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Teaching Students How to Evaluate Calculation Results

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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

- Motivation
- How evaluation is done
- How to teach it
- Reinforcing it in HW
- How well it works

- Not in textbooks
- Reliance on computers
- Experience is retiring!

Study Performed

- Interview 35 practitioners
- Ten firms
- Experience: 1-55 years

Categories of Evaluation Tools for Analysis Results

- Fundamental Principles
- Approximations
- Features of the Solution

- Structural Engineering
- Electrical Engineering
- Other Examples

- Statics
- Equilibrium always

- Mechanics of Materials
- Strain distribution
- Stiffness attracts load

- Simplify loading
- Simplify geometry
- Assume material behavior

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%

- Boundary conditions
- Continuity
- Fundamental principles

Use…

To…

- Anticipate graphical features
- Bound possible solution

T

= – M

C

C

= + M

T

+

M

–

Construct the moment diagram:

1.Sketch displaced shape

2.Deduce sign of moment from curvature

3.Construct diagram

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

Other Examples

- Fundamental Principles
- Approximations
- Features of the Solution

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

(a)

(b)

Which way will right end deflect (up or down)?

- 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

Reinforcing It in HWExample

Problem Statement:

An indeterminate beam experiences uniformly distributed load.

Objective:

Find vertical reactions.

Reinforcing It in HWExample

a) Guess the deflected shape

Not graded based on correctness, graded based on whether done

Reinforcing It in HWExample

b) Generate approximate solution

Assumption: load carried by nearest support

Reinforcing It in HWExample

c) Use computer for solution

Can use as “black box” if teaching how to evaluate results

Reinforcing It in HWExample

d) Identify expected features in computer solution

- Displaced shape features
- Internal force diagram features
- Reaction directions

Reinforcing It in HWExample

SFx = 0

SFy = 0

SM = 0

e) Verify fundamental principles in computer solution

Check equilibrium:

Reinforcing It in HWExample

f) Make comprehensive argument that computer results are reasonable

Features of Solution

√

√

Fundamental Principles

√

Approximate Result

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

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

Statement

Year

n

Average

2004

30

(ctrl)

Undergrads should be able to determine reasonableness of results

2005

46

2006

42

2007

29

2008

39

74%

74%

78%

Statement

Year

n

Affirmative

2006

42

I use metacognition more now than before course

2007

30

2008

40

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

3.5

3.6

50%

49%

67%

70%

66%

69%

69%

69%

69%

73%

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%

35%

46%

43%

44%

49%

65%

48%

71%

59%

68%

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%

- Evaluation of results can be taught
- Fundamental principles, approximations, features of the solution
- Metacognition might help

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