Foundations for the Future in Mathematics Education

James J. Kaput was a professor in the department of mathematics, at the University of Massachusetts Dartmouth. He was originally trained in mathematics (Category Theory), and became interested during the '70s in teaching teachers and reforming undergraduate education, and in the representational side of student learning. Under the auspices of the National Center for Research in Mathematical Sciences Education at Wisconsin, Dr. Kaput led efforts to understand how the core math curriculum might be fundamentally reorganized to democratize access to big ideas such as algebra and calculus. As part of this, he chaired the Early Algebra Research Group of NCRMSE's OERI-funded successor, and was an active researcher and leader in the development of algebraic reasoning in elementary grades mathematics. His NSF-funded SimCalc Project involved designing simulations for the learning of the fundamental ideas underlying calculus beginning at the middle school level prior to the learning of formal algebra. Dr. Kaput was on the editorial board of six mathematics education journals and was a founding co-editor of a new series of volumes sponsored by the Conference Board of the Mathematical Sciences on Research in Collegiate Mathematics Education. He was on many R& D project advisory boards, a consultant to a variety of federal education programs, and a frequent invited speaker at national and international meetings.David Carraher, senior scientist, TERC, is PI of the Early Algebra, Early Arithmetic Project and director of research for the Fulcrum Institute Project. His research looks at the long-term evolution of students' mathematical and scientific concepts, especially withrespect to how student thining meshes or clashes with canonical knowledge. Recent publications co-authored with A.D. Schliemann, cover topics such as "The transfer dilemma" (J.Learn.Sci., 2002), "The evolution of mathematical reasoning: everyday vs. idealized reasoning "(Devel. Rev., 2002), "Culture and Cognition" (in Matsumoto, 2002), and "Modeling Reasoning" (in Gravemeijer et.al., 2002). From his early work as professor of psychology and co-founder of the Learning Through Thinking Project in Brazil, through his recent work in introducing algebra to 8-11 year old students, Dr. Carraher has searched for research-grounded ways to improve mathematics and science education based upon how students reason. His books include "Street Mathematics and School Mathematics" (Nunes, Schliemann et al. 1993) and "Bringing Out the Algebraic Character of Arithmetic," (Schliemann, Carraher, & Brizuela, 2006).Maria Blanton is an associate professor of mathematics education in the department of mathematics, University of Massachusetts Dartmouth. Dr. Blanton is a mathematics educator whose research interests include both teaching and learning algebra in the elementary grades and the application of sociocultural theory in teaching and learning proof in undergraduate classrooms. Her particular focus in early algebra education has been on children's functional thinking and characteristics of classroom teaching practice that build elementary students' algebraic thinking. As PI on the project "Understanding Linkages Between Social And Cognitive Aspects Of Undergraduate Students' Transition to Mathematical Proof," she also studies how undergraduate students internalize public discourse and symbolizationsabout proof and argumentation and how teacher discourse supports this. Dr. Blanton has published numerous articles and invited chapters in mathematics education and has presented her research at over 50 national and international conferences.