New York University
Steinhardt School of Culture, Education and Human Development
Department of Teaching and Learning
Proposed Syllabus
MTHED-GE 2116 - 001
Teaching Elementary School Mathematics: Problem Solving and Procedures
Wednesdays 2:00 – 3:40 25W4 Room C-18
Professor: Anne Burgunder
Office: East Building, 239 Greene Street, Suite 415, NY, NY 10003
Phone: 908-407-8364
Email: [email protected]
Office hours: Tuesdays and Wednesdays 2:00 – 4:30
Catalog'Description:'!
This!course!will!be!focused!on!helping!teachers!to!develop!math!sense!through!problem!solving!&!procedures!while!
developing!skills!&!intuitions!for!creating!rich!learning!environments!and!engaging!contextual!tasks!for!elementary!school!
children!to!explore,!discover,!&!understand!mathematics.!Trends!in!mathematics!education!will!be!discussed!as!well!as!the!
implications!for!student!learning!&!accountability.!
!!
Course'Overview:'!
This!course!is!devoted!to!helping!future!teachers!prepare!to!engage!their!students!in!problem!solving.!!Participants!will!
examine!various!approaches!to!teaching!problem!solving!and!reflect!upon!how!these!theories!play!out!in!their!own!
problem!solving!experiences.!!In!order!to!prepare!children!to!become!better!problem?solvers,!teachers!have!
to!become!more!comfortable!with!the!messiness!and!non?linear!activity!of!problem!solving!and!problem?posing.!Ultimately,!it!
is!desired!that!future!teachers!become!better!problems!solvers!themselves!through!regularly!solving!problems!and!sharing!
solution!strategies!with!others.!!In!doing!so,!they!can!think!deeply!about!how!to!effectively!develop!a!classroom!environment!
that!promotes!in!children!a!disposition!to!mathematize!their!world!and!become!creative!and!flexible!problem!solvers.!!!
!
Problems,!by!definition,!are!hard!to!solve.!One!has!to!engage!in!problems!solving!regularly!in!order!to!become!more!
comfortable!with!the!inquiry,!investigation,!strategies,!models!and!tools!that!problems!solvers!use.!In!addition!to!solving!a!
number!of!problems,!it!is!important!to!be!familiar!with!certain!“classic”!math!problems!because!the!structures!of!these!
problems!are!replicated!in!numerous!related!problems.!!!
!
Strategies!are!broad!ideas!that!facilitate!investigation.!They!are!not!solely!mathematical,!!Some!of!the!strategies!that!will!be!
addressed!in!this!class!are!psychological.!Others!are!organizational,!and!others!simply!commonsense!ideas!that!apply!to!
problems!in!any!field.!!!
!
Models!are!very!specialized!tools!that!are!used!in!problem?solving!to!facilitate!reasoning.!They!allow!for!the!user!and!the!
audience!to!“see”!not!only!the!solution,!but!also!the!interrelated!ideas!that!exit!within!the!solution!path.!A!few!of!the!models!
that!will!be!utilized!in!this!course!are!the!open!number!line,!the!ratio!table,!and!the!area!model.!We!will!discuss!professional!
practices!that!are!ethical!and!equity?based.!!
!
Some!assumptions!that!form!the!basis!of!this!course:!
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All!people!(adults!and!children)!have!the!capacity!to!learn!mathematics!with!understanding.!
It!is!the!teachers’!role!and!responsibility!to!plan!well!and!engage!their!students!in!meaningful!mathematical!activity.!
Engaging!students!in!rich!mathematical!tasks!can!and!allow!them!to!actively!make!meaningful!connections!between!
and!among!content!and!contexts.!
Too!few!math!classes!allow!students!the!time!and!freedom!to!engage!in!problem?solving.!!Time!limitations!and!testing!
pressures!should!not!prevent!teachers!from!allowing!children!to!engage!in!meaningful!math!activity.!!
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No!one!knows!all!they!need!to!know!in!order!to!teach!mathematics!well.!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.!
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!right!way);!
o inquiring!into!mathematics,!mathematics!learning,!mathematics!teaching,!and!the!mathematics!of!children!is!
powerful;!
o learning!from!reflecting!on!planning!and!teaching,!observing!teachers!and!children,!!and!looking!at!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.!
This!course!is!designed!to!prepare!future!elementary!school!math!mathematics!teachers!with!the!goal!to!help!develop!
your!mathematical!and!pedagogical!understandings!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:!
• Understand!the!differences!between!and!the!role!of!problems,!exercises!and!experiments!in!learning!mathematics.!
• Increase!awareness!of!the!difficulties!and!the!benefits!of!incorporating!of!using!a!problem!approach!to!learning!
mathematics.!!
• Develop!a!tool?box!of!strategies!that!allow!for!teachers!to!overcome!the!difficulties!of!problem?solving!and!facilitate!a!
positive!and!productive!environment!of!supporting!natural!mathematics!activity.!
• Increase!awareness!of!the!dominant!instructional!approaches!to!teaching!through!problem?solving!and!consider!how!
sequence!and!structure!facilitates!or!restricts!flexibility!and!facility!of!engaging!in!problem?solving.!
• Develop!an!ability!to!use!various!strategies!and!tools!of!problem?solving.!
• Improve!your!understanding!of!important!models,!concepts!and!procedures!including!alternative!computation!
techniques.!!!
• Continue!to!develop!an!understanding!of!the!nature!of!mathematics!learning,!what!is!important!and!how!it!is!
practiced!globally.!
• 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.!!
• Increase!your!ability!to!create!a!thriving,!supportive!classroom!mathematics!community!
'
Required Reading:
Texts:
Van de Walle, John A., Karen Karp, and Jennifer M. Bay-Williams. "Elementary and middle school mathematics: Teaching
developmentally." (2007).
Fosnot, Catherine Twomey, and Marteen Dolk. Young mathematicians at work: Constructing Multiplication and Division.
Portsmouth, NH: Heinemann, 2001.
Case studies and additional readings as assigned including but not limited to:
Cuoco, Al, E. Paul Goldenberg, and June Mark. "Habits of mind: An organizing principle for mathematics curricula."
Journal of Mathematical Behavior 15.4 (1996): 375-402.
Charles, Randall I., and C. A. Carmel. "Big ideas and understandings as the foundation for elementary and middle school
mathematics." NCSM Journal of Mathematics Education Leadership 8.1 (2005): 9-24.
Course Format:
Classes will be conducted using direct instruction, small and large group discussions, and small and large group
activities.
Blackboard: This course has a Blackboard site. The syllabus, details about assignments, and any other general course
information will be 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.
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. Semester-long Project: Compile a Binder of Materials and Readings and Problems to support Problem
Solving and the Common Core Practice Standards
You will be required to gather and organize materials over the course of the semester that will serve as the backbone of
an educational program that will assist developing a a problem based approach to teaching mathematics. Your goal is to
craft a positive, intellectually rigorous, affirming, and respectful educative experience in the subject for your imagined
future students in a specific grade level. The educational program should reflect your understanding of rich tasks
differentiating instruction to meet students’ needs within and across the various dimensions of their developmental
profiles and identities. This assignment also will require you to think about and apply what you have learned through
your readings and in class experiences. You will turn in drafts and receive feedback on your educational program
throughout the semester to ensure you are on the right track. A more in-depth description of this project will be
provided in class and will be posted on the course Blackboard site.
You will present your educational programs 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 constructed in class and via Blackboard. 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 Blackboard 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 Study
One case study 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 the case. (200 points)
Note: Required, Non-graded Assignments
Notebook for problems and readings.
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 Blackboard. 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 notes 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. Keep your notes brief – just including what you need and do
not exceed 1-2 pages.
Problems and Posting Problems.
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. You should also reflect on the
problems. What big ideas are being developed thought the problem? Indicate in the margins whether the problem
is one that you would use with students in the future. You may be asked to post your problem solutions on
Blackboard, a private Facebook group, or Twitter. Constructive feedback on all postings is expected.
*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 problem-solving and procedures.
Interviews.
You will 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.
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 DF
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
• It is well developed with content that is specific, interesting, appropriate and convincing
• It has logical transitions that contribute to a fluent style of writing
• It has few, if any, mechanical, grammatical, spelling, or diction errors
• It 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
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 at the beginning of class on the date they are due, unless you have made other arrangements
with me before the due date. DO NOT leave a paper in my mailbox, outside my office door, or under my door UNLESS
this is an arrangement we have agreed upon.
Bring a clear copy of your work with you to class. 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 hard copy formats UNLESS
specifically stated. Electronic Submissions should always be named in the following way:
FIRSTNAME_LASTNAME_COURSENAME_ASSIGNMENTNAME.doc
for example:
AnneBurgunder_Tching Algebra_Reflection1.doc
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;
• submit the same work for two or more different courses without the knowledge and the permission of all
professors involved;
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•
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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:
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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 Blackboard 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.