Context-rich problem for cooperative group problem solving - Electric Force
This is a problem that students are asked to solve in cooperative groups during a 50 minute period. This problem occurs within the first week of studying electrostatic forces during the second semester of introductory physics for biology students. Students relate concepts from the first semester of physics, specifically forces, vectors, and free-body diagrams, to the electric force. While students work in groups of 3 or 4 to co-construct the solution to the problem, a coach who is either a graduate student or advanced undergraduate student, coaches a group as necessary.
After the groups work on co-constructing solutions and a class discussion of part of the solution, detailed solutions to the problem are handed out as the students leave.
Students should learn to analyze a situation governed by the electrostatic force and integrate the use of that force into their conceptual framework of forces. In addition students should continue to learn organized and logical procedures for constructing quantitative solutions using appropriate mathematics.
Context for Use
This is for use in a discussion section of 10-20 students in an introductory physics class at the university. The educational level is that students have taken the first semester of an introductory physics course. This activity is appropriate for students with a reasonable knowledge of algebra. Memorization of equations is discouraged by providing students will all fundamental equations and restricting students to them. The group problem solving activity takes approximately 35 minutes followed by a class discussion comparing and contrasting a selected part of the solution put up on the board by a representative of each group. This type of activity is relatively easy to use in other settings.
Description and Teaching Materials
You are working in a lab doing research on atmospheric pollution. Your group is trying to determine what unusual types of chlorinated molecules might exist in the upper atmosphere. You have been asked to determine where a chlorine ion of effective charge -e would situate itself near a carbon dioxide ion. The carbon dioxide ion you are investigating is composed of 2 oxygen ions, each with an effective charge -2e, and a carbon ion with an effective charge +3e. These ions are arranged in a line with the carbon ion sandwiched midway between the two oxygen ions. The distance between each oxygen ion and the carbon ion is 3.0 x 10-11 m. Assuming that the chlorine ion is on a line perpendicular to the axis of the carbon dioxide ion and that the line goes through the carbon ion, what is the equilibrium distance for the chlorine ion relative to the carbon ion on this line? For simplicity, you assume that the carbon dioxide ion does not deform in the presence of the chlorine ion. Looking in your trusty physics textbook, you find the charge of the electron is 1.60 x 10-19 C.
Context-rich group problem for Electrostatics (Acrobat (PDF) 37kB Mar31 09)
Teaching Notes and Tips
Difficulties include recognizing the need to independently add the components of vectors, recognizing that equilibrium means that the some of the force on an object is zero, having an organized process of doing algebra, debugging algebra using unit analysis.
Formative assessment during the class includes observing if all the students are engaged in the task and contributing and asking students questions about content or process while coaching individual groups. Assessment after the discussion session includes both group and individual performance on a test of related material using context-rich problems, performance on a multiple choice test targeting specific conceptual misconceptions, performance on standardized tests of the concepts involved, and performance on a final examination of written problems that link several of the concepts and processes involved.
References and Resources
University of Minnesota Physics Education Group
. Includes descriptions of how to build context-rich problems, organizing cooperative group sessions, and an archive of context-rich problems.