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## Peter Appelbaum

E-mail: pappel@frontier.wilpaterson.edu

Address:17 Essex Avenue, Montclair, NJ 07042

Phone: (201) 744-6913, (201) 595-3123 office

School: William Paterson CollegePeter Appelbaum is a professor of mathematics and science education at William Paterson College of New Jersey. He has for some time been interested in the politics of mathematics education: his doctoral dissertation in Social Foundations at the University of Michigan, "Popular Culture, Professional Discourse, and Mathematics Education," was about the ways in which people construct commonsense notions of what mathematics "is." Peter attended the Geometry Forum's Summer Institute in Swarthmore, PA in 1993.

Peter is interested in developing thematic units based on individual and group interdisciplinary projects. He has been using a 5-week planning model that includes three major components:

- Part I is introductory, begins with open-ended exploratory activities, and requires that students identify questions they want or need to answer and begin to note directions for pursuing them;

- Part II is a 3-week period during which students formulate a project, research it, and then put together an exhibition or presentation based on their research;

- Part III is math for math's sake, in which a kind of archaeology of mathematics is generated - students are given explorations, puzzles, games, and other activities that help them celebrate the mathematics learned during the unit.
This model is popularly described in a book called

How Big is the Moon, by Baker/Semple/Stead - Heinemann.Peter is also seriously interested in three other aspects of curriculum:

Peter plans to design resources this summer that can be used later to team up with math teachers in Northern New Jersey to adapt them as necessary and obtain feedback on their use.

- Integrating mathematics across the curriculum.

- Social justice issues as related to mathematics in society. "Here one can see curriculum as positioning the student in various roles viz-à-viz the subject matter. In most curricula the student is positioned as 'mathematician' and is expected to adopt the perspective of one who 'does' mathematics. What this means has been debated and has wide interpretations. A second option is the citizen-mathematician. Here the student needs to know mathematics to be an informed member of a democratic community - e.g., to be able to understand graphs in a newspaper, to be able to vote on school budgets or placements of toxic waste dumps. Another important option is the student as
subjectof mathematics - how math is used to turn the person into an object of study, how people and things are objectified through mathematical models, etc. In this object-orientation we might also lump in the de-mathematization of society through implicit mathematics that happens (invisibly?) through technology - the automatic cash registers at MacDonalds, scantrons at supermarkets, automated tellers, CAD programs, - in which the mathematics is donefor usas we no longer know what exactly is being done. What are the implications of these different positionings of students? Can curricula be developed that include all perspectives? Are there other important perspectives (especially in light of issues of pluralistic, multi-cultural societies)?"

- Alternative assessment as an integrated component of curriculum development rather than an add-on that evaluates the success of the curriculum. "[C]urriculum development won't change anything if the assessment is reduced to tired notions of 'evaluation.' I want to promote a transformation of what we want students to know and so on through changing our notions of what it means to 'show that one knows'."

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