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Contemplative Mathematics: Leading Math Discussion Groups

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  1. Introduction

    Introduction to Socratic Mathematics (Preview Content)
    2 Topics
    |
    1 Quiz
  2. Sessions
    Session 1: Figurate Numbers
    2 Topics
    |
    1 Quiz
  3. Session 2: Square Numbers
    2 Topics
    |
    1 Quiz
  4. Session 3: Co-primality
    3 Topics
    |
    1 Quiz
  5. Session 4: Co-primality and Fractions
    2 Topics
    |
    1 Quiz
  6. Session 5: A Numerical Puzzle
    2 Topics
    |
    1 Quiz
  7. Session 6: Another Numerical Puzzle
    2 Topics
    |
    1 Quiz
  8. Session 7: The Bridges of Köningsberg
    2 Topics
    |
    1 Quiz
  9. Session 8: Patterns in Graphs
    2 Topics
    |
    1 Quiz
  10. Session 9: Chromatic Graphs
    2 Topics
    |
    1 Quiz
  11. Conclusion
    Concluding Remarks
    1 Topic
  12. End of Course Test
    End of Course Test: Contemplative Mathematics
    1 Quiz
Lesson Progress
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  • First Discussion Questions: Remember that the goal here is to seek out truth together, and convince yourselves that you’ve found it. As the facilitator, part of your responsibility is to make sure that everyone in the group is heard and on board!
    • Can you order the graphs from fewest lines to most lines? Can there be more than one graph with the same number of lines?
    • In the top two rows, the graphs above and below each other are the same graph. So the top left-most and the middle left-most are the same graph. Given that, can you conjecture what counts when distinguishing graphs? Could you draw any of those graphs in different ways?
  • Second Discussion Questions: If you’re happy with the discussion about when graphs are the same or different, here are a few more that you can play with to tease out some more properties of graphs. Let’s see if we can find some rules to categorize them!
    • The graphs on the top are all happy graphs, and the graphs on the bottom are all sad graphs. Can you come up with a rule to sort graphs into happy and sad?
    • There are exactly twelve different happy graphs that have four dots. I’ve drawn four of them for you. Can you find the other eight?
    • How many happy graphs are there with exactly three dots? How many with exactly two? How many with exactly one?
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