Looking at Mathematics Differently

This course was about changing the way we look at mathematics and the world around us. We looked at mathematical problems through different lenses and connected it across disciplines. We shared our thinking and heard the thinking from others, allowing our mathematical understanding to become deeper and our perspectives to change. Here is a look at some highlights of our favorite activities of the class this trimester.

Poetry in Mathematics

You are probably wondering if you read that correctly...poetry in mathematics...could it be?

That's right, your eyes are not tricking you!

It was such a fun way to connect across disciples, think about numbers differently, and display our mathematical knowledge. We analyzed the numbers in the picture above and discussed them. This led to us learning about prime numbers. Then, we heard mathematical poetry in the form of Spoken Word on prime numbers by Harry Baker and discussed what made that poem special, funny, mathematical, and creative. Conversing in depth about how the poet deliberately personified the numbers and looked at them differently. We all appreciated the thought behind the poem and decided to used our mathematical knowledge and creativity to write our own poems with our own style, perspective, and flow. We picked a number and gave it a try! Finally, sharing what we had written (in true Spoken Word form) to our audience. The creativity that spilled out of each of these mathematicians was truly phenomenal!

Perspective

When we look at a mathematical problem, we analyze it our own way, oftentimes uniquely. Let's use the picture above to point this out. There might be something that you notice about one of the numbers that someone else didn't notice. The ability to explain our thinking, reasoning, and rationale is such an enormous part of mathematics. Some of our underlining principals in this course were:

• we believe everyone can learn math at a high level
• math is visual (even when we think it might not be)
• math is all around us (along with lots of wonder and curiosity)
• we value communication and connections
• math is open and it can take many forms, strategies, and perspectives
• we value mistakes

Powerful Questions to develop a Deep Level of understanding in Mathematics

• How do you see that idea?
• Why does that answer make sense?
• Why does that method work?
• How is that method or strategy connected to others?
• How can that idea be represented in different ways?
• Can you prove it?
• Can you justify your thinking?
• Can you predict what would happen if...?
• Did you make any interesting mistakes?

From Jo Boaler, Stanford University