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Katharine Beals
Philadelphia, PA
Katharine Beals is the author of the forthcoming Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School (Shambhala/Trumpeter, September, 2009)
Recent Activity
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Katharine commented on the article |It's hard to keep track of these moving goal posts! But, for an excellent conceptual math curriculum, consider Singapore Math.
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Katharine commented on the article |
It's specifically the(potentially patronizing) Western/nonWestern dichotomy I'm wondering about; not the much more likely possibility that some cultures are more into abstraction than others. (For example, it seems likely that to me that the subculture of U.S. academics is more into abstraction than other U.S. subcultures).
Even if we have lived in other cultures, it's hard to know how abstract the thinking is unless we've mastered the native language.
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Katharine commented on the article |
Yes. The question, again, is whether the statement "2+2=4", when it is a mathematically well-defined rather than a mathematically nonsensical statement (which was implicit in my initial question but which I now feel the need to state explicitely!), is true in all possible universes.
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Katharine commented on the article |
Abstraction (in particular, from measurement systems, everyday use of language, everyday use of math...) does not imply "objectivity", as you put it, but it does imply abstraction from everyday culture.
I've always thought that the notion that "Westerners" are more into abstraction than non-Westerners is a rather Western-centric idea, particularly since most of the people who push it seem to be Westerners. Do you know any ethnographies conducted by non-Westerners that reach such conclusions?
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Katharine commented on the article |
To clarify, what Ira said was:
"If you asked mathematicians what 2+2 is, you would get a range of answers, questions, and demands for more clarification. It's hardly cut and dry. I can absolutely guarantee that NO mathematician would answer "4" without qualifying the answer with additional information."
I then said:
"Find me a math professor (a mathemtician, not a philosopher!) who says, specifically, that 2+2 doesn't equal 4 in all possible universes, and I'll eat my hat."
Note that Ira is making a claim about what "NO mathematician would do;" I'm asking him to find ANY mathematician who believes that 2+2 doesn't equal 4 in ANY possible universe.
You're also reading too much into what I said about philosopohers. There are some really good mathematician/philosophers out there.
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Katharine commented on the article |
I know a lot of talented math buffs (the subjets of my forthcoming book) who are extremely frustrated by the practices you describe (which are unique to the U.S., and certain schools in Canada, Britain and Australia). They are severely underchallenged, especially with today's Reform Math (where the actual math is much, much easier than it used to be), hate working in groups, and resent being asked to teach math to other students. We are at risk of marginalizing (and under-preparing with respect to students from other countries) the next generation of potential mathematicians.
There are no randomized studies showing that social skills improve when students are forced to work in groups; if there were, then presumably my generation (which didn't do much work group at all), and students in non-Anglophone countries, have weaker social skills than younger Americans do.
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Katharine commented on the article |
I've taught math for a number of years, to a number of different students from different cultural backgrounsd, and have *never* encountered a student who needed to know my definition of number (i.e., that I wasn't referring to numbers on uniforms) in order to answer 2 + 2 = 4.
Have you?
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Katharine commented on the article |
apples and oranges! "nominal scales" use a different definition of number from that used in the statement "2 + 2 = 4"
From the paragraph that follows the one you cite from:
"Each number merely represents a category or individual. For example, numbers on baseball or football uniforms are only nominal. Having the number "1" on your uniform does not necessarily mean you are "numero uno" (the best) in your sport. Social security numbers are also nominal. All they do is name or classify the individual."
In making statements like 2+2=4, people are not referring to numbers on uniforms. If they were, then the statement would be no more meaningful than "too plus too equals for"!
Speaking of postmodermism and math, have you read Sokol's "Fasionable Nonsense"?
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Katharine commented on the article |
But he doesn't actually deny that 2+2=4. Find me a math professor (a mathemtician, not a philosopher!) who says, specifically, that 2+2 doesn't equal 4 in all possible universes, and I'll eat my hat.
I'm a big fan of foundational problems (computation theory; model theory; incompleteness the unprovability of certain mathematical statements--have you taken courses in any of these?) And I'm all for openness, as long as its meaningful!
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Katharine commented on the article |
What you're calling "assumptions" mathematicians would call "axioms". Euclidean geometry uses one set of axioms; Lovbachevskian geometry (where there are no parallel lines) uses another. Mathematicians use both systems; there's no contradiction or baloney. I learned both systems in 9th grade geometry, and was intrigued by their conceptual coexistence. It's actually rather beautiful. Ask a mathematician!
