Park City Mathematics Institute
Mathematics Education Research Program
Elementary Mathematics Laboratory

Instructor and Facilitator: Deborah Loewenberg Ball, University of Michigan

The Elementary Mathematics Laboratory (EML) is a new PCMI program (initiated in 2003), focused on elementary level mathematics. The goal of EML is to investigate how essential ideas and ways of working that characterize mathematics at advanced levels might be made accessible to young students, and how students might learn practices essential to mathematical work. A corollary problem is the mathematical knowledge needed for teaching: What do teachers have to do and "be" mathematically in order to engage students in such mathematical work?

The core of the program is a two-week summer school course for approximately 20 fifth grade students from Park City Schools. The content focus for the 2004 summer will be explored in the context of decompositions of the square, connecting arithmetic, geometric, and algebraic representations and ideas. Important topics will include factorization, primes, squares; and rectangles. The mathematical emphasis will be placed on looking for and identifying patterns, generalizing, use of definitions, and justification.

The classroom will be set up as a teaching laboratory with space for observers and documenters in the periphery. EML Participants will attend each class session and will also be involved in the planning and analysis of the class before and after the lessons. Participants will discuss the mathematical ideas and skills in which the students are engaged, and the sorts of mathematical moves and habits that they exhibit, are developing, or lack. Parallel to this will be an analysis of the mathematical problems faced by the teacher, and the mathematical moves needed to teach the class. Our focus will be on what is involved in trying to teach mathematics in a way that preserves the essence of the mathematics and that are accessible to and "do-able" by 10-year-olds. Observations and artifacts gathered from the lab class each day will provide resources for this investigation and analysis.

EML is a design and analysis laboratory, developed to provide a data-rich environment in which the disciplinary perspectives and expertise of mathematicians, mathematics educators, and K-12 teachers can be brought to bear on problems of teaching and learning mathematics. Participants will be engaged in the design and analysis of the student lessons but will not participate directly in teaching the class.

There will be available space for visitors from the PCMI community - or larger Park City community - to attend the class sessions as well as the EML planning and analysis sessions as observers. In addition, the EML students and participants will make a cross-program presentation near the end of the second week of the program.

Research Goals
As a research and development laboratory, the EML is intended to develop knowledge and usable products based on investigations of the following three questions:

  1. What are key issues involved in trying to represent mathematics with integrity at the elementary level? One example that emerged during the summer of 2003 was the intricate work involved in developing mathematically rigorous and yet usable definitions; a second was the mathematical judgment involved in estimating what it might take to pursue a student question.
  2. What kinds of disciplined mathematical work are possible for typical ten- and eleven-year old students? What mathematical ideas can be made accessible, and what mathematical skills can they learn to use to pursue and work with those ideas? Again, an example from the 2003 summer lab class was the way in which the children were able to work carefully on definitions; another was the children's capacity to learn to read and make use of charts and other tables that captured records of their work.
  3. In what ways can the records of the lab class be studied in order to develop knowledge of mathematics for teaching? The EML will study artifacts of the lab class, with an eye toward identifying and probing the issues named above. Particularly rich examples will be tagged, and, after the summer, developed into draft selections for further development.

Participants will be by invitation only and limited to 15. The participants will represent variation across these categories: mathematicians, researchers in mathematics education, other scholars, teacher educators, and teachers.

2003 Photo Album  private - in password protected area

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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540.
Send questions or comments to: Suzanne Alejandre and Jim King