
This book evolved out of research that began more than 25 years ago, based on a
National Science Foundationsupported project investigating the question: what
is needed, beyond having a mathematical idea that enables students to use it in
everyday problemsolving situations! (Lesh, Landau, & Hamilton, 1983). Large
portions of this research involved creating mathematically rich situations that
were similar to the old television program Candid Camera. That is, we
videotaped students in "real life" problemsolving situations that were thought
to be typical of those in which elementarybutpowerful mathematical constructs
are useful in the everyday lives of students, or their friends or families. As we
observed and analyzed students' mathematical thinking in such real life
problemsolving situations, our research teams gradually developed far more
sophisticated notions about (a) the nature of situations where mathematics is
useful beyond school, and (b) the nature of the understandings and abilities that
contribute to success in the preceding situations. We came to recognize the
importance of a broader range of elementarybutdeep mathematical
understandings and abilities, compared to those emphasized in standardized
tests, textbooks, and teaching.
This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education. On the level of emphasizing practical problems, it clarifies the nature of some of the most important elementarybutpowerful mathematical or scientific understandings and abilities that Americans are likely to need as foundations for success in the present and future technologybased information age.
Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching features an innovative Web site housing online appendices for each chapter, designed to supplement the print chapters with digital resources that include example problems, relevant research tools and video clips, as well as transcripts and other samples of students' work:
http://tcct.soe.purdue.edu/booksULandULjournals/modelsULandUL modeling/
This is an essential volume for graduatelevel courses in mathematics and science education, cognition and learning, and critical and creative thinking, as well as a valuable resource for researchers and practitioners in these areas. 
