Wednesday, January 17, 2018

TOK 2, Day 50 (1/17): Ethical Frameworks and Ethical Dilemmas

Today, Let's look a bit more formally at the various frameworks.  We can use this prezi by Ha Le to guide our discussion.  

Then, we should explore this super-in-depth Ethics Prezi by Daniel Santella

Remember to finish reading  the great (if a bit long) article, "The Moral Instinct," by one of my favorite public intellectuals, Steven Pinker. We will talk through that article on Friday.

Tuesday, January 16, 2018

TOK 1, Day 50 (1/16): Elegance and Beauty in Mathematics

First, let's return briefly to Fractals to apply the principles we learned to a real-world problem:

How Long is the Coastline of Great Britain?
This question is also the title of one of Mandelbrot's original treatments of the topic.

Then, we can shift our focus to the fascinating relationship between mathematics and beauty.  As we watch the videos and play the games, consider:

  1. What is the role of mathematics in Beauty?
  2. What is the role of beauty in Mathematics?
  3. Why should it be that a more complicated solution that gives the same answer should be considered "less correct?"

Friday, January 12, 2018

TOK 2, Day 49 (1/12): IRW

To do:
  • Update CAS Reflections
  • Finalize CAS Activities
  • Revise EE 
Each of you will be going to meet with Ms. Lawler about finalizing your CAS requirements.

Thursday, January 11, 2018

TOK 1, Day 49 (1/11): Formal Systems & Fractals

First, let's talk a bit about math as a Formal System, which is any rule-bound system that seeks internal consistency.  Have fun solving these "word" problems, and consider the meaning of the following key mathematical terms:

  • axiom
  • theorem
  • rule

Then, we will discuss the wonderful world of Fractals.

Creating Fractals

To begin, you will attempt to make some fractals of your own.  You will need:
  • A large piece of paper
  • A pencil
  • A ruler
  • Perhaps a protractor
Follow the rules to create your fractal.

What do you notice about the image that you are creating? What can we say about these diverse images?  What would a definition of fractals be?

Fractals in Nature
For Benoit Mandelbrot, who gave fractals their name and their theory, one of the most startling aspect of what seems at first to be a purely mathematical exercise was the frequency with which we encounter fractals and fractal-like structures in nature.

Take a few minutes to consider, and try to list ten examples of natural fractals.

Finally, consider this TEDTalk from Ron Eglash, "The Fractals at the heart of African design"

More Fractal Resources:
"Scientists find evidence of mathematical structures in classic books"

Wednesday, January 10, 2018

TOK 2, Day 48 (1/10): Ethics as an Area of Knowledge

Let's begin by watching the following video, explaining the famous "Trolley Problem", a thought experiment to demonstrate some key ethical dilemmas:

After you watch the video, think and discuss:

  1. How would you behave in the first example?  What motivates this decision?
  2. How about in the revised example?  What, if any, difference is there in your reaction?  What creates this difference?
  3. What other modifications to the problem can you come up with that would focus the dilemma in other interesting ways?
  4. Finally, this dilemma is not realistic, but we should think about real-world instances of "trolley problem" thinking at work.  Here's one of my recent favorites. (other take here and here)
And now you smart enough to get this Existential Comics cartoon:

I will send you away today with a great (if a bit long) article, "The Moral Instinct," by one of my favorite public intellectuals, Steven Pinker.

If we have time, or later, we should explore this super-in-depth Ethics Prezi.

Tuesday, January 9, 2018

TOK 1, Day 48 (1/9): Next Steps in EE


Finish Discussions on the Framework for Learning.

  • Remember:
    • You are responsible for documenting your own learning, and for making these records exist in a way that is useful for future reference.
    • I will be using the gradebook and your blog's comments section as my primary means of giving you rich feedback.
    • I will be happy to talk at any time with you about "how you are doing" in class, and how you might continue to improve.
  • First Round Grade Conferences will occur beginning the week of Feb 19. (We'll sign up for time slots as the date approaches)

Extended Essay
  • 1/11, 1/16: Return to Maths as an Area of Knowledge
  • Natural Sciences OPPs 1/18, 1/22

Monday, January 8, 2018