Cathleen Galas wrote:
Teachers can usually easily ascertain whether a child's answer on that kind of test is a careless mistake or a complete lack of
understanding.
Maybe things have changed by I remember Kurt van Lehn (whose CMU AI thesis was on arithmetic mistakes) telling me that he once gave a talk about analysing subtraction mistakes to a large group of educators and he was surprised by the responses. Typical was "wow, it never occured to me you could figure out why a child made a mistake in arithmetic". And to be fair to teachers, the BUGGY program he and others built to analyze subtraction mistakes was very clever.
The best teaching practice would have the children analyze the
mistakes
they made in the test and then classify them as "careless mistake--I need to slow down and check", or "IDKY (I don't know (understand) YET)". Just the analysis of the mistake and figuring out whether one needs additional work with that concept is valuable learning.
Interesting point. We are used to the idea that mistakes in programming are bugs that need to be debugged by the child. But I'm not sure how often that viewpoint is generalized to math and other topics.
Best,
-ken