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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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  • How does Andrew define “the art of mathematical rhetoric”? How does his example of “a gallery of student work” demonstrate concrete ways students can practice this art and get better at it?
  • How can you lead your math students from the point of observing and critiquing individual students’ work into the exercise of recognizing common techniques from multiple samples, and drawing generalizations from them? Could the Socratic method be used here?
  • Did you or your group pause and attempt to figure out the chicken and cow problem? If so, did you come up with the algebraic argument or the pictorial argument—or was there another way of finding the answer? Did you discover anything about yourself or your group? Did you or the group think outside the box, and did you find the more creative solutions more appealing?
  • Andrew’s challenge is for teachers to give more opportunities in the classroom for students both to present their own ideas well and to critique or assess other students’ arguments. How might some of the methods given in the lecture (“a gallery of student work,” nominating another student, competing for the most compelling argument presented for the same correct answer) provide you with a springboard for taking up this challenge? If your students are younger, how can you adapt these ideas to begin to develop their practice of rhetoric?