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In a recent post on math-teach@mathforum.org in response to my comments about pedagogical content knowledge, Jonathan Groves wrote, in part: Perhaps it is tricky to define constructivism precisely and to know exactly what it is. I am not even sure if I know exactly what it is though I do have at least an idea of what it is. I have learned some about constructivism in some education classes I took at Austin Peay State University when I originally was trying to become a high school math teacher (which I later abandoned so that I can graduate in four years and teach college instead). But the constructivism I learned I remember vaguely, and I learned some more about it when I was completing my online faculty training for Kaplan University, where I will begin teaching math online on March 25. The faculty training consisted not only on information on how to use their online system for their online classes and about Kaplan University itself and some of their expectations for faculty but als...

In a recent post to the math-teach@mathforum.org list-serve, Bill Marsh wrote, in part: I continue to think that guided discovery can be a powerful teaching tool, of definitions, as well as of proofs, but I should emphasize that in GUIDED discovery there will be a teacher in the room who knows the theorems that are coming and some of the pitfalls on the way to getting them. If you don't know how to use them, power tools can dangerous. If you don't like them or have to use them, you won't use them very much. Unless you use them a lot, you are unlikely to learn how to use them well. If you don't know how to use them well, you may underestimate what can be done with them. Suppose students arrive in a seventh grade math class to see 1+2+3 = 6 on the board. After a moment or two, the teacher might mention that numbers like six are called perfect and ask if anyone can say what's going on. I'd expect that pretty quickly someone would suggest adding up all the div...

In response to one of Wayne Bishop's usual assaults on someone who deigns to write or speak positively about progressive mathematics education, Bill Marsh wrote , in part: Wayne follows Wu by starting with one way of doing something, then dogmatically claiming and perhaps believing that it is the only way. This happens on both sides of the math wars, usually in the weaker form of merely claiming there is only one best way. I wrote back to Bill, a mathematician with whom I generally agree about educational issues: I wonder what you mean when you say "This happens on both sides of the math wars." Assuming that the antecedent of "this" is "claiming and perhaps believing that it is the only way," I would suggest that I've yet to see someone on MY side of the Math Wars debates take the view that there is only one way to do or think about anything, particularly when it comes to teaching and learning mathematics. The anti-progressive side has been pullin...

Sometimes there's nothing to add other than my wish that the speaker succeed in not only being heard, but heeded, and my gratitude for having been around when an intelligent, articulate, and above-all humane person once again holds the most powerful elected position on the planet.

A recent commentary " It's Not All About Class Size " appeared from Ken Jensen on the discussion list of the National Council of Supervisors of Mathematics (NCSM): I agree with the assertion that, "it is possible that smaller classes will actually widen the domestic achievement gap between the haves and have-nots." and the explanation as to why this may occur is well thought out. However, the article is void of any suggestions as to how we might increase achievement for all- both raise test scores and close the gap. I would like to propose that a teacher with a well developed sense of best instructional practices does much more to increase achievement for all students than lowering class sizes. In fact, I would want this teacher's class to be full to the brim so that as many students can take advantage of this learning environment as possible, and I would expect this teacher to raise the achievement level of all his or her students in spite of the large s...

The following was recently posted on math-teach by the always-remarkable Professor Wayne Bishop, who never saw a progressive educational idea he didn't despise: http://www.coreknowledge.org/blog/2009/02/03/21st-century-snake-oil/ 21st Century Snake Oil Published by Robert Pondiscio on February 3, 2009 in Core Knowledge, Curriculum and Education News. Tags: 21st century skills, Alfie Kohn, content knowledge, critical thinking, Curriculum, Jay Greene, Tony Wagner. Yesterday, Alfie Kohn; today Tony Wagner. Jay Greene goes after the education guru on his blog and in an op-ed in the Northwest Arkansas Morning News. The Fayetteville Public School system has purchased 2,000 copies of Wagner's The Global Achievement Gap and is holding a series of public meetings, according to Greene, on how Wagner's vision for 21st century skills "might guide our schools." Be afraid, says Jay. Be very afraid. It's hard to get people to think critically about people who push a focus...