PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
Building coherence in circular and complex trigonometry with inquiry-based modeling
Page: 1101
The trigonometry is first framed on a right triangle, next on a unit circle with a parametrized pair of coordinates (r cos t, r sin t), and then on a complex frame, r (cos t + i sin t) unifying the Cartesian pair (Ekici, 2010). Students often struggle in understanding the connections and the transitions among triangle, circle, and complex trigonometry which serve as a critical mathematical foundation in many STEM fields. It is a challenge for students and teachers to coordinate the multiplicity of these trigonometric frames to develop coherent meanings. To support this transition, dynamic manipulatives using GeoGebra are here developed for student experimentation in modeling with modified circular and complex trigonometric functions. The results show that inquiry-based modeling using these multiple yet interconnected frames facilitate the emergence of coherence observed while validating these trigonometric models.