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Ms. Juretic Pries

Theory of Knowledge

TOK Unit Outline:

Unit Objectives:

  • to understand the axiom-theorem structure of mathematics

  • to understand the implications of this structure for mathematical truth

  • to understand the role of logic in mathematics and the link to rationalism

  • to be able to discuss possible links between mathematics, science, art, and language

  • to understand why mathematics may be regarded as an extremely creative discipline

Day 1: Introduction to Mathematics

  • BR: Read the G.H. Hardy quote on the overhead. What do you think of Hardy’s assertion that he had never done anything “useful”? Do his words regarding the value of creating suggest similarities between math and the arts? How do you plan to add to knowledge in your lifetime?

  • Activity: Math!

Day 2: Is Mathematics the “Language of the Universe”?

  • BR: Choose 3 words that best describe the essence of mathematical knowledge.

  • Reading: “Is Mathematics the “Language of the Universe”?

  • Assign unit project: Interview a Math Teacher, due on: _______________

  • Activity: write a poem in mathematical language

Day 3: Mathematics: Invention or Discovery?

  • BR: Do you think that intelligent aliens would come up with the same mathematics as us, or might they develop a completely different kind of math?

  • Poem share

  • Reading: “Math: Invention or Discovery?”

  • Writing Prompt: Do you think that the full expansion of pi, which goes on forever, exists “out there,” and that we are gradually discovering more about it? Explain your answer.

Day 4: The Nature of Mathematics

  • BR: Evaluate this quote by Jack Handy: “Instead of having ‘answers’ on a math test, they should just call them ‘impressions,’ and if you got a different ‘impression,’ so what? – Can’t we all be brothers?

  • Reading + Questions in Groups: “The Nature of Math”

  • Exit Quiz

Day 5: Math as a Creative Art

  • BR: Consider the following quote by Henri Poincare: “The useful combinations (in math) are precisely the most beautiful.” What do you think he means by this?

  • Activity: Beauty and Elegance in Math

  • Reading + Questions in Groups: “Math as a Creative Art”

Day 6: Mathematics and Certainty

  • BR: Some philosophers have suggested that rather than think of mathematical entities as being either objective or subjective, we should think of them as having ‘social existence.’ Consider the game of chess: In what sense does it exist? Does it still exist if no one is playing chess? What about if no one is thinking about chess? Would it still exist if we destroyed all the rulebooks on how to play chess? Most people would probably say that, even if no one played chess for a year, there would still be certain statements about it that are true and others that are false. However, if the human race disappeared, it wouldn’t make much sense to say that the game of chess still existed.

    • Although Romeo and Juliet are fictional characters, it is true to say that Romeo loves Juliet and false to say that he hates Juliet. In what ways are mathematical objects similar to fictional characters and in what ways are they different?

  • Unit project share (teacher interview)

  • Reading + Questions in Groups: “Mathematics and Certainty”

  • HW: finish reading questions

Day 7: Unit Review

  • Quick Read: “The Number System is Like Human Life”

  • Review for tomorrow’s exam

Day 8:

  • Binder Check

  • Unit Exam

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