Robots in Motion, Robot Algebra Project

The Robots In Motion (RIM) research project stems from The Robot Algebra Project. The Robot Algebra project is a collaborative project the University of Pittsburgh’s Learning Research and Development Center (LRDC) and Carnegie Mellon’s Robotics Academy (CMU) to develop instructional materials designed to significantly improve robotic education’s ability to use robotic project based learning activities to increase students’ mathematical competency. The goals of this project are to:

  • Test and iteratively improve project based instructional units which, when implemented effectively in educational settings, significantly increase students’ algebraic reasoning abilities
  • Design the units & support materials in ways that are educative to both the educator and the student
  • Evaluate the extent to which the unit & support materials have met goals one and two
  • Increase the field’s understanding of how policy and organizational features shape instruction and learning outcomes.

Project Description

Robotics education has the ability to excite and engage students in science, technology, engineering, and mathematics (STEM). Robots are intrinsically motivating to students and introduce a rich range of STEM concepts. Mathematics is a fundamental component of STEM careers and that is our focus. Our team has a multiyear collaboration studying robotics education and has observed how a single 30-minute robotics activity designed for middle-schoolers can in rapid-fire touch upon measurement, geometry, algebra, and statistics concepts. In such an activity, there is no time to focus instruction on any one mathematical concept, and we were not surprised that students made no mathematical progress over a full semester of engagement with such activities even though the instructor attempted to focus student attention on the mathematics. Our approach is to focus on one foundational mathematical construct, proportional reasoning, for an entire robotics unit, and indeed build it up over multiple robotics units. Proportional reasoning is a foundational mathematics concept that relates to a wide range of situations in everyday life and in the workplace, such as those that involve unit rates, mixtures, or scaling. Proportional reasoning is also central in understanding how a robot’s movements can be controlled, as the relationships between the physical construction of the robot, the values used to program the robot, and how the robot actually moves are often proportional in nature. Moreover, students need to understand rates, ratios, and proportions to develop algebraic ways of thinking.

Testing Initiatives

During the summer of 2012 a set of teacher support materials were developed for teachers using the curriculum. The development team believes that teachers using the materials should participate in certified professional development programs to learn how to use the teacher support materials. The Robotics Academy includes training on RIM in their LEGO NXT training programs. During the fall of 2012 we will test the materials with 10 regional middle schools. This testing will be used to inform the next round of curriculum improvements.

Project Development and Resources

This project developed three instructional units designed to foreground measurement, direct proportionality, and indirect proportionality through robotics activities.

  • Unit 1 B-U-G – In this unit, students learn about the iKnowMATION Corporation, a company that makes robots and needs to develop a process to ensure that their robots drive straight, turn accurately, and travel the correct speed. Students are required to develop testing methodologies that insure that a new robot travels the correct distance, turns the correct angle, and travels the correct speed. In this activity measurement is foregrounded.
  • Unit 2 Asteroid 2012 JN4 – In this unit, students are tasked to program a robot on an asteroid that needs to explore specific areas of the asteroid. The robot has a limited power supply and therefor students need to program the robot accurately on their first attempt. The lessons focus on direct proportional relationships involving distance, turning, and speed. While solving the challenge students will explore the difference between using a unit rate or scaling strategy to solve the challenge.
  • Unit 3 Bots-in-Sync – In this unit, students are asked to program several robots with different physical characteristics, different size wheels and different robot sizes, to dance in synchrony. Students will use lessons they learned while solving the B-U-G and Asteroid units to solve this challenge. Students will quickly find that they need to solve both direct and indirect proportional relationships to make the robots dance synchronously.

Abstraction Bridges

Through our Robots In Motion units, students are exposed to core mathematics ideas and problem solving strategies in ways that build upon and extend their mathematical thinking. However, we believe addition intervention is required to develop mathematical fluency because of the following issues with the problem-based units:

  • Insufficient time to develop fluency with these mathematical concepts
  • Lacking direct connections with what they are learning in their mathematics classrooms.
  • Lack of easy assessment opportunities for the facilitators to evaluate individual student progress
  • Lack of connections with high stakes testing (of importance to some informal organizations)

We believe that robotics units can build up a core understanding, but additional work is required to generalize the learning. In particular, we believe additional assessment/practice opportunities are required. These paper-based word problems are called Abstraction Bridges—they act as a bridge from contextual mathematics in robotics problem solving to generalized mathematical problem solving abilities. They have the following form:

  • Activities that can act as warm-ups as students are shuffling into the after-school setting, or as simple challenge problems to work on at home between sessions. Only one would be assigned at a given time (i.e., not worksheets filled with problems), but they would be assigned every day for regular practice.
  • Some of these paper-based activities will involve robotics contexts, and many will make connections to other problem situations.
  • Although not as complex as the problems to be solved in our robotics units, neither will these units be rote, mindless kind of mathematics worksheets. More formally within the mathematics education framework, these problems will involve Procedures with Connections, a kind of problem generally associated with better learning outcomes (Stein, et al., 2007).

Below are sample problems, drawn from existing mathematics education resources:

Abstraction Bridge Problem – Rectangle Fractions

About how big is 4/5 of this rectangle? Show your answer by shading in the rectangle?

What other fractions are near 4/5 in size? Explain your answers.

Abstraction Bridge Problem – Graffiti Growth

You are doing a scientific study of graffiti in your local park. On the first day of spring, there is no graffiti. On the second day, there are two drawings. On the third day, there are four drawings. You couldn't check on the fourth day, but on the fifth day, there are eight drawings.

If this keeps up, how many graffiti drawings will there be on day 10? On what day will there be 40 graffiti drawings? How do you know?

A future goal of this project is to develop a larger database of ratio and proportion problems and make them available to educators. The problems will range in contexts, mathematical concept, and difficult. These problems will be distributed through a teacher-useable/managed database. More specifically, we will:

  • Build a website that allows educators to add, sort, and rate abstraction bridge word problems for educators to use with students
  • Develop a structure in the database that helps educators to quickly identify different types of problems in the database, i.e., ratio word problems, graphs, tables, proportional algebra problems, fractional relationship problems also sort the problems based on themes (robots, sports, shopping)
  • Rate the problems from novice, beginner, intermediate, advanced
  • Continually upgrade of the database based on educator usage and research (similar to the way Amazon or Netflix provides suggestions based on prior usage and rating patterns)