My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by Keisler https://www.math.wisc.edu/~keisler/calc.html. Two of my colleagues in Belgium are similarly teaching TIC at two universities there. I am also aware of such teaching going on in France in the Strasbourg area, based on Edward Nelson's approach, though I don't have any details on that.
Which schools, colleges, or universities teach true infinitesimal calculus?
A colleague in Italy has recently told me about a conference on using infinitesimals in teaching in Italian highschools. This NSA (nonstandard analysis) conference was apparently well attended (over 100 teachers showed up).
In Geneva, there are two highschools that have been teaching calculus using ultrasmall numbers for the past 10 years.
Anybody with more information about this (who to contact, what the current status of the proposal is, etc.) is hereby requested to provide such information here.
Note 1. On Gerald's suggestion, also of interest would be any educational studies comparing the two approaches (the one using infinitesimals and the one using epsilon, delta). That is, in addition to the study Sullivan, Kathleen; Mathematical Education: The Teaching of Elementary Calculus Using the Nonstandard Analysis Approach. Amer. Math. Monthly 83 (1976), no. 5, 370–375.