Wednesday, November 22, 2017

11/21 The intersection of History and Mathematics

My goal for this week in Math Club was to do something low key after AMC 8. Originally, I had been thinking about some tangram or panda block puzzles. I also had seen a recent Infinite Series video with a interesting triangle puzzle embedded within it that I thought looked promising.

But as often occurs, I ended up going in a different direction. Earlier last week I was thinking about what educators mean by "humanizing math".  The main claim is that mathematics is cold and sterile which I don't find totally convincing especially in the context of math circles. But some of the of the ideas bundled in with this subject are really interesting. In particular I liked this paper  about using Math History to humanize a classroom. This dovetails with my worry that kids don't really understand the trajectory of their Mathematics education in the same way as other subjects and tend to view Mathematics as a complete set of knowledge rather than a developing field that people still work within.  Even I as a student, couldn't imagine what Mathematics research really looked like.

So I started researching Mathematics History videos that might be a good fit for a session. I found several candidates.  My initial pick was "The Story of Maths"  a BBC documentary that looked promising.  But after picking out the clips when I went to prepare I found that they had all be taken down from youtube due to copyright issues.   It turns out I can borrow the DVD version of this from the library which I will remember for the future.  So instead I went with the following lecture given by Dr. John Dersch:

What I like about this talk is that it covers a lot of ground and gives a good historical framework. Conversely, it lacks flashy visuals and does assume a college level background. So I prepped by starting with a talk with the kids where I had them guess when various mathematical discoveries occurred ranging from addition, to algebra to geometry to calculus.  That set the stage for video. I also liberally stopped the video and talked about various topics. This was especially true when I thought the subject was new i.e. logarithms or derivatives.  This led to several tangents that might be fun to do a whole session on:

  • How did 17th century mathematics calculate square roots or logarithms?
  • Why can't you solve a 5th degree polynomial in a general fashion?
  • Fermat's Last Theorem.
  • Egyptian Fractions

Overall, I thought this went really well. If I repeat this topic, I do hope to find a better video resource or perhaps develop a slide deck of my own.  I also wonder if I could thread various historical discoveries in during a year i.e. a talk on Babylonian tables, or Napier's bones.

Image result for clock image

To round things out before this started I actually went to back to clock problems. This was strategic since I had noticed some of the kids were really interested in when the clock hands coincided already and had been looking up tables of the values online.  (If I repeat and this wasn't already the case I would ask kid to observe during school beforehand.)  The day really started with me drawing clocks on the whiteboard and having a few kids talk about what they already knew.  I was hoping they had noticed a regular pattern but since that wasn't the case we worked on that in club.  One focus I asked a few questions to point out was that here is a point of coincidence at every hour except 11. We then developed the basic equation to discover the actual values.   

m  = h * 5 + m / 12 

I was surprised that this seemed fairly new to everyone and the basic process of solving was not as smooth as expected especially developing the minute to hash mark ratio. I plan to return to ratios at some point.    On the bright side kids quickly found the method for find when the hand form a straight line by the times we were done.

This time I gave out a sample MOEMS test to prep for the first one of the series.  I'm probably going to do it in two weeks which means I'll have to continue to slide the other ones around in order to balance activities out. I'm actually very curious to see how the kids do on it.

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