It would appear that one of Montessori's grandest accomplishments is not only to remove tests and grades, but to ASSURE that no standardized test can ever be used to MEASURE their progress, or lack thereof.
Montessori vaguely claims that studies have been done which "prove" that children in their schools WOULD score higher than public schools IF they were actually given a grade.
Some of the best Education Mafia doubletalk I've ever heard.
Montessori students DO "feel" like they know math, which reminds us of the following obserevation from William Bennett:
Percent who feel "I am good at math" on IAEP Math:
US 68%, 494 Spain 60%, 495 Ireland 49%, 509 UK 47%, 511 Korea 23%, 542
The same phenomenon is now occurring with PISA, though on a grander scale