New York University
Steinhardt School of Culture, Education and Human Development
Department of Teaching and Learning
Proposed Syllabus
MTHED UE/ GE 1041/2031.001
The Teaching of Rational Numbers
Mondays and Wednesdays 4:55PM - 6:55PM Bldg:East, Room:300
Professor: Anne Burgunder
Office: 239 Greene Street, Suite 434, NY, NY 10003
Phone: 908-407-8364 (mobile)
Email: [email protected]
Office hours: Mondays 12:00 – 4:00 and Wednesdays 10:00 – 3:00, (Please phone or text before coming to my
office to insure that I am there).
Catalog Description:
This course provides a link between teachers' mathematical knowledge & understanding of the major skills &
concepts of ratios, proportions, percent, decimals & fractions to the effective & appropriate teaching of these topics
in grades 5-12.
Course Overview:
Building understanding of Rational Number for diverse adolescent learners in urban contexts is the primary focus of
this course. Students will examine pedagogically driven models of teaching and learning, using multiple lenses, in order
to construct practical, grounded, and equity-based approaches to their professional practice.
This course is based upon the following assumptions:
All students have the capacity to learn mathematics with understanding and deserve to have teachers who
work toward this end.
There are on-going, major changes in mathematics teaching in US schools. Through this course we are
trying to bring about a practice of mathematics teaching that rarely exists in US schools today. Therefore,
this course will likely challenge images you may have of what it means to teach mathematics.
Learning to teach mathematics well is a life-long endeavor, much longer than the duration of a course or
two. This course is another step in that process.
No one knows all they need to know in order to teach mathematics well. This should not be taken as
discouraging; rather, this assumption is based on an appreciation that:
o learning and teaching are problematic (i.e., there is no single right way);
o inquiring into mathematics, mathematics learning, mathematics teaching, and the mathematics of
children is powerful;
o learning from one's teaching and student work is possible and productive;
o and, developing an evolving vision of what school mathematics might be is a characteristic of good
teachers of mathematics.
Good teachers know how to think about the problems of teaching and the kinds of things to do and pay
attention to in order to teach more effectively. They make informed decisions and justify them based on a
deep understanding of the related issues of mathematics, mathematics learning, and mathematics teaching.
Often good teachers' lessons do not accomplish the teachers' goals; however, they know how to learn from
the previous lessons so that the next attempt is better informed and effective.
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This course is designed to prepare 5-12 mathematics teachers with the goal to help develop your
mathematical and pedagogical understandings of rational numbers and proportional reasoning for that grade
range.
This is part of your professional education. Approaching the course from the perspective of a college
student trying to merely be successful in completing the course will limit what you take from the course.
Approaching it instead as a math learner and a beginning professional in the field of education - evaluating
what you understand and working toward deeper understanding of what you need to learn - will provide you
with a strong foundation as you begin your career.
Learner Objectives:
Students will …
Use models as tools for helping students reason mathematically.
Examine ways in which the Common Core Practices will increase your ability to create a thriving, supportive
classroom mathematics community.
Learn a variety of productive ways of including all students in mathematical discourse.
Closely examine the Common Core Content and become knowledgeable of how rational numbers and
proportional reasoning develop throughout the grades.
Make connections and draw comparisons between whole number operations and rational number
operations.
Increase awareness of students’ difficulties in developing a sophisticated comprehension of rational number
concepts.
Develop an understanding that proportional reasoning is not the same (necessary) as setting up a
proportion.
Increase awareness of the dominant instructional approaches to teaching rational number and consider how
these facilitate or restrict flexibility and facility of rational number use.
Develop an understanding of different interpretations of rational number, include various constructs, i.e.
ratios, measures, operators and part-whole relations.
Improve understanding of important rational number concepts and procedures including alternative
computation techniques.
Continue to develop an understanding of the nature of mathematics learning, think deeply about what is
important and how various cultures approach this topic differently.
Explore student invented algorithms and their place in the math classroom.
Develop an inquiry approach to mathematics learning and teaching and an ability to reflect on these
domains.
Required Reading:
Texts:
Ma, Liping. Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental
Mathematics in China and the United States. New York: Routledge, 2010.
Lamon, Susan J. Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and
Instructional Strategies for Teachers (3E). 2012.
Fosnot, Catherine and Dolk, Maarten. Young Mathematicians at Work; Constructing Fractions, Decimals, and
Percents. Portsmouth: Heinemann. 2002
Case studies and additional readings as assigned.
Course Format:
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Classes will be conducted using direct instruction, small and large group discussions, and individual, small and
large group activities.
NYUClasses: This course has an electronic site. The syllabus, details about assignments, and any other general
course information are available on the site as well. In addition, postings will be made regarding events or other items
of importance regarding this course. Please also feel free to use the site to continue conversations started in class or raise
new points for discussion during future class meetings. Please use the Blog Tab to do so.
Course Requirements
1. Reading Assignments and Class Participation
It is important that you read assigned materials in order to foster interesting and productive class discussion. The reading
assignments for each week are listed in the course calendar. Readings are to be completed for the day indicated. Please
bring each day’s readings, and your notes and questions about the readings, to class with you.
Adapted from Maznevski, M. L. (1996, January). Grading class participation. Teaching Concerns: Newsletter of the Teaching Resource Center for
Faculty and Teaching Assistants. Charlottesville: The University of Virginia. Available from
http://trc.virginia.edu/Publications/Teaching_Concerns/Spring_1996/TC_Spring_1996_Maznevski.pdf.
Class participation in the form of attendance, comments, questions, and active engagement in classroom discussion
is required for this course. Attendance will be taken at every class. Because we only meet once per week, missing more
than one class (especially unexcused) will significantly affect your overall grade. [300 points]
2. Final:
This course does not have a final. Instead you are to submit a 5 page reflection of your learning throughout this course
that will serve to facilitate what you feel are key rational number ideas that will form the backbone of a mathematics
course for a chosen grade band. A more in-depth description of this project will be provided in class and will be posted
on the course NYUClasses.
You will present your thoughts to the class at the end of the semester. These presentations will be graded based on a
combination of scores from your peers’ assessment of the presentation and by my own assessment of the presentation.
The rubric for these assessments will be co-constructed in class and via NYUClasses. Presentations should run about
10 minutes. [400 points].
3. Media and Technology Critique
For this assignment, you will investigate one of the multiple media, electronic and technology modalities that have
become part of adolescents’ daily lives: calculators, solftware, television, film, music, social networking websites and
platforms (i.e., Facebook, SecondLife, MySpace, Twitter, text messaging), video games, etc. You will then write a 1-2
page critique that addresses how this modality can support teaching and learning of algebra, as well as how teachers can
build media and technology literacy regarding less positive aspects of this modality among adolescent learners. More
details will be given in class.
Your papers will be posted on NYUClasses for our course. This will give us an opportunity to contribute to critical
conversations in the field in a public forum. [100 points].
4. Case Studies
1-2 case studies (as time permits) will be assigned in order to allow you to “experience,” and reflect upon different
approaches to classroom instruction and pedagogy to and supporting student learning.
Clear directions will be provided on how to approach the reading and reflection of each case. [200 points each]
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Note: Required, “Non-graded” Assignments
Notebook for problems and readings.
5. Read and Write.
Students are expected to read the assigned readings prior to class and to come to class either understanding the
main ideas in the reading or with questions about what was not fully understood. These readings will come primarily
from the required texts. The others will be available on NYUClasses or through the NYU Library. In some cases,
the readings will reinforce what you learned in class. However, in other cases, the readings will set the stage for
activities and class discussions.
For each reading, you will produce a summary that will help you when you are teaching. Each set of notes will
consist of the most important ideas from the chapter that you want to review when you are teaching and, where
relevant, page numbers with annotations for items you may want to use (e.g., “pg 34 problem 5 –good assessment
problem for…”). Do this in a way that is potentially useful to you. However, the text must be clear enough for the
course instructor to read and understand. Keep your written reflections brief – (*1-2 pages) [POINTS VARY]
6. Problems and NYU Classes.
In addition to reading, problems and activities will be assigned each week. These problems should also be
completed before class and the work should be clearly marked in your notebooks and submitted through NYU
Classes. In addition to doing the problems, you should also reflect on the problems. What big ideas are being
developed thought the problem? What are you learning from engaging in the problem? Indicate whether the
problem is one that you would use with students in the future.
*You are to do problems without the use of any formal algorithms. It is expected that you work on this outside of
class and bring your work to the next class meeting. Be prepared to talk about your solutions or ideas, along with
any questions you had. The purpose of these assignments is to give you an opportunity to reflect on the
instructional options that are available to teach rational number concepts and procedures.
In addition to reading, taking notes on what you have read and completing problems and activities you are to post
responses to discussions on NYU Classes. [POINTS VARY]
7. Interviews.
You may be asked to plan and conduct interviews with children that focus on their mathematical thinking related to
a specific concept. Written reports will be periodically required. However, for any general interview when a written
report is not required, you must bring the student work samples with you to class along with your notes from the
interviews. This will be the basis of our class discussion. [POINTS VARY]
Grading Scale and Rubric: Steinhardt School of Education Grading Scale
There is no A+; A (93-100); A- (90-92); B+ (87-89); B (83-86); B- (80-82); C+ (77-79); C (73-76); C- (70-72);
D+ (65-69); D (60-64); There is no D- ; F(Below 60); IP (Incomplete/Passing); IF (Incomplete/Failing);
N (No Grade)
Letter Grade Rubric
A—Outstanding Work
An "A" applies to outstanding student work. A grade of "A" features not simply a command of material and
excellent presentation (spelling, grammar, organization, writing style, etc.), but importantly, sustained intellectual
engagement with the material. This engagement takes such forms as shedding original light on the material,
investigating patterns and connections, posing questions, and raising issues.
An "A" paper is excellent in nearly all respects:
• It is well argued and well organized, with a clear thesis
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• It
• It
• It
• It
is well developed with content that is specific, interesting, appropriate and convincing
has logical transitions that contribute to a fluent style of writing
has few, if any, mechanical, grammatical, spelling, or diction errors
demonstrates command of a mature, unpretentious diction
B—Good Work
A "B" is given to work of high quality that reflects a command of the material and a strong presentation but lacks
sustained intellectual engagement with the material.
A "B" paper shares most characteristics of an "A" paper, but
• It may have some minor weaknesses in its argumentation
• It may have some minor lapses in organization and development
• It may contain some sentence structures that are awkward or ineffective
• It may have minor mechanical, grammatical, or diction problems
• It may be less distinguished in its use of language
C—Adequate Work
Work receiving a "C" is of good overall quality but exhibits a lack of intellectual engagement as well as either
deficiencies in the student's command of the material or problems with presentation. A "C" paper is generally
competent; it is the average performance. Compared to a "B" paper, it may have a weaker thesis and less effective
development.
• It may have serious shortcomings in its argumentation
• It may contain some lapses in organization
• It may have poor or awkward transitions
• It may have less varied sentence structures that tend toward monotony
• It may have more mechanical, grammatical, and diction problems
D or F—Unsuccessful Work
The grade of "D" indicates significant problems with the student’s work, such as a shallow understanding of the
material or poor writing.
• It presents no clear thesis
• It displays major organizational problems
• It lacks adequate support for its thesis
• It includes irrelevant details
• It includes confusing transitions or lacks transitions altogether
• It fails to fulfill the assignment
• It contains ungrammatical or poorly constructed sentences and/or demonstrates problems with spelling,
punctuation, diction or syntax, which impedes understanding
An "F" is given when a student fails to demonstrate an adequate understanding of the material, fails to address the
exact topic of a question or assignment, or fails to follow the directions in an assignment, or fails to hand in an
assignment.
Pluses (e.g., B+) indicate that the paper is especially strong on some, but not all, of
the criteria for that letter grade. Minuses (e.g., C-) indicate that the paper is missing some, but not all, of the criteria
for that letter grade.
Other Important Details
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Accommodations for NYU Students with Disabilities:
Any student attending NYU who needs an accommodation due to a chronic, psychological, visual, mobility and/or
learning disability, or is Deaf or Hard of Hearing should register with the Moses Center for Students with Disabilities at
212 998-4980, 240 Greene Street, www.nyu.edu/csd.
Attendance Policy:
Attendance is mandatory. Material is presented in class that is unavailable in assigned readings, so it is necessary that you
attend every class. There are no texts or notes than can substitute for the discussion and interaction that will take place in
class. Please be on time for class. You are responsible for turning in assignments when they are due and for knowing
information announced in class, whether or not you were in class on any particular day. It is your responsibility to obtain
handouts, assignments, and information you missed when absent.
Turning in Assignments:
All papers and projects are due according to posted due dates listed on NYUClasses for each assignment , (unless
you have made other arrangements with me before the due date). Assignments are to be submitted through
NYUClasses. DO NOT email me or text me your assignment, leave a paper in my mailbox, outside my office door, or
under my door UNLESS this is an arrangement we have agreed upon.
I use TurnItIn to scan your documents for original content. Make sure that you site your sources correctly so that there
is no question of plagiarism.
Bring a clear copy of your work with you to class – when asked. I will be collecting your work each class period. Always
keep a copy of any assignment that you turn in. Papers must be submitted in both electronic and (when asked) hard
copy formats UNLESS specifically stated. Electronic Submissions should always be named in the following way:
FIRSTNAME_LASTNAME_COURSENAME_ASSIGNMENTNAME.doc
for example:
Anne_Burgunder_Tching Rational Num_Reflection1.doc
Note: Spaces may be substituted for underscores:
Anne Burgunder Tching Rational Num Reflection1.doc
MAKE SURE TO INCLUDE YOUR NAME AND THE COURSE NAME AND DATE ON ALL YOUR
PAPERS
PAPERS THAT ARE NOT PROPERLY NAMED WILL BE RETURNED TO YOU.
The following is adapted from the NYU Steinhardt Student’s Guide (p. 24) and from the Policies and Procedures of
the NYU Expository Writing Program (available from
http://www.nyu.edu/cas/ewp/html/policies___procedures.html):
The relationship between students and faculty is the keystone of the educational experience in the Steinhardt School
at New York University. This relationship takes an honor code for granted. Mutual trust, respect, and responsibility
are foundational requirements. Thus, how you learn is as important as what you learn. A University education aims
not only to produce high quality scholars but also to cultivate honorable citizens.
Academic Integrity: is the guiding principle for all that you do; from taking exams, making oral presentations, to
writing term papers. It requires that you recognize and acknowledge information derived from others, and take credit
only for ideas and work that are yours. You violate the principle of academic integrity when you
cheat on an exam;
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submit the same work for two or more different courses without the knowledge and the permission of all
professors involved;
receive help on a take-home examination that calls for independent work;
“collaborate" with other students who then submit the same paper under their individual names.
give permission to another student to use your work for a class.
plagiarize
Plagarism: one of the gravest forms of academic dishonesty in university life, whether intended or not, is academic
fraud. In a community of scholars, whose members are teaching, learning, and discovering knowledge, plagiarism cannot
be tolerated. Plagiarism is failure to properly assign authorship to a paper, a document, an oral presentation, a musical
score, and/or other materials, which are not your original work. You plagiarize when, without proper attribution, you do
any of the following:
•
•
•
•
•
•
Copy verbatim from a book, an article, or other media;
Download documents from the Internet;
Purchase documents;
Report from others’ oral work;
Paraphrase or restate someone else’s facts, analysis, and/or conclusions;
Copy directly from a classmate or allow a classmate to copy from you.
For a very helpful self-test on what constitutes plagiarism, please visit http://www.indiana.edu/~istd/practice.html. This
link also will be available on the NYUClasses site.
Syllabus:
While some portions of my syllabus are non-negotiable, I approach it as a working document that should reflect the
needs of the class community, of which we all are members. I reserve the right to make adjustments to this syllabus
should the need arise, and you should know that you, too, have the right to make suggestions for modifying its content.
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