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Teaching Math Classically

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  1. Introduction
    Teaching Math Classically—Introduction: How to Teach Mathematics Well (Preview Content)
  2. Lessons
    Lesson 1: The State of Math Education in America (Preview Content)
    3 Topics
    |
    1 Quiz
  3. Lesson 2: How to Improve Math Education in the US
    3 Topics
    |
    1 Quiz
  4. Lesson 3: The Trivium and Mathematics Education
    3 Topics
    |
    1 Quiz
  5. Lesson 4: The Grammar of Mathematics
    3 Topics
    |
    1 Quiz
  6. Lesson 5: Mathematics, Memory, and Retained Learning
    3 Topics
    |
    1 Quiz
  7. Lesson 6: Cultivating a Reflective and Collaborative Faculty
    3 Topics
    |
    1 Quiz
  8. Lesson 7: Strategies for Reforming a Math Program
    3 Topics
    |
    1 Quiz
  9. Lesson 8: Teaching Math with Socratic Dialogue—Part 1
    3 Topics
    |
    1 Quiz
  10. Lesson 9: Teaching Math with Socratic Dialogue—Part 2
    3 Topics
    |
    1 Quiz
  11. Lesson 10: Rhetoric in the Mathematics Classroom
    3 Topics
    |
    1 Quiz
  12. Lesson 11: Taking a Liturgical Audit
    3 Topics
    |
    1 Quiz
  13. Lesson 12: Constructing Mathematical Arguments
    3 Topics
    |
    1 Quiz
  14. Lesson 13: Mathematical Proofs Students Should Know
    2 Topics
    |
    1 Quiz
  15. Lesson 14: The Beauty of Math and Poetic Instruction
    3 Topics
    |
    1 Quiz
  16. Lesson 15: Teaching Math as Storytelling
    3 Topics
    |
    1 Quiz
  17. Lesson 16: Essential Elements for Teaching Math
    2 Topics
    |
    1 Quiz
  18. Lesson 17: Mathematics as a Humanities Subject
    4 Topics
    |
    1 Quiz
  19. Interviews
    Interview: Andrew Elizalde on Math Education
  20. Interview: Andrew Elizalde on How He Became Interested in Mathematics
    1 Topic
  21. Interview: Andrew Elizalde on His Journey into Classical Education
    1 Topic
  22. Interview: Bill Carey on Teaching Math Classically
  23. End of Course Test
    End of Course Test: Teaching Math Classically
    1 Quiz
Lesson Progress
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  • Do you agree with the idea that students should memorize or be familiar with a “canon” of great proofs? Why or why not? What benefits can students derive from having seen these proofs presented clearly?
  • Why does Andrew call Euclid’s proof of the infinitude of primes “beautiful”? How can you communicate such appreciation for mathematical concepts to your students?
  • What is it about the proof of the Pythagorean theorem that Andrew presents that makes it so appealing? Would strictly visual proofs—ancient or otherwise—be more helpful or less helpful for your students? What are some pros and cons for a pictures-only format for proofs?
  • Andrew suggests we should make certain that before students use something, they understand where it came from. Looking back on your own math education, did you understand (for example) the fundamental theorem of calculus before you ever made use of it? How did that knowledge—or lack of it—affect how you learned its principles? How can you translate your own experience into a beneficial one for your math students?