New York City Department of Education
New Explorations into Science, Technology and Math
111 Columbia Street, New York, NY 10002
Voice: (212) 677-5190 Fax: (212) 260-8124 www.nestmk12.net
(IA) Principal Mark Berkowitz
Mr. Greg Farrell, Upper School Assistant Principal of Supervision
E-mail Address: gfarrell@schools.nyc.gov
CURRICULUM LETTER: MATH RESEARCH
Mr. Baum
mbaum3.weebly.com
mbaum3@schools.nyc.gov
Dear Students,
What does it mean to distribute a resource fairly? What is the best way for a group to
make a collective decision (ex. electing a politician) when each individual has his or her own
preference? How many different ways are there to walk from the NEST+m campus to the
Brooklyn bridge (and which way is most efficient)? We all share intuitive ideas about fairness,
representation, efficiency, and other social and ethical norms. Our individual definitions of
these concepts, though, do not always align – even close friends ultimately disagree about
which outcomes are “fair” in life. One major goal of this class is to learn how to have these
arguments using mathematical logic. Using math to talk about these kinds of “big” questions
means much more than finding and quoting statistics to support an argument. Nor will
mathematics necessarily give us one satisfactory answer to any of our questions. In this course,
we will learn how to use the language and methods of math to come up with reasoned
solutions to any number of our questions. Equally as important, we will learn how to
communicate those answers to our peers.
Introduction and Course Outline
The goals of the course are thus two-fold: to apply our mathematical knowledge in
researching a question and then to adequately convince others that our answers make sense.
For the first goal, we will learn how the practices of mathematical modeling can give us
productive ways to talk about very complex, real-world problems. The models we will learn
about are not perfect: like any model, they rely on simplifying assumptions and depend greatly
on how we define our variables. Part of doing good research is listening to whether our peers
think our assumptions and definitions are valid. Presentation and discussion are thus a vital part
of the class.
During the year, we will weave mathematics into discussions about what it means to
make a “good” mathematical argument. Students are expected to be active listeners and to
respond constructively to solutions and arguments, whether given by the instructor, other
students, or the authors of course materials. Below you can find two outlines for the year: one
describing how we will learn the research process and one listing (in tentative chronological
order) the mathematical topics we will cover.
The Research Process:
One focus of this class is to introduce students to thinking, writing and presenting mathematics.
This is done through a series of small writing assignments building up to larger mathematical
research papers and in-class presentations. Students are encouraged to submit their papers to
the NYC Metropolitan Math Fair as well as other research competitions.
I. Introduction to Mathematical Writing
➢ Writing Up Solutions to a Problem
➢ Creating New Questions from a Question
➢ Extended Solutions to a Problem
➢ Summarizing Math Magazine Articles
II. Intermediate Mathematical Writing
➢ Writing a Mini-Research Paper
III. Advanced Mathematical Writing
➢ Writing a Complete Research Paper
1. Problem Statement
2. Introduction
3. History
4. Mathematical Background
5. Investigation
6. Summary
7. Applications and Extensions
8. Reference
Math Topics:
Students should come away from the class with the tools needed to develop mathematical
arguments that answer their own questions. Part of the content of the class will come from
student interest. We will however, learn about prominent cases where mathematicians have
found ways to apply number reasoning to issues like fair division, negotiations and voting. We
will also add to our toolbox the methods of more “pure” mathematics, including discrete math
and probability. We will tentatively end the class with a discussion about the mathematics of
infinity. Our class will, tentatively, progress through these topics as follows:

Fair division; Voting schemes; Apportionment; Introductory probability; Introductory
problems in Game Theory; Permutations and combinations; Symbolic logic and logical
fallacies; Infinite sets and cardinality
Classroom Policies
Materials: Students will be trusted in this class to use the materials that will enable them to
participate and take notes. Students will also need pencils, erasers, paper (loose-leaf or from a
notebook) and a calculator to do problems in class. Students will also need to take notes during
class.
Expectations: Class starts after the bell rings. At that time, students are expected to be in their
seat with their homework and notebooks out. Students who come in after the bell must
provide a late pass. A note must be provided for excused absences. Student who are
excessively late or absent will be notified to the Assistant Principal and the student’s guidance
counselor.
Participation: This class will rely heavily on student participation. All students are expected to
contribute to class discourse. While this will often mean that students should be prepared to
add their voice to a discussion, students will be able to participate by sharing thoughts in
writing as well. All sincere and respectful questions, suggestions, and critiques are welcome.
We will all pay careful attention to our tone, both verbally and in writing. Critiques of peer work
should be constructive (which includes asking for clarification), respectful, and should respond
to the content of the work being critiqued. The instructor will moderate discussions to ensure
that many voices come across.
Hall Pass Policy: Students must ask permission first before going to the bathroom.
Scholastic Dishonesty: Scholastic dishonesty is an academic violation and is absolutely not
tolerated. Student will be referred to the Dean and appropriate action will be taken. Since this
is a research course, students are expected to cite their sources, whether with a formal
bibliography in a research paper and certain smaller writing assignments or with informal
citations in homework assignments. Failure to cite a source in a paper may be considered
plagiarism and can result in automatic failure and appropriate disciplinary action.
School Tone: Students are prohibited from chewing gum, wearing hats, and having or playing
card trading on school property. Please keep cell phones on silent mode and in backpack. Cell
phones can only be taken out when instructed by your teacher. First offense is a warning.
Second offense will result in confiscation of the item. It will be given to the Assistant Principal
or the Dean and only the parent can pick it up. Confiscation of playing cards will not be
returned.
Tutoring Hours: Mr. Baum is available during lunch periods 3 in RM 361 and 6 in room 317.
After school tutoring hours will be posted on the bulletin board by Mr. Gold’s office (RM. 363).
Grading Policy
Homework (including short writing assignments) – 25%
Homework will be assigned during class and is due on the date(s) specified by class time, unless
otherwise specified. Assignments will vary: students should expect to read articles and
mathematical solutions (and write short responses), write their own short arguments or
critiques, and create solutions to math problems. Unlike traditional math courses, emphasis will
be placed not only on “showing work” in solutions but also on the style and presentation of the
solution. As such, we will do fewer problems for homework, but students should spend some
time thinking about how whether their solutions look, in a sense, “professional”.
Quizzes – 25%
We will have roughly 2-3 quizzes per quarter. As with homework, quizzes will consist of fewer
problems than students may be used to in a math class. Students will be graded on the clarity
and presentation of their solutions. Additionally, students may be asked to write short
paragraphs on a quiz. Any students who have difficulty hand-writing on a quiz should make
alternative arrangements with Mr. Baum.
Peer Review and Class Participation – 25%
Part of making strong mathematical arguments is being able to communicate solutions to
peers. We thus will rely on each other to make sure that our research continues in promising
directions. Students are thus expected to share their thoughts on problems presented by Mr.
Baum and by their peers. In addition to this kind of every day class participation there will be
formal Peer Review assignments corresponding with the quarterly projects (see below). These
written assignments will consist of thoughtful and critical responses to at least one quarterly
project done by a fellow student or student group.
Quarterly Projects – 25%
Each quarter students are expected to complete independent research assignments. More
details will follow, but the projects will consist of two in-class presentations (to conclude the
first and third quarters) and two written research papers (a five-page paper to conclude the
second quarter and an eight-to-ten-page paper to conclude the fourth quarter). Mr. Baum will
provide suggested topics for research assignments on the class website, and students are
absolutely allowed to develop their own topics for the quarterly projects. Quarterly projects will
typically be due ONE WEEK PRIOR to the end of a quarter to allow adequate time to complete
Peer Review.
Class Resources
The class website can be found under the “Math Research” tab at the top of Mr. Baum’s site –
http://mbaum3.weebly.com. The site will include current information on homework
assignments, notes on best practices for research developed in class, and links to other sites
that pose interesting problems (possibly for use as research topics).
Concluding Note
Students may be uncomfortable with the idea of a math class that involves writing. That is
perfectly normal. Ample time will be spent developing writing and presentation skills in class.
Any student (or parent) who has questions or concerns (or is simply a little nervous) about class
expectations should please, please see Mr. Baum or reach out via e-mail at
mbaum3@schools.nyc.gov.
Thank you, and I look forward to a great year!
Sincerely,
Mr. Baum