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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)
    3Topics
    |
    1 Quiz
  3. Lesson 2: How to Improve Math Education in the US
    3Topics
    |
    1 Quiz
  4. Lesson 3: The Trivium and Mathematics Education
    3Topics
    |
    1 Quiz
  5. Lesson 4: The Grammar of Mathematics
    3Topics
    |
    1 Quiz
  6. Lesson 5: Mathematics, Memory, and Retained Learning
    3Topics
    |
    1 Quiz
  7. Lesson 6: Cultivating a Reflective and Collaborative Faculty
    3Topics
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    1 Quiz
  8. Lesson 7: Strategies for Reforming a Math Program
    3Topics
    |
    1 Quiz
  9. Lesson 8: Teaching Math with Socratic Dialogue—Part 1
    3Topics
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    1 Quiz
  10. Lesson 9: Teaching Math with Socratic Dialogue—Part 2
    3Topics
    |
    1 Quiz
  11. Lesson 10: Rhetoric in the Mathematics Classroom
    3Topics
    |
    1 Quiz
  12. Lesson 11: Taking a Liturgical Audit
    3Topics
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    1 Quiz
  13. Lesson 12: Constructing Mathematical Arguments
    3Topics
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    1 Quiz
  14. Lesson 13: Mathematical Proofs Students Should Know
    2Topics
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    1 Quiz
  15. Lesson 14: The Beauty of Math and Poetic Instruction
    3Topics
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    1 Quiz
  16. Lesson 15: Teaching Math as Storytelling
    3Topics
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    1 Quiz
  17. Lesson 16: Essential Elements for Teaching Math
    2Topics
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    1 Quiz
  18. Lesson 17: Mathematics as a Humanities Subject
    4Topics
    |
    1 Quiz
  19. Interviews
    Interview: Andrew Elizalde on Math Education
  20. Interview: Andrew Elizalde on How He Became Interested in Mathematics
    1Topic
  21. Interview: Andrew Elizalde on His Journey into Classical Education
    1Topic
  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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  • Have you in your classroom ever overemphasized the strictly logical, deductive approach to mathematics? If you recognized this issue, how did you rectify it? If you might still be leaning too far in that direction, how can you instead develop your students’ mathematical intuition and imagination? If you have used the Socratic method, how has it helped your students understand the broader process of doing math?
  • If you have been able to use Socratic dialogue in the classroom, have you seen its character-shaping work in your students? Have you found that the general civility among the students as they work together has improved? What about the students’ ability to problem-solve and think critically? Has Socratic dialogue shaped you as a teacher? In what way?
  • Andrew’s example of Socratic dialogue with the graphing of rational functions has a number of steps and involves shepherding students slowly through the unveiling of the concepts. How tempting would it be for you to jump in and show the students how to find right answers? How would you rein in your more impatient students who want to race ahead of the others? How can you cultivate scholé for yourself and your students with the Socratic method?
  • As you preview the topics you need to cover in your classroom in the future, what are some concepts that will lend themselves to Socratic dialogue? Plan how you can devote at least one class period—and possibly several more for additional concepts—to helping your students understand an idea through the Socratic method. Do you anticipate any specific issues as you guide them through this? How can you overcome those issues?