Thursday, July 21, 2016

Creativity & Beauty in Mathematics

This book has me so fired up about math! Glad you're joining in for Chapter 3 of Mathematical Mindsets by Jo Boaler. If you missed the first couple of chapters, you can catch up here:
Summary
Math is often thought of as a performance subject. Students must perform by getting answers correct. However, mathematicians view math as beautiful, aesthetic, and creative. What? Boaler focuses on the beauty of math, particularly in nature. The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it. Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth. Written as a rule, the expression is xn = xn-1 + xn-2. Put the squares with those widths, forming a spiral:
Look at the symmetry of these beautiful flowers!
And look how amazing this picture is (taken by Cassini) of the south side of Jupiter! It reminds me of a natural mandala; what a fun connection to show students! You can read more about mandalas here.
Just as noticing the beauty of math in nature, mathematics must be relevant and real to students. Conrad Wolfram (2010) proposes that working on mathematics has four stages:

  1. Posing a question
  2. Going from the real world to a mathematical model
  3. Performing a calculation
  4. Going from the model back to the real world, to see if the original question was answered. However, 80% of school mathematics is spent on stage 3: performing a calculation by hand (something employers do not need workers to be able to do; there are computers)
Wolfram suggests that teachers spend more time on stages 1, 2, and 4. Employers need people who can think and reason!
My Takeway
Math must be seen as real and meaningful. Students need to be convinced of the importance of math in their own lives. There's a terrific picture book, A Day with No Math by Marilyn Kaye. A young boy wished there was no math, awaking to find all numbers gone. It's a funny story that makes the point about math in our everyday lives.
Three Tips for the Classroom
Emphasize the creativity & importance of math by sharing ways it is used in the arts, sports, videogames. . . I discovered this cool website, Get the Math,  all about algebra in the real world. There are videos and information about how professionals use math in music, fashion, videogames, restaurants, basketball, and special effects. Student can take interactive challenges related to those careers.
 Focus on problem solving.  Incorporate teamwork, encourage using a variety of strategies. Allow students to struggle and revise. When CCSS were first rolled out, we didn't even bat an eye because our students were so used to explaining their thinking orally & in writing, sharing strategies, and persevering. (However, it takes parents more time to become comfortable with this!) I use monthly problem solving booklets with my kids and although it's often painful at the beginning of the year, by mid-year, they love crossing out their bloopers and showing multiple possible solutions! Click on the picture below to learn more!
Focus on patterns, connections, and relationships in math. Limit the amount of timed tests.
Lots to think about this week! Thanks for stopping by!

7 comments:

  1. I love your ideas! I immediately checked our public and school library for that book and it isn't anywhere. Whomp, whomp...super sad face. I'll keep looking!

    I also love your Get the Math website! Thanks for giving me fabulous ideas in theory and that I can use in practice!

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    1. Oh no, I'm sad it isn't in your library!! :( Definitely keep looking! I know; Get the Math looks like a great site to share with students! Thanks for stopping by!

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    2. Diddo on the "whomp, whomp . . . super sad face." The book must be out of print. It is $200 on Amazon. :o(

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  2. Such great resources Kathie! Thank you! I also love what you said about your students learning that explaining their thinking and thinking deeply just came with the territory. I wish more teachers would embody this principle. What powerful math students we would have!

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    1. Thanks, Shametria! I wish more teachers would have student explain their thinking, too! :) Thanks for stopping by!

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  3. Thanks for the video share. Sometimes students just see math as number crunching. It is good to show how that math is much more than that. Love the nature images.

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    1. I love the mathematical beauty in nature, too!! It's so amazing to see math concepts all around us :)

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