Steinhardt School of Culture, Education, and Human Development
Department of Teaching and Learning
MTHED-UE 1043/MTHED-GE 2033: The Teaching of Secondary School Mathematics
Jasmine Y. Ma
[email protected]
212-992-7658
404 East Building, 239 Greene St.
Office hours: By appointment
Thursdays 2:00p-4:50p
301 East
Fall Semester, 2014
Course Description
Developing the skills of classroom planning, management, & implementation for effective
instructional practices in grades 7-12. Topics include lesson plan development &
implementation, different models of teaching, assessing student understanding & the use of
instructional technology. Students also visit schools, observe teachers in the classroom & use
these observations as the basis for discussions of effective teaching practice. This course requires
a field component where students are involved in tutoring & microteaching.
Course Overview
This methods course is designed to support the professional development of prospective middle
and high school mathematics teachers about to embark upon their student teaching. Mathematics
is a subject that is notoriously difficult for many people, and by the time they are in middle or
high school these students might need to learn not just the math content, but also that they can be
successful mathematics students at all. The goal of the course is to help you learn to teach the
content in ways that make significant mathematical ideas accessible to all students and that
support students in developing mathematical proficiency. As defined by the National Research
Council, mathematical proficiency includes both ability (e.g., to reason logically, solve nonroutine problems, and communicate about mathematics) and attitude (e.g., a disposition to
question and explore). In the course we will analyze artifacts (video and written cases) of
teaching, focusing on the role of mathematical tasks, tools, and the teacher in developing
students’ mathematical proficiency. We will engage in a number of mathematical activities and
examine our own beliefs about mathematics, teaching, learning and students. The course asks
you to look at mathematics and teaching from the perspective of a teacher, with a focus on
anticipating, eliciting, analyzing, and building upon student thinking. You will begin the work of
teaching as you get to know students and their communities, design lessons, start planning a
curriculum unit, and consider appropriate strategies for assessment. You will also practice
implementing pedagogical strategies in front of your colleagues and receive feedback on your
teaching. As you develop your pedagogical repertoire, you will also begin to develop your
pedagogical knowledge of mathematical content typically taught during middle and high school,
such as rate of change and functions.
Course Objectives
• Develop a stance on what counts as mathematics, and why we teach it;
• Understand mathematical big ideas and how they cut across content areas;
• Develop appropriate instructional strategies for supporting mathematics learning goals;
• Learn how to anticipate and analyze students' mathematics reasoning and strategies, and plan
for next steps;
• Assemble strategies for teaching secondary mathematics to all students, given the
complexities of different classrooms;
• Evaluate, adapt, and design learning activities and trajectories in secondary mathematics that
potentially foster and motivate all students’ learning;
• Become more reflective with respect to your own and others’ teaching, and develop
strategies for learning from your own and others’ experiences.
Required Texts
Boaler, J., & Humphreys, C. (2005). Connecting mathematical ideas: Middle school video cases
to support teaching and learning. Portsmouth, NH: Heinemann. [B&H]
Horn, I. (2012). Strength in numbers: Collaborative Learning in Secondary Mathematics.
Reston, VA: NCTM. [SiN]
You are responsible for acquiring the required texts. All texts are available on reserve at the
library. If you have difficulty accessing the readings, please let me know.
There will also be a number of articles and book chapters made available through NYUClasses.
Optional Text
Weinberg, P. J., & Weinberg, C. (2008). The first-year urban high school teacher: Holding the
torch, lighting the fire. Lanham, MD: Rowman & Littlefield Publishers. [WW]
Additional Suggestions
Cohen, Elizabeth G. (1994). Designing groupwork: Strategies for the heterogeneous classroom.
New York, NY: Teachers College Press.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring
mathematical success for all. Reston, VA: NCTM. (You can get this ebook for $5!!!)
Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M., & Wray, J. (2013). Elementary and
middle school mathematics: Teaching developmentally (8th ed.). Boston: Pearson.
Wieman, R., & Arbaugh, F. (2013). Success from the start: Your first years teaching secondary
mathematics. Reston, VA: NCTM.
In-Class Requirements
• Be prepared to actively participate and take notes
• Bring some version (hard copy or digital, NOT ON YOUR PHONE) of the assigned reading
• Scratch paper- blank, ruled, and graph
• Pens and pencils, eraser (at least one functioning version of each)
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Fieldwork
As a part of this course you are required to conduct 30 hours of mathematics classroom
observations in a local middle or high school. These hours should be spread out around 3-4
hours per week for 8-10 weeks. If you are currently doing your student teaching, you do not
need a separate placement. These observations are experiences that will be used in class
discussions and in your assignments.
Resources and forms for your fieldwork:
http://steinhardt.nyu.edu/apprentice/default/resources
To get a field assignment, fill out this survey:
http://www.surveygizmo.com/s3/1790740/Field-work-Placement-Request-Fall-2014
Assessment and Grading
1. Active participation in class activities and contribution to discussions (30%)
The quality of this class (and your learning) depends on your: attendance, close reading of
the assignments, preparation for class, and engagement in and contributions to class activities
and discussion. I will take attendance and keep notes on your participation in class. This is
where you show that you have done the reading assigned for the week. I expect you to be
engaged the entire 3 hours of the course (we will typically have a 5-10 minute break in the
middle). This means that you should not be checking email or your phone during class time.
Positive, substantive contributions make your thinking available to the class, raise new
questions, and challenge the group and yourself. I really encourage you to speak up, share
your ideas, question what you do not understand, and make proposals in class. You cannot go
wrong by engaging genuinely. In this course, it is important that you be willing to make your
mathematical and pedagogical ideas public, for everyone, including yourself, to learn from.
This means that others will be doing the same, and how you attend and respond to one
another also counts as contributions.
Your regular attendance is expected. Please be on time for class. This means that you are in
your seat and ready to go at 2pm. 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. If you have an extenuating circumstance and you will have to miss class,
come late, or leave early, please let me know as soon as you can. Absences will be excused at
the discretion of the instructor. Please contact me as soon as you anticipate missing class.
Each unexcused absence will result in a 2% reduction of your final grade. Unexcused
tardiness or early departures count as unexcused absences. 3 or more absences may result in
no credit for the course.
2. Weekly assignments (20%)
Most weeks we will have an assignment, in addition to reading, that will be a combination of
mathematics/mathematics instruction tasks (some will reinforce and apply ideas from
previous lessons; others will prepare for the following class) and writing (reflection and
commentary). These are listed in the course outline, but may also be assigned in response to
what happens in class.
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3. Investigation of teaching context (15%)
As a teacher, it is important to know as much as you can about your workplace and the
students. For this project you will conduct a thorough investigation of 3 aspects of your
teaching/observation context: the school, students, and your students’ communities.
Important dates for ITC:
October 16: School
October 30: Students
November 13: Community
4. Micro-Teaching (20%)
Each student will plan and teach a launch for a mathematics lesson for the class.
Micro-Teaching will be documented (including videotaping) and analyzed.
Important dates for Micro-Teaching:
October 2: Task Analysis (3 points)
October 9: Plan (5 points)
October 30: Perform! (2 points)
November 13: Transcript (1 point)
November 20: Commentary (9 points)
5. Fieldwork Case (15%)
Instead of a final exam, students will write up and present their own case of an episode from
their fieldwork experiences. Students may focus on one or two themes from the course for
their cases, which should raise some questions but also take an informed, justified stance.
The case should draw from course readings, experiences, and assignments.
Late assignment policy:
All assignments are to be uploaded to NYUClasses by 9am the day of class, unless I state
otherwise. Under extenuating circumstances you may make other arrangements with me before
the due date. Late assignments will be penalized 10 (out of 50) points for each day.
Rubrics for each component are attached at the end of this document. Your final grade will be
determined by the sum of points accumulated for each component (participation, weekly
assignments, and final project), according to Steinhardt School of Education Grading Scale.
A
93-100
C
73-76
A-
90-92
C-
70-72
B+
87-89
D+
65-69
B
83-86
D
60-64
B-
80-82
F
Below 60
C+
77-79
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Course Bibliography
Aguirre, J. M. & Bunch, G. C. (2012). What’s language got to do with it? Identifying language
demands in mathematics instruction for English language learners. In S. Celedón-Pattichis &
N. G. Ramirez (Eds.), Beyond good teaching: Advancing mathematics education for ELLs
(183-194). Reston, VA: NCTM.
Arcavi, A. (2002). The everyday and the academic in mathematics. Journal for Research in
Mathematics Education, 11, 12-29.
Boaler, J. (1993). The role of contexts in the mathematics classroom: Do they make mathematics
more “real”? For the Learning of Mathematics, 13(2), 12-17.
Boaler, J., & Humphreys, C. (2005). Connecting mathematical ideas: Middle school video cases
to support teaching and learning. Portsmouth, NH: Heinemann. [B&H]
Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in
schools. British Journal of Developmental Psychology, 3, 21-29.
Celedón-Pattichis, S., & Ramirez, N. G. (2012). Elements of an effective mathematics
community for ELLs. In S. Celedón-Pattichis & N. G. Ramirez (Eds.), Beyond good
teaching: Advancing mathematics education for ELLs (19-37). Reston, VA: NCTM.
Chapin, S. H., O'Connor, C., & Anderson, N. C. (2003). Classroom discussions: Using math talk
to help students learn, grades 1-6. Sausalito, CA: Math Solutions.
Civil, M. (2002). Culture and mathematics: A community approach. Journal of Intercultural
Studies, 23(2), 133-148.
Cohen, Elizabeth G. (1994). Designing groupwork: Strategies for the heterogeneous classroom.
New York, NY: Teachers College Press.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., . . . Human, P.
(1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth,
NH: Heinemann.
Hodgen, J., & Wiliam, D. (2006). Mathematics inside the black box. London: GL Assessment.
Horn, I. (2012). Strength in numbers: Collaborative Learning in Secondary Mathematics.
Reston, VA: NCTM. [SiN]
Jackson, K. J. (2009). The social construction of youth and mathematics: The case of a fifth
grade classroom. In D. B. Martin (Ed.), Mathematics teaching, learning, and liberation in the
lives of black children (pp. 175-199). New York: Routledge.
Jackson, K. J., Shahan, E. C., Gibbons, L. K., & Cobb, P. A. (2012). Launching complex tasks.
Mathematics Teaching in the Middle School, 18(1), 24-29.
Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven: Yale
University Press.
National Research Council. (2001). Adding it up: Helping children learn mathematics.
Washington, DC: National Academy Press.
New York State P-12 Common Core Learning Standards for Mathematics Retrieved from
http://schools.nyc.gov/NR/rdonlyres/C0971909-165F-46F5-B209F3425A90C5E8/0/p_12_common_core_learning_standards_mathematics_final.pdf
Ramirez, N. G., & Celedón-Pattichis, S. (2012). Second language development and implication
for the mathematics classroom. In S. Celedón-Pattichis & N. G. Ramirez (Eds.), Beyond
good teaching: Advancing mathematics education for ELLs (19-37). Reston, VA: NCTM.
Smith, M. S., Hughes, E. K., Engle, R. A., & Stein, M. K. (2009). Orchestrating discussions.
Mathematics Teaching in the Middle School, 14(9), 548-556.
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Smith, M. S., & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research
to practice. Mathematics Teaching in the Middle School, 3(5), 344-350.
Taylor, C. S., & Nolen, S. B. (2008). Classroom assessment: Supporting teaching and learning
in real classrooms (2nd ed.). Upper Saddle River, NJ: Pearson Education, Inc.
Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M., & Wray, J. (2013). Elementary and
middle school mathematics: Teaching developmentally (8th ed.). Boston: Pearson.
Weinberg, P. J., & Weinberg, C. (2008). The first-year urban high school teacher: Holding the
torch, lighting the fire. Lanham, MD: Rowman & Littlefield Publishers. [WW]
Wieman, R., & Arbaugh, F. (2013). Success from the start: Your first years teaching secondary
mathematics. Reston, VA: NCTM.
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MTHED-UE 1043/MTHED-GE 2033: The Teaching of Secondary School Mathematics
Ma, Fall 2014
Course Outline
*20140904*
Topic
Week 1
9/4
Week 2
9/11
Week 3
9/18
Week 4
9/25
Due
Introductions
Images of Teaching and Learning Mathematics
The Work of Teaching Mathematics
What Does it Mean to Learn Mathematics?
Aspects of Equitable Mathematics Teaching and Learning:
Being "Smart"
Who Can Learn?
Students Make Sense
Groupworthy/Complex tasks
Launching tasks
Reading:
Lampert Ch 1-2
Hiebert Ch 3 Role of Teacher
CCLSM Intro & Practices
Assignment:
1) What's the mathematics?
2) sign up for an observation placement
Reading:
Wieman (10-17): Learning Mathematics
SiN Ch 1: Classrooms as Learning Environments
SiN Ch 2: Equitable Mathematics Teaching
SiN Ch 3: Mathematical Competence and Status
Assignment:
Resources and Responsibilities
Reading:
SiN Ch 4: Groupworthy Tasks
Jackson et al.: Launches
* Smith & Stein (1998), Mathematical Tasks
Assignment:
Task Preparation
Strands v CCLSMP
MTHED-UE 1043/MTHED-GE 2033: The Teaching of Secondary School Mathematics
Ma, Fall 2014
Week 5
10/2
Week 6
10/9
Week 7
10/16
Week 8
10/23
Talk in the Mathematics Classroom
Students Learning from Each Other
Students' Resources for Learning
Phases of Planning
Reading:
Chapin 2: Talk Moves (selections)
Aguirre & Bunch
Assignment:
Micro-Teaching: Task Analysis
Reading:
B&H Ch 1-2: Intro, Border 1 (building on S ideas)
SiN Ch 5: Positive Interdependence
* Smith (Orchestrating discussions)
Assignment:
Micro-Teaching: Plan
Reading:
Civil (2002 JRME)
Arcavi (2002 JRME)
Boaler (1993)
UDL video
*Carraher, Carraher, & Schliemann
Assignment:
ITC 1: School
Reading:
B&H Ch 3: Border 2 (algebraic rep'n)
SiN Ch 6: Teacher's Role
Assignment:
Planning 1: The Task
MTHED-UE 1043/MTHED-GE 2033: The Teaching of Secondary School Mathematics
Ma, Fall 2014
Reading:
NONE
Week 9
10/30
Micro-Teaching Performances
Week 10
11/6
Language and Learning Mathematics
Academic Language
Week 11
11/13
Student Reasoning
Assessment of Learning in Progress
Week 12
11/20
Assessment and grading
Assignment:
Micro-Teaching: Perform
ITC 2: Students
Reading:
Ramirez & Celedón-Pattichis
Celedón-Pattichis & Ramirez
Assignment:
Planning 2: Developing Assessments
Reading:
B&H Ch 4: Defending Reasonableness
Hodgen and Wiliam
Assignment:
Micro-Teaching Transcript
ITC3: Community
Reading:
Van de Walle Chapter 5
edTPA handbook
*Taylor & Nolen Ch 10
Assignment:
Micro-Teaching: Commentary
11/27: Thanksgiving Break
MTHED-UE 1043/MTHED-GE 2033: The Teaching of Secondary School Mathematics
Ma, Fall 2014
Reading:
Jackson (2009) Social Construction of Youth & Math
Week 13
12/4
Student Identities and Dispositions
Week 14
12/11
Planning Over the Long Term
EXAM
WEEK
TBD
Assignment: Fieldwork Case Presentations
Assignment:
Planning 3: Orchestrating Discussion
Reading:
WW selections
Assignment:
Planning 4: Curricular Planning
Other Important Information
Accomodation 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 212 998-5980, 240 Greene Street. See
www.nyu.edu/csd.
Academic Integrity
The relationship between students and faculty is the keystone of the educational experience in
The Steinhardt School of Culture, Education, and Human Development 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 to also 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 prior permission from your
professors;
• Receive help on a take-home examination that calls for independent work;
• Plagiarize.
Plagiarism, 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 other's 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 more on academic integrity see http://steinhardt.nyu.edu/policies/academic_integrity.
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Grading Rubrics
1. Active participation in class activities and contribution to discussions (30%)
Participation will be scored each week based on these criteria, then averaged at the end of the
semester.
Exceptional
(30 points)
Excellent
(25 points)
Considerations for scoring
Has made connections
between readings,
assignments and
activities from this and
prior weeks;
Participation elevates
the tone of class and
learning of all students.
Has clearly read
assignments carefully
and thought deeply
about them; Participated
in class activities and
contributed
substantively to
discussion.
* Promptness to class
* Preparation for class, including closeness
of reading
* Active participation in class activities
* Quantity and quality of contributions to
class discussion
2. Weekly assignments (20%) and Fieldwork Case Presentation (15%)
The weekly assignments and fieldwork case presentation will be graded on a scale of 0-50 points
for each assignment. Unless otherwise stated, the grading of an assignment will be done
according to the following rubric. At the end of the semester, assignment grades will be averaged
and scaled.
Exceptional
(50 points)
All parts were completed
thoroughly and
thoughtfully, following the
guidelines. Made
connections to readings,
assignments, and/or course
experiences.
Excellent
(45) points
All parts of the
assignment were
completed well,
following the guidelines.
Considerations for scoring
* Completion of all parts of the
assignment
* Adherence to assignment
guidelines
* Work makes sense or is well
justified with evidence
* Work shows effort and original or
creative thinking
3. Investigation of teaching context (15%)
The 3 parts of the ITC will each be worth 5%. These will be graded on a 100 point scale, with a
rubric similar to that for the weekly assignments. I will be looking for evidence that you have
investigated the context carefully, and that you have answered all of my questions thoroughly
and thoughtfully.
4. Micro-Teaching (20%)
The Micro-Teaching assignment has 4 main parts. Task Analysis (3%), Planning (5%),
Performing (2%) and the transcript and commentary (10%). Rubrics for each of these parts will
be distributed along with the assignments.
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