Enriching K-12 Math Education Using LEGOs

摘要

Abstract 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.