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 twoweek 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 "doable" by 10yearolds. 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 datarich environment in which the disciplinary perspectives and expertise of mathematicians, mathematics educators, and K12 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 crossprogram presentation near the end of the second week of the program. Research Goals
Participants 2003 Photo Album private  in password protected area PCMI@MathForum Home  IAS/PCMI Home
