the author

I am Judah L. Schwartz, a failed retiree.

Along with colleagues and students, I have been writing prize-winning educational software for more than thirty years. For several decades I taught physics at the Massachusetts Institute of Technology and taught and did research on mathematics and science education there and at the Harvard Graduate School of Education (HGSE) (1).

After retiring from MIT and Harvard, I taught pre-service and in-service teachers of mathematics for nine years at Tufts University.

For the past  three years (2014-17) I taught a course entitled "The Art & Craft of Posing Problems & Making Conjectures" in the Mathematics for Teaching masters' program at the extension school of Harvard University.

The course on problem posing has now evolved into a two course sequence. The first of the two courses, "Posing Problems with Interactive Images I: Objects and actions" is being taught in the Fall 2018 semester at Harvard. The second course "Posing Problems with Interactive Images II: Reflective Teaching: will be taught in the Spring 2019 semester at Harvard.

Please send any comments or questions to me at

(1) A description of my teaching & research activities at HGSE taken from their website

Judah L. Schwartz is a retired Professor of Education who taught courses on the teaching and learning of mathematics, assessing mathematical attainment, and ethical and philosophical issues arising from the use of technology in education. His research interests include the use of microcomputer software environments to improve the teaching and learning of math and science, and the application of cognitive science to the study of math and science education. Schwartz has written extensively about educational technology and is the author of educational software for science, mathematics, and language. He did his undergraduate and graduate work in theoretical physics and mathematics. He also has a long-standing interest in alternative modes of assessment.

Schwartz is the author or coauthor of such software programs as The Semantic Calculator; M-SS-NG L-NKS; What Do You Do with a Broken Calculator?; The Geometric Supposer Series; Sir Isaac Newton's Games; The Calculus Toolkit; The Visualizing Algebra Series; The Newtonian Sandbox; The Function Supposer Series; The Function Family Register; Unsolving...; Get Off the Plane!; Focus on Locus; The View from the Top; Calculus Unlimited; and the <inCOMMON> software series.

His print publications include: The Prices of Secrecy: The Social, Intellectual, and Psychological Costs of Current Assessment Practice”, The Geometric Supposer: What Is It a Case Of?, ed., Software Goes to School: Teaching for Understanding with New Technologies, ed., Assessing Mathematical Understanding and Skills Effectively (AMUSE)”

He is a retired Professor of Engineering Science & Education at the Massachusetts Institute of Technology.