- s3mthartford

# Inquiry-based Modeling of Periodical Orbits in Building Coherent Conceptions of Trigonometry

Updated: Jun 19, 2019

Researcher: Celil Ekici.

Inquiry-based Modeling of Periodical Orbits in Building Coherent Conceptions of Trigonometry across Euclidean, Cartesian, Vector, and Complex Frames

Teaching trigonometry in college often builds on supporting students across a number of conceptual orientations building on triangles, circles, functions, vectors, complex numbers as mathematical objects. Students often struggle to make the conceptual jumps and understand connections among Euclidian, Cartesian, and Complex frames of trigonometry and develop intuitions for more advanced conceptions such as Fourier Analysis.

While Euclidean approach builds on measuring triangles without even requiring negative numbers in modeling direction of measurement of lengths and angles, circle trigonometry builds and expands on a Cartesian frame in modeling a circular point with a pair of coordinates expressed by a pair of cosine and sine functions parametrized by an angle. Here, inquiry-based modeling is used to help students build coherence between the circle trigonometry, vector and complex trigonometry in modeling periodic functions with modified circular orbits.

**RESEARCH PROBLEM:** How do inquiry-based modeling of periodic functions with modified circular orbits help students develop coherent understandings and connections between the circle trigonometry, vector, and complex trigonometry?

**DATA COLLECTION TIMELINE:**
Fall 2018: Developed, piloted, and refined the IBL modules on a modified circular approach to facilitate transitions between circles, functions, and complex frames
Oct-Nov 2018 & Feb- March 2019: Building and refining student-centered experimental tasks and objects for inquiry-based modeling of trigonometry incorporating technology such as GeoGebra.
April 2019: Refine the assessment of student learning outcomes including concept maps to track conceptual connections to build coherence.
Summer 2019: Analyze student work and refine modules and assessments.
Fall 2019: Teach the course again and collect student data refining IBL modules and their assessment tools. Conduct focus group sessions. Involve outside observers and video recordings of class sessions on student learning and interactions with each other.