One of the problems in American Education, I've come to believe, is that people confuse labels and concepts--and, by extension, definitions with conceptual information.
Mistaking labels for concepts, they ssume that a child who doesn't know what a "number sentence" is doesn't understand the concept of number sentences, or that an autistic child who doesn't know what "because" means doesn't understand cause and effect.
Or they teach biological terms like "endoplasmic reticulum" as definitions to memorize ("the part of the cell that assembles proteins and sends them to the nuclear membrane") rather than as biological entities (an organ within the cell that uses its structure in particular ways to cooperate in particular ways with the rest of the cell).
Then, mistaking concepts for labels, they avoid having children memorize detailed, concept-rich networks of facts like those of the Philogenic Tree or the Periodic Table. ("Mere facts"--right up there with "mere calculation").
In short, concept/label confusion leads people to understimated children (especially children who are gifted and/or autistic) whose conceptual understanding exceeds their vocabulary, to teach rote meanings stripped of underlying concepts, and to avoid teaching concepts whose grounding in detailed factual information causes people to mistake them for mere labels.
Saturday, July 31, 2010
One of the problems in American Education, I've come to believe, is that people confuse labels and concepts--and, by extension, definitions with conceptual information.
Thursday, July 29, 2010
Tuesday, July 27, 2010
"One of the first personal accounts of autism, and still the best." Oliver Sacks' assessment of Clara Claiborne Park's The Siege is as true now as it was when he made it. Clara passed away on July 3rd, 43 years after publishing this classic memoir about her autistic daughter, Jessica Park (now an acclaimed painter), and 9 years after publishing its sequel, Exiting Nirvana.
Sunday, July 25, 2010
In her latest New York Times Op-Ed piece, Susan Engel and co-author Marlene Sandstrom, both of Williams College, discuss ways to reduce bullying in schools. Claiming that
a growing emphasis on standardized test scores as the primary measure of “successful” schools has crowded out what should be an essential criterion for well-educated students: a sense of responsibility for the well-being of othersEngel and Sandstrom argue that "educators need to make a profound commitment to turn schools into genuine communities." Besides ensuring that they and their students have "conversations about relationships every day," and that students know that "kindness and collaboration to be every bit as important as algebra and reading," teachers should
structure learning activities in which children are interdependent and can learn to view individual differences as unique sources of strength. It’s vital that every student, not just the few who sign up for special projects or afterschool activities, be involved in endeavors that draw them together.In other words, besides having students get together to talk about relationships, teachers should also have students get together for academic tasks.
look at Norway, where the prevention of such incidents became a major emphasis of the school system after three teenage victims of bullying committed suicide in 1983. There, everyone gets involved — teachers, janitors and bus drivers are all trained to identify instances of bullying, and taught how to intervene. Teachers regularly talk to one another about how their students interact. Children in every grade participate in weekly classroom discussions about friendship and conflict. Parents are involved in the process from the beginning.But what's egregiously missing from this Norwegian comparison is any mention of Norwegian school children working cooperatively on academic assignments.
Friday, July 23, 2010
|Final 5th grade fractions unit problems (left or top: Investigations; right or bottom: Singapore Math):|
|(Investigations in Number, Data and Space Student Activity Book p. 68 of Unit 4, "What's That Portion?"; Primary Mathematics 5A, p. 96, Unit 4, "Multiply and Divide Fractions")|
Tuesday, July 20, 2010
An article in Newsweek, excerpted on JoanneJacobs, discusses the creativity crisis in America and how schools can go about addressing it. Its recommendations, unfortunately, risk taking schools further down the unpromising garden path along which they've already been wandering for quite some time now.
When you try to solve a problem, you begin by concentrating on obvious facts and familiar solutions, to see if the answer lies there. This is a mostly left-brain stage of attack. If the answer doesn’t come, the right and left hemispheres of the brain activate together. Neural networks on the right side scan remote memories that could be vaguely relevant. A wide range of distant information that is normally tuned out becomes available to the left hemisphere, which searches for unseen patterns, alternative meanings, and high-level abstractions.Consistent with the idea that in creativity, the left brain is as important as the right, the article makes several observations:
Having glimpsed such a connection, the left brain must quickly lock in on it before it escapes. The attention system must radically reverse gears, going from defocused attention to extremely focused attention. In a flash, the brain pulls together these disparate shreds of thought and binds them into a new single idea that enters consciousness. This is the “aha!” moment of insight, often followed by a spark of pleasure as the brain recognizes the novelty of what it’s come up with.
Now the brain must evaluate the idea it just generated. Is it worth pursuing? Creativity requires constant shifting, blender pulses of both divergent thinking and convergent thinking, to combine new information with old and forgotten ideas. Highly creative people are very good at marshaling their brains into bilateral mode, and the more creative they are, the more they dual-activate.
*The age-old belief that the arts have a special claim to creativity is unfounded. When scholars gave creativity tasks to both engineering majors and music majors, their scores laid down on an identical spectrum, with the same high averages and standard deviations. Inside their brains, the same thing was happening—ideas were being generated and evaluated on the fly.
*Creativity isn’t about freedom from concrete facts. Rather, fact-finding and deep research are vital stages in the creative process.
*From fourth grade on, creativity no longer occurs in a vacuum; researching and studying become an integral part of coming up with useful solutions.
*What’s common about successful [creativity training] programs is they alternate maximum divergent thinking with bouts of intense convergent thinking, through several stages. Real improvement doesn’t happen in a weekend workshop. But when applied to the everyday process of work or school, brain function improves.
*The European Union designated 2009 as the European Year of Creativity and Innovation, holding conferences on the neuroscience of creativity, financing teacher training, and instituting problem-based learning programs—curricula driven by real-world inquiry—for both children and adults.
*In China there has been widespread education reform to extinguish the drill-and-kill teaching style. Instead, Chinese schools are also adopting a problem-based learning approach.
*Researchers say creativity should be taken out of the art room and put into homeroom.
Working in small teams, the fifth graders first engaged in what creativity theorist Donald Treffinger describes as fact-finding. How does sound travel through materials? What materials reduce noise the most? Then, problem-finding—anticipating all potential pitfalls so their designs are more likely to work. Next, idea-finding: generate as many ideas as possible. Drapes, plants, or large kites hung from the ceiling would all baffle sound. Or, instead of reducing the sound, maybe mask it by playing the sound of a gentle waterfall? A proposal for double-paned glass evolved into an idea to fill the space between panes with water. Next, solution-finding: which ideas were the most effective, cheapest, and aesthetically pleasing? Fiberglass absorbed sound the best but wouldn’t be safe. Would an aquarium with fish be easier than water-filled panes?So here's my prediction: our education experts will read this article and conclude that we need more, not fewer, assignments across the curriculum that ask students to Be colorful! Be creative!, and more, not fewer, open-ended, real-world, group projects.
All of which will fail to inspire creativity, it turns out, not just in our left-brained math and science buffs, but in students in general.
Monday, July 19, 2010
An article in last week's Education Week reports that schools are falling behind in their computer science offerings at the same time that the demand for programmers has risen. Computer science advocates are now calling for more computer science offerings in public schools.
Proponents of computer-science education say a major hurdle is simply getting school officials and others to understand what the field is, and isn't.
"One of the biggest problems is schools confusing computer literacy with computer science," said Barbara J. Ericson, the director for computing outreach and a research scientist at the Georgia Institute of Technology, in Atlanta.
"A lot of places don't understand the difference," agreed Ms. Cuny of the NSF, which is providing grants to support a variety of programs and research undertakings on computer-science education. "They're not teaching kids how to be creators of technology—they're teaching them how to be users of technology."Sounds a bit like the confusion between teaching science and teaching science appreciation, and it's nice to see that the computer science advocates, unlike many of the science advocates, understand the difference.
Learning to *use* computers is easy. Learning to *design* computer hardware or to write software that handles edge cases properly and not just the “happy path” is difficult. Millennials think they’re smarter than the boomers and the boomers’ parents merely because they can use the technology. They forget that the boomers and the generations before them invented the technology that the millennials are using.
- Internet (ARPAnet): 1960s, created by a team at MIT who were born late in the Silent Generation.
- First email message: 1969, sent by a Boomer.
- First cell phone: 1973, invented by Martin Cooper, Silent Generation.
- World Wide Web, first HTTP communication, 1990, Tim Berners-Lee, a Boomer.
As for music recording and playback: the pulse-code modulation that makes it possible was patented in 1937 by a member of the Greatest Generation. The first digital speech transmission was in 1943; computerized digital recording was invented in 1957.
If we don’t provide the STEM grounding necessary to understand the technology already in existence (how and why it works, not how to use it), I don’t see how future generations will be able to invent anything of substance.
Without pointers, for example, you'd never be able to work on the Linux kernel. You can't understand a line of code in Linux, or, indeed, any operating system, without really understanding pointers.
Without understanding functional programming, you can't invent MapReduce, the algorithm that makes Google so massively scalable.
Pointers and recursion require a certain ability to reason, to think in abstractions, and, most importantly, to view a problem at several levels of abstraction simultaneously. And thus, the ability to understand pointers and recursion is directly correlated with the ability to be a great programmer.
What he says about pointers and recursion enforcing and testing a certain way of thinking is a very important point, in my opinion.As our problems of the week here have shown, Seth has good reason to be scared. In connecting geometry proofs with computer programming, he raises an important point: is the American education establishment, with all its calls to teach "higher level thinking skills," no longer interested in logical reasoning?
But what I found really disturbing from helping to teach that course was that it was possible, indeed universal, that the students who came from the best high schools and had the most experience had never been exposed (consciously) to problems of recursion. Why is it that e.g. the Towers of Hanoi problem has to wait until college to be taught? Students need to be hit with this when they're younger, before their brains start to rot.
I really wish that when people talk about the need for computer in schools, the focus would be not just on computers, but computers as a way to teach how to think about breaking up a problem. But I'm an old-fashioned fart, so I still think that one of the best preparations for programming is geometry, and the process of proving a theorem. I'm scared to ask if that is still taught in high schools.
Saturday, July 17, 2010
David Brooks, for one, thinks it should be more left-brained--at least when it comes to business. (When it comes to education and Asperger's Syndrome, Brooks' bias is more right-brained). In his July 12th New York Times Op-Ed piece, he divides the business world into princes and grinds. Guess which ones are left-brained.
If you go to business conferences, you know that at lunch it is definitely better to be seated next to a prince than a grind. Princes, who can be male or female, are senior executives at major corporations.
They are almost always charming, smart and impressive. They’ve read interesting books. They’ve got well-rehearsed takes on the global situation. They can drop impressive names as they tell you about their visits to the White House, Moscow or Beijing. If you’re having lunch or dinner with a prince, you’re going to have a good time.Or the grinds?
Grinds, on the other hand, tend to have started their own company or their own hedge fund. They’re often too awkward to work in a large organization and too intense to work for anybody but themselves.
Over lunch, they can be socially inert. You try to draw them out by probing for one or two subjects of interest to them. But as often as not, you find yourself playing conversational ping-pong with a master of the monosyllabic response.
Every once in a while you’ll run into one who can’t help but let you know how much smarter he is than you or anybody else in the room. Sitting at this lunch is about as pleasant for him as watching a cockroach crawl up his arm. He’d much rather be back working in front of his computer screen.
Since the princes are nicer and more impressive, it is easy to be seduced into the belief that they also are more trustworthy. This is false. During the last few years, for example, the princes at Citigroup, Bear Stearns, Goldman Sachs and Lehman Brothers behaved with incredible stupidity.Or the grinds?
...The smooth operators at the big banks were playing with other people’s money, so they borrowed up to 30 times their investors’ capital.
The social butterflies at the banks got swept up in the popular enthusiasms... The well-connected bankers knew they’d get bailed out if anything went wrong.
The hedge fund loners often behaved with impressive restraint.
[They] usually had their own money in their fund, so they typically borrowed only one or two times their capital.
...[They] knew they were on their own and regarded their trades with paranoid anxiety.In short:
In finance, as in other realms of business life, social polish doesn’t always go with capitalist success. Often it is the most narrow, intense, awkward people who start the best companies, employ the most people and create the most value.And guess which group Brooks thinks is doing better under today's recovery?
Sadly, this recovery has been great for princes and horrible for grinds... The big companies are posting excellent earnings. They’re sitting on mountains of cash.In short:
The aspiring grinds, meanwhile, are dead in the water. Small businesses are not growing. They are not hiring. They are struggling to stay alive. (Though my friend Paul Downs, a small business owner who blogs for the New York Times, thinks things are improving).
The princes can thrive while the government intervenes in the private sector. They’ve got the lobbyists and the connections. The grinds, needless to say, don’t... [They] try to stay far away and regard the interlocking network of corporate-government schmoozing with undisguised contempt.But the problem has spread beyond the grinds. Because "very few grinds are bringing new ideas to scale and hiring workers to enact their us-against-the-world schemes," we have "an economy that is inching toward recovery but that is not creating much in the way of new innovations and new jobs..."
For jobs to recover, the grinds have to recover... Maybe the real issue is how we are going to light a fire under the country’s loners, its contrarians and its narrow, ambitious outsiders.
Thursday, July 15, 2010
|Two ways to sum up a chapter on fractions, decimals, and percents:|
1. "Problems without Numbers," from Chapter I of Hamilton's Essentials of Arithmetic: Second Book (intended for students in the "sixth, seventh and eighth years"), p. 79
2. "Time to Reflect," from Unit 4 of the 6th grade Everyday Mathematics Student Math Journal Volume I, p. 161.
Tuesday, July 13, 2010
As I look back on J's past year, one thing that stands out to me is how minimal and inadequate his official autism-related therapies were. Our regional autism center no longer provides any therapy at all, limiting its services to evaluations (and even for these there's quite a long waiting list). So all of J's official therapies have happened at school. Here, OT has been minimal, and speech therapy is conducted by an itinerant generalist untrained in autism-specific language deficits. I asked for more; nothing happened; I have yet to sign our 9-month-old IEP. I could have spent more time fighting; instead I spent the time I had working with J myself.
A few months ago it looked like a new opportunity had opened up: the new Kinney Center for Autism Education and Support at nearby St. Joseph's University was offering a social skills group for adolescents with autism. We called up, there was an opening, we faxed over evaluations and went through an accelerated intake. They couldn't wait to meet J. But then they did. "He doesn't comply with directions," the psychologist told me after he interviewed J with my husband, "and so he doesn't meet the requirements of our social group. We need kids who will follow directions." He promised to let us know if some other program opened up that might be appropriate for J.
So my ears pricked up the other morning when I heard the following words on WHYY's Morning Edition:
The long hot days of summer can pose challenges for families of special needs children. Parents have to find activities or camps where their child feels safe, welcome, and continues to learn. A new camp at Saint Joseph's University is trying a unique approach. It's especially designed to accommodate children with autism and pairs them with their typical peers.Gee, they didn't tell us about this program, I thinks to myself, as I continue listening:
Executive director Michelle Rowe says having a mixed group of kids means opportunities for learning. "What that does it it allows the kids with autism to learn from their typically developing peers. In translation, that means that children with autism can benefit from learning what kinds of things are expected socially at different ages."Sounds great, I says to myself. A great opportunity, as well, for typical kids to learn about autism and about how to interact with autistic peers. But then I hear more:
"The kids can be in the pool and also be interacting with each other – we take them for five hours a day, we expose them to a lot of fun, but also, they can't help but learn in the process."
As excited campers chatter about their favorite activities, it is nearly impossible to determine which children have Autism, and which don't:Nearly impossible to tell which ones have autism?? Only a tiny disability?? Tell that to a parent of an autistic child. Or take a look at J, so capable, yet so mischievous that he would never be admitted to this camp. Of course, that's precisely what's going on.
[Sounds of kids' voices.] "I like it all!! We go swimming every day, we go to the play ground most of the days." "I like talking with my friends, I like swimming, and I like snack time." "Playing basketball!"
This is the first year for the camp, and the kids with autism are in the majority, but Rowe hopes to have more of a 50 – 50 mix in the future. She says the concept is also beneficial for typical kids, who learn to feel comfortable around people with disabilities. 7 year-old Ian sums it up:
Ian: "Kids with autism just have a tiny disability, not like a big difference, we're all the same in a couple of ways."
Indeed, besides the fact that the Kinney people didn't tell us about Camp Kinney at the time they evaluated J, there are an number of clues here suggesting that they handpicked the autistic campers to be minimally disabled--at least in ways that would inconvenience the staff and disturb their non-autistic peers. Consider, for example, how easy it was for one of the college undergraduate counselors to diffuse a child's temper tantrum:
St. Joseph's Psychology major Amber Leyton says learning about behaviors and explosive temper tantrums associated with Autism in a classroom is one thing – dealing with them first hand is another. But Leyton had no problems diffusing a situation when a young camper had a meltdown because he couldn't spend time with a counselor named Drew:What this program seems to be striving for, as much in its admissions policies as in its hoped-for outcomes, are individuals like John Dorfman:
Leyton: "At first, it was just waiting for him to level out a little bit, and it was explaining to him, over and over the situation: if you calm down, you can eat your lunch, you can go see Drew, over and over again, the schedule, what was going to happen, and what was expected of him."
These kinds of situations [as in Drew's tantrum] are familiar to counselor John Dorfman from first-hand experience – he has autism. He says he wants to inspire the campers with his own story:So long as potential providers resist providing intensive therapy and opportunities for peer interactions to the many, many individuals with more severe or challenging forms of autism, everyone but the families of such children can remain in happy denial, congratulating themselves on how openly they welcome autistic kids into their worlds and how open-mindedly they appreciate what a tiny disability autism really is.
"Anything is possible! When I was in 9th grade, everyone was skeptical that I was even going to make it to college, and here I am, going into my senior year helping the other kids, it's really a great thing."
I emerge from these thoughts in time to hear the program's closing remark:
Michelle Rowe says they had to turn away applicants this year, but hope to expand the program next summer.Isn't it pretty to think so?
Sunday, July 11, 2010
In this latest case it's hard to say what's more shocking: that the "expert" in question thinks she's qualified to make recommendations about general classroom pedagogy, or that the publication in question has given her a forum for doing so.
The expert in question: Martha Nussbaam, a professor of Law and Ethics at the University of Chicago Law School.
The publication in question: The New Republic.
In a July 1st opinion piece entitled "The Ugly Models", Nussbaum criticizes American liberals, specifically President Obama and New York Times columnist Nicholas Kristov, for extolling the virtues and successes of the Chinese and Singaporean education systems.
Alluding to "the Chinese government’s ferocious opposition to political dissent," Nussbaum writes:
Obama and Kristof and all the other U.S. proponents of Singapore and China’s educational systems apparently aren’t thinking very hard about the relationship of those policies to democratic debate and democratic autonomy. Indeed, they are glorifying that which does not deserve praise.Nussbaum offers just one reason why these education systems don't deserve praise:
By their own internal accounts, [educators in China and Singapore] do a great deal of rote learning [sic] and “teaching to the test.”Given that educators in the US have been making the same claims about US education from time immemorial, this presumably qualifies us as steadfast "Ugly Models" as well. But Nussbaum doesn't go there.
Instead, she implicitly concedes that there is a bright side to this Sino-Singaporean critical self-awareness, namely, an inkling of possible reform:
In recent years, both nations have conducted major educational reforms, concluding that a successful economy requires nourishing analytical abilities, active problem-solving, and the imagination required for innovation. In other words, neither country has adopted a broader conception of education's goal, but both have realized that even that narrow goal of economic enrichment is not well served by a system focused on rote learning.Nussbaum elaborates Singapore's reform attempts in particular:
Singapore, similarly, reformed its education policy in 2003 and 2004, allegedly moving away from rote learning toward a more “child-centered” approach in which children are understood as “proactive agents.” Rejecting “repetitious exercises and worksheets,” the reformed curriculum conceives of teachers as “co-learners with their students, instead of providers of solutions.” It emphasizes both analytical ability and “aesthetics and creative expression, environmental awareness … and self and social awareness.”The problem, Nussbaum explains, is that these reforms remain theoretical:
Observers of current practices in both Singapore and China conclude that the reforms have not really been implemented. Teacher pay is still linked to test scores, and thus the incentive structure to effectuate real change is lacking.Here, Nussbaum herself waxes pragmatic:
In general, it’s a lot easier to move toward rote learning than to move away from it, since [this kind of progressive education] requires resourcefulness and perception, and it is always easier to follow a formula.
In Singapore, nobody even attempts to use the new techniques when teaching about politics and contemporary problems. “Citizenship education” typically takes the form of analyzing a problem, proposing several possible solutions, and then demonstrating how the one chosen by government is the right one for Singapore.
Singapore and China are terrible models of education for any nation that aspires to remain a pluralistic democracy. They have not succeeded on their own business-oriented terms, and they have energetically suppressed imagination and analysis when it comes to the future of the nation and the tough choices that lie before it.Nussbaum doesn't entertain the possibility that the U.S. education system might already be achieving precisely these results without help from Singapore and China.
Friday, July 9, 2010
Wednesday, July 7, 2010
Two recent segments on NPR remind me of how important it is to qualify carefully what you're calling for--especially when your advice is directed at the education establishment, where phrases--whether it's "conceptual understanding," "higher-level thinking," or "project-based learning"-- are routinely distorted to serve pre-existing agendas.
The early education learning environment, whether in the home or in a school, should provide a rich variety of activities that will foster physical, mental, emotional, and social development.But there's a distinct difference in both the ingredients and the efficacy of America's Head Start vs. France's écoles maternelles. As E.D. Hirsch explains in The Schools We Need and Why We Don't Have Them (p. 46):
Head Start has not been primarily an academic program. Though momentary academic benefits have sometimes been measured, they are not securely fixed and they quickly fade.
And this core includes, among other things, content-based civics instruction....Preschool programs elsewhere in the world do achieve long-term academic benefits for disadvantaged students. In France, early schooling permanently boosts educational achievements of low-paid workers and immigrants from North Africa. What, then, makes the academic benefits of early education endure in some countries but fade in our own? A few contrasts: Head Start lasts three hours, is staffed by nonprofessionls, and is nonacademic. The école maternelle (attended by over 90 percent of French three and four-year-olds) lasts all day and goes twelve months a year, is staffed by professionals, and has well-defined academic goals. Children then enter a grade-school system that also has a well-defined academic and cognitive core.
Monday, July 5, 2010
Saturday, July 3, 2010
Every time a new line of cribs or high chairs is recalled because of loose nuts and bolts or other safety concerns, my first reaction is: haven't people been making these things long enough to know how to make ones that don't fall apart? The problem, of course, isn't that manufacturers yet haven't figured out how to make a safe crib, but that they're constantly trying out new designs to cut costs or look appealing. If it ain't broke, don't fix it just doesn't apply. Instead: the older the appliance, the more likely it is to still be working. One might say the same things about math pedagogy.
Thursday, July 1, 2010
I. Final percent problem in Bits and Pieces III: Computing with Decimals and Percents, p. 78: