ED 429: Mathematics and the Curriculum
Peter Appelbaum, Arcadia University

Welcome!
... to Mathematics and the Curriculum. In this course, we will do a great deal of investigation into current ways of thinking about mathematics education, and their implications. I have prepared a number of topics that I believe are central to teaching and learning mathematics, including:

• Recent NCTM Principles & Standards compared with the PA and some international standards
• Backlash against the Standards movement
• Diversity, equity, and mathematics teaching & learning
• Literature-based mathematics education
• The design of mathematical investigations, especially in light of assessment opportunities, and mathematical investigations into politics and everyday life.

• Increased attention to problem solving and topics other than arithmetic; decreased attention to drill & practice
• Social rather than psychological analyses of classroom practices
• Mathematics as a social-cultural resource for meaning as opposed to a commodity to be collected, consumed, and spent
• Teaching as curriculum leadership

One tricky thing is for us all to appreciate that the expertise we are developing in mathematics education goes way beyond our individual classrooms or other professional work. This course is preparing us to think about and consult on mathematics education issues in a broad sense, and to develop leadership skills with that in mind. So you are going to be challenged to talk with people who teach different grade levels, to understand your own professional work within this larger context, and to consider ways in which you can apply what we are learning to school-wide, district-wide, state-wide and other levels of mathematics education professional development. I can't wait! It will be a lot of fun to find out what you are interested in this semester!

Textbooks
I ordered the following books at the bookstore:

• Secada, Walter, Elizabeth Fennema & Lisa Byrd Adajian (eds.). 1998. New Directions for Equity in Mathematics Education. Cambridge/NCTM.
• Cooney, Thomas, Stephen Brown & John Dossey. 1999. Mathematics, Pedagogy & Secondary Teacher Education. Heinemann.
• Moon, Jean & Linda Schulman. 1995. Finding the Connections: Linking assessment, instruction and curriculum in elementary mathematics. Heinemann.

A number of readings will be on-line (such as the NCTM and PA Standards) or handouts; so make sure you work out access to the internet either at home, your work site, your public library, or on campus, and stay abreast of what has been passed out in class. Contact Peter right away if you need help with this.

Assignments/Grades

Each of these will be 25% of your grade:

Contributions beyond minimal expectations of attendance and participation

Literature circle

Classroom action/research project

Assignment of your choice

Contributions beyond minimal expectations of attendance and preparation are supremely important for all concerned. This is a seminar, which only works well if participants ask questions of each other, help each other to develop ideas, and are patient when others don't understand. As we work to introduce "communication" standards into our mathematics education practices, it is important for us to experiment with different kinds of communication ourselves.  Class members will also rotate facilitating class discussion of readings. 

Active engagement with the texts is essential and required. Our texts require you to try things out or carry out explorations as you read them; you must do this so that we can talk about your experiences and use what you thought about as the jumping off point in class for further analysis. Class discussion will make no sense if you are not prepared. Being prepared is also a sign of respect for me and the other students.

Literature circle You will choose a work of literature from my collection and form a group based on reading choice. The group will design a participatory event for the whole class. 

Classroom Action/Research Project In this assignment, you research your own practice.  You identify a teaching strategy or assessment strategy you would like to pursue developing in your own work, or another area of focus of professional growth for the semester.  You keep a regular journal of your daily or weekly efforts to pursue this new style of teaching or teacher-researcher project in which you reflect on your progress, the types of dilemmas and issues that arise, and the ways in which you seek to answer your ongoing questions.  You regularly describe how you are applying the readings and discussions of this course to your project.  The format of your final portfolio/progress report is up to you.  However, what you turn in should clearly demonstrate that you have regularly applied our course content to this project.  Include as well descriptions and plans for two new action/research projects you will do next year. There are several dates for progress report/ideas to be turned in as a portfolio or as a typed paper.  

Assignment Options -- Choose One (collaboration encouraged)

Connections Essays  A total of EIGHT essays (approximately every other week with one final statement).  You write a reflective essay in which you make a CONNECTION that links the readings, what we discuss and do in class, and your own personal life (present or past).  Describe the connection, and form an opinion.  Write about how the connection impacts on your beliefs and expectations for teaching and education.  Discuss how you think your own personal life experience has affected your opinion.  Essays should be approximately 2-3 typed pages.  This can also be done as a dialogue journal: two people write back and forth responding to each other about the material of the course; you turn in your dialogue three times during the semester. The dialogue journal should accomplish the same goals of connecting, forming an opinion, but most of all reflecting on what in your personal experience has led you to believe as you do.

Bibliographic Analysis Report on a Researchable Issue/Topic  You identify a research area that you are interested in and read current research in this area.  You analyze in your report the types of research that have been done, the ways in which people have explored the issues, and gaps in the literature or questions that seem to be left open.  Do not summarize articles but instead interpret them in the context of the existing research. Your report is an annotated bibliography and analysis of the current research in this area, distributed to all class members.  Obtain initial approval of the topic before starting; the final paper should be 8-14 pages.

Creative Project  You pursue a creative form of expression for representing an area of concern or interest developed during this course.  Examples from past semesters: An interpretive dance, a painting, a documentary video, a spoof video, an environmental studies lab in a school, a quilt, a collection of storytelling performances, a multicultural mask interactive exhibit, a mathematical novella.  Along with your work, provide some written program/guide that helps others understand what to look for in the work that you have created.  If you need to schedule class time, please do so as far in advance as possible.  Remember that this assignment is equivalent to the others, and demands serious reflection on the course material; evidence of work over an extended period of time on the project (which may include conceptual development) must be included in the product of your efforts.

Essay Midterm You type responses to 3-4 questions that ask you to synthesize and apply the material of our course.  Tentative dates: pass out midterm before Spring vacation, due the day after Spring vacation.

Exit Interview You meet with Peter Appelbaum during the last week of class or during the final exam week and talk about the course.  I ask you to discuss the themes of our course, how you have synthesized and applied the topics and ideas of our course, the questions you have now at the end of the course, and your plans for projects that continue your investigation of the course material.  You are graded on how well you can synthesize the content of our course and apply it to your own career plans.

Media Project You analyze media presentations of mathematics & society in order to prepare an exhibition for the class to learn from.  Possible projects include: watch and videotape kids’ TV and create a montage emphasizing key representations in these programs; listen (watch) / (video) tape contemporary music videos and create a presentation that effectively demonstrates the representations in contemporary music; research a case study of mass media reporting on a current mathematics topic (e.g., newspapers, television documentaries, etc.) and prepare a report or presentation.  This asks you to go beyond the regular expectation that you view some suggested educational programs.  You must speak with me to check on the initial idea, and at a mid-point to make sure you are meeting my expectations.

Outside-of-Class Discussion You facilitate an ongoing, outside-of-class discussion on the teaching and learning of mathematics.  (a) Internet option: You join a listserv (I have some suggestions) during the first two weeks of the semester.   Find a way to become an active contributor, influencing the trends of discussion and introducing new questions.  Print out records of your email and the resulting threads of discussion that ensue.  (b) Face-to-face option: Facilitate a series of meetings on mathematics education of current teachers and/or administrators whom you recruit to participate.  Take notes on the issues and ideas that are discussed, and especially conflicts that arise regarding what is best for children, schools, and families.  Multiple meetings should take place with the same people.  On March 3^rd, turn in a progress report and portfolio, including a two-page reflection on your work with this project, and a series of goals that you have for this project for the rest of the semester.  I will provide a tentative “grade” to help you meet my expectations.  On April 28^th, turn in a final portfolio documenting your work with this project, and the experience of learning by leading.  Carefully describe two or three projects that have grown out of your work in this assignment that you will begin to implement in the next year.

Contact Information
Peter Appelbaum
 

Taylor 312A	215-572-4476
M, Th 2:00-3:30 & by appointment	appelbaum@arcadia.edu

Tentative Schedule

Date	Topic(s)	Reading for Today	Due Today
Jan 13	Welcome and Orientation		Buy those textbooks!
20	MLK DAY	NCTM Standards PA Standards CIEAEM Manifesto; see also this year's conference
27	Current Professional Recommendations, pt. 1	NCTM Standards Electronic Version Mathematically Correct Mathematically Sane Illuminations Website Annenberg guide to math/science reform On-line Journal of School Mathematics	Action/Research initial ideas; Selection of literature circle book
Feb 3	Current Professional Recommendations, pt. 2	PA Performance level handbook.; Surf the net using my list of websites and the Math Forum. Further investigations into current professional recommendations based on last week's discussions	Initial collaborative assignment ideas
10	Thinking about teaching mathematics	Cooney et al. Chapter 1; Moon & Schulman Chapter 1-3; Walter handout on problem posing; Appelbaum on critical thinking; Math in the News Project	Literature Circles
17	Developing topics across the mathematics curriculum; Group workshop on action/research project design	Cooney et al. Chapter 2	Working draft of the design of your project
24	Assessment issues	Moon & Schulman, 4-6; Mathematics Assessment Resource Service; Secondary Mathematics Assessment Database	Design of your project due. Literature Circles
Mar 3	Designing teaching	Cooney et al. Chapter 3	Literature Circles

  Spring Vacation   

***REVISED TENTATIVE SCHEDULE***...***REVISED TENTATIVE SCHEDULE*** 

Mar 17

Designing teaching

Cooney et al. Chapter 3

Literature Circles

24	Portfolio and self-assessment; Genre	Moon & Schulman, 7-8; Gerofsky handout	Literature Circles
31	Analyzing subject matter; Reporting on Assessment; Group workshop on action/research project	Cooney et al. Chapter 4; Moon & Schulman, 9	Literature Circles; Working portfolio of your project checkpoint; Literature Circles
Apr 7	New directions for equity in mathematics	Mathematics Equals Opportunity; Secada et al. Part I, 1,2,3	Project Checkpoint due
14	Curricular theorizing on equity issues; Mathematical modeling as a feature of the curriculum Planning for 4/28	Secada et al. Part I, 4,5,6,7; Cooney et al. Chapter 5
21	Self-scheduled action/research workshops; Planning for 4/28	Self-selected readings pertinent to project
28	Festival of Mathematics		Festival of Mathematics Education
May 5	Exam Period: Festival Debriefing; Posing Mathematically; Future plans	Cooney et al. Chapter 6	Action/Research Progress Report due

What are you going to read over the summer????