Teaching Students How to Evaluate Calculation Results

1. Teaching Students How to Evaluate Calculation Results James Hanson, Ph.D, PE Rose-Hulman Institute of Technology ASEE Illinois-Indiana Section Conference March 27, 2009

2. Overview • Motivation • How evaluation is done • How to teach it • Reinforcing it in HW • How well it works

3. Motivation • Not in textbooks • Reliance on computers • Experience is retiring!

4. How Evaluation is Done Study Performed • Interview 35 practitioners • Ten firms • Experience: 1-55 years

5. How Evaluation is Done Categories of Evaluation Tools for Analysis Results • Fundamental Principles • Approximations • Features of the Solution

6. How to Teach It • Structural Engineering • Electrical Engineering • Other Examples

7. Fundamental Principles(for Structural Engineering) • Statics • Equilibrium always • Mechanics of Materials • Strain distribution • Stiffness attracts load

8. Fundamental Principles Example

9. Approximations(for Structural Engineering) • Simplify loading • Simplify geometry • Assume material behavior

10. Actual Approximate P/3 P/3 P/3 w = P/L L/4 L/4 L/4 L/4 L Mmax = PL/6 Mmax = PL/8 Difference= – 25% Approximations Example

11. Features of the Solution(for Structural Engineering) • Boundary conditions • Continuity • Fundamental principles Use… To… • Anticipate graphical features • Bound possible solution

12. T = – M C C = + M T + M – Features of Solution Example Construct the moment diagram: 1. Sketch displaced shape 2. Deduce sign of moment from curvature 3. Construct diagram

13. Electrical Engineering Examples Fundamental Principles: Circuit analysis governed by Ohm’s Law and Kirchoff’s Current Law Approximations: DC circuit with capacity approximated as open circuit DC circuit with inductor approximated as a short Features of the Answer: Ripples in frequency response of filter relates to order of the filter Thanks to Dr. Yoder, ECE Dept, RHIT

14. How to Teach It Other Examples • Fundamental Principles • Approximations • Features of the Solution

15. How to Teach It Metacognition Def: Sequence of steps followed by a person to monitor and improve that person’s own cognitive performance in an area How: Set up student so intuition leads to wrong conclusion, then ask to reflect on why went wrong

16. (a) (b) Metacognition Which way will right end deflect (up or down)?

17. Reinforcing It in HW • Guess part of the solution (instructor choice) • Generate approximate solution (text prob?) • Use computer for solution • Identify expected features in computer solution • Verify fundamental principles in computer solution • Make comprehensive argument that computer result is reasonable • Compare guess with solution and reflect on why similar/different • Guess part of the solution (instructor choice) • Generate approximate solution (text prob?) • Use computer for solution • Identify expected features in computer solution • Verify fundamental principles in computer solution

18. Reinforcing It in HWExample Problem Statement: An indeterminate beam experiences uniformly distributed load. Objective: Find vertical reactions.

19. Reinforcing It in HWExample a) Guess the deflected shape Not graded based on correctness, graded based on whether done

20. Reinforcing It in HWExample b) Generate approximate solution Assumption: load carried by nearest support

21. Reinforcing It in HWExample c) Use computer for solution Can use as “black box” if teaching how to evaluate results

22. Reinforcing It in HWExample d) Identify expected features in computer solution • Displaced shape features • Internal force diagram features • Reaction directions

23. Reinforcing It in HWExample SFx = 0 SFy = 0 SM = 0 e) Verify fundamental principles in computer solution Check equilibrium:

24. Reinforcing It in HWExample f) Make comprehensive argument that computer results are reasonable Features of Solution √ √ Fundamental Principles √ Approximate Result

25. Reinforcing It in HWExample g) Compare guess with solution and reflect on why similar/different Graded based on candor and depth of reflection, not how similar or different

26. 3.1 3.3 3.6 3.5 3.3 2006 33 3.0 Metacognition improved performance in this course 2007 23 3.1 2008 32 3.1 4 – Strongly Agree 1 – Strongly Disagree How Well It WorksAttitude Statement Year n Average 2004 30 (ctrl) Undergrads should be able to determine reasonableness of results 2005 46 2006 42 2007 29 2008 39

27. 74% 74% 78% How Well It Works Behavior Statement Year n Affirmative 2006 42 I use metacognition more now than before course 2007 30 2008 40

28. Statement n Average (Respond 1 yr after course) 2006 39 I use fundamental principles, approx, and features of soln to evaluate in other areas of civil 2006 39 I now use metacognition … than before the course 5 – Almost Always 5 – Much More 1 – Much Less 1 – Never How Well It Works Behavior 3.5 3.6

29. 50% 49% 67% 70% 66% 69% 69% 69% 69% 73% How Well It Works Cognitive Structural Mechanics I Course (Required) Correctly Identify Most Reasonable Correctly Explain Why Reasonable Term n Fall 2004 (Ctrl) 34 Fall 2005 48 Fall 2006 44 Fall 2007 30 Fall 2008 42 Practitioners 8 92% 72%

30. 35% 46% 43% 44% 49% 65% 48% 71% 59% 68% How Well It WorksCognitive Structural Mechanics II Course (Elective) Correctly Identify Most Reasonable Correctly Explain Why Reasonable Term n Winter 2004 (Ctrl) 9 Winter 2005 9 Winter 2006 17 Winter 2007 11 Winter 2008 16 Practitioners 8 65% 58%

31. Summary • Evaluation of results can be taught • Fundamental principles, approximations, features of the solution • Metacognition might help

32. Acknowledgements Sponsor Grant: DUE-0341212 Participating Firms Center for Structural Engineering Education http://www.rose-hulman.edu/csee Questions or comments: james.hanson@rose-hulman.edu