# 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?

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)
SinFong
Sarah
Yanira
Neil

Group 2 (Mutilated Checkerboards)
Syed
Latina
Joseph M
Julia
Sidney

Group 3 (Mutilated Checkerboards)
Stacy
Rushdha
Joseph R
Jian

Group 4 (MIU Game)
Marina
Victor
Leonardo
Farjana

# 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
WeBWorK – none
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.

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 – the 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

# Exam #2 Grades are posted

You can find them on the Grades page (send me an email if you don’t remember the password).  The exams will be returned on Tuesday.

Best,
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 – amazing 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:

Best,
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.
WeBWorK – none
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.

### QUESTIONS 1-9, RATE THE HELPFULNESS OF VARIOUS ACTIVITIES.

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.

 Question HELPFULNESS RATING 0-4 (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.

### QUESTION 10, WHAT COULD BE DONE TO IMPROVE YOUR EXPERIENCE OF THE COURSE.

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).

Best,
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

# Exam 2 Review Sheet UPDATED

Exam 2 will take place next Thursday 10/23.  The review sheet was updated 10/16/14 to remove the material from Chapter 6, Proof by Contradiction.  Two problems were removed (#8 and #12 on the previous version).  No new problems were added.

The review sheet can be found on the Handouts page.

Best of luck with your studying,
Prof. Reitz