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Assessment criteria and tools to evaluate students' performance in the course (E2)
Course description of Secondary Math Methods Course (including evaluation criteria)

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Overview

Goals

Course requirements

Course Evaluation

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Overview

This course will be an introduction to mathematics education. Various issues regarding the nature of mathematics, the process of learning mathematics, methods of teaching mathematics and other variables affecting mathematics instruction will be raised and analyzed. The course is addressed to prospective and in-service mathematics teachers at all levels of schooling, doctoral students in mathematics education as well as any other person interested in mathematics education. However, doctoral students enrolled in the class should expect some additional and/or alternative assignments and requirements (described only in part in this course description and needing to be negotiated individually with the instructors at the beginning of the course).

One of the major thrusts of the course is a critical examination of the nature of mathematics, as a necessary premise for the discussion of fundamental issues such as: what should we teach in school mathematics? how should we teach mathematics? This will be done through a variety of means, including the participants' engagement in a variety of learning situations as students themselves, readings in various areas of mathematics and mathematics education, and examining selected teaching materials and/or experiences. These experiences will always be followed by reflections, writing and discussions aiming at enabling each participant to discover and/or refine his/her own beliefs about mathematics and the learning and teaching of mathematics. As we re-examine the nature of mathematics and mathematics education, we will also look at recent reform proposals, particularly the NCTM Standards, as well as teaching approaches that have been suggested in the mathematics education literature, to become aware of their assumptions, potential and limitations.

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Goals

The main goals of this course can be articulated as follows:

• students will gain a better appreciation of the nature of mathematics, and especially become aware that math is a more humanistic domain than it is usually perceived and that it involves much more than dealing with numbers
• in light of this new appreciation of the nature of mathemetics, students will begin to question what we should teach in school mathematics and why, and will develop strategies to approach these questions in the context of your future teaching
• students will come to appreciate the importance of affective issues in the learning and teaching of mathematics (including the role of teachers and students' beliefs)
• students will experience as learners various "teaching strategies" that could be used in mathematics instruction (such as cooperative learning, journals, exploration, various forms of assessment, creating a community of learners, etc.) and come to appreciate their pedagogical values and shortcomings as well as possible uses in their own teaching
• students will gain an understanding and appreciation of the nature and rationale of alternative approaches to teaching mathematics based on a constructivist/inquiry paradigm in contrast to a traditional approach to teaching mathematics
• students will gain an understanding and appreciation of the nature and rationale of the most recent recommendations for school mathematics reform, as articulated in the National Council of Teachers of Mathematics "Standards", and their implications for the teaching of specific math topics
• students will become familiar with some key issues in mathematics education and the literature about those issues
• students will be encouraged to approach the teaching of mathematics in a more innovative and meaningful ways in their own student teaching experiences, as well as their future teaching

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Course requirements

Class Participation

The format of the course will be that of a seminar, and therefore depends on students' full participation. Thus, attendance to class is an essential pre-requisite. In case you are unable to attend a specific class, please let the instructor know as soon as possible; in addition, make arrangements with a classmate to make sure that you receive information about what went on in the class you missed as well as a copy of all the material distributed in that class (the list of the participants' phone numbers and addresses will be collected and distributed at the beginning of the course).

Class Journal

An important component of the course is the class journal. Each week we will all be expected to bring to class our personal "journal entry" in an appropriate number of copies so that it can be shared with all the other members of the class. This entry will consist of a page or so of our thoughts, ideas, comments regarding the learning and/or teaching of mathematics. For example: you may comment on some of the readings assigned or recommended, you may relate some interesting learning or teaching experience, or you might elaborate on your reflections or reactions to some of the activities done in class. The journal will create an additional medium for communication among the class participants and allow us to touch on issues and concerns for which we may not have an opportunity to deal with explicitly in our class sessions.

Readings

Three texts have been required for this course:

• National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
• National Council of Teachers of Mathematics (1991). Professional Standards for Teaching Mathematics. Reston, VA: National Council of Teachers of Mathematics.
• Owens, D.T. (Ed.) (1993) Research Ideas for the Classroom: Middle Grades Mathematics. New York, NY: MacMillan (co-sponsored by NCTM) AND/OR
• Wilson, P.S. (Ed.) (1993) Research Ideas for the Classroom: High School Mathematics. New York, NY: MacMillan (co-sponsored by NCTM)
• Borasi, R. (1992). Learning Mathematics through Inquiry. Portsmouth, NH: Heinemann.

(NOTE: Copies of earlier versions of my book will be loaned to students' in the course upon request; the NCTM books can be bought directly from NCTM at a 20% discount by NCTM members -- full-time students can become NCTM members and receive copies of at least one of the journals published by the association at half of the regular price.)

In addition, several articles and portions of books will be assigned in the course of the semester; a collection of these readings is available (at cost) as a "course manual" from the University of Rochester Bookstore.

Doctoral students enrolled in the course will also be expected to do additional readings from the following "classic" books:

• Kline, M. (1980). Mathematics: The Loss of Certainty. New York: Oxford University Press.
• Schoenfeld, A. (1985). Mathematical Problem Solving. New York: Academic Press.
• Brown, S.I. & Walters, M.I. (1990). The Art of Problem Posing. Hillsdale, NJ: Erlbaum.
• Grouws, D.A. (Ed.) (1992). Handbook for Research in Mathematics Education. New York: MacMillan.

Weekly assignments

A variety of assignments will be given each week (involving reading, writing as well as other kinds of tasks) and expected to be completed ON TIME as the following class will often assume and make use of them. Therefore NO LATE ASSIGNMENTS will be accepted, except if previously arranged with the instructors. The weekly assignments, when involving a written component, are not intended to be finished, polished reports, but rather they are meant to be ways to think on paper, so that your reflections can be recorded and shared with other members of the group. Therefore, they will not receive a letter grade, but having completed them satisfactorily will affect the final grade in the course (see Evaluation section for more detail).

Major assignments

Though there will be no final comprehensive paper or exam, a few "major assignments" will be given throughout the semester:

• Midterm take-home exam: This will consist in an in-depth analysis of one classroom experience (to be selected among several assigned for reading in previous assignments) in light of the NCTM Standards and the principles of an inquiry approach to teaching mathematics. This assignment is intended to support prospective teachers in making sense of the instructional implications of the reform promoted by many constituencies today's, and synthesize what they have learned in the course up to this point.
• Original mathematical investigation: Each student will be asked to develop independently a mathematical inquiry on a topic of his/her own choice. The results of this inquiry will be shared with the rest of the class in both an oral presentation and a written report (to be explain in more detail at the appropriate point in the course).
• Final project: This project is intended to synthesize and consolidate what was learned in the course by means of an experience that involves some "innovative teaching". There will be several options to choose from to fulfill this requirement, although in each case the student will be expected to develop and implement a short but innovative teaching experience and report its results in a written report.
• "What have I learned" paper: At the end of the course, every student will be asked to look back at the experiences and readings done during the semester and articulated the major insights about the learning and teaching of mathematics that they gained as a result. Among other things, this paper will provide the instructor with each student's own self-evaluation.

While further information on these assignments will be provided at an appropriate time later in the course, the deadlines for each of these assignments will be already indicated in the tentative syllabus that will be distributed at the beginning of the course, so that students can set aside the necessary time for them. Contrarily to the weekly assignments, each of the "major" assignments describe above will be graded.

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Course Evaluation

Students' evaluation will be based for 60% on their participation to the class sessions, their contributions to the class journals, and their compliance with the weekly assignments, and for the remaining 40% on their performance in the four major assignments. More specifically:

• class participation: 26 points (i.e., 2 points for every class attended with full participation in the activities and/or discussions)
• journals: 12 points (i.e., 1 point per journal entry contributed)
• weekly written assignments: 22 points (i.e., up to 2 points per assignment when completed on time and satisfactorily)
• midterm take-home exam: 10 points
• report on an original investigation: 10 points
• final project: 10 points
• "What have I learned" paper: 10 points

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