A Hobbit Post

I saw a quote by Steve Jobs on Twitter today:

“Why join the navy when you can be a pirate?”

I googled the quote to confirm that it was Steve Jobs and if Wikiquote can be trusted and without going to deeply into the true origins of any quote, it seems it can be safely attributed to him.

Cheesy mantras about “teaching like a pirate” aside, this describes my current feelings about being an educator pretty well. The politics and red tape related to education right now are very frustrating and discouraging to me and I find it much more appealing to do something independently. I have more thoughts on this, but I have other things I need to be doing right now so that is all I will write for the moment.

Yarr.

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Hilbert Space Invaders

As an adjunct at a two-year college, I have been given a class called “Foundations of Quantitative Reasoning” to teach on several occasions. Essentially it is a throw-away breadth of knowledge class that the college offers students who don’t need any specific math classes for their degree but still need a course in “quantitative reasoning”. The supplied textbook is a hodge-podge, Frankenstein’s monster of a book that starts the first chapter with the basics of formal logic and set theory and, in what could be called the paragon of awful transitions, switches to units and percentages in the subsequent chapters. The idea was to create an overview of “real-world math”, but the result gets on my nerves as much as the phrase that describes its goal.

Anyway. Enough complaining. I’ve made the course my own and had fun with it.

One of the things I did was take the “Mathematics and Art” chapter of the book and use it to help introduce students to the idea of doing math as a recreational activity. I integrated that chapter with the previous chapter about fractals, talked about the dreaded Cult of the Golden Ratio, threw in a few Vi Hart videos and ta-daaa: arts and crafts day in a college math course that is secretly some of the most interesting math my students did in that course. (And they didn’t complain about it either….mostly.)

While researching different ideas for this lesson, I came across the Wikipedia entry for Hilbert Curves.

This idea must have stuck in my mind because some months after that math-art lesson I found myself doodling during a meeting.

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After I made the third iteration of the curve, I noticed that if I continued my grid a little more, I could enclose the shape in a pleasing manner. After I colored it in with my pencil, it reminded me of an enemy ship in Galaga. Or a space invader. Hilbert Space Invader.

I went back and extended the second iteration as well.

Summers are a slow time at the tutoring center where I work full-time and so I found myself making a grid on construction paper.

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Then I realized I had drawn too many boxes, so I erased a few.

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It turns out I still had too many, but I didn’t realize that until later. I was so concerned about recreating what I had doodled on my meeting agenda, I wasn’t really thinking about the curves were made in the first place. I feel like my intelligence fluctuates and today was a low day, because then I forgot how to make the curve completely and had to scribble for a while.

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Ignore the prime factorizations, I was tutoring a very kind, older woman yesterday who was taking an algebra class to, in her words, “keep her mind from atrophying”. Which I found very impressive. I’d tell you how old she was, but I didn’t want to be rude yesterday, so I didn’t ask her. So finally I remembered how I had done the curve and started sketching. I tried to connect the middle of each square for the lines. I almost used a ruler to keep the edges straight, but my personality has too much lazy and not enough perfectionist to take the time to do that. Here are some stages of the work.

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It was at this point that I realized I still had too many squares. Oops. Like I said, low day. I cut out the grid.

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Then I drew a second level curve on the leftover piece.

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Then I cut out the shapes to make the invaders.

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I wasn’t sure what to do with the first iteration of the curve since it actually looks like this.

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And there didn’t seem to be a good way to cut it out, so I left it as the square. I’m open to suggestions. Here they are on my whiteboard.

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I’ll probably spend way too much time today making more and then recreating a space invaders scene on the whiteboard. I’m thinking about trying to make space invaders clone, but with my Hilbert Space Invaders instead. Also, I wasn’t sure at first if Hilbert Space Invaders was really the proper term for them since technically the shapes come from Hilbert Curves, but I couldn’t come up with a funny play on words that involved Hilbert Curves. However! I figure since a Hilbert space is a generalized n-dimensional space (if I understand the wiki article correctly) then my curves are invading a 2-d place that could be considered a Hilbert space. I think Hilbert Space Invaders turns out to be a good name.

So anyway, that’s what I’ve been wasting my time on.

 

 

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Reservations, Table for One

I know I was supposed to post Part 2 of my thoughts on that BuzzFeed quiz. I had it half written, but I didn’t like the tone/content as it was. I’m working on it. There are some thoughts in it that I want to share, but it needs tweaking. In the meantime, this post is almost a direct copy-paste from an assignment I had to write for the training class I am currently taking to teach online courses at my job. It’s a first draft and I didn’t try to go back and reword or reorganize anything. Just me, letting my thoughts out.

I feel a little like a hypocrite teaching this online calculus class this summer. Teaching online feels like—mercenary work? I don’t know how to describe it, I can’t find the right metaphor. Teaching online feels like something I shouldn’t do as a teacher, but it is necessary if I am to make money and still be able to fulfill my other responsibilites.  I am very engaged with the #mtbos community on Twitter. That is, the “math-twitter-blog-o-sphere” which has quite a few professional math and science educators who are always discussing pedagogy, classroom design, management, and even social justice issues. One of the big things that I–and many other math teachers–have an issue with is Khan Academy. It isn’t the company itself or the videos–KA helped me pass Differential Equations as an undergraduate–but that KA is being held up as “the future/savior of education” by the media, Bill Gates, and others when really the site has some serious pedagogical flaws in its underpinnings and philosophy. Gamification of learning, presentation method of knowledge, etc. But here I am, linking to KA videos as I get ready to teach this online calculus course this summer.

This is partly out of necessity. My supervisor wants to use the KA videos, and I was given the class so close to the beginning of the semester, I don’t really have time to make my own lecture videos. But even if I do (and I plan to for the Applied Calculus I course I will be designing for the training class and implementing in the Fall) I feel as though I am comprising my integrity as a mathematics eductor if I simply give students links to videos and reading assignments. I can’t just say “Here, read this, watch that, answer these questions, quiz next week.” There is more to math than that. There is more to math teaching than that. I have a few ideas of my own–I annotate the reading with questions and I link to Desmos (a free online graphing calculator software) with small activities to help students work through concepts. But I feel there is still an aspect missing. How do I create a problem based task for students in an online class? I reached out today on Twitter to the #mtbos today and asked for advice/help/resources. A principal of an online high school in Tennessee responded and emailed me some examples and ideas. (By the way, that interaction reinforced for me the importance/value of being an eductor on twitter.) I will be using what he sent me as well.

I enjoy teaching a lot. I view my profession as a craft and I take pride in being good at it and getting better at it. One part I enjoy is the interaction with the students. This enjoyment stems from my gregarious personality and maybe a little narcissm. I like to entertain the students as well as teach them. It feels to me that this aspect of teaching that I enjoy so much will be lost in an online format. I can record my own videos and that does transmit some of my personality and style, but it feels more canned. I like to interact to what the students say and get a sense for how they are feeling. It may be that teaching online is just a different type of enjoyable and I need to find the positives about it. I am looking forward to trying.

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