This session explores routines where students analyze correct and flawed sample solutions to consolidate their mathematical thinking in Building Thinking Classrooms environments. By centering reasoning over answer-getting, errors become key tools for discussion, reflection, and deeper understanding.
In this session, we provide geometric definitions for all six trig functions and connect secants, tangents, and chords with the secant, tangent, and sine functions. From these definitions we use geometry (e.g., Pythagorean Theorem, similar triangles) to generate trigonometric identities.
Students often learn procedures before developing intuition for the structures symbols describe. Through hands-on modeling, participants explore how structure, pattern, motion, and constraint strengthen spatial reasoning, problem solving, and mathematical understanding.
