Without having surveyed much of the literature, my [ersonal impression is that it's more of a rural-urban thing these days.
I spent two years in a flat on Balestier Rd. Singapore's education could be a model in almost any area...
I'm aware of my own ethnocentricity. That said, I was speaking mostly from personal experience, having lived in the Caroline Islands, The Mariana Islands, and a sprinkling of SE Asian's locations.
I don't think abstract thinking and concrete thinking are by any means mutually exclusive. But I do think some cultures value abstration more than others. You seem to have just agreed with me on that by suggesting that the idea was Western-centric. But then, I read too much into your words...
I don't really feel the need to produce an cluster of ethnographies to sustain the idea that some cultures value abstraction more than others. But I'll have to keep my eyes open now for support for that idea.
Social skills (I'll have to search the literature on that sometime) are a smaller part of the picture than academic skills. I think there's considerable support for the idea that participating in cooperative learning activities results in a stronger set of academic skills for the students. I'll quote Johnson, Johnson, and Stanne (2000):
Cooperative learning has been around a long time (Johnson, 1970; Johnson & Johnson, 1989, 1999). It will probably never go away due to its rich history of theory, research, and actual use in the classroom. Markedly different theoretical perspectives (social interdependence, cognitive-developmental, and behavioral learning) provide a clear rationale as to why cooperative efforts are essential for maximizing learning and ensuring healthy cognitive and social development as well as many other important instructional outcomes. Hundreds of research studies demonstrate that cooperative efforts result in higher individual achievement than do competitive or individualistic efforts. Educators use cooperative learning throughout North America, Europe, and many other parts of the world. This combination of theory, research, and practice makes cooperative learning one of the most distinguished of all instructional practices.
I thought the question had something to do with culture and education...
I've said that this discussion was entertaining. I don't really have a problem with the idea that 2+2=4 (or that if I give Sue 2 counting bear and I give Bob 2 counting bears and I ask them to tell me in their own little kindergarten words how many counting bears they have together, they should say "four"). I'm not sure how that impacts my understanding of Jon's article.
I've reread Sylvia's comment at the top of this subthread from August 2. I take her to be saying that the emphasis we place on memorizing math facts (2+2=4, 6x5=30, etc.) is cultural. And that it is problematic because simple memorization, which for so long has been the measure of academic success, is no longer a sufficient skill in isolation. The value we place on it has changed.
Students need to be required to manipulate those math facts within some context. If I've been in my classroom four years and every year they bring a new computer, someone might expect me to have four computers now; but they have to understand the idea that in the third year they began taking the oldest one with them when they left, so that no matter how many years in a row they add a computer, I'll never have more than three. That's context. Sylvia's example is perfect. The track may be a mile around, but walking around it twice and then walking around it two more times just gets you back to where you parked; it doesn't leave you four miles away (even if an abstract 2 plus an abstract 2 is four is "all possible universes").
And Sylvia is absolutely right about testing compliance. If a kid puts five on the test and has a brilliant explanation (one that shows that she can manipulate the numbers just fine) about how she was imagining cans of juice and her friend always comes over unexpectedly and she has to get an exit glass and divide the four cans of juice up five ways - well, the State education people couldn't give a rip and the answer is still wrong and I have to explain to the kid that she should have put "four" because that's what the people in Charleston expect her to put. Tests have their limitations. We only give the tests for cultural reasons - to measure something we value.
Sylvia is guilty of hyperbole. But memorization of isolated abstract facts is being downgraded in state content standards all over America. Not many people care about other possible universes. And none of my students at the elementary school where I teach at the moment are mathematicians. I don't even have one whose parents are mathematicians. But a couple of my school's kids have been identified as "gifted."
As for the argument between Katherine and Ira regarding the predictability of the behavior of mathematicians (how they'd answer a particular question) - I suspect the answer you'd get would depend on how the question was phrased. And the line of argument seems to have become an exercise in refining the question. And now, in order to be sure of my own answer I have to go study other universes. But since I'm not a mathematician, I answer probably doesn't matter...
Fair enough.
So you'd take an answer from a mathametician-philosopher?
Hi Shelly,
The disabilities law, IDEA, covers a number of categories of disabilities. I have to disagree with you and say that for the most part it is both useful and concrete. If a child is autistic, has a psychosis, is legally blind, has some inconvenient medical condition (for example, epilepsy), has Down Syndrome, or has an IQ of 65 and difficulty coping with their environment - in all of those cases the concept of disability seems both useful and appropriate.
You are correct regarding learning disabilities. IDEA's 2003 reauthorization left the concept of "learning disability" in a state of foggy flux. Without going through the issues in any detail, the old discrepancy model based on comparing IQ and achievement has been put out of its considerable misery and replaced with, well, nothing in particular. We're encouraged (but not required) to use a model called RtI (Response to Intervention) and the education community is feeling its way through just how that should work at the moment. IDEA 2003 basically leaves individual states to define "specific learning disability" as they see fit - and in some cases the states have passed that on to individual school districts. The result is the possibility of literally hundreds slightly different definitions of learning disability - and a situation where a child has a disability in New York (and in some parts of New Jersey) but not in Pennsylvania.
To be fair, there is more smoke (and heat) than light surrounding the scientific research on learning disabilities. Dyslexia, for example, is an ill-defined concept that I don't think is even mentioned in the DSM-IV. In the last few years there've been controversial assertions that some of the genetics underlying dyslexia has been identified. One group promised that in less than a year we'd have a cheek swab that could be used to test newborns for dyslexia; they made that promise in early 2006 and their year is over, but I haven't heard of the swab yet.
The growing field of cognitive neuropsychology is shedding a little light on reading disorders by using MRI results. And it's hard to deny that there's some real neurological disorder behind many reading problems. At the moment, that knowledge doesn't help a school psychologist on the ground here in my part of Central Appalachia to sort out which kids qualify as having that disability and which kids don't.
Do gifted kids face discrimination? I've said already on this page that giftedness is not a disability. The idea of discrimination implies a status, a legal standing that I have no qualms about extending to blind children, or to kids with autism, or to students with measurable and significant cognitive deficits, but that I'm not at all sure should be extended to students who qualify as gifted.
We've used the word "best" a lot. Let's just give kids "the best we have." That's a noble sentiment. And when I enter a classroom my goal is to give the children in it the "best" I have that day - in that room, and in me. That's different than giving a particular child the best possible education. In a world where we all share limited resources and where education is funded by society in general, the courts have repeatedly ruled that no one is entitled to the best possible education - just to an appropriate one, at public expense.
As educators struggle to bring pedagogy and educational environments into the 21st century, students don't have to be gifted in order to be bored. The changes that are needed for gifted students are needed for MOST students. Central themes in that include: technology integration, more rigorous content standards, increased professional development for teachers, and a focus on higher level thinking skills in the curriculum. It's a problem that's faced by most kids, not just gifted ones. And (to answer your closing question) we need to restructure education in general, not just gifted education.
http://educationalissues.suite101.com/article.cfm/digital_natives_and_digital_immigrants
Ira says that 2+2 doesn't always have to equal four: it's a qualified truth.
Katherine wants Ira to find a math professor who will stipulate to the idea that 2+2 does not equal 4 (which doesn't strike me as quite what Ira said). And Katherine says that if Ira finds such a math professor, it proves only that the math professor is a closet philosopher. If I were Ira, I wouldn't spend much time looking...
Without investing the time to read Ira's citations (I have a life), I thought he was pretty convincing. And I thought Katherine was circular: all mathematicians agree with her; if they don't, they're not pure mathematicians.
I think we've all agreed that education (its value in a society, its pedagogy, etc.) is culturally defined. The math discussion has been entertaining; I just can't decide if it has a point in the context of Jon's article.
I will say this: the ability of pure mathematicians to articulate great truths abstractly (which I take to mean hypothetically, in the absence of any real context) is something that I see as a cultural exercise in itself. Most great truths can be articulated concretely or abstractly. You can talk about materialism and the nature of reality or you can talk about Plato's Cave. You can talk about Grace or about the Prodigal Son. Some cultures prefer the concrete presentation. Most Western European cultures prefer abstraction. And that preference is in itself cultural. Even for mathematicians, I think...
Jon said: In other words, unlike special education, there is no legal mandate to offer services to children identified as gifted and/or talented.
There may not be a Federal mandate (although I think giftedness is covered by "child find"), but many states have a mandate within state law. Giftedness amy not be treated as a disability, but it is an exceptionality and school districts are required to provide gifted services in WV, I think...
The idea of providing a curriculum that challenges and/or meets the needs of all students sounds to me like differentiated instruction (DI), which has become a major focus of professional development and curriculum design in the last few years. Carol Tomlinson is one of the more popular authors on the subject. I've been sent to three or four workshops on it in the past three or four years - and the general ed teachers I work with have been required to attend with me.
DI comes in flavors. There's DI intended to cater to different learning styles to ensure that kinesthetic learners don't have to rely on auditory or visual processes alone. There's DI intended to address the level at which students get challenged. The math lesson may be on probability; the curriculum we use will provide the teacher with a variety of tasks (of varying difficulty) that can be used with their students.
Both the math and the reading curriculum my district uses in the elementary grades build DI into each lesson.
Rate is a different issue. The adoption of a spiral concept in curriculum design makes *rate* seem like a problematic concept. Instruction is cyclical: we may spend a couple of weeks working on learning and using central tendencies in statistics with the fourth or fifth graders, then the curriculum moves to addition of improper fractions for a week, then it spends some time reinforcing student knowledge of geometric shapes and their properties, and a few weeks later it cycles back around to central tendencies.
Chances are good that the second and third graders are working on exactly the same concepts (though with simpler problems) if their teachers are on track with the pacing guides.
If a student came to me at any grade level (I've taught K-12) and said that they understood chapter 11 and had finished the work in it, and they asked me if they could go on to chapter 12 WITHOUT the rest of the class, I'd say no. The reasons are simple. I need that student to participate in cooperative learning and group activities for the sake of the other students (whom they can help in ways that I can't) and for their own sake (because being a peer tutor has been show to produce a more secure set of skills in a student).
It's not that there is material to cover and the student could finish early, it's that there are standards (content standards) to meet. I'm happy if the kid can excede the standards for central tendencies; I'm not happy for the kid to move on to geometry while the rest of the class is still in statistics. In addition to math skills, I have to think about the student's social skills - their ability to work with with others.
DI can and should lead to engaging each student at their level. But it doesn't (and shouldn't) lead to anyone finishing the year's math curriculum sometime in March...