Getting Started

Welcome to NerdCave Mathematics Courses.

These help make abstract math concepts more concrete:

Desmos (Graphing Calculator + Classroom Activities)

  • Great for visualizing functions, transformations, derivatives, etc.
  • Desmos Classroom lets you build interactive activities (like card sorts and exploration sliders).
  • 🌐 https://teacher.desmos.com .

GeoGebra

  • Interactive geometry, algebra, calculus, and statistics tools.
  • Especially strong for dynamic construction and exploration of theorems.
  • 🌐 https://www.geogebra.org

Symbolab or WolframAlpha

  • For step-by-step solutions—ideal for practice, checking, and differentiated support.
  • Helps students understand how answers are derived.

ChatGPT (with Markdown & LaTeX)

  • Use for generating practice problems, markdown explanations, or full problem sets tailored to students’ level.
  • Students can also ask it questions if taught how to prompt correctly.

Khan Academy

  • Free and comprehensive video-based lessons with quizzes.
  • Ideal for independent revision or flipped classroom models.
  • 🌐 https://www.khanacademy.org

📊 Assessment Tools

Make formative and summative assessment smoother:

  • Edpuzzle – Embed questions in math videos for active engagement.
  • Quizizz / Kahoot / Blooket – Game-style quizzes to review topics and prep for tests.
  • Google Forms + Autograders (e.g., Flubaroo) – Create quizzes that mark themselves.

📘 Lesson Design Strategies

“Low Floor, High Ceiling” Tasks

  • Choose problems that all students can begin, but few can fully solve (e.g., visual calculus puzzles or estimation challenges).
  • NRICH and YouCubed offer some great examples.

“Concept First, Procedures Later”

  • Use real-world contexts or visualizations before introducing notation-heavy formulae.
  • Example: Use slope of a ramp to explore derivatives before jumping into rules.

Spiral Review Boards

  • Weekly tasks that cycle back to older topics so they stay fresh over time.

📚 Professional Resources

  • Five Practices for Orchestrating Productive Mathematics Discussions by Smith & Stein – Focuses on questioning strategies.
  • YouCubed by Jo Boaler (Stanford) – Research-backed methods to improve engagement and growth mindset in math.
    • 🌐 https://www.youcubed.org
  • AMS/MAA Calculus Texts & Projects – Enriches with historical and theoretical perspectives for advanced students.

đŸ§Ș Calculus Classes

3Blue1Brown’s “Essence of Calculus” YouTube Series

  • Visually intuitive explanations of fundamental calculus ideas—excellent for deep conceptual understanding.
  • 🌐 https://www.3blue1brown.com
Calculus AB →