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Steinhardt School of Culture, Education, and Human Development
Department of Teaching and Learning
The Teaching of Geometry, Grades 7-12
Instructor: Arnon Avitzur
[email protected]
Spring Semester, 2015
Course Description
The course provides a link between teachers' mathematical knowledge & understanding of
the major skills & concepts of geometry to the effective & appropriate teaching of these topics in
grades 7 through 12.
Course Overview
This course will support students’ developing understandings of the pedagogical and
mathematical issues underlying the teaching and learning of geometry in grades 7-12. The course
will sample topics central to geometry, promoting deep mathematical understandings as well as
related pedagogical content knowledge. Students will have opportunities to reflect on their own
mathematical learning and problem solving strategies. At the same time, they will connect these
experiences to theoretical and practical issues, drawing from current research on teaching and
learning geometry. The course integrates the use of tools for teaching geometry, including digital
technologies, such as The Geometer's SketchPad.
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 is an on-going, major effort to reform 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 might 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 right way);
o Inquiring into mathematics, mathematics learning, mathematics teaching, and the
mathematics of students is powerful;
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 more effective.
This course is designed to prepare 7-12 mathematics teachers with the goal to help
develop your mathematical and pedagogical understandings for that grade range.
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This course 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.
Course Objectives
Develop a stance on what counts as geometry, and why we teach it;
Develop an understanding of big ideas in geometry and the connections between
geometry and other mathematical domains;
Solve geometry problems and construct geometry proofs from the secondary curriculum
in multiple ways, while considering relevant pedagogical implications;
Anticipate and analyze students' geometry reasoning and strategies, and begin to develop
appropriate instructional strategies for supporting learning goals;
Increase awareness of common difficulties students face in making sense of geometry
concepts;
Become more reflective with respect to your own and others’ teaching, and develop
strategies for learning from your own and others’ experiences.
Required Texts
Driscoll, M. (2007). Fostering geometric thinking: A guide for teachers, grades 5-10.
Portsmouth, NH: Heinemann.
Other Requirements
The Geometer's SketchPad or GeoGebra available on your computer
(If you don’t want to buy GSP, there is a cheap student version and perhaps a trial one)
Laptops for use in the classroom
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Course Outline (always tentative)
Week
Topic
Week 1
02/02/2015
What geometry is and why teach it
Geometric Habits of Mind
Week 2
02/09/2015
The Van-Hiele theory
Common Core Geometry Standards and the NY Regents
02/16/2015
NO CLASS
Week 3
02/23/2015
Concept image and concept definition
Using examples in Geometry
Weekly #1 - Van-Hiele and CCGS are due
Week 4
03/02/2015
Discovering invariance
Dynamic Geometry Environment
Weekly #2 - Examples are due
Week 5
03/09/2015
Lesson analysis
Weekly #3 - DGE constructions are due
03/16//2015 NO CLASS
Week 6
03/23/2015
Congruence and similarity
Shape hierarchy
Weekly #4 - Lesson analysis is due
Week 7
03/30/2015
Thinking about student thinking
Micro-teaching #1 proposal is due
Week 8
04/06/2015
Micro-teaching #1
Week 9
04/13/2015
Theorems
Proof
Week 10
04/20/2015
Constructions
Micro-teaching #2 proposal is due
Week 11
04/27/2015
Micro-teaching #2
Week 12
05/04/2015
Micro-teaching #2 (continued)
Problem-solving in geometry classes
Week 13
05/11/2015
Micro-teaching reflections are due
Final presentations
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Assessment and Grading
1. Active participation in class activities and contribution to discussions (30%)
The quality of this class (and of 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. Good
contributions to classroom discussion do more than simply push the conversation along.
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. 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%)
Weekly assignments will be a combination of Geometry/Geometry 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.
Late assignment policy:
All assignments are due at the beginning of class on the date they are due, unless I have
stated otherwise. Under extenuating circumstances you may make other arrangements with
me before the due date. Late assignments will be penalized 1 point for each day.
3. Micro-Teaching (50%)
Each student will plan and teach parts of two geometry lessons for the class. Micro-teaching
#1 (10%) will focus on discovery and examples, and Micro-teaching #2 (25%) will
incorporate all the ideas studied in the class.
Instead of a final exam, students will reflect on and present analysis and commentary on their
Micro-Teaching experiences (15%).
Rubrics for each component can be found 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 micro-teaching)
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Grading Rubrics
Participation (30 points):
Excellent
(30 points)
Good
(25 points)
Adequate
(20 points)
Has clearly read
assignments carefully
and thought deeply
about them;
Participated in class
activities and
contributed
substantively to
discussion
Was late to class; Has
read assignments;
Participated in class
activities and
contributed
substantively to class
discussions.
Was late to class; Has
read most of the
assignments;
Participated in class
activities and
contributed to class
discussions.
Poor
(15 points)
Was late to class or
absent (unexcused);
Has not read
assignments;
Participated in class
activities; Made very
few (or no)
substantive
contributions to class
discussions.
Weekly Assignments (20 points):
The weekly assignments (unrelated to Micro-Teaching) will be graded (0-5 points for each
assignment). Unless otherwise stated, and only if applicable, the grading of an assignment will
be done according to the following rubrics. At the end of the semester assignment grades will be
averaged and scaled.
5 points
All parts of the
assignment were
done thoroughly
and thoughtfully,
following the
guidelines.
4 points
All parts of the
assignment were
done well,
following the
guidelines.
3 points
2 points
1 point
Most (but not all)
parts of the
assignment were
completed
adequately,
following the
guidelines.
Only some parts
of the assignment
were completed,
overlooking some
of the guidelines.
Only a very small
part of the
assignment was
completed,
overlooking most
of the guidelines.
Micro Teaching (50 points):
The Micro-Teaching assignments have three main parts.
(1) Micro-Teaching #1 (10 points),
(2) Micro-Teaching #2 (25 points)
(3) Final presentation (15 points).
Micro-Teaching #1 and #2 each has three parts (draft/proposal, instruction, commentary).
Rubrics for each of these parts will be distributed along with the assignments.
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The 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
AB+
B
BC+
The Teaching of Geometry
93-100
90-92
87-89
83-86
80-82
77-79
C
CD+
D
F
73-76
70-72
65-69
60-64
Below 60
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Accommodation 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.
The Teaching of Geometry
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