“Internet Instructor, Tireless Grader, Endless Self-Assessment Tests, and Game-Based Learning (GBL) With Real-World Applications For Improving STEM Education”

Subhash Kadiam, Ahmed Mohammed, Duc T. Nguyen*

Old Dominion UniversityCivil & Environmental Engineering, 135 KAUFNorfolk, VA 23529

http://www.lions.odu.edu/~amoha006http://numericalmethods.eng.usf.edu/people.html#Duc_Nguyenhttp://www.lions.odu.edu/~amoha006/Fillinterms/FILLINTERMS.htmlhttp://www.eng.usf.edu/~kaw/download/Assembly_procedure2_256.wmv

Table 1:Objectives and Outcomes of the Developed SMM Module

Background Outcomes 1,2,3,4,5

SIMULATION/COMPUTATIONOutcomes 2,3,4,5

INTERACTIVE VISUALIZATION Outcomes1,4,5

VISUALIZATION Outcomes1,4

STIFFNESS MATRIX METHOD (SMM) MODULE

Concepts: (a) Element local

matrices (b) Element global

matrices (c) Assembly

process (d) Boundary

conditions (e) System of linear

equations (f) Structural

responses

Derived formulas Detailed step-by-step Procedures for items

(a,b,c,d,e,f)

Visual plots of un-deformed structural model

For items(a,b)

For items(e,f)

For items(c,d)

Visualization of deformed structure

Visualization of impact of Node Numbering System of

the structural stiffness matrix bandwidhOptimum Node Numbering

system To minimize the bandwidth of the assemble structural stiffness matrix

Practicality

Viscompana

Connectivity

Hierarchical

Figure 2: Layout of Stiffness Matrix Method (SMM) Module.

Out-come Unacceptable Marginal Acceptable Excellent

1Little/no knowledge of what data is required to create a structural model/problem.

Can identify some data required to create a structural model.

Can identify most data required, but have difficulty to follow interactive instructions to (visually) create a structural model.

Can identify all data required and to visually/interactively create a structural model.

2

Inadequate ability to identify the degree-of-freedom (dof), size and rotational matrices associated with a particular truss/beam/frame element

Know to identify the dof and size of element matrices, but can’t compute numerical values of element stiffness matrix in local references

Can compute the element stiffness matrix in local references.

Know to transform element stiffness matrix from local to global references.

3

Inadequate ability to determine the locations of element stiffness within the “structural” stiffness matrix. Also does NOT know how to impose “boundary conditions”

Know to place the locations of element stiffness matrices in a structural stiffness matrix. However, still confuse to handle “over-lap” terms.

Know how to “assemble” the structural stiffness matrix. Still have some difficulty to impose “boundary conditions”.

Completely understand the assembly process, including properly imposed “boundary conditions”.

Out-come Unacceptable Marginal Acceptable Excellent

4

Can’t recognize the roles of linear equation solver (to solve for nodal displacements). Have no ideas to compute member-end-actions, support reactions. Have no abilities to interpret the obtained results.

Know to compute the nodal displacements, and member-end-actions.

Know to compute all structural responses. However, still have some difficulty to interpret the computed results.

Know to compute all structural responses, and have abilities to interpret the computed results.

5

Can’t identify important parameters that have impacts on the structural responses. No abilities to apply the SMM software to conduct “what if” studies. Can’t identify/fix errors made in preparing the structural model.

Can identify some important parameters for conducting “what if” studies.

Can identify most (or all) important parameters for “what if” studies.

Can conduct all “what if” studies, interpreting the computed results and be able to identify/fix potential errors made in earlier phase (such as preparing the input structural model).

Cont’d

Figure 3: Deflections and reactions for support “settlements” example.

Figure 4: Self-Assessment Test: Frame problem (Students will enter his/her answers in the textbox provided).

Figure 5: Self-Assessment results and graded score are included in each student’s email.

Comparisons of Students’ Performance Test Scores In Spring ‘2007 and Spring ‘2008 Semesters - Surveys and Results:

Overall Comparison of Class Average Tests' Scores in Spring'07 and in Spring'08

78.53

71.24

88.483.37

0

10

20

30

40

50

60

70

80

90

100

take home in class

Year

Ave

rage

Stu

dent

s pe

rfor

man

ce

Spring'07 without SMM Modules, 34students

Spring'08, with SMM Modules, 47students.

Figure 6: Overall comparison of Class Average Tests’ Scores in Spring’07 and in Spring’08.

17.03%

24.7124.7137.83 improvements in an in-class exam. A total of 34 students

participated in Spring’07, and 47 students participated in Spring’08 survey, respectively.

Results of "Voluntary" Computer Self-Assessment SMM Test Scores

0

20

40

60

80

100

120

29 x 47

Number of Students

"Vol

unta

ry"

Com

pute

r Se

lf-A

sses

smen

t SM

M T

est S

core

s

Notes:a) Total Number of students = 47.b) ‘x’ = unknown number of students who volunteerto take computer self-assessment test. ‘x’ could be any numberbetween [29 – 47].c) Number of students who got computer automatically graded scores equal or exceeding 80%.

Results of "Voluntary" Computer Self-Assessment SMM Test Scores

0

20

40

60

80

100

120

29 x 47

Number of Students

"Vol

unta

ry"

Com

pute

r Se

lf-A

sses

smen

t SM

M T

est S

core

s

Notes:a) Total Number of students = 47.b) ‘x’ = unknown number of students who volunteerto take computer self-assessment test. ‘x’ could be any numberbetween [29 – 47].c) Number of students who got computer automatically graded scores equal or exceeding 80%.

Figure 7: Results of “Voluntary” Computer Self-Assessment SMM test scores.

Figure 8: Surveyed results of effectiveness of the developed SMM modules.

The ratings (for the following questionnaire) can be quantified as: A = 4 points (Definitely Agree), B = 3 points (Agree), C = 2 points (Not Sure), D = 1 point (Not Agree)

Questions Selected Rating

The developed web based Stiffness Matrix Method (SMM) modules will:

1. Improve students' ability to solve SMM homeworks' problems. A B C D

2. Improve students' performance scores in SMM (take-home) exam. A B C D

3. Improve students' performance scores in SMM (in-class) exam. A B C D

4. Improve students' ability for better understanding of SMM lecture

materials. A B C D

5. Help students to have more interests (through graphical displayed inputs

and colorful output plots) in learning/practicing SMM materials. A B C D

6. Help students to accurately assessed (through automated, self-grading

assessment tests) his/her understandings about the SMM module. A B C D

7. Help students to identify his/her errors in calculating some

"intermediate" steps of the entire solution process. A B C D

Figure 9: Results of “In-class” test on SMM module.

Figure 5 A preliminary chess-like game is being developed as an innovative and effective way to explain a difficult topic such as "fill-in terms" in simultaneous linear equations (SLE) covered in the course Numerical Methods. This game illustrates how to minimize fill-in terms during factorization phase of SLE (Choleski) procedures.

An Applied Problem in a Numerical Methods Course

Autar Kaw

Department of Mechanical EngineeringUniversity of South Florida

http://numericalmethods.eng.usf.edu

Sponsored by National Science Foundation

Why incorporate real-life problems in courses?

– Train students in state-of-the-art research in emerging technologies.

– Real world application of course work increases comprehension.

– Encourage that education and research are of equal value and are complementary parts of an integrative engineering and science education enterprise.

Trunnion

Hub

Girder

Bascule Bridge THG

Trunnion-Hub-Girder Assembly Procedure

Step1. Trunnion immersed in dry-ice/alcoholStep2. Trunnion warm-up in hubStep3. Trunnion-Hub immersed in dry-ice/alcoholStep4. Trunnion-Hub warm-up into girder

Fulcrum Assembly Movie

Trunnion Stuck in Venetian Causeway Bridge

When the trunnion was inserted into the hub, the trunnion got stuck before it could be fully inserted.

Consultant calculations show sticking should not have occurred.

TDD

FT o18880108 F80 of re temperaturoomat //1047.6 6 oo Finin

-0.01504")188)(1047.6)(363.12( 6 D

"363.12D

Clearance needed was 0.015” or more

Thermal Expansion Coefficient Variation with Temperature

0

1

2

3

4

5

6

7

-400 -300 -200 -100 0 100Temperature (oF)

Coe

ffic

ient

of T

herm

al E

xpan

sion

(10-6

in/in

/o F)dTTDD

c

a

T

T

)(

Knowing that thermal expansion coefficient varies as shown, as compared to the consultant’s estimate,

the magnitude of contraction you would calculate is

1. Less2. More3. Same4. undeterminable

Less

More

Same

undeterm

inable

0% 0%0%0%

0

1

2

3

4

5

6

7

-400 -300 -200 -100 0 100Temperature (oF)

Coe

ffic

ient

of T

herm

al E

xpan

sion

(10-6

in/in

/o F)

dTTDDc

a

T

T

)(

Roughly estimate the contraction using trapezoidal rule

0

1

2

3

4

5

6

7

-400 -300 -200 -100 0 100Temperature (oF)

Coe

ffic

ient

of T

herm

al E

xpan

sion

(10-6

in/in

/o F)

dTTDDc

a

T

T

)( Ta=80oF; Tc=-108oF; D=12.363”

Estimating Contraction Accurately

dTTDDc

a

T

T

)(

Change in diameter (D) by cooling it in dry ice/alcohol is given by

0150.6101946.6102278.1 325 TT

Ta=80oF; Tc=-108oF; D=12.363"

ΔD =-0.0137"

The area under the curve, that is,

6.75

15.25 22

.529

.25

0% 0%0%0%

-25

y

x

f(x) Area of this triangle is 22.5 units

Area of this triangle is 6.75 units

5

2

)( dxxf

1. 6.752. 15.253. 22.54. 29.25

The number of significant digits in 0.0023406 is

4 5 6 7

0% 0%0%0%

A. 4B. 5C. 6D. 7

Coefficient of Thermal Expansion vs Temperature

Temperature Instantaneous Thermal

ExpansionoF min/(in oF)

80 6.47

60 6.36

40 6.24

20 6.12

0 6.00

-20 5.86

-40 5.72

-60 5.58

-80 5.43

-100 5.28

-120 5.09

-140 4.91

-160 4.72

Temperature Instantaneous Thermal

ExpansionoF min/(in oF)

-180 4.52

-200 4.30

-220 4.08

-240 3.83

-260 3.58

-280 3.33

-300 3.07

-320 2.76

-340 2.45

Microsoft Excel Used for Regression With Default Format

What is your predicted value of the thermal expansion coefficient at T=-300oF?

Thermal Expansion vs Temperature

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

-400 -300 -200 -100 0 100 200

Temperature (oF)

Coe

ffic

ient

of t

herm

al

expa

nsio

n (m

in/in

/o F)

015.60062.0101 25 TT

The difference between predicted and observed values

015.60062.0101 25 TTDefault Format in Excel for Regression

T = -300oF61026.3 in/in/oF

T = -300oF 61007.3 in/in/oF Observed Data at

Predicted Value at

Microsoft Excel Used for Regression with Scientific Format

What is your predicted value of the thermal expansion coefficient at T=-300oF?

Thermal Expansion vs Temperature

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

-400 -300 -200 -100 0 100 200

Temperature (oF)

Coe

ffic

ient

of t

herm

al

expa

nsio

n (m

in/in

/o F)

0150.6101946.6102278.1 325 TT

The difference between predicted and observed values

Scientific Format in Excel for Regression

T = -300oF61005.3 in/in/oF

T = -300oF 61007.3 in/in/oF Observed Data at

Predicted Value at

0150.6101946.6102278.1 325 TT

Summary of what formatting does in Excel

in/in/oF

T = -300oF 61007.3 in/in/oF Observed Data

0150.6101946.6102278.1 325 TTT = -300oF

61005.3

Scientific Format in Excel for Regression

015.60062.0101 25 TTDefault Format in Excel for Regression

T = -300oF61026.3 in/in/oF

A scientist finds that regressing the data below is a perfect fit to a straight

line. The missing data at x=17 is

-2.44

4 2. 34.

35.

0% 0%0%0%

x 1 3 11 17y 3 7 23 ??

1. -2.4442. 2.0003. 34.004. 35.00

So if dipping in dry-ice/alcohol is not a good medium, what is?

f

room

T

T

dTDD

fT

dTTT80

69211 10015.6101946.6102278.1363.12015.0

010 88318.010 74363.010 38292.010 50598.0)f( -2-42-73-10 T T T T ffff

An equation solver gives the roots of the above equation

as 1688,-128,-802. The acceptable solution is

1688 -12

8-80

2

All of th

e above

0% 0%0%0%

010 88318.010 74363.010 38292.010 50598.0)f( -2-42-73-10 T T T T ffff

1. 16882. -1283. -8024. All of the above

A cubic equation has three roots. At least one root is known to be complex.

The cubic equation has

one rea

l root a

nd tw

...

two re

al ro

ots an

d o..

three

complex

roots

three

real

roots

0% 0%0%0%

1. one real root and two complex roots

2. two real roots and one complex root

3. three complex roots4. three real roots

For more information

• http://numericalmethods.eng.usf.edu OR just do a Google search on numerical methods undergraduate

The Only Advice

If you don't let a teacher know at what level you are by

asking a question, or revealing your ignorance you will

not learn or grow. You can't pretend for long, for you will

eventually be found out. Admission of ignorance is often

the first step in our education.

Steven Covey - Seven Habits of Highly Effective People

Acknowledgements.

The authors would like to express their gratitude for the financial support provided by the National Science Foundation, through the NSF Grants #0530365 (Sept.2005-Sept.2008; PI=Prof. Chaturvedi; Senior Investigator=Prof. Nguyen), #0717624 (Jan.2008-Dec.2010; PI=Prof. Kaw; Co-PI=Prof. Nguyen), and #0836916 (Feb.2009-Jul.2010; over-all PI=Prof. Nguyen).

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CA 94103.

2. B.S Bloom, Taxonomy of Educational Objectives, The Classification of Educational

Goals, “Handbook I” Cognitive Domain,” David McKay Co., New York., 1986.

3. D.T. Nguyen, Finite Element Methods: Parallel-Statics and Eigen-Solution, Springer

Publisher, 2006.

4. D.T. Nguyen, Parallel-Vector Equation Solvers for Finite Element Engineering

Applications, Kluwer Academic/Plenum Publishers, 2002.

5. O.O.Storaasli, J.M, Housner and D.T Nguyen, “Parallel Computational Methods for

Large-Scale Structural Analysis and Design, Guest Editors,” Computing Systems in

Engineering, an International Journal, vol. 4, no. 4-6, August, October, December 1993.

6. S.D.Rajan, Introduction to Structural Analysis and Design, John Wiley & Sons, Inc,

2001.

7. A.D.Belegundu and T.R.Chandrupatla, Optimization Concepts and Applications in Engineering, Prentice-Hall, 1999