Another point in the NYT article discusses the use of calculators beginning in the early grades.  I have seen its use taught as early as 2nd grade.  These students never learn how to do the basic arithmetic operations independently.  The rationale for doing this is that they can learn to do "real" problems, without worrying about the size of the numbers. As a result, when I ask 11th graders to calculate a mean for 5 numbers all below 10, where the answer is a whole number, they want to use a calculator!  Another consequence of the constructivist approach is that by not learning how to solve basic arithmetic problems, they fail to develop a good number sense, to appreciate when an answer is likely or unlikely,
 
Riki Koenigsberg
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