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

**Assignment (Due Thursday, 11/6/14)**. Your assignment has three parts:

**First, read** the section titled “Mathematics and Culture” (pages 3-5) in Lockhart’s essay, (click here). Â *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. Â Your response should be **at least 300 words.**Â Your responseÂ should represent your own thoughts and opinions on what you read, and can include responsesÂ 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 oneÂ quote that you think stands out in the reading. Â 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”. Â What do you think he means? Â 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 or question about your game, and bring it with you to class on Thursday 11/6 (do NOT post it here)**.Â Consider Lockhart’sÂ example of a triangle drawn inside a rectangle. Â He described the process of playing around with this picture, until he arrives at the basic idea for calculating the area of a triangle. Â 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. Â Think aboutÂ the game youÂ worked on last week (the MIU game, the bridges and walking tours game, or the mutilated checkerboards game). Â Each of these games 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. Â You’ve had a chance to play with it a bit, and try some different challenges. Â Now what? Â 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?Â **Write down a conjecture or question about your game, and bring it with you to class on Thursday 11/6 (do NOT post it here).**

Here is anÂ example: Let’s imagine that you have just been introduced to the game Tic-Tac-Toe. Â After playing it for a while, you might come up with one of the following:

Question:Â Is the corner the best move, or theÂ center?

Conjecture: The person who goes first always wins.

Conjecture: It’s impossible to win, no matter who goes first.

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