Published on February 16, 2014; Permalink; Tags: Mathematics • Assignment • Robotics
This post was published as part of an assignment in EDSE 338 in the Faculty of Education at the University of Alberta.
The above scenario has been paraphrase from an 1984 article by Sawada that explores how robots can be used in primary grade mathematics classrooms as a tool for inquiry-based explorations. Although this particular example is intended to be a bit tongue-in-cheek it does require students to use various mathematical concepts that are covered by the Program of Studies during the primary grades, e.g. estimation, mental mathematics, distance, and direction. Sawada offers various compelling examples of how robots can be used in a primary grade mathematics classroom to enhance teaching and learning, to differentiate instruction, to personalize the learning experience and to solve authentic real-world problems. All of these aspects play a central role for effective teaching and learning and for motivating students of all abilities. If mathematics thinking is about understanding concepts and foster a certain way of thinking (Ben-Hur, 206) and if we use computers in mathematics for tedious and repetitive calculations (Wolfram, 2010) then robots are the physical manifestation of mathematical concepts and calculations (Sawada, 1984). What this means is that a robot becomes an physical manifestation of a students mind, or in Sawada’s own words “[the robot] carries out the child’s thought in the world of the child”.
It is remarkable that although the Sawada paper was published three decades ago, and although the specific robot technology described in the paper is since long obsolete the ideas Sawada articulated are not only timeless but even more relevant today with robotics programs appearing in an increasing number of schools. Unfortunately, however, often students are not given the opportunity to use robots in a classroom setting until junior high or high school level. Sawada argues, however, that already in elementary school children can benefit from using robots in the classroom as a tool for exploring and learning about mathematical concepts. From my own experience children as young as 7 can learn how to program computers, I am currently teaching a gr. 4/5 robotics class of very capable students, when writing his paper Sawada himself had his 6 year old son program a robot, and every year tens of thousands elementary school aged children (from grades 3) participate in the FIRST robotics program. Clearly, not only are elementary school students highly capable when it comes to computer programming and robotics they also have a lot to gain by being offered the opportunity to explore mathematics through this type of technology.
Incorporating robotics into the mathematics education of primary grades exposes students to all the mathematical processes required by Education Alberta in the Program of Study, all of which are central to good quality mathematics teaching and learning. Specifically,
2 steps forward
3 steps forward
5 steps forward
which corresponds to \(2 + 3 = 5\). By programming and executing the two different version of the program students can verify the answer, i.e. both journeys are the same, and make connections between the addition operation and displacement in the physical world.
turn 90 degrees to the left
In reality, however, it might turn out that an uneven surface or extra grippy tires interact (or interfere, if you will) with the turning robot changing the actual angle the robot ends up turning. This is authentic problem solving, while the theory can give you a prediction (the robot should turn 90 degrees to the left), interactions with the physical world requires the predictions to be adjusted.Ben-Hur, M. 2006. Concept-rich mathematics: Building a strong foundation for reasoning and problem solving.
Meyer, D. 2010. Math class needs a makeover. Accessed on Feb 15, 2014. URL: http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html
Sawada, D. 1984. Computer power in primary grades: Mathematics with Big Trak. The Arithmetic Teacher
Tunis, H.B. 1994. A Tribute to the "Arithmetic Teacher". The Arithmetic Teacher 41(9):512. (URL: http://www.jstor.org.login.ezproxy.library.ualberta.ca/stable/41196095. Accessed on February 16, 2014)
Wolfram, C., 2010. Teaching kids real math with computers. Accessed on Jan 20, 2014. URL: http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers.html
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