Appelbaum, ED 528B, Arcadia University, Spring 2006

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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. - out of print, so we will share my copy, make selective photocopies as needed, etc.

Appelbaum Peter. in press. Embracing Mathematics: On becoming a Teacher and Changing with Mathematics. manuscript; I'll make copies as needed.

Participation, Contributions, and Leadership: This course expects you to do more than simply show up to class. We will be working on mathematics investigations together, sharing ideas for what to do when we interview students, supporting each others' efforts to confront difficult subjects, etc. Missing class means more than trying to make up what you missed: everyone else does not get your input into their own work and we can never make that up; you do not get others; input into your work, and we can never make that up. In addition to attending class, coming having read materials and ready to discuss it, with questions for the group, with connections to your own work, etc., we need you to contribute in significant ways, but suggesting new avenues of thought or exploration, by introducing resources and materials to the class, by initiating projects for the group to take on, etc.

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. You are expected to meet once per week at least 10 times for at least 30 minutes over the course of the semester. 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. I will also have several assessment challenges that I will introduce as we go along. You are asked to videotape your work and view it yourself, and occasionally 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 (March 20): Turn in your working portfolio with a statement that includes: (a) weekly plans and reflections, including revisions based on email feedback from Peter; (b) what you have learned so far about your student(s); use evidence from your portfolio to explain how you know what you know; (c) 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? (d) an explanation for how you have been learning to distinguish between how you think mathematically and how your student(s) think mathematically. (e) Your analysis of what aspects of this work are primarily related to mathematical content and which aspects are primarily related to something else. Explain. Checkpoint 2 (April 24): (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, using a five-part structure that will enable you to develop an inquiry, pursue it, connect with the world outside of our class, and pull out of that work important learning and understanding. Your goal is to learn more about yourself as a mathematician. Your portfolio should include all work and reflection on your mathematical explorations, including background/kitchen work (starts and stops, initial ideas, work that seems to lead nowhere, places where you recognize progress, etc.), Diningroom work (rewriting of your work in more public form), reflections on your tendencies and dislikes as a mathematician, etc. Please see the separate Investigation portfolio specifications sheet. Your portfolio is due April 3rd.

Action Project. In the last part of the course, growing out of your work with the mathematics investigations and the flexible interview project, you will have the opportunity to take action based on what you have identified as most significant for your learning in this course this semester. Please see the separate Action Project specifications sheet.

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. (It is similar to asking a colleague to look at a student's written work on a worksheet and give his or her opinion.). We are not judging your teaching or your students' quality of work. We are developing skills of clinical and flexible interviewing.

Professional Visit: I would like to visit you in your current professional work at least once this semester. Arrange a date with me before March 6th, 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.

Jan 23 Opening: What's this course about? The nature of clinical education in professional work

30 Math Investigation: Opening; Corwin handout; Appelbaum handout, Prologue, Chapters 1 & 2

Feb 6 Math Investigation: Developing a Project; Appelbaum handout, Chapter 3; Hersh handout

13 Math Investigation: Developing a Project; Appelbaum handout, Chapter 4; Mason handout

20 Math Investigation:: Doing Your Project; Appelbaum, Chapter 5; Brown, Part 1 (Chapter 1)

20 Math Investigation: Work Out into World; Flexible Interview Checkpoint 1 due; Winnicott handout

Apr 3 Math Investigation: Archaeology; Appelbaum, Chapter 8; Investigation Portfolio due

10 AERA/AAACS - Peter in California for conferences, April 7-11; readings TBA, based on the direction that our work takes

17 Taking Action Workshop; readings TBA, based on the direction that our work takes

24 Taking Action Workshop; readings TBA, based on the direction that our work takes; Flexible Interview Checkpoint 2 due

Peter Appelbaum

Taylor 312A

(215) 572-4476 fax: -4075

appelbaum@arcadia.edu

Office Hours:

Monday & Wednesday 2:00 - 3:30

& by appointment

I am also available after class.

Participation, Contributions, and Leadership	20%
Flexible Interview Project, Checkpoint 1	15%
Flexible Interview Project, Checkpoint 2	15%
Investigation Portfolio	30%
Action Project	20%