As a professor teaching undergraduate and graduate math at the university, I paid no attention to K-12 at all. Not only was it irrelevent to my professional ambitions, but there were, so I thought, experts whose views were much more informed than mine. Then my older son started attending PS41, our neighborhood elementary school, which was in the famous District 2 run by nationally known educator Anthony Alvorado. By the third grade things were serious. Instead systematic addition and subtraction, they were drawing pictures and solving "brain teasers" (simple word problems) by trial and error. There was no progression of ideas; the third and fourth grade books being practicall identical. I tried to share my misgivings with the Principal, but got was told (for the first, but not the last time) that research had shown that the "conceptual, problem solving" makes kids do better later on.
Around that time, I got an email asking me to endorse the Klein letter asking the US Secretary of Education (Richard Riley at the time) to put mathematics experts "in the loop" in making K-12 math curriculum recommendations. Though I did not know much about the national politics of math education, clearly something was wrong and this modest request was easy to agree with: I signed. A while later, community activist Elizabeth Carson noticed the signature of a local mathematician and contacted me to see whether I might help her push for better curricula District 2. At her suggestions, I started probing: what were the curricula District 2 was using? What was the research supporting them? Who was chosing the distruct 2 curricula and what was their process? The answers were disturbing . . .
The NCTM and related standards are called fuzzy because of their
studied bureaucratic vagueness. For example, the
Number and Operations standard for Kindergarden through
second grade says that by the end of second grade, kids should
be able to "understand and represent commonly used fractions,
such as 1/4, 1/3, and 1/2." Is this anything more than memorizing
an association of the symbol "1/4" with a picture of a quarter
of a pie? Should the kid understand that putting
three of these quarters together gives 3/4 of a pie?
The three items under "Compute fluently" are "develop
and use strategies for whole-number computations,
with a focus on addition and subtraction;" (What is a "strategy"?
What are the non-focus computations?), "develop fluency with basic
number combinations for addition and subtraction;" (memorize
simple sums and differences?), and "use a variety of methods and
tools to compute, including objects, mental computation, estimation,
paper and pencil, and calculators." What about adding, say 56 to
78, the normal way (write 56 above 78, add 6 to
8 to get 14, write the 4 underneath and carry the 10, add one
ten (the carry) to the 5 and 7 tens giving 13 tens, then write
the 13 in front of the 4 to get 134.)? The NCTM "standard"
hints that kids should learn something like this, but it
does not actually say so. Moreover, with all those "stragegies"
and "understandings" going on, how would the teacher have time?
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