Tag: lockhart’s lament

Videos – Ismail Akram

Part 1:

Vi Hart’s “How to Draw a Perfect Circle” had similar traits to Lockhart’s Lament.¬†While Lockhart emphasised trial and error and exploration into concepts, the pen’s character and voyage for adventure hearkened to that same concept. While some may have thought it was frustrating to see the pen constantly fail or go against Vi Hart’s instructions, the end result sparked a eureka moment. I think I’ll remember how to draw a perfect circle because of the zaniness of the pen’s quirky deviancy.

I thought this video was clever in explaining a paradox. The supposed pi=4 illusion is easily explained by asking “what’s a circle?” That alone was simple enough to disprove this sophistry. I can’t help but make a connection to our course in making sure our arguments while (dis)proving something must be logical and not fall into fallacies.

I found this video to be creative and amusing. Our standard way of proving something is chalk on blackboard, this is just another engaging way in learning the Pythagoras Theorem in a more hands on approach. We’re not simply told this is true but shown; that and asked to try it ourselves!

 Part 2: How to Draw a Perfect Circle

Initially I felt intrigued by the video, who wouldn’t like to know how to draw a perfect circle? Then I see this weird conversation between Vi Hart and a super determined pen. After various struggles from the pen I did feel a little bored, wondering “why am I watching this again?”

Vi Hart then interrupts the pen’s crazed state and simply shows us how to draw the circle in the end. While it was funny, the actual answer kind of came about at a halt. The video still did achieve that “aha!” moment, so that actual lesson in drawing a circle did click and stick in my head.

I learned to draw a perfect circle, although it’s not too different from most techniques out there (the idea of rotating paper isn’t new). I also frowned slightly when she drew against the natural curvature of her hand to draw said circle. Coming from a slight architectural background; it’s much better to draw with the natural curve of your wrist than go against it.

I don’t have any particular questions, it was a simple how to video. I would initially ask why the quirky beginning but that adds to the charm of the lesson.

 

Part 3: Lockhart

This video actually taught me something important about teaching; make it fun! Despite the dorky dialogue and zany frenzy of the pen; I bet kids would love a video like this. Imagine teaching a child a simple technique for drawing (whether it be for arts or graphs) and have it click in their heads in an engaging and humorous manner. It’s definitely teaching, but is it maths? Probably not. I can’t imagine it being super relevant to the work we’ll be doing in class other than working through our proofs and concepts.

As I talked about in Part 2; this reminded me of Lockhart’s Lament where he talked about trusting our youth to make mistakes through trial, error and exploration. The pen reflects that sentiment.

 

OpenLab #5: Lockhart’s Lament

In 2002, a mathematician named Paul Lockhart wrote an essay¬†called “A Mathematician’s Lament,”¬†a passionate criticism of mathematics education in America. ¬†It has become widely known among mathematicians and mathematics educators – not everyone agrees with everything he says¬†(though many do), but everyone seems to have something to say about “Lockhart’s Lament,” as it is called. ¬†For this week’s assignment, you will read a short excerpt (three pages) from his essay and respond to the prompts below.

Assignment (Due Friday, 10/14/16). Your assignment has three parts:

First, read the section titled “Mathematics and Culture” (pages 3-5) in Lockhart’s essay, (click here). ¬†If you’re interested, I encourage you to read more, starting at the beginning – but this is not required.

Second, write a response to what you read and post it in the comments below.  Your response should be at least 300 words. Your response should represent your own thoughts and opinions on what you read, and can include responses to any or all of the following:

  • What is one thing that you agree with in the reading? Explain why.
  • What is one thing that you do not agree with? Explain.
  • Choose one¬†quote that you think stands out in the reading. ¬†Give the quote, and explain why you chose it.
  • Have you ever had an experience of mathematics as art?
  • On page 5, Lockhart describes mathematics in schools today as “heartbreaking”. ¬†What do you think he means? ¬†Do you agree? How do your own math experiences in school compare to his description?

Third, and most important, I want you to write down a conjecture about the Bridges and Walking Tours game, and bring it with you to class on Friday¬†10/14 (do NOT post it here).¬† Consider Lockhart’s¬†example of a triangle drawn inside a rectangle. ¬†He described the process of playing around with this picture, until he arrives at the basic idea for calculating the area of a triangle. ¬†He contrasts this with a traditional math class, in which the formula is given to students without providing them any opportunity to explore the problem on their own. ¬†The bridges and walking tours game¬†is a little like the triangle-rectangle picture – it’s fun to play around with, but you may not be sure what the point is. ¬†You’ve had a chance to play with it a bit, and try some different challenges. ¬†Now what? ¬†Your job is write down a conjecture (a guess!) or a question about your game. If you could have one question answered about your game, what would it be? If you wanted to be a master of your game, and be able to solve any challenge that was given to you, what would you need to know?¬†Write down a conjecture or question about your game, and bring it with you to class on¬†Friday¬†10/14¬†(do NOT post it here).

Here is an¬†example: Let’s imagine that you have just been introduced to the game Tic-Tac-Toe. ¬†After playing it for a while, you might come up with one of the following:
Conjecture: The person who goes first always wins.
Question: Is the corner the best move, or the center?
Conjecture: It’s impossible to win, no matter who goes first.

ps. ¬†Paul Lockhart retired from being a first-rate research mathematician in order to teach math at a private elementary school here in Brooklyn,¬†Saint Ann’s School, where he says “I have happily been subversively teaching mathematics (the real thing) since 2000.”