MTE 482 / 598 – Fall 2007
Methods of Teaching Mathematics in Secondary School
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Numbers 80921 / 80941
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Instructor: |
Dr. Michael Oehrtman |
Office Hours: |
TTh: 3:00-4:30pm |
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Class Time: |
Tuesday and Thursday, 12:15-1:30pm |
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Location: |
PSA 303 |
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Class Website: |
http://math.asu.edu/~oehrtman/mte482 |
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Required
Texts:
Course
Description: This course will address issues of teaching
secondary
school mathematics content. The nature of our activities will be guided
by
current research about what it means to “know,”
“learn,” and “do” mathematics as well as from the
recognized national and state academic standards for secondary
mathematics. The
course is organized around the integration of topics in learning
theory,
mathematics content, and pedagogical techniques. The three units we
will cover
are
Unit 1: Platonism / Proportional Reasoning / Lesson Planning and Assessment
Unit 2: Constructivism and Cognition / Algebra / The Structure of Classroom Activity
Unit 3: Socially Mediated Thought / Functions / Cooperative Learning
Teaching
Experiences and Writing Assignments: You will be given several
opportunities to teach in your field placement this semester receiving
feedback
from me, your peers, and your mentor teacher. If you are not enrolled
in a field placement this semester, you are responsible for finding a
mathematics teacher, subject to my approval, either in a school or at
ASU that will allow you to observe throughout the semester and complete
the assignments. A major portion of
these
experiences will involve your preparation of products such as lesson
plans, classroom
activities, and assessment items and reflection on their implementation
through
analyses of video of your teaching, written self-evaluation, and
revisions of
lesson materials. I will use the following rubrics to grade written
assignments
on a ten-point scale (with more substantial or important assignments
scaled to
20 points):
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Rubric for Classroom Materials |
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Scoring Criteria |
Points |
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Correct and appropriate mathematical content. The ideas you present should always be geared at increasing the power of your students’ mathematical abilities and reasoning. Provide a balance between attention to procedures and their underlying concepts. |
3 |
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Appropriate incorporation of current course concepts. You must show thoughtful application of the material being covered in class and submit a product reflecting all of the criteria requested in the assignment. |
3 |
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Clarity. Materials meant for students should include instructions and layout understandable to students. Material for teachers such as lesson plans should be clear and usable without any additional explanation. |
3 |
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Correct punctuation, grammar, and mathematical typesetting. |
1 |
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Total Score (add points from each
category) |
10 |
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Rubric for Reflections on Implementation of Materials and Interviews |
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Scoring Criteria |
Points |
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Description of how things went. Provide a clear and detailed description of what happened in the classroom, interview, etc. |
3 |
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Critical application of current course concepts. Use the ideas we cover in class help you evaluate and make sense of what has happened. |
2 |
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Ideas for improvement. The most important part of becoming an effective teacher is reflecting on ones own practice for ways to improve, and this should never end! How could you do things better? |
3 |
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Clarity, punctuation, grammar, and mathematical typesetting. |
2 |
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Total Score (add points from each
category) |
10 |
Problem Analyses: At the beginning of each unit, you will be given
a set of
challenging problems related to the mathematical content for the unit
(Proportional Reasoning, Algebra, and Functions). Over the following
3-4 weeks,
you must work with your classmates to solve these problems, then
individually write up the solutions. Your work must be neat and include
sufficient exposition to make the solution clear to a student (for
example, a
sequence of equations without explanation will most likely receive zero
credit).
Reading
Assignments and Discussion Boards: Much of this course will be
built around
theoretical and practical considerations of issues of teaching and
learning. In
addition to the NCTM Principles and Standards we will use a variety of
additional sources, including major readings from Plato, Piaget, and Vygotsky. Between the time a reading is assigned
and
discussed in class, you will participate in a discussion board, posting
your
reactions to the reading and to your colleagues' ideas. You will
probably
submit several posts for a given discussion, but each one should fit
into one
of the following categories:
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Types of Posts and What They Should Contain |
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In-depth reaction to an important issue raised in the reading. Do not just repeat, summarize, agree, or disagree with something, but go beyond what was said providing justification and fresh examples or alternatives. Also, explain why the issue is important/relevant if it is not immediately obvious. |
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Connections to other content we have covered in the class or ideas that you have encountered in other settings. Go beyond saying something is similar or different, but explain how. Place different perspectives in dialogue with each other. |
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Reflection on how you can apply what you have learned from the reading to your own practice as a teacher. Avoid vague statements and build a clear picture of how you want your classroom style to emerge. Give specific examples and reasons why you think that will help students learn. |
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Thoughtful response to a classmate's post. Point out additional examples, justifications, or subtleties that may have been originally missed. As with an original post, do not just repeat, summarize, agree, or disagree, but try to move the discussion forward. It is ok to disagree as long as it is done respectfully. |
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Well constructed synthesis of an entire thread in the discussion. Bring together the big ideas in a way that the issues become clearer. Categorize various sides of an issue or debate, point out differences in use of terminology, propose resolutions, and place everything into a bigger framework. |
The discussion boards associated with course readings
will be
assigned a maximum number of points. The totals from all assignments
will well exceed the 250 points in this category toward your final
grade, so you do not need to earn the maximum on each assignment to
earn these points. Each original post can earn
up to 10
points toward this total according to the following rubric:
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Rubric for Scoring Discussion Boards |
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Criteria |
Points |
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Writing: Original and strong writing. Be creative and use appropriate punctuation, grammar, and rhetoric. |
required |
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Relevance: The posting should cover issues relevant to the class and the reading. and should meet most, if not all, of the criteria described in the previous table for a given type of post. |
0-2 |
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Clarity: The
main point of the post should be obvious. One way to do this is to
carefully organize your writing. If you use a metaphor, be explicit
about what it means and why you think it is appropriate. Don't use
jargon without explicit definitions (unless we as a class have come to
agreement on a definition). Make sure that pronouns have clear
antecedents (the pronouns "this," "these," "that," and "those" are
particularly abused). |
0-2 |
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Justification:
Make sure that you provide a strong rationale for your
claims. Explain why you think something is the case or why you agree or
disagree with something. If you give an example, explain why your
example supports your argument. |
0-2 |
| Completeness:
Fully develop your ideas and explore their implications.
Rather than hop from topic to topic, try to dig deeply into one idea
per post. Note that length does not imply completeness; try to cover
the topic concisely. |
0-2 points |
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Perfection:
If all points are awarded in the previous criteria and the
points made in the post are so good that it should have been
included in the
original reading, an additional couple points may be awarded. |
0-2 |
Midterms and Final: The midterms will be taken outside of the
regularly
scheduled class times at the Mathematics Testing Center (PSA 21) and
the final
will be given at the time and location established by the university.
You will
be provided additional information at a later date. These exams will
assess
your understandings of the mathematical content, readings, and written
assignments
covered in the class. They will mostly cover content from the unit just
covered
but will also contain some aspects of cumulative comprehensiveness.
Grades
will be determined as follows:
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150 |
Written Assignments |
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A+ |
970 and above |
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150 |
Problem Analyses |
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A |
930 - 969 |
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250 |
Discussion Boards |
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A- |
900 - 929 |
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150 |
Midterm I |
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B+ |
870 - 899 |
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150 |
Midterm II |
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B |
830 - 869 |
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150 |
Final |
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B- |
800 - 829 |
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C+ |
770 - 799 |
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1000 |
Total |
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C |
700 - 769 |
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D |
600 - 699 |
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E |
below 600 |
Graduate Credit: If you are
taking this course for graduate credit (MTE 598, SLN 80941), the
written assignments (including all field placement assignments) will be
replaced by an individual research project. You will need to speak with
me about ideas for your project and submit a 1-2 page proposal no later
than September 11. Upon approval, you will complete the project during
the course of the semester. The project should involve implementation,
evaluation, and refinement of activities you develop based on the
theoretical and practical foundations of this course. A final report
should include an abstract, an introduction, a review of relevant
research literature, a description of the activities, report and
analysis of the results, a description of modifications to the
activities based on the outcomes of your analysis, conclusions, and
references. You will work independently but should consult me regularly
throughout the semester to make sure you are progressing appropriately
and for feedback. The final paper is due on December 4, however, I
strongly recommend that you submit a draft before Thanksgiving so that
you may incorporate my feedback into a final version. Finally, please
note that grades for MTE 598 will be on the standard A, B, C, D, E
system (no plus/minus grades).