Teaching and Learning Trochoid Curves: The Importance of LEGO® Drawing Robots and Educational Robotics in Tertiary Mathematics Education

Abstract

An innovative, STEAM-based educational approach uses LEGO^® robots to improve the visualisation and understanding of trochoid curves in tertiary mathematics education. The method involves a two-step process: first, the curves are drawn based on the classical definition of trochoids using a custom-designed LEGO^® robot that employs LED light to trace the shapes. Then, the same process is replicated with a marker, with the robot controlling the movement of the drawing head to reproduce the curves accurately. To deepen students’ comprehension and visualisation, Desmos dynamic geometry software was used in parallel to draw all three types of trochoids (prolate, curtate, and cusped). This hands-on technique aims to make these motion curves more tangible and engaging within a classroom setting. A quantitative experiment involving 94 first-year IT BSc students was conducted during the spring semester of the 2024/2025 academic year using a quasi-experimental design. We had one control group and two experimental groups. One of the experimental groups did not use educational robotics; participants could only see how the robots worked via video. The other experimental group gained first-hand experience by building and testing LEGO^® drawing robots. The aim was to evaluate the effectiveness of an innovative teaching method that used educational robotics to improve understanding of the mathematical properties of trochoids, compared to traditional teaching methods and presentations containing short videos. The Mann–Whitney U test was used in all cases during hypothesis testing. Only watching videos of drawing robots does not have a statistically significant effect on learning outcomes. In this case, the effect size was only 0.12. However, the results of the group performing educational robotics activities showed a statistically significant difference compared to the other two groups, with large effect sizes (0.68 and 0.7). Our results suggest that visualisation using LEGO^® robots significantly improves students’ knowledge of parametric curves. Educational robotics offers promising opportunities because it is an attractive and interactive teaching tool. Its great advantage is that it combines abstract mathematical concepts with modern technology, thus creating an effective learning environment.