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Enriching K-12 Math Education Using LEGOs

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2011 ASEE Annual Conference & Exposition


Vancouver, BC

Publication Date

June 26, 2011

Start Date

June 26, 2011

End Date

June 29, 2011



Conference Session

K-12 and Pre-College Engineering Poster Session

Tagged Division

K-12 & Pre-College Engineering

Page Count


Page Numbers

22.629.1 - 22.629.17



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Paper Authors


Irina Igel Polytechnic Insititute of New York University

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Irina Igel received the B.S. degree in Mathematics with a minor in Computer Science from NYU, Poly, Brooklyn, NY, in 2009. Upon graduating she received an Adjunct Instructor position at the Department of Mathematics at NYU, Poly, teaching undergraduate math courses to incoming freshmen. She is currently serving as a teaching Fellow at the Bedford Academy HS under NYU, Poly’s GK-12 program funded by NSF and CBRI consortium of donors. She is perusing the M.S. degree in Mechanical Engineering with emphasis on Control and Dynamical Systems. Her research interests include cooperative control of multi-agent systems, flocking and shoaling behavior in live animals, and distributed consensus algorithms analysis and computation.

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Ronald Leonel Poveda Polytechnic Institute of New York University

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Ronald Poveda received the B.S. degree in Mechanical Engineering,
Summa Cum Laude, from the Polytechnic Institute of NYU, Brooklyn, NY, in 2009. Upon graduation, he started research for a Ph.D. degree in Mechanical Engineering in the Composite Materials and Mechanics Lab (CMML). He is currently serving as a teaching Fellow at the Mott Hall Bridges Academy under NYU, Poly’s GK-12 program funded by the NSF and CBRI consortium of donors. In the summer of
2008, he held a mechanical engineering internship position with Motorola, Inc., performing mechanical testing and evaluation of scanners and other mobile
devices in Holtsville, N.Y. His largely experimental research is focused on parametric studies of novel lightweight composites and simulations of functionally-graded materials under load.

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Vikram Kapila Polytechnic Institute of New York University Orcid 16x16

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Vikram Kapila is an Associate Professor of Mechanical Engineering at Polytechnic Institute of NYU, Brooklyn, NY, where he directs an NSF funded Web-Enabled Mechatronics and Process Control Remote Laboratory, an NSF funded Research Experience for Teachers Site in Mechatronics, and an NSF funded GK-12 Fellows project. He has held visiting positions with the Air Force Research Laboratories in Dayton, OH. His research interests are in cooperative control; distributed spacecraft formation control; linear/nonlinear control with applications to robust control, saturation control, and time-delay systems; closed-loop input shaping; spacecraft attitude control; mechatronics; and DSP/PC/microcontroller-based real-time control. Under Research Experience for Teachers Site and GK 12 Fellows programs, funded by the National Science Foundation, and the Central Brooklyn STEM Initiative (CBSI), funded by the Brooklyn Community Foundation, Xerox Foundation, J.P. Morgan Chase Foundation, Motorola Foundation, White Cedar Fund, and NY Space Grant Consortium, among others, he has conducted significant K-12 outreach to integrate engineering concepts in science classrooms and labs of several New York City public schools. He received Polytechnic’s 2002 and 2008 Jacobs Excellence in Education Award and 2003 Distinguished Teacher Award. In 2004, he was selected for a three-year term as a Senior Faculty Fellow of NYU, Poly’s Othmer Institute for Interdisciplinary Studies. His scholarly activities have included three edited books, four chapters in edited books, one book review, 43 journal articles, and 92 conference papers. Moreover, he has mentored 67 high school students, over 170 K-12 teachers, 21 undergraduate summer interns, and 11 undergraduate capstone-design teams, and graduated eight M.S. and four Ph.D. students.

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Magued G. Iskander Polytechnic Institute of New York University

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Magued Iskander is Associate Professor and Graduate Adviser of the Civil Engineering Department at Polytechnic Institute of NYU, Brooklyn, NY. Dr. Iskander is a recipient of NSF CAREER award, Chi Epsilon (Civil Engineering Honor Society) Metropolitan District James M. Robbins Excellence in Teaching Award, Polytechnic’s Distinguished Teacher Award, and Polytechnic’s Jacobs Excellence in Education Award (twice). Dr. Iskander’s research interests include Geotechnical modeling with transparent soils, foundation engineering, and urban geotechnology. He makes extensive use of sensors and measurement systems in his research studies. Dr. Iskander has published 10 books, 90 papers and graduated six doctoral students, 27 masters students, 12 undergraduate research assistants, and supervised the research activities of three school teachers and nine high school students

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Enriching K-12 Math Education Using LEGOsTo address mathematical and scientific obstacles of any era, prize-based competitions arefrequently organized. Such competitions generate widespread interest and open multiple fronts toovercome the obstacle. Although this strategy has a long history, it has regained currency asevidenced through the Millennium Prize Problems and the Netflix Million Dollar ProgrammingPrize. In a similar vein, a proliferation of competitions, e.g., Future City, FIRST LEGO League(FLL), etc., are being directed at K-12 students, to engage their interest in science and math.Recent years have seen an accumulation of evidence that participation in FLL contest providescompelling learning experiences to students and imparts critical academic, life, and professionalskills to them. In a Brandeis University Study, students reported that participation in FLLcontests enhanced their interest in science and math and increased their confidence andmotivation in school work.However, increasingly, educators have focused on transitioning these robotic experiences froman after-school activity into classroom. In pre-college math classes, students must learn abstractalgebraic and statistical concepts, graphical interpretation, as well as incorporating problem-solving and measurement methods. The challenge of teaching abstract concepts in K-12environment arises from the lack of motivation that students exhibit when faced with having tocomprehend material that appears to be unrelated to their everyday experiences. Yet, many mathprinciples are inherently incorporated into performing simple tasks with a LEGO robot. Forexample, as students develop strategies for the locomotion of a robot traveling a specifieddistance, a math lesson on the geometry of a circle can be used to connect the distance traveledby the robot to the circumference of its wheels.This paper will present illustrative LEGO-based math activities developed under a NSF GK-12Fellows Program. The activities, developed by engineering graduate Fellows in partnership withK-12 teachers, are grade appropriate and address pertinent math learning standards of the cityand state. For example, through the exploration of the mathematical constant “phi—the goldenratio” students learn its mathematical source the Fibonacci sequence and its ubiquity in nature,from snails’ shells to the works of da Vinci. Next, students program a robot to move around agrid in the Fibonacci sequence pattern to view a physical interpretation of how numerical valuesincrease as the robot follows the sequence. In another lesson, students explore the value of theconstant “pi” by programming a robot to draw circles of various sizes. Next, they determine thedistance the robot moves around the circle, “the circumference,” and divide it by the diameter tofind pi. In yet another lesson, students learn representation of “spring” measurement data interms of statistical quantities such as the mean, mode, and median. A spring-mass system is usedwith a LEGO Mindstorms setup involving an ultrasonic sensor for distance measurement. Thesame setup is used for a lesson on graphing an equation such as Hooke’s Law to understand therelationship between force and displacement. Full paper will present details of these and otherlessons as well as assessment of their effectiveness.

Igel, I., & Poveda, R. L., & Kapila, V., & Iskander, M. G. (2011, June), Enriching K-12 Math Education Using LEGOs Paper presented at 2011 ASEE Annual Conference & Exposition, Vancouver, BC. 10.18260/1-2--17910

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