Three-Dimensional Interactivity of Polar Functions Through Arduino and Joysticks

This article presents an action-research study with a quasi-experimental design aimed at evaluating the academic impact of integrating polar-graphics programming into an interactive three-dimensional environment using Arduino and joysticks, for learning trigonometric functions at the upper-secondary level. The intervention draws on Seymour Papert's second big idea —constructionism: learning by building shareable artifacts— and on Project-Based Learning (PBL), and was designed as a structured instructional sequence of four 50-minute sessions. The study was conducted at the Lázaro Cárdenas del Río Preparatory School of the BUAP Bachillerato General, with a total of 120 fifth-semester students distributed into an experimental group (n = 58) and a control group (n = 60). The triangulation of five instruments —pre-test/post-test, Student's t-test, portfolio of evidence, analytic rubric, and a 10-item Likert survey— revealed significant results: the post-test recorded an efficiency of 94% in the experimental group (relative improvement ≈198%; t = 9.12, p < 0.001, Cohen's d = 1.31); 93% of portfolios reached high quality, with equations of considerable complexity and complete assembly of the device; and 95% of Likert responses rated the project as a means that gives real meaning to the abstract concept of trigonometric functions within a three-dimensional environment. It is concluded that combining constructionism and PBL with visual programming environments and open-source hardware constitutes an effective strategy for meaningful learning of trigonometry in the intervention's academic unit.

Constructionism; Project-Based Learning; Arduino; Processing; polar functions; STEM; interactive 3D visualization

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