Tuesday, August 9, 2016

Pattern Finding in Spain

I am currently in Granada which is home to the Alhambra - a fortress from the Moorish times in Spain.  Today I did a bike tour of the city and walked around the old town, snapping some photos along the way of patterns I saw.  Here are a few of my favorites:

Check out that symmetry!

How many different polygons can you find here?

When does this pattern repeat?  

What types of symmetries do you notice here?

While I had initially planned on using this in geometry next year, I found out that I will not be teaching geometry this upcoming school year.  Now the question is, how can I implement what I have learned in my classroom starting this year?

Here are some ideas in no particular order:

  1. Math history: Math has a great history - a history that is actually shared with students who are under-represented in my school.  I can do a better job of incorporating that history in my classroom.  There is a great TED talk about why we use "x" to represent the unknown that I can certainly use in my classroom. 
  2. Math "Excursions": There are fun things to do in math that maybe aren't in the MN math standards.  These fun topics can certainly be tied back to common core math practice standards (which MN doesn't know about/acknowledge) and they are worth while to do because it give students another access point to high level mathematics.  I would like to do a 2-3 day excursion on Islamic Patterns
    1. Start with a little slide show action - incorporating the images I have taken here in Spain and with a little history/culture about why these patterns are in Islamic art.
    2. Give students a pattern and ask them to re-draw it using some scaffold (like a circle, maybe a circle with other circles on it to give them a type of grid. 
    3. After they struggle with it, give students a compass and a ruler and walk them through the process of creating the pattern. 
      1. I think it is important here to bring back the vocabulary - definition of a circle, equilateral triangle, hexagon, regular shapes, bisect, etc. 
      2. You could also relate it to fractals and show students how to keep putting shapes inside a shape.  This could be a good arithmetic sequence problem (when will you have 100 stars on your paper)
    4. Provide students with a pattern and allow them to be creative.  At one point in the class our instructor asked us to "see what we could do" with a pattern we had created.  It was really challenging to think of what makes sense to try to do and what doesn't make sense. We also were asked if we were to make a tile that would repeat itself, what shape would you need to make that tile - how big would it have to be?  Also, a brain teaser!
I would be interested in other people's thoughts on culture in math.  How much do you try to incorporate others' cultures in the math?  

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