Resources for Robot Competition Success...Overall Robotics Interest Math Interest Math Value for Robotics Pre Post + Results – Gains in Robot/Math Attitudes • Team E2 – Used

Resources for Robot Competition Success Assessing Math Use in

Grade-School-Level Engineering Design

Eli M. Silk1, Ross Higashi2, and Christian D. Schunn1

June 27, 2011

1 University of Pittsburgh 2 Carnegie Mellon University

© Adriana M. Groisman, 2007 FLL Photo Archive, usfirst.org

•  Popular, engaging context for integrated STEM problem solving (Verner & Ahlgren, 2004)

•  But ... do teams use math? (Cardella, 2010; Gainsburg, 2006)

•  Does using math help in the competition? (Titus et al., 2008)

•  Does using math help in other ways? (Melchior et al., 2009)

Robot Competitions – Is Math Useful?

ASEE - 6/27/11 Eli M. Silk 1

Distance = Motor Rotations × Wheel Circumference

© Adriana M. Groisman, 2007 FLL Photo Archive, usfirst.org

•  Local competition

•  16 teams –  Tell me about... –  your team –  your solution

•  4 Focus Teams –  Pre/post surveys –  Problem solving

•  12 items

–  Attitudes (13 items) •  Robotics interest •  Math interest •  Math value for

robotics

Method – Ask Teams at a Competition


Results – What Strategies do Teams Use?

•  Sensor-Based (n = 3) –  Move until touch sensor pressed

•  View-Mode (n = 3)

•  Guess-Test-Adjust (n = 6)

•  Calc-Test-Adjust (n = 4) –  Explicitly math-based –  Measurement –  Prediction (1-rotation-distance)


Sensor Based 19%

View Mode 19% Guess

Test Adjust 38%

Calc Test

Adjust 25%

31

1 2 3 4

Interactive Servo Motor

Technology

The three Interactive Servo Motors provide the robot with the ability to move. Using the Move [Move] block automatically aligns their speed so that the robot moves smoothly.

Built-in Rotation SensorThe Interactive Servo Motors all have a built-in Rotation Sensor. The rotational feedback allows the NXT to control movements very precisely. The built-in Rotation Sensor measures the Motor rotations in degrees (accuracy of +/- one degree) or full rotations. One rotation is 360 degrees, so if you set the Motor to turn 180 degrees, the hub will make half a turn.

ViewTest the Rotation Sensor’s ability to measure distance.Connect the Motor to the NXT.Select View in the NXT display.

Select the Motor rotations icon.

Suggestions for useThe built-in Rotation Sensor in each motor along with the Power confi guration in the Move or Motor blocks in the Software (see page 53-55) allow you to program different speeds for your Motors and move the robot accurately.

Select the port in which you have placed the Motor.Now try to attach a wheel to the Motor and measure the rotations by pushing the wheel over the fl oor.

Results – Which Strategies are Successful?

•  Sensor-Based –  Least successful

•  View-Mode –  Most reliable and most

reliably successful

•  Math-Based –  Mid-level overall

success on average –  But highly variable –  What’s going on?


Ran

k in

the

Com

petit

ion

22

19

16

13

10

7

4

1

View−Mode

Guess−Test−Adjust

Calc−Test−Adjust

Sensor−Based

View Mode

Guess Test

Adjust

Calc Test

Adjust

Sensor Based

!

!

!

!!!!

!!

! !

!

!!

!

!

Max

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re in

the

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petit

ion

0

10

20

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View−Mode

Guess−Test−Adjust

Calc−Test−Adjust

Sensor−Based

Results – Is Using Math Successful? •  Top 2 performers

–  Both middle/experienced •  2 low-performers

–  Both elementary/rookies •  Success depends on how

(well) the math is used

•  Focus Teams –  #1 Team M2

•  Middle, exp. mentor/students –  #6 Team M1

•  Middle, exp. mentor/students –  #17 Team E2

•  Neighborhood team •  Rookie mentors and

students


View Mode

Guess Test

Adjust

Calc Test

Adjust

Sensor Based

Results – Gains in Problem Solving

•  Both math-using (E2 & M2) teams improve from pre to post

–  Middle school teams higher at pre

•  Team M2 –  Make efficient and reliable

movements •  Simpler programs (up, back)

–  Use math in optimizing strategy •  Focus on highest point-value

missions •  Practice timing and sequence •  Take strategic penalties

–  Comparable to Team M1 •  Team M1 from similar suburban

school environment, with experienced mentors and students, access to multiple robots, etc.


Prop

ortio

n C

orre

ct

0.0

0.2

0.4

0.6

0.8

1.0

Team E2 Team M1 Team M2

Pre Post *

E2 M1 M2

Stro

ngly

Nega

tive

Nega

tive

Neut

ral

Posit

iveSt

rong

lyPo

sitive

Overall RoboticsInterest

MathInterest

Math Valuefor Robotics

Pre Post

Results – Gains in Robot/Math Attitudes

•  Team M2 – Used a math

strategy

– High across the board at pre and post

– But didn’t improve


Overall Robot Interest

Math Interest

Math Value

for Robots

Stro

ngly

Nega

tive

Nega

tive

Neut

ral

Posit

iveSt

rong

lyPo

sitive


MathInterest


Pre Post


•  Team M1 – Used a guessing

strategy

– Not as high at pre

– But also didn’t improve



Math Interest

Math Value

for Robots

Stro

ngly

Nega

tive

Nega

tive

Neut

ral

Posit

iveSt

rong

lyPo

sitive


MathInterest


Pre Post

+


•  Team E2 – Used a math strategy

– Not as high at pre •  Similar to M1 at pre

– But made positive gains

•  Similar to M2 at post

– Even though not successful in competition (17/22)



Math Interest

Math Value

for Robots

Stro

ngly

Nega

tive

Nega

tive

Neut

ral

Posit

iveSt

rong

lyPo

sitive


MathInterest


Pre Post


•  Team M2 – high across the board at pre and post, but didn’t improve

•  Team M1 – not as high at pre as M2, but also didn’t improve

•  Team E2 – not as high at pre (like M1), but make gains across the board (like M2 at post) –  Even though not successful in the competition


Team M1 (guessing strategy)

Team M2 (math strategy)

Team E2 (math strategy)

Stro

ngly

Nega

tive

Nega

tive

Neut

ral

Posit

iveSt

rong

lyPo

sitive


MathInterest


Pre Post

Stro

ngly

Nega

tive

Nega

tive

Neut

ral

Posit

iveSt

rong

lyPo

sitive


MathInterest


Pre Post

+

Conclusions & Discussion

•  Summary of results –  25% (4/16) of teams used math in their solutions –  Using math had highly variable competition success

•  Top 2 teams and 2 low-performing teams •  The most reliably successful strategy was the View-Mode strategy

–  Using math did lead to problem solving gains –  Using math unsuccessfully still resulted in attitude gains

•  Why (under what conditions) does math lead to success? –  Success was about fine-tuned, simple, reliable movements

•  So the math only helpful if it supports that –  But the math can also be helpful in other optimization aspects

•  Success even when teams don’t perform well in the competition –  Elementary teams may not have the background to do well –  But just trying the math seems to have benefits to interest and value

ASEE - 6/27/11 11 Eli M. Silk

Thank You

Eli M. Silk [email protected]

References Cardella, M. E. (2010). Mathematical modeling in engineering design projects. In R. Lesh, P. L. Galbraith, C.

R. Haines & A. Hurford (Eds.), Modeling Students' Mathematical Modeling Competencies (pp. 87-98). New York: Springer.

Gainsburg, J. (2006). The mathematical modeling of structural engineers. Mathematical Thinking and Learning, 8(1), 3-36. doi: 10.1207/s15327833mtl0801_2

Jansen, B. R. J., & van der Maas, H. L. J. (2002). The development of children’s rule use on the balance scale task. Journal of Experimental Child Psychology, 81(4), 383-416. doi: 10.1006/jecp.2002.2664

Köller, O., Baumert, J., & Schnabel, K. (2001). Does interest matter? The relationship between academic interest and achievement in mathematics. Journal for Research in Mathematics Education, 32(5), 448-470. doi: 10.2307/749801

Melchior, A., Cohen, F., Cutter, T., & Leavitt, T. (2005). More than robots: Evaluation of the FIRST Robotics Competition participant and institutional impacts, Waltham, MA: Center for Youth and Communities, Brandeis University.

Misailidou, C., & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. Journal of Mathematical Behavior, 22(3), 335-368. doi: 10.1016/S0732-3123(03)00025-7

Tapia, M., & Marsh, G. E. (2004). An instrument to measure mathematics attitudes. Academic Exchange Quarterly, 8(2), 16-21.

Titus, N., Schunn, C. D., Walthall, C., Chiu, G., & Ramani, K. (2008). What design processes predict better design outcomes? The case of robotics teams. Paper presented at the Seventh International Symposium on Tools and Methods of Competitive Engineering (TMCE 2008), Izmir, Turkey.

Verner, I. M., & Ahlgren, D. J. (2004). Robot contest as a laboratory for experiential engineering education. ACM Journal on Educational Resources in Computing, 4(2), 2-28. doi: 10.1145/1071620.1071622


Documents

Resources for Robot Competition Success...Overall Robotics Interest Math Interest Math Value for Robotics Pre Post + Results – Gains in Robot/Math Attitudes • Team E2 – Used