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Ira Socol
A grad student/educational researcher in the College of Education at Michigan State University focusing on Universal Design Technologies on one hand and the structure and history of education on the other. Former police officer, network administrator, architecture student, graphic designer. Author of microfictions and books. Historian at heart.
Blackberry addict. Student of Critical Theories. Fan of James Joyce, Seamus Heaney, Arsenal, the New York Mets, Derry City, French Cinema. Believer in the possibility of change.
Recent Activity
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Ira commented on the article |There was a time when a district hired an administrator to solve problems. Now that administrator outsources all of her responsibilities, and people cheer?
All through the DC school system there are great teachers who, if empowered by Rhee rather than denigrated by "the witch with the broom," could have already begun to turn these schools around.
But unfortunately Rhee, with her TFA background, despises teachers, and thinks that education is meaningless (if education is meaningless in the preparation of teachers, what value might it have in any other field?). With that kind of built-in attitude there will continue to be zero cooperation within the DC schools, and students will continue to suffer.
So, yes, this is a political argument, not an educational one. Look for hyped (and possibly faked) test scores soon (a la Joel Klein) along with the hiding of any negative information (a la Rod Paige). Plus, be prepared for the next barrage of press-releases and NYTimes and WaPo stories on "The DC Miracle" coming from the anti-union flaks of the Republican Party.
Then, look five years from now. Rhee will be a "senior fellow" at the Heritage Foundation, spouting off on Diane Rheam, and the DC schools will still suck.
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Ira commented on the article |But no, I don't read intentionally fraudulent academic writing. I have other things to do with my time.
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Ira commented on the article |
Wait! A student would have to know your definition of "number" in order to answer that question? I thought this was "absolute" and "culture free"?
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Ira commented on the article |
Kline and Hersh both say this. Read, it'll give you something to chew on.
and
"Believe it or not, sometimes 2 + 2 does not equal 4. It depends on what type of measurement scale you are using. There are four types of measurement scales - nominal, ordinal, interval, and ratio. Only in the last two categories does 2 + 2 = 4."
Thus, even on number lines, 2+2=4 is only sometimes true. You need a formal set of, yes, culturally applied, rules to make 2+2=4.
I understand the desire to have something absolute and "always true" in the world. And I am sure it is stunningly frustrating for a pure rationalist to argue with a post-modernist like me, but I challenge you to dig deeper into this.
As Bain's book demonstrates, the shattering of the knowledge system created by K-12 math and science teachers is the first task of professors at top universities.
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Ira commented on the article |
Katharine,
PJ Davis in Mathematics (1988) provides a primer for you http://www.people.ex.ac.uk/PErnest/pome22/Davis%20%20Applied%20Mathematics%20as%20Social%20.doc
"Take any statement of mathematics such as ‘two plus two equals four', or any more advanced statement. The common view is that such a statement is perfect in its precision and in its truth, is absolute in its objectivity, is universally interpretable, is eternally valid and expresses something that must be true in this world and in all possible worlds. What is mathematical is certain. This view, as it relates, for example, to the history of art and the utilization of mathematical perspective has been expressed by Sir Kenneth Clark ("Landscape into Art"): "The Florentines demanded more than an empirical or intuitive rendering of space. They demanded that art should be concerned with certezza, not with opinioni. Certezza can be established by mathematics".
"The view that mathematics represents a timeless ideal of absolute truth and objectivity and is even of nearly divine origin is often called Platonist. It conflicts with the obvious fact that we humans have invented or discovered mathematics, that we have installed mathematics in a variety of places both in the arrangements of our daily lives and in our attempts to understand the physical world. In most cases, we can point to the individuals who did the inventing or made the discovery or the installation, citing names and dates. Platonism conflicts with the fact that mathematical applications are often conventional in the sense that mathematizations other than the ones installed are quite feasible (e.g., the decimal system). The applications are of ten gratuitous, in the sense that humans can and have lived out their lives without them (e.g., insurance or gambling schemes). They are provisional in the sense that alternative schemes are often installed which are claimed to do a better job. (Examples range all the way from tax legislation to Newtonian mechanics.) Opposed to the Platonic view is the view that a mathematical experience combines the external world with our interpretation of it, via the particular structure of our brains and senses, and through our interaction with one another as communicating, reasoning beings organized into social groups.
"The perception of mathematics as quasi-divine prevents us from seeing that we are surrounded by mathematics because we have extracted it out of unintellectualized space, quantity, pattern, arrangement, sequential order, change, and that as a consequence, mathematics has become a major modality by which we express our ideas about these matters. The conflicting views, as to whether mathematics exists independently of humans or whether it is a human phenomenon, and the emphasis that tradition has placed on the former view, leads us to shy away from studying the processes of mathematization, to shy away from asking embarrassing questions about this process: how do we install the mathematizations, why do we install them, what are they doing for us or to us, do we need them, do we want them, on what basis do we justify them. But the discussion of such questions is becoming increasingly important as the mathematical vision transforms our world, often in unforeseen ways, as it both sustains and binds us in its steady and unconscious operation. Mathematics creates a reality that characterize our age."
Other "open" readings on the same issues
http://www.economics.pomona.edu/widner/courses/econ58/ps/whatmath.pdf
http://markelikalderon.com/wp-content/uploads/2006/12/EpistemicRelativism.pdf
http://www.members.tripod.com/~jan_dejnozka/peano_russell_quine_number.pdf
And I'd urge you to go the the library, and if you are resisting Kline, read Reuben Hersh's "What is Mathematics, Really?" (1997)
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Ira commented on the article |
Katharine, you keep asking. Each time you've asked I've not just reached for my bookshelf but put "culture and mathematics" into Google Scholar, pulling up tens of thousands of articles on this issue - most by, yes mathematicians.
It is nothing new. I have a friend who wrote his 1962 Masters Thesis in Math on this subject, and I know it is spoken of constantly in our math education program (which is tied to a 'fairly reputable' mathematics department).
I'd again encourage you to read Morris Kline's work - going back to the early 50s - or to look at the "NYU School" exploring the "fictions of mathematics." I think you will enjoy the conversations.
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Ira commented on the article |
Greg,
I appreciate all of your questions - I guess I'm saying that we understand prime numbers because we give special status to points on the number line which correspond to numerals. And I say that as someone who, as a kid, was confused by this. "Of course I can divide 13 by something other than 1: 10x1.3=13 Of course, I was classed as "retarded." As Silvia suggests, our simplistic K-12 view of math punishes creative math thinkers (as we do in every subject) or those who bring any different viewpoint to the topic.
It goes much further. Why is the Fibonacci sequence so essential in the UK and Ireland and barely taught in the US? Does understanding the golden mean" have an absolutely different value depending on hemisphere (as Pullen might suggest - based on his comments here), or is that choice cultural? Isn't the 1.06 multiplication table the most important to memorize in Michigan (sales tax rate)? or the 1.0975 table most important in New York City? And, as you say, considering the speed of light - is there not indeed a conceptual change when you switch between feet, meters, and nautical miles?
All of this creates confusion for those "not from "normed" backgrounds." I wrote a blog post a year ago about the confusion created simply because the US writes sports scores "backwards" from the rest of the world, or writes the dates reversed from the rest of the world. Strange little cultural decisions which make life harder for certain groups. Our world is full of them. Our curricula are full of them. Our tests are full of them.
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Ira commented on the article |
Actually Katharine, the mathematicians I know all understand the cultural construct and the sense of "rules." Once you get past 'high school math' this all becomes obvious. No mathematical system works without a shared understanding of its rules.
Whether you read Kline from 1953 or Lave from 1988 or anyone before or since, you'll get the picture.
Let's take a very simple notion - the "prime number." What makes it "prime"? Yes, you've got the answer, but that requires you to believe that, say, the number "1.3" is somehow fundamentally different than 1.0, 3.0, 13.0, or 130.0. Which is not "a fact" but a cultural choice.
This is why any math major knows that there are different geometries, etc, depending on the choice of accepted rules. We are not really stuck with Newtonian Physics, you know.
> And Mark, get your face out of your hands. It is ok to learn new things.
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Ira commented on the article |Jon,
I love when we have both facts and observations to work with, I think you've done a great job of laying out the situation.
Of course I could comment in many ways, but I'll say what I see from a "life prep" perspective in my work with Michigan's Voc/Rehab agency.
Students from minority groups and impoverished communities lack the tech skills they need to survive when they leave high school, and this is because, while few - if any - schools are doing enough, the poorer the school, the less they are doing. And thus, we widen the digital divide daily.
Here's what I see, Students do not know how to use their mobile phones, their email, their voice mail or to text message. Oh, they have all these things - the poor are far more likely to have phones than computers - but since schools neither allow those phones in nor teach their use, they can not use them appropriately.
So Voc/rehab must teach the basics: How to choose a "resume appropriate" email address. How to create an employer friendly voice mail greeting. How to text your boss or email a co-worker. How to properly check email spelling. How to use Jott or Dial2Do to text from a car. How to properly search, look up an address, judge search results. Not to mention how to support their own reading and writing with online supports. All the things any decent school should be teaching in fifth grade. And V/R agencies really don't have the time or resources to do this well, or do this for enough kids. It is hard to make up for ten years of educational malpractice in a couple of week training course.
So by not teaching these skills, the rich kids - those from the iPhone/BlackBerry households - get these skills from family, and those traditionally "out of power" fall further and further behind.
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Ira commented on the article |
Its not, but you insisted that there's nothing "cultural" about math, I was trying to show you that you were wrong.
All learning, all testing,is culturally constructed. To pretend otherwise is absurd.
