mazur4 provides many conceptual questions. There are many good questions in Lillian McDermott and Peter Schaffer’s book, Tutorials in Introductory Physics and Homework Package.5 In addition, Tom O'Kuma, David Maloney, and Curtis
Hieggelke6 have published ranking tasks, which make excellent conceptual questions for informal groups, in their book Ranking Task Exercises in Physics: Student Edition.
A B A B
Chapter 9: Course Structure for Cooperative Problem Solving
123
There are other advantages to starting slowly with informal groups in your lecture.
First, it gives you a baseline from which to judge whether CPS is successful for you.
Before you start CPS, you can collect some data from your course. For example, you could collect student answers to informal-group questions. You could also give the Force Concept Inventory7 to your students as a pretest and posttest so you can compare your students’ gains with national norms for this test at similar
institutions.8 You can also examine a sample of problem solutions from each test to determine the kinds of errors are your students making and how well they are expressing themselves.
Second, you may need time to review the available problem-solving frameworks, and modify these frameworks to match your preferences (see Chapter 14). It is be helpful to practice demonstrating your preferred framework when you solve problems in lecture. We have found professors often have difficulty putting themselves in the minds of students and demonstrating a competent framework.
Remember, the “problems” in introductory physics are not real problems for you. It is difficult to ask yourself continually: “What would I do next if I didn’t know how to solve this problem already?”
Remember the 2nd Law of Instruction. Don’t change course in midstream. We do not recommend starting CPS in the middle of a course. The students have already set their behavior patterns and will resist any changes.
ENDNOTES
1 For examples of problem-solving labs, go to our website:
http://groups.physics.umn.edu/physed/Research/PSL/pslintro.html.
2 For more information about Technology Enhanced Active Learning (TEAL) classrooms ant MIT, go to http://web.mit.edu/edtech/casestudies/teal.html.
3 For the data supporting this statement, see Heller, P., Keith, R., & Anderson, S.
(1992). Teaching problem solving through cooperative grouping. Part 1: Groups versus individual problem solving, American Journal of Physics, 60(7), 627-636.
4 Mazur, E. (1992). Peer instruction: A user's manual, Upper Sadler River NJ, Prentice Hall.
5 McDermott, L.C. and Shaffer, P.S., (2002). Tutorials in introductory physics and homework package, Upper Sadler River NJ; Prentice Hall
6 O’Kuma, T.L., Maloney, P.D., & Hieggelke, C.J. (2000). Ranking task exercises in physics: Student edition, Upper Sadler River NJ, Prentice Hall
7 Hestenes, D., Wells, M., & Swackhamer, G. (1992). Force concept inventory, The Physics Teacher, 30, 141-158
124
Part 2: Using Cooperative Problem Sobving8 Hake, R. (1998). Interactive-engagement vs traditional methods: A six thousand student survey of mechanics test data for introductory physics courses. American Journal of Physics, 66: 64-74.