Cooperative Problem Solving In Physics A User's Manual

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Cooperative Problem Solving in PhysicsA User’s ManualWhy? What? How?STEP 1Recognize the ProblemWhat's going on?STEP 2Describe the problem in terms of the fieldWhat does this have to do with . ?STEP 3Plan a solutionHow do I get out of this?STEP 4Execute the planLet's get an answerSTEP 5Evaluate the solutionCan this be true?Kenneth HellerPatricia HellerUniversity of MinnesotaWith support from the National Science Foundation, University of Minnesota, and U.S.Department of Education Kenneth & Patricia Heller, 2010

AcknowledgmentsIn reaching this stage in this work, we gratefully acknowledge the support of the University ofMinnesota, the U.S. Department of Education FIPSE program, and the National ScienceFoundation. This work would not have existed without the close cooperation of the Universityof Minnesota School of Physics and Astronomy and Department of Curriculum and Instruction.We have incorporated the suggestions of many faculty members from both Physics andEducation at the University of Minnesota and other institutions that have communicated with usat workshops, meetings, and by e-mail. This work has depended on the efforts and feedback ofmany graduate student teaching assistants in the School of Physics and Astronomy over theyears. Much of this development is directly based on the research of the graduate students inthe University of Minnesota Physics Education Program: Jennifer Blue, Tom Foster, CharlesHenderson, Mark Hollabough, Ron Keith (deceased), and Laura McCullough. We are indebtedto our colleagues in the Physics Education community for their ideas, insights, and research.Finally we would like to thank Arnold Arons for his inspiration and guidance that has lasted alifetime.

Table of ContentsChapter 1. IntroductionHow to Use This BookCourse Content and Structure for Cooperative Problem SolvingImplementing Cooperative Problem SolvingOur Laws of Instruction and other Frequently Used Icons13459Chapter 2. Connecting Students, Physics, and Problem SolvingWhy Teach Physics through Problem Solving?What Students Typically Learn Through Problem SolvingWho Benefits?1315171822Chapter 3. Combating Problem Solving that Avoids Physics27Part 1 – Teaching Physics Through Problem SolvingHow Context-rich Problems Help Students Engage in Real Problem SolvingThe Relationship Between Students’ Problem Solving Difficulties and the Designof Context-Rich ProblemsHow to Discourage Students from Memorizing FormulasChapter 4. Building Physics into Problem SolvingWhat Is a Problem-solving Framework?A Physics Example: The Competent Problem-solving FrameworkExample of an “Ideal” Student’s Problem SolutionProblem Solving as A Series of TranslationsInitial Objections to Teaching a Problem-solving FrameworkChapter 5. Reinforcing Student Use of a Problem-solving Framework28313337384044535559Flow-Charts of Problem-solving DecisionsInstructor Problem Solutions on Answer SheetsPutting Together the Scaffolding for Students616868Chapter 6. Why Cooperative Problem Solving (CPS)75The Dilemma and a SolutionA Framework for Teaching and Learning Introductory Physics:Cognitive ApprenticeshipCourse Structures and Cognitive ApprenticeshipPart 2 – Using Cooperative Problem SolvingChapter 7. Cooperative Problem Solving: Not Just Working in GroupsTwo Examples: Traditional Groups and Cooperative GroupsElements of Cooperative LearningAchievement for Traditional and Cooperative Groups: SummaryChapter 8. Group Problems and Managing GroupsGroup Structure and ManagementAppropriate Group Problems75768387898991949797105Chapter 9. Course Structure for Cooperative Problem-solving SessionsScheduling: Continuity of Group InteractionsWhat Resources Are Needed to Implement CPSi109110111

Appropriate Course GradingConsistent Grading of Problem SolutionsGetting Started115117120Chapter 10. Results for Partial and Full Implementation of CPSImprovement in Problem Solving PerformanceImprovement in Knowledge OrganizationImprovement in Students’ Conceptual Understanding of Forces and Motionas measured by the Force Concept Inventory (FCI)Improvement in Students’ Conceptual Understanding of Forces and Motionas measured by Open Response Written QuestionsPart 3 – Teaching a CPS Session125125130132135145Chapter 11. Preparation for CPS Sessions147Assign Students to Groups with RolesPrepare Problem & Information SheetWrite the Problem SolutionPrepare an Answer Sheet (Optional)Prepare Group Functioning Evaluation Sheets (as Needed)Prepare MaterialsChapter 12. Teaching a CPS Session149150152154154157159Opening Moves (Steps 0 – 2)Middle Game (Steps 3 – 4)End Game (Steps 5 – 7)159161163Chapter 13. Coaching Students During Group WorkMonitor and DiagnoseIntervene and CoachCoaching Dysfunctional GroupsCoaching Groups with Physics Difficulties165166166167171Part 4 – Personalizing a Problem-solving Framework, Problems, and SolutionsChapter 14. Personalize a Problem Solving FrameworkStep 1. Clarify the SituationStep 2. Gather Additional InformationStep 3. Construct Your Problem-solving FrameworkStep 4. Reconcile Your Framework with Your Textbook Framework (if necessary)Step 5. Evaluate Your FrameworkChapter 15. Building Context-Rich Problems from Textbook ProblemsReview of the Properties of Context-rich ProblemsConstructing a Context-rich Problem from a Textbook ProblemPractice Building Context-rich Problems from Textbook ProblemsChapter 16. Judging Context-Rich Problem Suitabilityfor Individual or Group WorkProblem Difficulty TraitsDecision Strategy for Judging the Suitability of Problems for Their Intended UsePractice Judging Context-rich 19222

Bibliography229AppendicesAppendix A: Survey of DepartmentsAppendix B: Context-Rich Mechanics ProblemsAppendix C: Context-Rich Electricity and Magnetism ProblemsAppendix D: Problem Solving Laboratoriesiii235239261271

1Chapter 1IntroductionIn this chapter: How to use this book. Course content and structure for Cooperative Problem Solving. Preparation to implement Cooperative Problem Solving (CPS). Steps needed to adapt CPS. What to expect after implementing CPS. Our “Laws of Instruction” and frequently used icons in this book.The most effective teaching method depends on the specific goals of acourse, the inclination of the instructor and the needs of the students,bound by the constraints imposed by the situation. There is no known"best" way to teach. Cooperative Problem Solving is one teaching tool that mayfit your situation. It is not the "magic bullet" that, by itself, will assure that all ofyour students achieve your goals for the course. It is, however, based on a solidresearch foundation from cognitive psychology, education, and physicseducation. We have over two decades of experience testing and refiningCooperative Problem Solving at it is used by many professors teachingthousands of students and different institutions. Cooperative Problem Solvingcan be used as the major focus of a course, or as a supplement in combinationwith other teaching tools.What is Cooperative Problem Solving (CPS)? This book is designed to answerthis question. First lets describe what you would see if you observed a 50minute class engaged in Cooperative Problem Solving. As they walk into theclass, students sit in groups of three, facing each other and talking. Theinstructor begins class by talking about 5 minutes, setting the goal for thissession. For example, the instructor might remind the class that they have juststarted two-dimensional motion, that the problem they will solve today wasdesigned to help them understand the relationship between one-dimensional andtwo-dimensional motion, and they will have 35 minutes to solve the problem.The instructor also informs the students that at the end of 35 minutes, onemember from each group will be randomly selected to put part of their solutionon the board. The instructor then gives each group a sheet with the problem

2Part 1:Teaching Physics Through Problem Solvingand all the fundamental equations they have studied in class to this point intime.The class is quiet for a few minutes asstudents read the problem, then there isa buzz of talking for the next 30minutes. No textbooks or notes areopen. Group members are talking andlistening to each other, and only onemember of each group is writing on apiece of paper. They mostly talk aboutwhat the problem is asking, how theobjects are moving, what they knowand don’t know, and what they need toassume, the meaning and application ofthe equations that they want to use, andthe next steps they should take in theirsolution. There are disagreements about what physics applies to the problemand what that physics means in this situation.The instructor circulates slowly through the room, observing and listening,diagnosing any difficulties the group is having solving the problem, andoccasionally interacting with the groups that the instructor judges need help.This pattern of listening to groups and short interventions continues for about30 minutes. At the end of that time, the instructor assigns one member fromeach group to draw a motion diagram and write the equations they used to solvethe problem on one of the boards on the walls. That member can ask for helpfrom the remaining group members as necessary. The instructor then tells theclass to examine what is on the board for a few minutes to determine thesimilarities and differences of this part of each group’s solution. The instructorthen leads a class discussion that highlights the similarities and differences andclarifies which are correct and which are incorrect. As the students are aboutleave class, the instructor hands out a complete solution to the problem.Almost everyone looks over the solutions. Some groups celebrate and othersgroan.The description above gives a image of a CPS class but does not include all thepreparations and scaffolding that go along with implementing CPS. In theremainder of this chapter we first outline how to use this book. This is followedby an outline of how CPS influences both content and course structure. Thenext section in this chapter includes a checklist for preparing to implement CPS,a brief outline of the steps needed to adapt CPS, and what to expect afterimplementing CPS. Finally, the last section of the chapter introduces some“laws of instruction” and icons that are frequently used in this book.

IntroductionHow To Use This BookThis book has four parts, described briefly below:Part I. Teaching Physics Through Problem solving. These six chaptersprovide background about the unsuccessful problem-solving strategies ofbeginning students, how context-rich problems and a problem-solvingframework help students engage in real problem solving, and why CooperativeProblem Solving (CPS) is a useful tool for teaching physics through problemsolving.Part 2. Using Cooperative Problem Solving. These four chapters describethe foundation of cooperative problem solving and provide detailed informationabout how to implement CPS for maximum effectiveness. This informationincludes what are appropriate group problems, how to manage groups, and thecourse structure and grading practices necessary to implements CPS. The lastchapter provides the research evidence that CPS improves both students’problem-solving skills and their conceptual understanding of physics.Part 3. Teaching a CPS Session. These three chapters provide informationabout how to prepare for a cooperative problem solving session, how toimplement the session, and how to monitor and intervene with groups as theyare solving problems.Part 4. Personalizing a Problem solving Framework and Problems.These three chapters provide some advanced techniques building upon knowledge fromprevious chapters and assuming that you have already tried using cooperative grouping.This part provides details on how to construct a problem-solving framework foryour students, how to write context-rich problems, and how to judge or adjustthe difficulty of a context-rich problem.The second page of each part summarizes the purpose and content of eachchapter of that part (pages12, 80, 134, and 164). You may want to read thesesummaries before you to help guide your reading.Random AccessWe have tried to write this book so that you can jump in anywhere you find anissue of interest. Of course you can also read it straight through. For toachieve that flexibility, each chapter contains frequent references to other relatedchapters. There is also some repetition of content to allow this type of randomaccess reading.Endnotes and ReferencesThe endnotes at the end of each chapter provide comments as well as referencesto seminal research papers or research reviews if you are interested in pursuing a3

4Part 1:Teaching Physics Through Problem Solvingsubject further. Since the research articles and reviews often apply to more thanone chapter, a bibliography is provided at the end of the book. To keep the listof references to a minimum, we have left out many important papers and booksthat can be found in the references of those cited.Course Content and Structure for Cooperative Problem SolvingTopics CoveredThe use of Cooperative Problem Solving (CPS) hasonly minor implications for how many topics you canincorporate into your course, and none, as far as weknow, for the order of those topics. Those decisionsmust be based on other factors such as the success ofyour students in meeting the goals of your course. CPS has been designed forcourses with a goal of having the majority of students reaching the appropriatelevel of a qualitative and quantitative understanding of all of the topics in thecourse. There is no method of instruction or course structure that can besuccessful if the course content is presented toorapidly for the average student in the class to have achance of understanding it.Class Size and Course StructureThe Cooperative Problem Solving techniquesdescribed in this book can be used under conditions that are less than ideal. Weteach at a large research-orientated state university with over 2000 students persemester taking physics courses taught in this manner. About one quarter ofthese students are in algebra-based courses and the rest are in calculus-basedcourses. Essentially all of these students take physics because their majorrequires it. The number of physics majors in any of the introductory courses isnegligible.The courses at our University have the very traditional structure of three largefifty-minute lectures per week, accompanied by smaller two-hour laboratoriesand fifty-minute discussion sections. Many different professors teach the lecturesections with the help graduate and undergraduate teaching assistants primarilyresponsible for the coordinated laboratories discussion sections. The teachingpersonnel changes each semester. This is not the best structure for CPSinstruction but it is still effective.At other institutions where Cooperative Problem Solving has been usedeffectively, teaching situations range from large classes with separated lecture,laboratories, and discussion sections, to smaller classes with all functionsinterwoven, taking place in a single room. Naturally each professor adapts CPSto fit his or her teaching style and situation. These techniques are being used atlarge research-oriented universities, comprehensive state universities, privateuniversities colleges, and community colleges.

IntroductionImplementing Cooperative Problem SolvingIf you decide to teach a physics course using Cooperative Problem Solving(CPS), you need to be prepared to: Explicitly show students how to use the fundamental principles andconcepts of physics to solve problems (Chapters 4, 5 and 11). Use problems that require students to make decisions based on aworking knowledge of physics (Chapters 3 and 8). Have students solve problems while coached in groups, as well as solveproblems by themselves (Chapters 7, 12 and 13). Grade student problem solutions for communicating the application ofphysics while using sound problem solving techniques as well as thecorrectness of the solution. Grade students in a manner that emphasizesindividual achievement but does not discourage cooperation (Chapter9). Assume that all parts of the instructional process must be repeated everytime a new topic is introduced.Of course, "the devil is in the details." Successful implementation requiresattention to the learning process as well as the teaching process. In designingCooperative Problem Solving we tried many things that did not work, althoughthey seemed to be reasonable extensions of fundamental learning research orcommon sense experience. Even techniques that work well with one class maynot give as large an effect in another type of class. This is not surprisingbecause the learning process is complex. As with any complex system, theparameters that influence learning must be tuned for each particular set ofconstraints to achieve large effects. This book describes the sensitiveparameters that we have found in our research and development work. Theymust be matched to the goals and constraints of your situation.Overview of Adapting Cooperative Problem SolvingThere is no point in you making exactly the same mistakes we did in gettingCooperative Problem Solving to work. Based on the experience of faculty atother institutions that have adapted these techniques to their situations, wesuggest that you begin by following as much of our prescription as possible inyour situation. After you have tried it once, you will have a good idea of what tochange to make it work better for you.The following is an outline of what to do. The details and rationale are given inthe remainder of this book.Step Determine the most important goals for studentlearning in your class. For example, the goals below arethe top goals from a survey of the engineering faculty5

6Part 1:Teaching Physics Through Problem Solvingthat require their students to take introductory physics at the University ofMinnesota. See Appendix A for a copy of the survey. Know the basic principles underlying all physics. Be able to solve problems using general qualitative logical reasoningwithin the context of physics. Be able to solve problems using general quantitative problem-solvingskills within the context of physics. Be able to apply the physics topics covered to new situations notexplicitly taught by the course. Use with confidence the physics topics covered.Step Get or write context-rich problems that require students to: Directly use the physics concepts you want to teach; Directly address the goals of your course; and Practice their weakest problem solving skills.Appendices B and C contain examples of context-rich problems inmechanics and electromagnetism. See Chapter 3 for a description ofcontext-rich problems, Chapter 15 for how to write context-rich problems,and Chapter 16 for how to judge and adjust the difficulty of those problems.Step Adopt a research based, problem-solving framework that you wantyour students to use to solve problems. Make every step of the processexplicit to the students. Always demonstrate the same logical and complete problem-solvingprocess throughout the course no matter what the topic. Explain all the decisions necessary to solve the problem. Show every step, no matter how small, to arrive at the solution. Hand out or have on the web examples of complete solutions toproblems showing how you expect students to communicate theirthought process in problem solutions. Allow each student to make their own reasonable variations of theframework for their solutions.See Chapter 6 for additional information about demonstrating a problemsolving framework. Chapter 4 provides a description and example of aresearch based problem-solving framework, and Chapter 5 providesexamples of complete problem solutions using the framework. Chapter 14describes how to personalize a framework to match your preferences andthe needs of your students.

IntroductionStep Require that your students practice solvingproblems in small groups while you or anotherinstructor provide timely guidance. Use cooperative groups of three, or at mostfour. Structure the groups so that they really worktogether on the solution. Use a problem appropriate for group work.Make sure no notes or books are available to students while they solveproblems in groups. Grade the results of these group problems, only occasionally, for alogical and complete solution using correct physics reasonablycommunicated.See Chapter 7 for a description of how Cooperative Problem Solving isdifferent from having students work in groups, and Chapters 8 - 9 forappropriate group problems, structuring and managing groups, and grading.See also Chapters 11-13 for how to prepare for and teach a CooperativeProblem Solving session.Step Encourage students to solve homework problems by themselves usingcorrect physics communicated in a logical and complete manner. If homework is graded, make sure the gradedepends on logical and complete solutions, notjust a correct answer. If you cannot grade homework in this manner (wedon’t have the resources) make at least oneproblem on your tests an obvious modification ofa homework problem. Point this out to your students. A week or twobefore each test, give students a sample test to work on at home.See Chapter 9 for how to grade problem-solving performance.Step Give the same type of problems on your examinations that yourstudents solve in their groups. Grade them based on the student behavioryou wish to encourage Grade on an absolute scale to encourage student cooperation. Grade for well-communicated problem solutions presented in anorganized and logical manner. Give enough time to actually solve problems based on makingdecisions about physics and writing complete solutions.See Chapters 9 for how to grade problem-solving performance.7

8Part 1:Teaching Physics Through Problem SolvingAfter becoming comfortable with the basics of Cooperative Problem Solving,you can improve student achievement by using all of your course resources toaddress your goals. For example, all demonstrations can be presented asexamples of problem solving. In addition, laboratories can be structured so thatthey give students practice in problem solving that can be checked bymeasurement. See Appendix D or visit our rch.html) for more informationabout problem solving labs.What to Expect After Implementation of CPSIf the implementation of Cooperative Problem Solving (CPS) is going well, byabout half way through your term you should notice some changes in your class.When you visit discussion sections you will hear students talking to each otherabout physics concepts, and beginning to use the language of physics. Studentproblem solutions on exams will look neater and more organized and thus easierto grade. By the end of the term you will find that student drop-out rates, itthey were high, will have decreased. Student conceptual knowledge as measuredby objective exams such as the Force Concept Inventory will have improved.The problem-solving performance of your students will also improve. Yourstudents will be more willing to tackle new and unusual problems. They willtend to begin problems by thinking about what physics to apply. Typically, youcannot expect things to go smoothly until the second time you have taught acourse after you implement any significant change.Of course you will not be 100% successful and not all your students will likeCPS. Judge your success by comparing to results of previous classes. Researchshows that in traditional classes, about 20% of the students show significantimprovement. Our goal is to reach 2/3 of the students 2/3 of the time. In thebeginning, try not to worry if one of five groups is dysfunctional. That's an 80%success rate! Spend most of the time on most of the students. Next timearound you can try to tweak the course structure to reach the others. Makeincremental changes. Try to improve your results just a little bit each year.Students are usually the most conservative element in the educational process.They may not like how things are now taught, but they resist any changes. If thecourse is noticeably different than it was the previous year, students will blametheir difficulties on those changes. Be patient and supportive of your studentsat the beginning. You must believe that the changes are for the better. If youdon't have confidence in what you are doing, then you can't expect them to.Naturally you will meet the most resistance from students that have beensuccessful previously. Human beings do not like to change, especially if theyhave been successful. On the other hand, students who were expecting to havetrouble will be immediately grateful. As long as you are firm and positive andthe students are more successful than they imagined, they will be positive aboutthe changes at the end of the course. Interestingly we have found that thestrongest support for Cooperative Problem Solving comes from some of the

Introductionstudents who resisted the most at the beginning. In the hands of a very goodstudent this is a very powerful tool and they recognize it.Our Laws of Instruction and Other Frequently Used IconsTo guide the actual implementation of a course design, we have invented, onlyhalf seriously, four "Laws of Instruction" in analogy with the "Laws ofThermodynamics." In the same spirit as classical thermodynamics, these "laws"describe robust empirical observations that are based on the current state ofknowledge of human behavior and learning.1 The overriding principle of humanbehavior addressed by the laws is that most human beings do not like to changetheir behavior. As with thermodynamics, our “laws” are statistical in nature -you will certainly know of specific counter examples.Our Laws of Instruction are described below.If you don't grade for it, students won't do it.It would be wonderful if we lived in a world in which students were intrinsicallymotivated to learn new things, and our physics class was the only class studentswere taking. But it just isn’t so. Humans expend the minimum energy necessaryto survive. Students expend the minimum energy necessary to get what theyconsider a “good” grade.Doing something once is not enough.The most effective way for humans to learn any complex skill is apprenticeship.For example, a new apprentice would learn tailoring in a busy tailor shop, wherehe or she is surrounded both by master tailors and other apprentices, all engagedin the practice of tailoring at varying levels of expertise. Masters teachapprentices through a combination of activities called modeling, scaffolding,coaching and fading.2 Repetition of these activities is essential.Modeling. The apprentice repeatedly observes the master demonstrating (ormodeling) the target process, which usually involves many different but relatedsub-skills. This observation allows the apprentice to build a mental model ofthe processes required to accomplish the task.Scaffolding. Scaffolding is structure that supports the learning of theapprentice. Scaffolding can include a compelling task or problem, templates andguides, practice tasks, and collections of related resources for the apprentice.Usually scaffolding is removed as soon as possible but may need to bereintroduced later for a new context.Coaching. The apprentice then attempts to execute each process with guidanceand help from the master (i.e., coaching). A key aspect of coaching is thesupport, in the form of reminders or help that guides the apprentice toapproximate the execution of the entire complex sequence of skills, in their ownway. The interaction with other learners provides the apprentice with instantfeedback through peer coaching and a calibration of progress, helping focus the9

10Part 1:Teaching Physics Through Problem Solvingeffort needed for individual improvement.Fading. Once the apprentice has a grasp of the entire process, the masterreduces the scaffolding (i.e., fading), providing only limited hints, refinements,and feedback to the apprentice, who practices by successively approximatingsmooth execution of the entire process. The interplay between observation,scaffolding, peer interactions, expert coaching, and increasingly independentpractice helps the apprentice develop self-monitoring and correction skills andintegrate those skills with other knowledge to advance toward expertise.Problem solving is a complex mental skill. Like learning a complex physicalskill, students learn physics problem solving best in an environment in whichproblem solving is modeled, the process is scaffolded, they are coached in theprocess, and the structure and coaching fades as the students become betterproblem solvers. All of this should happen in what is called an environment ofexpert practice in which the student should be able to answer the followingthree questions at any time in the course:1. Why is whatever we are now learning important?2. How is it used?3. How is it related to what I already know?[See Chapter 6 for a more detailed description of cognitive apprenticeship.]Don't change course in midstream; structure early then graduallyreduce the structure.Humans are very resistant to change. It is easier on both instructors andstudents to start with what may seem a rigid structure (e.g., a problem-solvingframework, roles for working in groups), then fade gradually as the structure isno longer needed. It is almost impossible to impose a structure in the middle ofthe course, after you discover that students need it.Make it easier for students to do what you want them to do andmore difficult to do what you don’t want.Humans will persist in apreviously successfulbehavior until it is no longerviable for survival. Learninga new way of thinking is adifficult, time consuming,and frustrating process, likeclimbing a steep mountain.For most students, expert

Combating Problem Solving that Avoids Physics 27 How Context-rich Problems Help Students Engage in Real Problem Solving 28 The Relationship Between Students' Problem Solving Difficulties and the Design of Context-Rich Problems 31 . are solving problems. Part 4. Personalizing a Problem solving Framework and Problems.

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