Understanding Math – It’s All About Perspective

I love to explore TedTalks as there are so many interesting ones that expose you to new ideas. TedTalks are great to use with students as well, because they can spark conversations, provide some real-world applications, and engage students in learning. I am always looking for any math-related TedTalks, especially when I can connect them to concepts students might be about to explore or have already explored and I want to provide an interesting connection.

There was a newer talk posted by Roger Antonsen entitled Math Is the Hidden Secret to Understanding the World where he talks about how mathematics is all about patterns and the idea of finding patterns is how we use mathematics to understand the world. Asking the questions of how does this work, and why does this work.  Representing something with patterns and then changing the perspective of that pattern can lead to really interesting things.  One of my favorite lines of Antonsen’s is “If you change your perspective, and take another point of view, you learn something new about what you are watching, or looking at, or hearing”. He does a great example of looking at a very common equation: x + x = 2x and realizing that this ‘equation’ is actually two different perspectives – one additive, one multiplicative. He goes on to give several examples, and one the whole talk really brought out to me is this idea that if students are allowed to explore and describe and explain their own understanding of patterns in the ways that make sense to them, i.e. their representations, they might have a better understanding of the mathematics themselves. Representing numbers as patterns of pictures or sound – fascinating and engaging. When he looks at fractions from the perspective of music or sound, the ‘sound’ of 4/3 is really beautiful and makes sense. The different perspectives are what allow us to understand the mathematics.

Obviously, the Common Core comes to mind immediately – those Standards of Mathematical Practice that I love! If we look at just a couple things from these practices you can see Antonsen’s idea of changing perspective to understand and make sense of mathematics (and the world):

  • Students look at problems from multiple entry points (i.e perspectives)
  • Students reason abstractly – i.e. abstract what they know and apply it to make sense
  • Students model with mathematics – i.e. use different perspectives to represent something mathematically
  • Students look for and make sense of structure
  • Students look for and express regularity – (patterns)

Common Core practices really speak to Antonsen’s idea of understanding by finding patterns and using different perspectives to make sense of the world. He does a great job of both visually explaining, using mathematics as his example, of how changing perspective helps opens you up to understanding the world and becoming a more empathetic participant in it. It’s all about perspective.

Here is Antonsen’s TedTalk – worth a watch!