Grant Wiggins, via a kind reader’s email:
There is little question in my mind that national standards will be a blessing. The crazy quilt of district and state standards will become more rational, student mobility will stop causing needless learning hardships, and the full talents of a nation of innovators will be released to develop a vast array of products and services at a scale that permits even small vendors to compete to widen the field to all educators’ benefit.
That said, we are faced with a terrible situation in mathematics. In my view, unlike the English/language arts standards, the mathematics components of the Common Core State Standards Initiative are a bitter disappointment. In terms of their limited vision of math education, the pedestrian framework chosen to organize the standards, and the incoherent nature of the standards for mathematical practice in particular, I don’t see how these take us forward in any way. They unwittingly reinforce the very errors in math curriculum, instruction, and assessment that produced the current crisis.
Unfortunately, Grant Wiggins seems to have no idea
what is the mathematics part of the Common Core
State Standards. Wiggins cited a New York Times
piece by Garfunkle and Mumford. Here is a link
to a response by David Bressoud:
http://launchings.blogspot.com/2011/10/quantitative-literacy-versus.html
Wiggins also mentioned a treatment of “Big Ideas” by
Randall Charles. Unfortunately, these are
incoherent. Wiggins also mentioned a book by
George Polya. Polya’s book is a very nice book,
but one has to know more mathematics than Wiggins
knows to really understand it. Polya has six other
books on problem solving, at various levels of
sophistication. “How to Solve It” is the easiest,
and one can learn from it. However, if one is
going to write about what is in it, one better
know at least the next two volumes fairly well,
or one is likely to distort the meaning. Polya’s
own comment on his own work and work of his
coworker and good friend Gabor Szego is that
the two volumes of problems they wrote in the
middle 1920s is the best work of each. It is
asking too much for Wiggins to have read these
books, but he could learn that they contain
sequences of problems which build on a few
earlier ones, so students develop needed skills
along with ideas to put them to work. Polya’s
comment on this work with Szego is in the
introductory material in volume 1 of Szego’s
“Collected Works”.
The Common Core has a much more coherent treatment
of mathematics than appears in current textbooks,
so we will need better textbooks. We will also
need serious professional development for many
teachers. Finally, we will need better assessments.
Without all of these, there will be problems
with the Common Core Math Standards. However,
these are not what Wiggins wrote about.
I am not sure that the author, Wiggins, of the article knows what he is talking about. Having looked at previously proposed Wisconsin math standards (really poor) and the Achieve standards, the Common Core math standards are very similar to the Achieve standards, which are very decent. I am afraid as long as people who are not trained as mathematicians decide about the math standards we will have poor math education. This will put us at an economic disadvantage vis a vis the rest of the world.
An addendum to Richard Askey’s comments, which required some minimal goggling/amazoning on my part to clarify his comment.
Dr Askey refers to a two volume set from Polya after “How to Solve It”. I believe he is referring to “Mathematics and Plausible Reasoning, Vol 1: Induction and Analogy in Mathematics” and “Mathematics and Plausible Reasoning, Vol II: Patterns of Plausible Inference”.
Dr Askey also refers to another two volume set written with Gabor Szego. I believe he is referring to “Problems and Theorems in Analysis I: Series, Integral Calculus, Theory of Functions”, and “Problems and Theorems in Analysis II: Theory of Functions, Zeros, Polynomials”.
PS: Prof Askey is the editor, along with Gabor Szego of “Gabor Szego: Collected Papers ….”