ED 428B

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This is the catalog description for our course: Using tutoring and other clinical experiences, students examine alternative assessment, diagnosis of misconceptions, and personal projections of mathematical relationships upon the student. Videotaping of clinical experiences and readings on clinical educational approaches form the basis of personal projects.

The basic idea of our course is to approach mathematics education practice much in the same way that pyschoanalysts, social workers, and in general other reflective practitioners do their professional work. Clinical experiences will enable us to reflect on how we make decisions in our teaching practice: what constitutes information? what do we really know about our students? when are we learning about our students, and when are we projecting aspects of our own relationships with mathematics onto the students with whom we work? Often, assessment practices give us more information about ourselves than they do about our students.

Ginsburg, Herbert, Susan Jacobs, and Luz Stella Lopez. 1998. The Teacher's Guide to Flexible Interviewing in the Classroom: Learning what children know about math. Boston: Allyn & Bacon. ISBN: 0-205-26567-7.

Brown, Stephen I. 2001. Reconstructing School Mathematics: Problems with Problems and the Real World. NY: Peter Lang. ISBN 0-8204-5103-7.

Flexible Interview Project: For this course you will need to arrange a way to routinely plan assessment and instruction experiences with the same individual or small group of students. Your goal is to learn how to most successfully understand the way that each student is making sense of mathematical ideas, and how they live their lives mathematically. You will plan weekly experiences and apply your reflections on these experiences to future plans. You are asked to videotape your work in order for us to discuss your efforts in class. Email your reflection and the follow-up plan for the next encounter to me at appelbaum@arcadia.edu so that I can correspond with you prior to your next meeting with your student/s every week. Keep a portfolio of your work, including plans, reflections, copies of student work, analysis of student work, etc.

Checkpoint 1: Turn in your working portfolio with a statement that includes: (a) what you have learned so far about your student(s); use evidence from your portfolio to explain how you know what you know; (b) plans for the second half of the semester: what do you believe you need to do in order to learn more about your student(s)' relationship with mathematics, and why do you believe this? (c) an explanation for how you have been learning to distinguish between how you think mathematically and how your student(s) think mathematically. (d)What aspects of this work are primarily related to mathematical content and which aspects are primarily related to something else? Explain.

Final Checkpoint: (a) Provide a written portrait of this/these student(s)' relationship with mathematics. Use examples to illustrate each point you make. (b) Describe what you believe to be the best mathematical experiences that this/these student(s) could have next year; explain why you believe this based on documentation in your portfolio; (c) Describe two projects that you will undertake in your future teaching based on your work with flexible interviewing this semester. Explain how you have come to choose these projects based on your experiences this semester, and why you believe they will be valuable projects for you.

Investigation Portfolio: In and out of class we will work on mathematical investigations. Your goal is to learn more about yourself as a mathematician. Your portfolio should include all work and reflection on your mathematical explorations, including "back"/kitchen work (starts and stops, initial ideas, work that seems to lead nowhere, places where you recognize progress, etc.), "front"/diningroom work (rewriting of your work in more public form), reflections on your tendencies and dislikes as a mathematician, etc.

Checkpoint 1: Turn in your portfolio as evidence of your serious work in this area of the course. Include: (a) one example identified as work that you are proud of, with an explanation of why you are proud of this work; (b) one identified as an example of work that you believe you learned the most from; (c) one sample identified as an example of work that you would like to continue, with a plan for paths that you will try to take in continuing this investigation; (d) a written self-portrait of yourself as a mathematician.

Final Checkpoint: We will decide in class on what we think is the best way to present the portfolio for a final evaluation that adequately reflects your work this semester, along with a rubric for evaluating the portfolio.

Videotapes: We will be viewing and discussing videos of our work in class. I know this can be uncomfortable -- none of us wants to videotape ourselves, let alone show it to somebody else. Getting used to this is an important part of professional development in education. National Board certification requires it, and we may need to be prepared to pursue this in the future. We are a small group and nothing will go beyond our class. You may want to get permission from parents of students you are working with, but there is really no need for you to get special permission to videotape children you are teaching if it is part of your instruction and assessment; I believe this is part of your routine professional work, which can include discussing assessment issues with professional colleagues. We are not judging your teaching or your students' quality of work. We are developing skills of clinical and flexible interviewing. Videocameras can be borrowed for student use.

Talk Show Host Study: This is a non-graded semester-long project. Choose a radio or television talk-show host and analyze how they get their guests talking and revealing insightful information about themselves. How does s/he help the guest to demonstrate how he or she makes meaning and interprets ideas?

Professional Visit: I would like to visit you in your current professional work at least once this semester. Arrange a date with me at some point so that I can drop by, observe for a brief period of time, and just generally get to know the environment in which you work. This is not a time for evaluating your teaching; by visiting I will better be able to understand your efforts in our course.

We may read additional handouts from my book in progress if I can maintain my planned writing schedule.

Jan 12 Opening: What's this course about? The nature of clinical education in professional work

19 No Class -- MLK DAY; Appelbaum handout, "Preface (Chapter 0);" Walter, "Looking at Pizza with a Mathematical Eye."

16 Ginsburg et al., Chapter 7; Handout: Belenky, et al. "Separate and Connected Knowing" and "Connected and Separate Knowing: Toward a Marriage of Two Minds;" work on math investigations

23 Ginsburg et al., Chapter 8; Handout: Mason, "Everyone Can Start," "Phases of Work "; work on math investigations

Tuesday, March 2, 2004, “Why 0.999… is and is not equal to 1,” Bill Rosenthal, Assistant Professor of Curriculum and Instruction and Co-director of the Community School District 4, Hunter College Professional Development School Partnership, New York. Meet at Castle, 7:00 - 9:00

15 Flexible Interview Checkpoint 1 due; math investigations; Kirshner handout, "Exercises, probes, puzzles"

29 Investigation Portfolio Checkpoint 1 due; Appelbaum/Kaplan article, "An Other Mathematics;" Winnicott handout, "Sum I Am."

12 AAACS/AERA -- No Class; Readings TBA, based on the direction that our work takes: selections from Brent Davis, Julian Weissglass

19,26 Readings TBA, based on the direction that our work takes: Excerpts from Deborah Britzman, Sharon Todd, Alan Block, Alice Pitt, Valerie Walkerdine, and others

Peter Appelbaum

Taylor 312A

(215) 572-4476 fax: -4075

appelbaum@arcadia.edu

Office Hours:

Monday & Thursday 2:00 - 3:30

& by appointment

I am also available after class.

Peter Appelbaum and Rochelle Kaplan. 1998. An Other Mathematics. Journal of Curriculum Theorizing.

Peter Appelbaum. 1997. Target Number. Kicneloe et al., The Post-Formal Reader.