Tuesday, June 17, 2014

Capstone Book Club - Summer 14

Time for another installment of Read 'Em and Weep... no, that doesn't sound right. See a previous edition here.  Students grouped with others who read the same book, plus a group of readers with unique books. After they have a chance to discuss for a good bit, I ask the groups to think of what they want to say to the whole class about it. In a whole class circle, we discuss each book in turn. These notes are from the whole class discussion.

Accessible Mathematics:
shifts emphasize how to adjust your classroom… eg. multiple representations. Liked it b/c it wasn’t just changes. Like minimizing what is no longer important; calculators for example. A lot of specific examples… real life. $1.89 v easy numbers…
Love and Math:
Good for non-math majors so they can understand what we’re talking about. Example of symmetry: which is more symmetric a circular table or a round table? If you left the room and I turned. More of a story and Frenkel’s search for knowledge.
e: the Story of a Number
We agree that the beginning - the history of the mathematicians who worked on it - was very accessible. Could not follow the shifting representations of problems in the last few chapters. The end was significantly harder to understand. The part about the personal life of mathematicians was cool, and who winds up getting credit for achievements. Publish or perish keeps some people who deserve credit from getting it. Qualified recommendation. Music and logarithms. Some review that was helpful. Interesting to see how they discovered what we study, and how hard it was to find some of what we take for granted.
Euler: the Master of us All
Is Euler human? Today you have to be very specific, but Euler did so much in so many areas. He goes by topic, what was known before Euler, hen what Euler did. Proofs, but open to people who can handle logs and series. Highly, highly recommended. Popularized complex numbers. His proof writing was like Romeo and Juliet; the balcony just works. Blind for a lot of his life…
Review: Kyle Ferguson: plus some extenisve book notes.
    Gödel, Escher, Bach
    Really about Gödel and the incompleteness theorem. He’s trying to explain to a general audience. Tortoise and Achilles, a fable, then ties it into a serious discussion of the mathematics. He also ties in art, music, zen philosophy. Not a clear path to the Incompleteness Theorem, but about what is interesting along the way.

    A Journey through Genius
    Paint a picture of mathematics that is logically sound and aesthetically beautiful. He picks the best proofs, a bit of history about the man, then an explanation. You could read this in sections to understand something specific and the culture it came from. Not just about the applications, but appreciating it for what it is. Logic still holds true centuries later.
    Review: Jason Lohman

    The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Prob-
    lems, and Personalities by William Dunham
    Also by Dunham. Proofs and problems of mathematics, arranged alphabetically. Which is confusing vs historical order. Chose some really interesting proofs. Any natural number as distinct integers and odd integers.
    Review: Nate De Maagd. Includes some of his proofy highlights. (click through to Gdoc)
      Vision of Elementary Mathematics
      Good for non-math majors teaching elementary school. Good for visual learners, lots of diagrams. Also for getting kids to discover math on their own. Gives alternate perspectives that could help in talking to students. It’s a little repetitive. But we’d really recommend it.
      Mathematician’s Lament
      Problems with math teaching as it is right now in schools. The differences between teaching art and teaching math. The creativity is taken out of the math. There’s nothing to explore or discover. Like teaching art with only paint by numbers. Couple issues with some of the arguments: like teachers try to make it interesting but it already is interesting. Or you learn when it’s relevant to you, but he had argued against relevance. Also doesn’t describe how to make it better. Says math should be a free for all - against all structure. Everything he’s telling us is pointless. He’s against drill but favors real world problems. We teach definitions for no reason. (Quadrilaterals, for example. But then how do we communicate math?) Has a mathematician’s perspective, but he didn’t have a teacher’s perspective. What he offers doesn’t seem appropriate to most schools. The conversations at the end of each chapter were confusing. “What to do with elementary students?” “Just have them play games.” Strong opinions but no evidence. You should read it but it will make you frustrated.

      I feel like how we’ve been taught to teach does help handle a lot of these issues. It would work if everybody loved math like he does.
      The Joy of X
      Insightful and helps make math more accessible. Analogies from Sesame Street. “Fish, fish, fish, fish, fish, fish…” all the way up through complex numbers. Split up into 30 short chapters. From numbers to infinity. I liked the way he uses personal stories. Very readable. Not for diving into math but there’s a lot of stuff that helps clarify. Even for someone who struggled with math. But it won’t change your mind. Great book for college freshmen who have to start making some sense of math. Also good for middle school and high school teachers.
      The Math Book
      Looks intimidating but it’s an easy to read. A page and a picture. Goes through history including lots of things that you would not think of as math, like tic tac toe or mancala. Also see a lot of mathematicians come up multiple times, which is neat to see

      Students choose their own books and that really pays off. Very positive feedback this time around. We follow it up with a book swap, so you get to read a second book that is of interest to you, or at least to skim it. (That's why some people have more than one review linked.)

      Some of the reviews are fabulous; if you're interested by the blurb here I'd really recommend following up. And of course, if you have a chance to comment on a student blog, that's excellent.

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