Precision Low-cost Robotics for Math Education (Work In Progress)

A professor and several teachers in mathematics have collaborated with an engineering professor and his students at our university since 2011 in developing robots for math education. This project was started with the clear goal to develop low cost robots that use off-the-shelf commercial grade components and are thus easy to incrementally acquire, build, maintain and repair. Further, this robot, unlike currently available commercial education robots, would be built to be transparent in exposing the underlying math, physics, engineering, and technology principles. A group of engineering undergraduates first built low cost prototypes and explored alternatives for cost effective solutions. In a following semester, Seventeen ninth grade preengineering students worked in teams to build their own low cost robots (an improved version), program them and use them to draw various geometric shapes . This course was designed to enhance their interest in engineering and math, while providing a social context of empowerment, competition, and cooperation. The results indicate that these students benefited from the use of robots. Two papers document the research results of student interviews to evaluate the effectiveness of this course 4, . This will be described further below. In the 2103 ASEE conference paper, a two-boat problem was examined to demonstrate how robots can be used for solving complex math problems in an intuitive and incremental manner. The problem is visually and dynamically solved. Successive approximation is used to identify a trend and come close to a solution. After examining the problem from multiple perspectives, the students become comfortable that the result that they have gotten with the robots is near to the mathematically correct solution. Students can stop with the robotic investigation at any point and solve the problem algebraically. Earlier student interviews demonstrated that robots help students visualize challenging real world applications and secure multiple representations of a problem. They also develop a lasting handson experience in a social context and a better attitude towards math education and engineering realities. Building low cost robots that schools can afford would ensure access, availability and foster mainstream instruction with robots that would prepare our next generation in math and engineering principles. This latest paper is focused on the final phase of engineering research, to build in precision in robots so the distances traversed and angled turned are mathematically exact. Problem solving can be significantly supplemented with robotics, even if a robot is imprecise, goals that are well appreciated by high school students who are in a pre-engineering program. However, it is also essential to make the robot a tool for teaching math to all students, so interest in math and P ge 26242.2 engineering can be enhanced for all. This is required to make the robots useful in classroom environment for teaching mathematics. Several engineering enhancements already implemented and currently undergoing implementation will be covered in detail in the paper. These significantly improve the precision of the robot; here precision implies the yield of a repeatable solution. Ten graduate and undergraduate engineering students worked during this semester to improve accuracy and incorporate methods for error correction and detection to build a robot that solves a math problem much more accurately. Thus, the focus is not only making the problem solving exercise more repeatable and precise, but also enhance the eventual accuracy of the solution. This will be presented in more detail at the conference (as it is underway at present). Concurrent to this engineering effort, research is also underway to develop math lessons that can be incorporated in a class environment. This will be covered briefly in this paper. This will also be covered in more detail in the presentation. The presentation will also be supplemented with student and teacher surveys (contribution of the fourth author, an undergraduate engineering student with interest in education research). Background: Mathematics plays an important role in high school education as it helps students develop the skill of problem solving. Problem solving is a useful and necessary skill in STEM fields which high school students may have interest in pursuing in college and as a career. But there is a dichotomy mathematics is a precise science, and any problem solving engineering paradigm provides an optimal (or near optimal) solution. Anyone with an engineering perspective learns to appreciate this and continue to combine the two skills advantageously. However, not all students significantly develop this skill when learning math in their curriculum as they may not see the connection between the theoretical concepts in the subject and the practical problems associated with STEM fields. This lack of a connection could negatively affect the students’ performance and interest in STEM. Our initial focus was to develop the robot as a tool for problem solving . We also made sure that it is low cost and reliable so schools can afford to buy and repair. However, it soon became clear that the robot also should be precise, and accurate, for it to be useful as an educational platform to teach mathematics. The motivation for undertaking this paper’s research project thus stemmed from the desire to enhance high school students’ retention and interest in Mathematics. Such qualities would significantly improve their performance in STEM (Science, Technology, Engineering, and Mathematics) career fields and education in general. Our exploration showed that much research has already been performed by other researchers to facilitate high schools in fostering STEM interest with robots 6 . However, such robots have tended to be expensive (~$300) by standards of a typical high school in the US and elsewhere. Further, their role in exploring fundamental P ge 26242.3 principles of math is limited. Our experimentation with commercial educational robots showed that programming, and transparency into the underlying behavior, of such a robot is limited, with the results that are mathematically imprecise (and inaccurate). Our results on this are unpublished at present; however some related work is published in a graduate student’s blog . While there is universal agreement on the potential of robots to enhance STEM interest, the enthusiasm seems to be have been stymied by the non-availability of low cost and mathematically accurate robots. Perhaps the lure of commercial potential of high end educational robots has kept companies from exploring this option. There is still a large barrier for their use routinely in a class environment, because of their cost and sophistication, and the inability of a typical school to support teachers and students in their routine use. We believe that robots built with low cost and off-the-shelf components can reduce this barrier immensely. If, further, they are made (precise and) accurate, they will gain a major role in teaching math. This is based on the feedback we have received from all types of stakeholders, viz., parents, students, teachers, and administrators. A definite attempt will be made to quantify this with a survey in the near future. Our extended research group has parallel activities underway to facilitate (middle and) high schools in using robots to enhance Math education. This collaborative research project involves several faculty members from engineering, mathematics, education, and K-12. It has led to the development of several iteratively improved platforms. Our goal has been to increase interest in STEM-related fields in high school students as well as teaching system-level design and integration issues to engineering undergraduate students. Using low-cost, imprecise components, a group of undergraduate students first built functional platforms (four years ago); this highlighted several issues associated with the components. A group of high school students (in a pre-engineering program), with no prior programming and electronics knowledge, then built and used an improved platform to draw mathematical shapes on a large 6’ x 6’ canvas. These experiences led to continued research to further develop the platform’s precision and robustness. All of this is documented in earlier papers presented at education conferences and at our websites. Our low cost (under $100) robotic platform 1-3 allows for hands-on demonstration of mathematical topics, such as Geometry and Trigonometry, which are taught in the classroom. Our initial demos to math teachers and pre-engineering students demonstrated the problem solving capability of the robots, especially for visualizing and exploring multiple perspectives. Understandably, this meets well with the needs of pre-engineering students in high school, who also now understand the errors in real world representations of mathematical concepts 4 . But a typical student in a middle or high school math class needs an accurate representation of mathematical concepts, whether it is done with a graph sheet, a computer simulation, or a physical robotic simulation. Page 26242.4 Our low-cost robot is made out of off-the-shelf commercial components to keep the cost low; these components in turn have poor tolerance. Such poor tolerance leads to the solutions being imprecise during the robotic platform’s execution. In this work, we document our solution to compensate for the poor precision in distance traveled and angle turned; for this, we use engineering approaches, viz., feedback control algorithms and custom (automated) calibration, to achieve this, while still keeping the cost low and the platform simple to utilize. This work by a DIS (Directed Independent Study) student (3rd author) has provided significant improvement; further improvement is being actively pursued at the algorithmic and robotic level by tw