Can physical embodiment be used as a tool to improve a student's ability to estimate and approximate the answer to a math problem?

Project Description

- Team Members: Jonathan Vitale, Eric Carson, Tim Chang

- Subject: Mathematics

- Skills: Problem-solving, Teamwork

- Concepts: Estimation/approximation, Decimals, Angles, Decimals & Angles. A conceptual approach to problem-solving.

Research Background

Mathematics is not only an abstract symbol system, but a means for understanding and manipulating our world.  Yet constructing motivating and relevant applications can sometimes be a challenge for the mathematics educator.  Word problems and discovery scenarios can be constructed to demonstrate a single mathematical principle, but these are soon forgotten once the principle is abstracted.  On the other hand, robotics incorporates a diversity of mathematical principles as a means for creative expression and problem-solving.  In this project, we will discuss the design of a 6-8 week upper elementary school curriculum that focuses on the development of several mathematical skills in the context of robotics problem-solving using Lego Mindstorms NXT. 

Although robotics can be used to incorporate an almost unlimited range of mathematics, it is of critical importance to focus on concepts that will have the most relevance outside of the robotics context. Recent evidence suggests that imprecise, estimation abilities play a major role in a wide range of mathematical competencies.  Given the importance of developing a child’s number sense, our curriculum focuses on two mathematical systems where estimation is critical: (i) arithmetic with rational numbers - represented in decimal form and (ii) measurement of rotation - represented in degrees.  Both concepts are necessary when programming the robot’s motion path and will be integrated into the learning and teaching activities of robotics.

Methodology

To explore the relationship between estimation ability and problem-solving, two groups of students received distinct instructional approaches.  The first group of students embodied the concepts described above by simulating the movements of the robot with their own bodies.  The second group made precise measurements and calculations using standard tools and algorithms. 

Research Questions

1. Are students from the embodied group more likely to spontaneously apply strategies of embodiment by accounting for orientation and movement when encountering novel word problems?
2.  Are students from the embodied group more likely to avoid making errors based on the application of inaccurate visual heuristics?

6-week Class Outline

• Session 1: Intro to Robotics/Begin Building
• Session 2: Finish Building/Intro to Mindstorms programming
• Session 3: Decimals/Moving Forward
• Session 4: Angles and 90 degree turns
• Session 5: Converting angles to decimal turn rotations
• Session 6: Culminating activity/Student Presentations

          Detailed embodied curriculum schedule

Sample Embodied Curriculum

• Treasure Hunt (Adding decimals tasks)
• Treasure Hunt (Estimating angles tasks)
• Giving Directions
• Decimal Magnitude Task
• Angle Estimation
• Estimating forward distances

Related Study

Chan, M., Black, J., Han, I., Vitale, J., Xia, Q., Subramanian, M., Du, M. & Kang, S. (2007). "Look, it's turning!" Factors Affecting Structural and Functional Knowledge Acquistion in an Elementary School Robotics Classroom. In C. Montgomerie & J. Seale (Eds.), Conference Proceedings of World Conference on Educational Multimedia, Hypermedia and Telecommunications 2007 (pp. 1626-1631). Chesapeake, VA: AACE.