Learning to Solve Engineering Problems

1. David Jonassen Curators’ Professor University of Missouri Learning to Solve Engineering Problems

2. Assumptions Engineers are hired, retained, and rewarded for solving problems, not writing exams In order to prepare engineering students to be engineers, learning should be problem-based.

3. Why? • Authenticity - in everyday life and work, engineers constantly solve problems (especially ill-structured problems) • Intentionality - problems provide a purpose for learning (intrinsic motivation) • Conceptual anchoring - knowledge constructed while solving problems is more meaningful, more integrated, better retained, and more transferable • Ontology – knowledge that results from solving problems is more meaningful (not topic-based).

4. Issues in Learning to Solve Engineering Problems • What kinds of problems do engineering students normally learn to solve? • What do engineering students learn from that process? • How can we help students to better understand the problems they are solving so they can transfer what they know to new problems? • What kinds of problems should engineering students learn to solve? • How can we support learning to solve complex problems?

5. 1.What kinds of problems do engineering students normally learn to solve? Story Problems taught byWorked Examples

6. 2. What do engineering students learn from solving story problems? To mimic what they were taught

7. 2. What do engineering students learn from solving story problems? • count the number of variables in the problem • select an equation with that number of variables • plug the values into the equation • solve the equation for the answer

8. 2. What do engineering students NOT learn from solving story problems? What those equations mean

9. 2. What do engineering students NOTlearn from solving story problems? Conceptual understanding of the nature of the problem

10. Why? • Reliance on only quantitative representation (equations) • Successful problem solving requires • comprehension of concepts in problem • comprehension of interrelationships among concepts (mostly causal) • ability to visualize data • classify the deep structure of the problem (problem schema) • capacity to correctly sequence and evaluate the solution

11. 3.How can we help students to better understand the problems they are solving? • Help students to construct a problem schema for each kind of problem • Require students to analogically compare problems • Help students to understand mechanisms of causal relationships in problem • Use different forms of questions • Represent problems in different ways • Require students to model problems in different ways • Help students to argue for the best solution • Help students to regulate problem solving • Assess conceptual understanding of problems, not just correct answer

12. A. Help students to construct a problem schema for each kind of problem • What kind of problem is this? • Structural characteristics • Situational characteristics • Solution methods

13. InitialSpringComp-ression Represent problems as structure maps FinalSpringComp-ression InitialPotentialEnergy From Springs FinalPotentialEnergy From Springs Force Distance InitialPotentialEnergy Work FinalPotentialEnergy Spring Cons-tant Spring Cons-tant InitialPotentialEnergy From Height FinalPotentialEnergy From Height FinalTotalEnergy InitialTotalEnergy InitialHeight FinalHeight InitialKineticEnergy FinalKineticEnergy Mass Mass FinalVelocity InitialVelocity

14. Represent problems as structure maps

15. Represent problems as equation structure maps

16. Analyze conceptual elements of problems

17. B. Help students to analogically compare problems

18. Why analogically compare problems? • Surface Difference (FD) : Roller Coaster vs. Gun • Structural Similarity (PS) : Both Conservative systems

19. Why analogically compare problems? • Surface Similarity: Both Roller Coasters • Principle Difference: Conservative vs. Non-Conservative

20. C. Help students to understand causal relationships in problem using… • Animations • Simulations • Causal diagrams • Ask causal questions

21. Animations of Causal Relationships

22. Simulations demonstrate causality. Simulations alone are not enough for learning.

23. Causal Diagrams

24. Ask Causal Reasoning Questions Prediction

25. D. Use different forms of questions

26. E. Represent problems in different ways

27. F. Require students to model problems in different ways • Concept maps • Causal maps • Systems models • Simulation-building tools

28. Students model problems with concept maps

29. Model problems with expert systems D1: 'You know the mass of one mole of sample.'D2: 'You need to determine molar (formula) mass.'D3: 'Divide sample mass by molar mass.'D4: 'Multiply number of moles by molar mass.'D5: 'You know atomic mass units.'D6: 'You know molar mass.'D7: 'Divide mass of sample by molar mass and multiply by Avogadro's number.'D8: 'Divide number of particles by Avogadro's number'D9: 'Convert number of particles to moles, then convert moles to mass'D10: 'Convert mass to moles using molar mass, and then convert moles to molecules using Avogadro's number.'D11: 'Convert from volume to moles (divide volume by volume/mole), and then convert moles to moles by multiplying by Avogadro's number.’Q1: 'Do you know the number of molecules?' A 1 'yes' 2 'no'Q2: 'Do you know the mass of the sample in grams?' A 1 'yes' 2 'no'Q3: 'Do you know the molar mass of the element or compound?’ A 1 'yes' 2 'no'Q4: 'Do you know the number of moles of the sample?' A 1 'yes' 2 'no'Q5: 'Do you want to know the number of molecules?' A 1 'yes' 2 'no'Q6: 'Do you want to know the mass of the sample in grams?' A 1 'yes' 2 'no'Q7: 'Do you want to know the molar mass of the compound?' A 1 'yes' 2 'no'Q8: 'Do you want to know the number of moles of the sample? ’ A 1 'yes' 2 'no'Q9: 'Do you know atomic mass units?' A 1 'yes' 2 'no'Q10: 'Do you know the volume of a gas?' A 1 'yes' 2 'no’Rule1: IF q2a1 AND q8a1 THEN D2Rule2: IF (d1 OR q3a1) AND q2a1 AND q8a1 THEN D3Rule3: IF q4a1 AND q3a1 AND q6a1 THEN D4Rule4: IF q3a1 THEN D1Rule5: IF q3a1 THEN D5Rule6: IF q9a1 THEN D6Rule7: IF qq3a1 AND q2a1 AND q5a1 THEN D7Rule8: IF q1a1 AND q8a1 THEN D8Rule9: IF q1a1 AND q6a1 THEN D9Rule10: IF q2a1 AND q5a1 THEN d10

30. Students model problems with systems modeling tools

31. Simulation Builders Interactive Physics Dynamic Designer Working Model 2D

32. G. Help students to argue for the best solution • Argumentation an essential skill in problem solving, especially ill-structured problems (engineering ethics problems) • Also a remedial strategy for correcting misconceptions on well-structured problems

33. G. Help students to argue for the best solution

34. H. Help students to regulate problem solving (metacognition) • Have you solved similar problems before? • What strategy can you use to solve these problems? • What steps are you taking to solve the problem? • Can your answer be checked for accuracy? • Are you sure that your answers are correct? • Can the problem be solved in steps? • What strategy are you using to solve the problems? • Is there a faster method to solve the problem? • Are these problems similar to addition in any way? • What is the best method to solve the problem?

35. I. Assess Conceptual Understanding of Problem • Problem classification • Text editing • Jeopardy questions • Problem posing • Causal reasoning questions

36. Assess understanding with problem classification questions • What kind of problem is this? • A. kinematics • B. work-energy • C. Newton’s 2nd law • D. etc.

37. Assess understanding with text editing questions Multiple choice, but very challenging

38. Assess understanding with Jeopardy questions Students given fragment of solution to a problem, asked to identify scenario that correspond to solution.

39. Assess understanding with problem posing Take a look at the picture below. Create your own physics problem based upon this situation. You may use anything that you have learned from General Physics.

40. Assess understanding with causal reasoning scenarios • You have just received a shipment of three boxes, each containing one of the isotope sources for the three nuclear thickness gauges described above. Each box has a radioactive material label affixed. The sources all weigh the same amount. The boxes are the same size but have different weights. What is the likely reason for the different box weights? • a. The sources each emit radiation of different energy, so they each weigh differently because of the different shielding needed. • b. The sources each emit radiation of different penetrating ability, so they each weigh differently because of the different shielding needed to attenuate the radiation from each source. • c. The sources each have a different amount of radioactivity, so they each need a different amount/weight of shielding depending on the amount of radioactive material. • d. The sources each have a different half-life, so they each need different shielding depending on the half-life.

41. 4.What kinds of problems should engineering students learn to solve? • What kinds of problems do engineers solve? • Ill-structured, containing smaller well-structured problems • Non-engineering constraints (legal, economic, environmental) • Non-engineering criteria for success • Problem driven by multiple, often-conflicting goals • Require collaboration, teamwork, communication • Unanticipated problems emerge.

42. Design Problem Dilemmas Troubleshooting Decision making problems What kinds of problems are there? Strategic planning

43. How Do Problems Vary?

44. 5.How can we support learning to solve complex problems? PBL • Groby Industries designs and manufactures x-ray equipment for hospitals and laboratories. Lately, management has become dissatisfied with its market share for the x-ray cassettes used by its hospital customers. Groby has recently been undercut in the market because its closest rival has found a way to produce the cassettes more cheaply. Rather than simply cutting production costs to compete on price, management prefers to improve Groby's existing x-ray cassette design. The VP of the design department at Groby has tapped senior design engineer Alex Sparks to manage the project. Alex is meeting with four other engineers in the design department to discuss how to approach the problem. • "Okay, guys," Alex begins, "the marketing department did a customer survey and found out that their biggest complaint about our x-ray cassettes is that they are too heavy. The x-ray technicians at the hospitals handle a lot of cassettes during their shifts. They said that, in addition to positioning patients, transporting the x-ray cassettes is the most physically demanding part of the job. Our VP says that the best way to increase our sales would be to make the cassettes lighter."

45. "Well, if we just want to make the cassettes lighter," suggests Zac, "couldn't we just make the face plates thinner? They're pretty dense, right?” "The plates are currently 0.5 mm thick," replies Sunil, who was the lead designer for the current cassettes. "Sure, Charlie," Sunil continues, "but we won't be able to move in a direction that requires increasing a patient's exposure to get the same exposure on the film. We also have to keep the rigidity of the current plates." • "How would a patient get a higher exposure, Sunil?" asked Charlie. • "If the new plates absorb x-rays more than the current design, the patient will have to receive a higher exposure to get the same amount of exposure on the film." • "Does that mean we can reduce the patient exposure if we select a material that absorbs less than the current design?"asked Jocelyn.

46. Performance Goal

47. Argument • A. Determine performance problem (e.g., cassettes too heavy, cause injury) • B. Determine performance goal (e.g., modify cassette to be lighter, non-toxic, with same functionality) • C. Determine performance characteristics (e.g., lighter, stronger , faster, bending stiffness, x-ray transmission) for job • D. Identify solution options (e.g., substitute material with lower density, use less material)\ • 2. For each performance characteristic, determine the material properties that affect that performance • i. Identify primary material properties (elastic modulus, density, x-ray attenuation) that affect/control each requirement • ii. Identify secondary material properties (e.g., fracture toughness, compatability with people, poison danger) that affect/control each requirement • iii. Identify and map the factors that affect that property and the factors that will be affected by that property and how they are affected (see Figure 1) • iv. Which properties require a limiting value for the application? (e.g. fracture toughness must be at least 10 MPa√m) • vi. Which properties should be optimized (maximized, minimized)? (e.g. minimizing the density can minimize the weight, all else being equal) • vii. Rank properties in terms of importance • Viii.Determine interactions among requirements (e.g. density and elastic modulus cannot be varied independently with materials. Increasing thickness to increase stiffness increases the weight. You can find that the maximum E1/3/r minimizes weight) • Determine final ranked property list

48. Results of PBL • Disconnect between problems and exams: Students studied textbook for exams and Internet for problems. Solution: eliminate exams • Students’ major concern: what was on exams • Students came up with questions to help them figure out how to approach problem but failed to monitor effectiveness of strategy. • Most students had little idea of how much they learned from problems: Their conception of learning is so dominated by examination • Student approaches to problems: staple-together collaboration: Individuals in most groups retained roles throughout semester • Suggestions: • More lectures: begin each problem with a lecture on topic of case (not sure how much that will give away solution. • Stories from real engineers about similar problems they have solved (case-based reasoning) • Instructor provided model of ideal problem report as feedback after reports submitted

49. Solution: Engineering Collaboration Environment

50. Summary • Engineers solve problems • Engineering students should learn to solve different kinds of problems, including everyday, complex, ill-structured problems • Engineering educators should enhance student’s conceptual understanding of problems. • Instruction should help students to: • Identify kinds of problems • Analogically compare problem structures • Predict effects and infer causes • Argue for solutions