Teaching Problem Solving Skills

Transcription

1 Teaching Problem Solving Skills Kathleen Ropella Francisco Sotomayor After attending this session, you should be able to: Identify at least two problem solving tips and how to use them in class. Identify at least two problem solving mistakes and how to avoid them. Prepare and complete after-action review (with Wankat s strategies). During this session, think about: What is your favorite problem solving technique? When does it work well? When does it not work well? Which part of problem solving is most difficult for you? For your students? How should you approach answering questions without a right answer? Action items: Before student interactions, develop three questions students may ask. Review and complete the after-action review grid (see Resources page 4). Contact an Engineering Teaching Consultant to discuss problem solving skills. Plenary Resources: Concurrent Resources: Workshops/Seminars: tiny.cc/plenary tiny.cc/concurrent tiny.cc/seminars Center for Research on Learning and Teaching in Engineering crlte.engin.umich.edu

2 Teaching Problem Solving Skills Activities Role play scenarios (student and observer) Practice Problem #1 Write the 3 letters that should come next in this series: B A A C E E D I I E M M F Practice Problem #2 What would the seventh line in this pyramid be? Practice Problem #3 What is the next symbol in this sequence? CRLT-Engin Page 1

3 Role play solutions (for GSI ONLY) Practice Problem #1 Answer: The letters B, C, D, E, F form a sequence, so one can expect to have this sequence be continued. So the next element in the sequence would be G. This letter would go in the last place of the three letters asked. The two first letters should be the same, as the general pattern follows a 1-letter, 2-letter sequence. E is the fourth letter from A; I is the fourth letter from E, and M is the fourth letter from E. Therefore one can expect to have the fourth letter from M be the repeated letter in the first two places. This is letter Q. So the three next letters are: QQG. Practice Problem #2 Answer: The trick to solving the number pyramid is to forget any math you were trying to apply and instead, simply read the lines aloud. You ll notice that each line describes the line above it, so the third line, read two ones, describes the line above it, which is indeed simply two numeral ones. The fourth line reads: one two, one one again simply describing the line above it. Thus, the seventh line would read one three, one one, two twos, two ones, or: Practice Problem #3 Answer: The answer is not provided for this problem. While this problem has an intended solution, many solutions can be rationalized to this open-ended problem. Do your best to work with the student towards an answer you both agree is reasonable. Note: if you are interested in knowing the intended answer, see that the first picture is the number one and its mirror image. The second picture is the number two and its mirror image and so on. CRLT-Engin Page 2

4 Teaching Problem Solving Skills Resources Common mistakes of instructors 1 While there is no "right" or "wrong" way to help students to solve problems, there are some approaches that tend to be more or less effective than others. We present an (incomplete) list of mistakes that are very easy to make as an instructor. Even the best of instructors can find themselves committing errors such as these, so revisit this list often. Solving it for them Your job is not to show the student how a particular problem should be solved, but rather to help them discover for themselves an appropriate method for approaching the problem. This can sometimes be frustrating for both parties, as you will most likely know the answer from the beginning, and the student will often care only about obtaining such an answer. However, it is unlikely that deep learning will occur if the student does not make the mental connections for themselves. Letting the student consume too much time If you feel that you have given an appropriate amount of assistance to any individual student, you may want to suggest to the student that they think about the problem some more alone, and to come back later if no progress has been made. Often they will be able to figure out the solution on their own, which in the end is probably better anyway, as it makes them less dependent on the hints of the instructor. Giving discouraging feedback There is nothing more detrimental to a student s self-esteem than the discouragement of an instructor. Phrases such as "No, you're doing it all wrong" or "This is so simple, why can't you see it?" send a message that they are somehow deficient or incapable. Instead, try to convey that you understand their frustration, and are confident that they will discover the solution in due time. Not considering alternative approaches You may find that after several attempts to lead the student in the right direction, they are still unable to see the light. When this happens, feel free to stop for a moment and reevaluate the approach you are taking as an instructor. Take your time. You may realize that there is a simpler explanation than the one you have been trying to give. Giving bad advice When you feel rushed and are under pressure to serve several students, it is easy to explain something either too rapidly or altogether incorrectly. Students tend to hang on every word of their instructor, especially when seeking help, so such mistakes can easily throw them off track. If you feel that you are going too fast or are giving inconsistent answers, slow down and take smaller steps. As you are explaining a procedure or process, check frequently for student understanding. Not listening to the student fully It is common that people try to sense what the other is saying based on a few sentences at the beginning of the conversation, and cut them off midway. While it is important to gauge the reactions of the student, we must patiently listen to the students, and then respond. Students try to get a boost to their self-esteem by stating the basics (like the problem data) initially before coming to the problem. That does not mean they know the subject thoroughly. Conversely, just because the student is very tense does not mean that they do not understand the basics at all. 1 Prepared by Michael D. Moffitt and Shankara Kuppa for 2005 Engineering GSI Teacher Training. CRLT-Engin Page 1

5 Comparison of novice and expert problem solvers 2 Characteristic Novices Experts Memory Attitude Stores in small pieces Files few items Tries once then gives up Is anxious Stores in chunks or patterns Files ~50,000 items Is persistent Is confident Categorization Recalls superficial details Recalls fundamentals Problem statement Simple problems Has difficulty redescribing Is slow and inaccurate Jumps to conclusions Is slow Works backward Uses many techniques to redescribe Is fast and accurate May redefine several times Is fast (up to 4x faster) Works forward with known procedures Strategy Uses trial and error approach Uses a strategy Information Parts of harder problems First steps for harder problems Sketching Equations Solution procedures Progress of solution Approach when stuck Accuracy Evaluation of result Mistake or failure to solve problems Action Decisions Doesn t know what is relevant Cannot draw inferences from incomplete data Does NOT analyze into parts Tries to calculate Often does not sketch Memorizes or looks up detailed equations for each circumstance Uses uncompiled procedures Decides how to solve after writing equation Does not monitor progress Guesses Quits Is not concerned with accuracy Does NOT check Does not evaluate results Ignores mistakes Develops new problem solving methods Sits and thinks Is inactive Is quiet Does NOT understand process Has no clear criterion Recognizes relevant information Can draw inferences Analyzes parts Proceeds in steps Looks for patterns Defines and draws Explores alternatives Uses considerable time to sketch Presents abstract principles, shows motion Uses fundamentals to derive needed results Uses compiled procedures Conceptualizes equation and solution method as single procedure Keeps track of progress Checks off steps versus strategy Uses heuristics Perseveres Brainstorms Is very accurate Checks and rechecks Evaluates based on broad experience Learns from mistakes Is very active Writes questions or draws flow paths Subvocalizes (talks to self) Understands decision-making process Has clear criterion 2 Based on Wankat, P.C., & F.S. Oreovicz. (1993). Teaching engineering. New York: McGraw-Hill. CRLT-Engin Page 2

6 Wankat s Problem Solving Strategy The following is a sample strategy for solving problems 3. As you made the transition from novice to more expert problem solver by progressing from freshman year in college to graduate school, you have likely adopted a similar strategy. However, it is likely that you have not verbalized this strategy. When you act as a GSI, you should model a distinct strategy to students, and you should advocate that the students follow the approach. Even advanced students, those who can skip steps and those who resist such a formalized problem-solving approach, will eventually benefit from a disciplined approach to problem solving. 0 I can Motivation step work on student s self-confidence and remove anxiety as obstacle to problem solving. 1 Define List knowns and unknowns, draw figure correct figures are critical. 2 Explore Think about it, or ponder in a general sense. Is this a routine problem? What are alternative solution methods? What are some likely limits on the answer? 3 Plan Use formal logic to set up steps of the problem. Write appropriate equations for each step. Consider a flowchart for long problems. Solve without numbers. This step may be difficult for serial thinkers as opposed to global thinkers. 4 Do it Put in values and calculate answer. Novices want to do this first. Better problem solving skills will result if the Plan and Do it stages are separated. Enforce this! 5 Check Check for calculation errors, but also compare with limits determined in the Explore step. Also compare answer to common sense. 6 Generalize Almost never done by novices unless they are explicitly told to do it. What has been learned about the content? Could the problem have been solved more efficiently? Was there a term that could possibly be neglected in general? If problem was not solved correctly, what was done wrong? Students should get useful feedback and re-solve incorrect problems. 3 Based on Wankat, P.C., and F.S. Oreovicz. (1993). Teaching engineering. New York: McGraw-Hill. CRLT-Engin Page 3

7 Problem solving preparation and after-action review HW Problem Before problem solving session What will be my approach to solving this problem? 0 I can What is motivation? 1 Define List knowns and unknowns 2 Explore What makes this problem unique? Questions students may ask: Questions Answers After-action review Questions that students asked: Questions Answers What was my approach to solving this problem? What will I do differently next time? What did I learn? CRLT-Engin Page 4