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David Jonassen Curators’ Professor University of Missouri

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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.

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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).

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1. What kinds of problems do engineering students normally learn to solve? 2. What do engineering students learn from that process? 3. How can we help students to better understand the problems they are solving so they can transfer what they know to new problems? 4. What kinds of problems should engineering students learn to solve? 5. How can we support learning to solve complex problems?

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Story Problems taught by Worked Examples

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To mimic what they were taught

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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

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What those equations mean

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Conceptual understanding of the nature of the problem

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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

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A. Help students to construct a problem schema for each kind of problem B. Require students to analogically compare problems C. Help students to understand mechanisms of causal relationships in problem D. Use different forms of questions E. Represent problems in different ways F. Require students to model problems in different ways G. Help students to argue for the best solution H. Help students to regulate problem solving I. Assess conceptual understanding of problems, not just correct answer

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What kind of problem is this? Structural characteristics Situational characteristics Solution methods

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ForceDistance Work Initial Total Energy Final Total Energy Initial Potential Energy Initial Kinetic Energy Initial Potential Energy From Springs Initial Potential Energy From Height Initial Spring Comp- ression Spring Cons- tant Mass Initial Height Initial Velocity Final Potential Energy Final Kinetic Energy Mass Final Velocity Final Potential Energy From Springs Final Potential Energy From Height Final Height Final Spring Comp- ression Spring Cons- tant Represent problems as structure maps

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Represent problems as equation structure maps

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Analyze conceptual elements of problems

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Surface DFD Surface Difference (FD) : Roller Coaster vs. Gun Structural SPS Structural Similarity (PS) : Both Conservative systems

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Surface S Surface Similarity: Both Roller Coasters PD Principle Difference: Conservative vs. Non- Conservative

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Animations Simulations Causal diagrams Ask causal questions

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

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Prediction

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Concept maps Causal maps Systems models Simulation-building tools

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Students model problems with concept maps

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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 D2 Rule2:IF (d1 OR q3a1) AND q2a1 AND q8a1 THEN D3 Rule3:IF q4a1 AND q3a1 AND q6a1 THEN D4 Rule4: IF q3a1 THEN D1 Rule5:IF q3a1 THEN D5 Rule6:IF q9a1 THEN D6 Rule7:IF qq3a1 AND q2a1 AND q5a1 THEN D7 Rule8:IF q1a1 AND q8a1 THEN D8 Rule9:IF q1a1 AND q6a1 THEN D9 Rule10: IF q2a1 AND q5a1 THEN d10

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Students model problems with systems modeling tools

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Interactive Physics Dynamic Designer Working Model 2D Simulation Builders

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Argumentation an essential skill in problem solving, especially ill-structured problems (engineering ethics problems)engineering ethics problems Also a remedial strategy for correcting misconceptions on well-structured problems

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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?

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Problem classification Text editing Jeopardy questions Problem posing Causal reasoning questions

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What kind of problem is this? A. kinematics B. work-energy C. Newton’s 2 nd law D. etc.

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Multiple choice, but very challenging

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Students given fragment of solution to a problem, asked to identify scenario that correspond to solution.

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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.

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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.

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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.

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

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How Do Problems Vary?

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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."

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"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.

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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 E 1/3 /r minimizes weight) Determine final ranked property list

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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

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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

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