Monthly Archives: October 2014

OpenLab #8: 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 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). ¬†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 or question about your game, and bring it with you to class on Thursday 11/6 (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. ¬†Think about¬†the game you¬†worked on last week (the MIU game, the bridges and walking tours game, or the mutilated checkerboards game). ¬†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. ¬†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 Thursday 11/6 (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:
Question: Is the corner the best move, or the center?
Conjecture: The person who goes first always wins.
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.”

In-Class Group Project Activity 10/30/14 – Puzzle Making

Group Activity (25 min).  Get into your groups (group assignments appear below), arrange your chairs in a circle, and take 25 minutes to:

1.  Share your responses to OpenLab #7.  Compare your answers to the given examples (do you all agree on the solutions?).  Now share your own puzzles with the group, and discuss.

2.  Create three new puzzles, as tricky as possible (try to stump Prof. Reitz!).

Group work due after 25 minutes:  Each group will hand in a sheet of paper with the names of the groups members, the date, and the three new puzzles created by the group.  You do not need to submit solutions, but you do need to be able to solve the puzzles on request.

Reflection:  To be completed individually after group work is complete, and submitted on paper with your name and the date.  Take 5 minutes to write on the following prompt:

Briefly reflect on the process of working in a group by responding to each of these points:
1.  Describe something you learned.
2.  Describe something you contributed to the group.
3. ¬†How did today’s work¬†change your understanding of your assigned game?


Group Assignments

Group 1 (Bridges and Walking Tours)

Group 2 (Mutilated Checkerboards)
Joseph M

Group 3 (Mutilated Checkerboards)
Joseph R

Group 4 (MIU Game)

Week 9 Assignments

Written work, Due Tuesday, November 4th, in class:
Chapter 7 p129: 5, 9, 10, 12
**Chapter 8 p143: 3, 7, 18, 19
      **Chapter 8 has been extended to Tuesday, November 11th
OpenLab¬†–¬†OpenLab #8 due Thursday, November 6th¬†at the start of class

Class work: There will be group & individual work completed & submitted in class on Thursday 10/30/14, which will count towards your “Project” grade.

Midsemester Grades are posted

You can find your midsemester grades on the GRADES page.  Let me know if you have any questions.

A note about grading of written assignments.  These assignments are a mix of odd and even numbered problems in the book Рthe odd numbered problems have solutions in the back.  Unless otherwise stated, odd problems will be worth 4 points each and even problems worth 8 points.

Best regards,
Prof. Reitz

Upcoming Math Club Talks

Hi everyone,

The Math Club meets almost every Thursday during club hours (12:45 – 2:00) in Room N719. ¬†They have free pizza and cool talks about Math – fun, interesting and inspiring, and the topics should be accessible to all of you. ¬†You don’t have to be a member to attend – just show up! ¬†I wanted to call out two upcoming talks especially:

This Week (Thurs 10/23): 
Jonathan Ginsberg, Basic Concepts in Hyperbolic Geometry
If you are currently taking or plan to take Geometry I/Geometry II, check this out!

Next Week (Thurs 10/30):
Andrew Douglas, Proofs Without Words
This is a perfect talk for you guys Рamazing examples of proofs that involve ONLY pictures.  I strongly encourage you all to attend!

Here’s the Math Club site, with additional talks and info:

Prof. Reitz

Week 8 Assignments

Written work, Due Tuesday, October 28st, in class: Chapter 6 p. 116: 3,4,5,8,9
Odd problems are worth 4 points, even problems worth 8 points.
OpenLab¬†–¬†OpenLab #7 was posted last¬†Friday, 10/17, and will be due next TUESDAY 10/28.

Exam #2 will take place this Thursday, 10/23 (first half of class).

OpenLab #5 Survey Results

Thanks to everyone for completing the survey.  I want to share the results and make some observations.


Data.¬†I converted the ratings into a numerical scale from 4 = Extremely Helpful to 0 = Not At All Helpful. ¬†I calculated the average “helpfulness rating” for each question – the results are presented below, with the questions listed in order according to their rating.

(Extremely Helpful = 4,
Not at all = 0,
Don’t Know = not counted)
Lecture 3.8
Professor answering questions in class 3.8
Email contact with Professor 3.7
WeBWorK assignments 3.6
Group Work in class 3.4
Office Hours 3.1
Working with peers (friends, classmates, other students) outside of class. 3.1
OpenLab Assignments 2.8
Tutoring at CityTech 2.7

Observations. ¬†First, it’s interesting to see¬†that the top¬†two¬†items are about me talking to you in the room. ¬†I am curious to see if this shifts over the rest of the semester¬†as a) the course becomes more challenging, and b) you have more opportunity to work with one another. ¬†We’ll see! ¬†¬†The relatively low helpfulness rating for OpenLab assignments is not too surprising, as these are designed to supplement and contextualize the course content rather than contribute to it directly¬†– however, I¬†will¬†put some thought into changes that might¬†be made here (you will find, for example, that a number of the future OpenLab assignments will directly support¬†completion of your class project). ¬†I will also put some thought towards the timing of office hours, as I know the current schedule conflicts with other courses.


This question was short answer, but most of the responses fell into just a few different categories, summarized here.

Top Categories Number of responses
I’m happy with the class as it is 7
More advanced examples in class 2
More group work/more problem solving in class 2
Other 3

Observations.¬†The biggest news here is that most of you are pretty satisfied with the class so far. ¬†That’s great! ¬†But don’t get complacent, and don’t hesitate to give feedback or ask for help¬†as the semester continues, especially as we begin to explore proofs in earnest. ¬†I’ll take the comments regarding examples and group work on board as I’m planning future classes.

I plan to revisit this survey later in the semester, and I look forward to seeing how the responses compare.  If you have any questions, feel free to post them in a comment here or send me an email.

Best regards,
Prof. Reitz

OpenLab #7: Let the games begin

Hi everyone,

Based on your responses to OpenLab #6,¬†I have assigned each of you a game to work on (everyone got their first or second choice). ¬†Check the “Who is doing what” list below to see which game you will be working on. ¬†Then follow the appropriate link from the list below to view your assignment (detailed instructions are provided for each game).

Prof. Reitz

Links to assignments (Due TUESDAY, OCTOBER 28th – end of day):

Who is doing what:

Chiu,SinFong Bridges and Walking Tours
Conyers,Sarah Bridges and Walking Tours
Felamon,Marina MIU Game
Garcia,Yanira Bridges and Walking Tours
Hamza,Syed Mutilated Checkerboards
Jones,Stacy Mutilated Checkerboards
Kamath, Neil Bridges and Walking Tours
Laing,Latina Mutilated Checkerboards
Lee,Victor MIU Game
M Rafeek, Rushdha Mutilated Checkerboards
Mongo,Joseph Mutilated Checkerboards
Perez,Leonardo MIU Game
Rivera,Julia Mutilated Checkerboards
Ruiz,Joseph Mutilated Checkerboards
Sao,Sidney Mutilated Checkerboards
Shati,Farjana MIU Game
Sun,Jian Mutilated Checkerboards