thanks to...

This web site would not have been possible were it not for the many teachers, students and colleagues that I have worked with over the years. While I am indebted to all of them, my debt to some of them is particularly great.

My colleagues in the Balanced Assessment in Mathematics Project at Berkeley, Michigan State, Nottingham and Harvard who helped me to think hard about the posing of good questions. Indeed, many of the challenges on this website are drawn from the work of that project.

I am also deeply indebted to the world-wide GeoGebra community of mathematics educators whose continuing productions of materials is a source of inspiration for many of the challenges on this site.

Michal Yerushalmy, my former student and now friend and collaborator is a thoughtful and inventive mathematics educator and researcher who taught me much about the possible roles of thoughtfully designed software in mathematics education.

Daniel Chazan, another of my former students and now friend who has over the years served as a critical sounding board for ideas about mathematics and mathematics education. He has helped me better understand the real world in which many students live and the constraints under which many teachers teach.

The late James J. (Jim) Kaput was a mathematics educator who had a great influence on me. Through him I learned of the excellent work of colleagues around the world who struggle to make progress in this difficult field. 

The late I.M. Gelfand was a world-class mathematician that I had the privilege of knowing and working with for several years. Many readers will recognize the influence he had on my thinking by looking at his masterful little book entitled “Functions and Graphs”.

Marion Walter, a now-retired mathematics educator who raised the issue of problem posing to consciousness in the mathematics education community in general, and in me in particular.

My mentor, the late Jerrold R. Zacharias was a physicist and educator that I worked with and learned from for over two decades at the Massachusetts Institute of Technology. I owe to him whatever ability I have to keep my eye on important issues, be they scientific or pedagogical. He was never intimidated by power and position but always responded to the power of ideas no matter the position of those who presented those ideas.

Finally, I am grateful for the support offered by my wife, Joan Thormann, whose forbearance for my foibles is beyond my ability to understand.

Judah L. Schwartz