Math = Patterns

Fibonacci Sequence Powerpoint, Nicole Horlings, Oct 23 2017, Screenshot 

How on earth is a comparison between a pine-cone and the Parthenon relevant during math class? Well, to answer that question, I first need to ask you a different question:

How do you define math? 

Is the answer:

a) the study of numbers?
b) a set of rules?
c) a set of patterns?

While none of these answers are incorrect, the answer that you chose for this question is still important. As Dr. Boaler explains in this video, most people see math as numbers. This answer seems pretty obvious, since you can't do math without numbers, right? Well, the mathematicians who see math as a set of patterns probably wouldn't agree with the previous statement. Patterns, such as the spiral of a fern, exist in nature without requiring any numbers. The Fibonacci sequence is a special pattern that is extremely prevalent in nature, as well as in a variety of other locations, such as art and architecture. Thanks to this pattern, students could do an inquiry project based off of the question, "What similarities are there between a pine-cone and the Parthenon?"

But why is the way that you define math important?

Throughout my youth, I was implicitly taught that math is a set of rules about numbers. This made math feel abstract and disconnected from nature, which made it difficult for me to make connections between the concepts that I was learning about and how I could apply them to my life. I believed that I had to follow certain procedures to answer math problems, and felt closed off from exploration and inquiry.

As a teacher, it is important for me to view math from a different mindset. Defining math as a set of patterns opens it up to exploration and inquiry, allows for a variety of entry points for understanding, and directly connects math to nature. Suddenly, there are ways to study math in other subject areas such as music, dance, sports, and biology.

If you're still not convinced, just consider which came first: patterns that exist in nature, or the numbers that we use to describe the patters that we see?