Reference Angles v2 - Pedagogical Notes

🎯 Where This Came From

Four students taught unit circle lessons: Ana Fernandez, Aaron Hagaman, Katelyn Smith, Emma Stenger

Problems identified across their lessons:

Sign errors by quadrant — Ana's students got numerical values right but applied wrong signs (Q1-Q4 confusion)
Decimal bypass — Aaron's students memorized decimals instead of understanding triangle relationships and exact values
Coterminal angle confusion — Aaron's students couldn't "enter the circle" from angles like 405° or -135°
Students could work within the circle but struggled connecting it to real angle measures

Design goal: Build three targeted features, each addressing a specific misconception from field data.

Feature 1: Predict Signs Mode (purple button)

From Ana's feedback: "Requiring students to PREDICT the sign BEFORE they calculate"
Students choose +/− for sin/cos/tan, then check answers
Coordinates hidden as "( ?, ? )" until prediction checked
Correct predictions turn green, wrong turn red

Feature 2: Exact Values for Special Angles

From Aaron's feedback: "Fractions and triangle relationships are the conceptual core"
Shows √2/2, √3/2, ½ in bold white when at 30°/45°/60°/90°
Decimals shown below in muted gray (de-emphasized)
Prevents students from bypassing the conceptual understanding

Feature 3: All Quadrants Simultaneously

From Aaron's feedback: Students couldn't connect coterminal angles across quadrants
Shows reference triangles in all four quadrants at once
Color-coded by quadrant (Q1 amber, Q2 blue, Q3 violet, Q4 green)
Terminal quadrant gets larger dot to show "where you landed"

Predict mode doesn't track history: Can't see previous attempts or patterns across multiple angles
No guided progression: Students might skip straight to checking instead of reasoning through signs
Exact values only show magnitude: Students still need to apply quadrant rules for signs
All-quadrants view can overwhelm: Too much visual information for first-time learners
No connection to real-world contexts: Still abstract unit circle, not tied to periodic phenomena
Dark theme may not print well: If students want to annotate screenshots
No explicit coterminal angle labels: Doesn't show 45° = 405° = -315° relationship directly

What did you notice? What was confusing? What would make this better?

Click above to open the shared feedback document. Your instructor will review all responses this weekend.