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For all the talking points that Reform Math proponents deploy in response to the general criticisms, I haven't yet seen any talking points that respond to concerns about children on the autistic spectrum. Has anyone else?
Since it's well-documented--and generally agreed--that AS children require structure, direct instruction, and discrete tasks, and that many of them have the potential to excel in math, and since the education establishment's purported missions include (1) mainstreaming and (2) catering to different learning needs, I believe this is a fruitful message to keep plugging.
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11 comments:
"Since it's well-documented that AS children require structure, direct instruction, and discrete tasks, and that many of them have the potential to excel in math . . . "
This is true for all kids . . . the education establishment just ignores it.
(and, by the way, I love your blog!)
joelhylen, thanks for your comment; I've edited my post with what you point out in mind.
Katherine,
There is extensive research put out by the feds including the Dept of Ed's Access Center and nichcy.org (the National Dissemination Center for Children with Disabilities) on the need for systematic, explicit instruction in math for all students with learning disabilities and "at risk" kids.
Here's another cite on the same point:
http://www.ldonline.org/spearswerling/Components_of_Effective_Mathematics_Instruction
Many years ago, I was working on a PhD in Physical Oceanography and as part of that program I was one contributor on a three person research team. We were to develop software that would predict the drift of spoils deposited from dredging operations. One of my partners was from Mississippi and talked deep southern accent, while the other was from South Korea and knew absolutely no English.
The Mississipean was a brilliant FORTRAN programmer with a smattering of mathematics, the South Korean was a brilliant mathematician with a bit of programming ability, and I was somewhere in between with a smattering of 6 programming languages and a mathematics background in Engineering (not even close to the South Korean's math skills).
Surprisingly, we worked together quite successfully for over a year on the project and we never learned each others tongues. I actually had a little more success with Korean than I did with Mississippiean. Our Rosetta stone was math and programming. We concocted a mishmash of if/then statements smurgled in with equations so that we could communicate. I relate all this because it sparked a remarkable epiphany for me.
It is that Math is a universal language! And, it is indeed a language. It has its own grammar and sentence structure. It has it's own paragraphs and vocabulary. It differs from most spoken languages only in that it possesses far more precision in its ramblings.
As a math teacher (with this epiphany planted firmly in my brain) it has always amazed me that math 'educators' and 'modern' math curricula are so resolute in demanding language descriptions of mathematical concepts. It's bizarre to think that you can convey a remarkably precise mathematical concept in a notoriously fuzzy language like English.
With a high percentage of kids with learning disabilities (many of them with shades of Autism) and an equally high percentage of ELL kids I always strive to maximize the equation and minimize the language. It's a far crisper, delivery scheme, it seems. Math curricula based on heavy duty language skills are trying to deliver a finely machined bullet to its target by throwing it in the air and blowing on it.
Now if I had a bunch of suburban angels blessed with supportive parents, the whole language thing might make sense. But I've never understood why you would want to deliver Greek (math) to a Russian (generic ELL student) in English (U.S. language of choice for math teachers). Skip the English, I say, and go right to the math.
Actually, I've wondered at times if the math departments have actually been hijacked by the English departments in higher ed. Maybe the math folks need to go underground and take back their discipline, eh?
The new NSF funded high school curriculum, the CME Project, stresses "robust mathematical thinking" for ALL students. It was designed for the inclusive classroom that blends regular and special ed students.
We seem to be living in different worlds about the purpose of K-12 schools. Our focus is on how each student can best obtain needed math and science knowledge and skills to the best of his or her capability, interests, and needs.
The education focus on the heterogeneous classroom seems to be that the interaction of a diverse group is the primary goal, not individual learning.
Unfortunately, 'robust mathematical thinking' in many of these programs is encouraged to be expressed as robust English paragraphs of descriptive text.
Time after time I see (interesting, insightful) solutions from really bright kids that are not equipped with either the vocabulary/writing skills or the mathematical (notational) skills to tell me what they were thinking when they solved a problem.
It has been my experience that we wait far too long to give these kids the mathematical notational tools to express themselves (age appropriately) while we concurrently demand the kind of semantical precision in their mathematical expression that is beyond their current state in language arts. Not to flog a dead horse, but this is directly related to curricula bloat that displaces these things with the early introduction of distractions that can be deferred quite safely.
These programs hit them with a double whammy. What I get, every time, is the arithmetic 'explosion'. Stuff is all over a page. There's no sequence, no logical progression, no order, no way to find or track an error and no effective communication. It's not their fault. There is absolutely no attempt to tame this kind of thought sneeze in earlier grades because the goal is....
1. The answer
2. The English
Constructivism in mathematics is ELA with numbers in it.
"The education focus on the heterogeneous classroom seems to be that the interaction of a diverse group is the primary goal, not individual learning."
Yes, that does seem to be the goal. As the parent of a child with good social skills, I'm tired of hearing that teaching others is the highest good. These years are the only time my child has to learn. The group's progress is much slower than my child's progress could be in traditional, individualized instruction. When the content is too easy, my child gets bored and tunes out.
As a parent, I am not inclined to sacrifice my children's future for the nebulous tag of, "working so well with others." Fortunately, there still exist schools which believe in rigorous instruction which does not rest on group work. Changing schools has worked wonders.
"... it has always amazed me that math 'educators' and 'modern' math curricula are so resolute in demanding language descriptions of mathematical concepts. "
I think this is why teachers in my district love Everyday Math. They LOVE it--I suspect because they finally understand some things that they had only memorized before. The obvious problem is that their students are not building from the same base of computational competence. The students won't leave with understanding or competence.
"...they finally understand some things that they had only memorized before."
There you go. Spiraling works!
Trusting the spiral is a great way to avoid accountability. What school wouldn't love it. Just point to the kids who do well.
"I am not inclined to sacrifice my children's future for the nebulous tag of, 'working so well with others.'"
Many people don't set high goals for K-6 education. They think it's OK to focus on social goals. You can perhaps get away with this in some areas, but not in math.
Our schools pump kids along in K-6, but then really start to turn the screws in 7th grade. It's easy to blame hormones for problems, but I don't believe it. I think it has more to do with bad preparation. All I have to do is look at my son's friends. The ones who do well are the ones with parents who do a lot at home and have always set high expectations.
Schools know this. They know that their best students are the ones with helicopter parents. They know that it takes much more than a place to do homework and modeling an interest in education.
I suppose this has always been true, but I think it's worse nowadays. Math now requires support at home. I also think there is a bigger jump in expectations between 6th and 7th grades. K-6 schools seem to be in their own pedagogical la-la land. Pump the kids along and trust the spiral.
That would certainly include my support.
Cheers
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