Monday, March 5, 2012

Math for Good Thinking


I was listening to this Freakonomics podcast and they had Ellen Peters on. She said:
"Numeracy in general, what it should do, is it should help you to better understand information, first of all, and that kind of comprehension is sort of a basic building block of decisions across a variety of domains. But numeracy should also do other things. It should also help you just simply process the information more systematically. It should, in general, help you to get to better decisions that are more in line with the facts."

and I agreed, and felt hopeful about the world, but it was all a setup for her research conclusion that even or especially people with higher education have preexisting beliefs that are not affected by good thinking:
"Greater scientific literacy and numeracy were associated with greater cultural polarization: respondents predisposed by their values to dismiss climate change evidence became more dismissive, and those predisposed by their values to credit such evidence more concerned, as science literacy and numeracy increased."

This is concerning! I would like to believe that my math-teachers colleagues are making students into better thinkers. I am inclined to hope that hard science majors are less inclined to be biased by "values" than, say, MBAs, but everybody has been through high school and ought to be better than this.

I also recently read "Thinking, Fast and Slow" by Kahneman, which is wonderful. He talks about how he helped develop a textbook on rational thinking that was never adopted by Israel after they finally finished it. I would like to see a textbook like that. I think that could be the kind of textbook American schools could use. Do you know of any resources in this vein?

And this idea of our-subject-should-make-people-better-thinkers is not unique to math, of course. It's everywhere, and here's a relevant selection from a science point of view:
"We need a more scientifically literate populace to address the global challenges that humanity now faces and that only science can explain and possibly mitigate, such as global warming, as well as to make wise decisions, informed by scientific understanding, about issues such as genetic modification."

That's from an article series that makes the point that unfortunately, too often the result of science classes is not a really useful better understanding of science. Good stuff.

I think that cross-discipline work between math and ELA could be really valuable too, and is the sort of thing that should probably be done more. I'm thinking of things like analyzing the logical structure of an argument, looking at symbolic structures of logical fallacies, etc. I'm sure there are more good ideas in this realm. Perhaps what I mean is really better-structured, deeper, more cognitively demanding ELA.

I'm also thinking about this in relation to the Common Core hullabaloo, which I think is generally wonderful - who wouldn't be for deeper better standards that encourage real understanding of concepts? But then I see stuff like this: http://engageny.org/wp-content/uploads/2011/11/grade-4-handout.pdf which is supposed to be a *model* of Common Core-aligned work, and it kind of makes me retch. Am I wrong to retch? Is this an improvement on what's currently being done?

I hope the thread connecting all these things I've mentioned is evident to you! haha What are your thoughts? Are there really great math (etc.) curricula/texts being used now or being developed?

Ramblings on Learning Management Systems

This is seriously just very quickly edited text from an email I sent a while ago:



Date: 12 Dec 11 3:46 PM

First, consider two classes of skills or activities. One is "basic" skills that can be taught explicitly and practiced repetitively. I'm thinking of things like multiplying two-digit numbers, and I believe this class of skills can be taught and practiced really well with technology like Delta, Khan academy, etc. The second class are collaborative and "higher-level" skills that are best learned by working in teams on projects that have clear connections to the real world. I'm thinking of things like analyzing an issue, making a design, that kind of thing.

Now I grant that probably skills really lie on some continuous spectrum, but I think enough of the "basic" skills can be lumped together that the conceptual distinction can be useful.

To illustrate with math, problems with one correct answer are generally on the "basic" side and problems that admit of many solutions, like "design a system that uses data to evaluate NYC schools" or "engineer a device that solves this problem" are the other side. I feel like I want better names for these two categories. I propose "derivative" skills and "creative" skills. Derivative skills are skills you just learn from others, based on their work. Good. Also includes therefore knowledge of facts like "Mars is the next planet out in the solar system".

I think there is almost but not quite an analogy to pure and applied math. It falls apart because pure math of course has a creative leading edge, and applied math is about creatively using math to solve problems.

I think perhaps the pervasive corruption of debate on education is that some people seem to think that these two kinds of skill and education can succeed in isolation. And then you get kids with basic skills who can take a test but can't do anything creatively or solve problems in the real world, and you get kids who are creative but everything they create is complete crap because they don't have any supporting skills or knowledge.

I think that people who focus on derivative learning don't care much about the creative side because their kids do well on standardized tests. People focused on the creative side take one of two positions: they say either that basic skills are not important and shouldn't be tested, or that their kids learn them but somehow learn them differently through doing "rich" tasks.

And that last is my big gripe with some applications of constructivism, wherein educators set their students some rich task and expect it to take care of teaching the fundamental skills. I compare this to handing kids a chess board and expecting them to get good at chess just by messing with it. I'll have more to say about chess but first I'm curious if this all seems self-evident to you or if it seems like I'm missing something important. My claim here is that there are broadly two classes of important proficiencies, and that they might be best taught in two different ways.

**

Okay now the derivative skills form a foundation for further work, and I think it's fair to say that every student should have them. You should not have a few kids who know how to multiply and a few that always go to them to ask when they need something multiplied. (Never mind that this is effectively what a lot of managers do; I think we'd have a lot better managers if those folks had some skills too.) But this lack of even distribution of skills can easily happen with group work, as I'm sure you've seen. If somebody can already do it, I don't need to learn it. So I think that for many or all derivative skills, students should definitely demonstrate proficiency independently, and this will mean independent study and practice.

You can see that I'm getting toward learning management systems. What they already have is that they scale-ably (how is that spelled?) deliver individual interactive practice. They make attempts, to varying degrees, at delivering individual instruction (explanatory videos, etc.).

I think the as-yet unrealized great potential of technological solutions is to also deliver scale-able differentiation. They're the only possible solution I know of. One teacher can't work one-on-one with thirty kids at the same time. You're already doing much better than average because you can assign different kinds of problems on Delta to different students, but that still doesn't scale, because it is always more work for you to figure out what to assign and do so for every student individually.

What I envision is a system that incorporates some kind of machine learning with an internal representation of every student's current knowledge and skill set and customizes on the fly the experience that individual students have to optimize their progress toward educational targets.

What this means is: you don't tell students what exercises to do, and you don't tell the software what exercises to have the students do, you just sit the student down and tell the computer that the student needs to learn algebra, or whatever.

What would this be like? Well, it would be a little like Computer Adaptive Testing. If the student does something wrong, the computer makes an inference about what they know. If they do it right, the computer would make a different inference. So as an example, if you sit the student down to learn algebra and they already know it all, the computer will know that and tell you that the student is done. Bam. On to the next thing. But it isn't just Computer Adaptive Testing, it's Computer Adaptive Teaching, because based on what it infers about student knowledge the computer can offer different lessons, videos, activities, etc. to help move the student along.

This is a little bit like what School of One does; they have a huge library of computer (and classroom) lessons and assessments - but they spend a huge amount of time just deciding what each student should do the next day. Computer systems should be able to work this out more efficiently. Also, I think School of One has the wrong idea about the role and value of teachers. School of One makes sure to have teachers delivering lessons in the usual way, by talking and drawing on a board, so as to not "take anything away" from the teachers. But teachers shouldn't have to focus on these derivative skills. They should be facilitating the fun and interesting projects and other learning experiences, helping students with higher level skills. What they shouldn't have to do is worry that they can't get their kids to write a good essay because they don't know how to spell or capitalize properly.

What else is this like? It's a little bit like playing rated games against a chess computer. If I play and lose, my rating goes down and the next game I play is against the computer at a lower difficulty setting. This adjusting of difficulty makes it more fun for me (and there's a comparison to that idea of "flow" in matching difficulty to skill level) and by practicing I can get better at chess. But I would get better at chess more quickly if based on my play the computer also offered suggestions or lessons on how to play better in general. And this is possible.

So I imagine that we have a collection of lessons and a collection of assessments, and probably all or many of these are very short, like one question or a two-minute "lecture". (I'm not entirely sure that lessons and assessments really belong in separate bins; it might be better to have them all be together as "activities" or something to that effect.) And there's an internal space of concepts or proficiencies. This could be set up explicitly like "able to multiply six by seven" or "knows what thesaurus means" or "can find Atlanta on a map", or it could be completely generated by a machine learning algorithm and not necessarily correspond to our ideas of what the component skills are. The main point is that it will be more complicated than one value representing "skill in math" or something like that, the way your chess rating represents "skill in chess". But the system would learn based on user interactions that, for example, a student who can't do this also can't do that, or can do this but only after first doing that, and so on, so that a dynamic adaptive progression can be made for each student, and change as the student works.

I also think such a system would do well to incorporate ideas of carefully spaced repetition for maximizing retention in memory. Often a few repetitions at the right intervals are better than many repetitions in one bunch.

This is the outline of what I think could be a very good system for delivering real differentiated instruction in a way that scales across all students and can raise them all to very high levels of competency in basic skills. I think such an approach should be balanced with work on high-level rich tasks that build a whole suite of different skills, and I think it is in that realm that the importance of classroom teachers lies. In terms of time-share, I think it might be something like 30% individual work with technology, 70% collaborative project type work. (I think I'm not far off from what Khan has said on this.) (For one thing, the mental demands that this kind of computer work makes are very high. You can't just space out in the back of the room.)

I think that Delta and many similar projects are steps in the right direction toward enabling this kind of education, but I think there is a big missing piece and that piece is the kind of artificial intelligence approach that I outlined. So here's check-in number two: does it make sense, what I'm saying? Do you think it could be done? I think it would require a novel architecture, of course, but I think a lot of the components of Delta could fit into that architecture. What do you think would be the main hurdles of building something like this?

**

I think I sent you this link already: http://www.learningregistry.org/about because I think that project could also help form some of the content guts of a system like this. There is a lot of educational content out there, but solving the problem of getting that content to students at exactly the right time and evaluating whether they understand it is a difficult problem. It is a problem that I think could be solved by an approach like the one I'm describing. It looks like they have a name for systems of this type: a "learning management system".

added 2012.3.5: My best guess at what junyo is up to, with one of the founders of School of One, is that they're doing the big data machine learning data analysis buzzword xyz work toward some of the goals that I've mentioned for next-generation LMS.

Slang Equivalencies from Big L's "Ebonics"

This is just a cut down version of the lyric. Check out the song: Big L – Ebonics


weed smoke:lye
ki of coke:pie
lifted:high
new clothes on:fly
cars:whips
sneakers:kicks
money:chips
movies:flicks
crib:home
jacks:pay phone
cocaine:nose candy
cigarettes:bones
radio:box
razor blade:ox
fat diamonds:rocks
jakes:cops
got rubbed:got stuck
got shot:got bucked
got double-crossed:got fucked
bankroll:poke
choke hold:yoke
kite:note
con:okey-doke
got punched:got snuffed
to clean:to buff
bull scare:strong bluff
burglary:jook
wolf:crook
felony:F
got killed:got left
the dragon:bad breath
7:30:crazy
hit me on the hip:page me
angel dust:sherm
AIDS:the germ
chick gave you a disease:you got burned
max:relax
guns and pistols:gats
condoms:hats
critters:cracks
food:grub
victim:mark
sweat box:small club
ticker:heart
apartment:pad
old man:dad
studio:the lab
heated:mad
iron horse:train
champaign:bubbly
a deuce:a honey that's ugly
fine girl:dime
a suit:a fine
jewelry:shine
in love:blind
genuine:real
face card:hundred dollar bill
very hard, long stare:a grill
sneaking to go see a girl:creeping
smiling:cheesing
bleeding:leaking
begging:bumming
nutting:coming
taking orders:sonning
ounce of coke:onion
hotel:telly
cell phone:celly
jealous:jelly
food box:belly
to guerrilla:to use physical force
took a L:took a loss
show off:floss

Wednesday, December 28, 2011

Words from The New Kids by Brooke Hauser

The new kids: Big dreams and brave journeys at a high school for immigrant teens
Brooke Hauser

I read this book about the International School @ Prospect Heights (17K524) for my work reading group book club thing. It's a book of stories. I haven't read any fiction in a while. I guess I read some Douglas Adams over the summer. Maybe what I mean is, I haven't read any mundane fiction in a while. Not that the stories of the students and teachers are mundane - they follow the ordinary rules of physics is all. They're good stories. They give you a human view of a lot incredible lives. But it isn't a book of ideas, unless the idea is "let's have empathy" - and that isn't a bad idea.

It did have some interesting words!
umber
sable ponytail: seems to be just an ordinary ponytail
vitiligo: I had wondered about this and am glad to have a word for it now.
brackish (okay I do know what this means...)
atelier
scrim
Tibetan Spicoli: this one is interesting... it seems like the only place this phrase has ever been used is in this book. Is it a typo? Is it just overwhelmed by other uses? Seriously the only other reference I can find is some joker garbage on urban dictionary...
kitten heels
Les Brown: comical motivational speaker?
liminal space between
ebullient: cheerful and happy; I knew that...
skein (noodle): like a ball (skein) of yarn...
arrondissement: district of Paris
stupefaction (I guess I know this one too)
chafing-dish: those things they use to keep food hot at buffets
Batusi: THIS IS REALLY FUNNY
compas (re: bachata)
tulle (re: taffeta)
chignon
T-zone (cosmetics): apparently your forehead down to your nose makes a "T"?

Tuesday, December 27, 2011

Thoughts on Now You See It by Cathy Davidson

Now you see it: How the brain science of attention will transform the way we live, work, and learn
Cathy Davidson

The main point of this book is that every individual has a limited perspective and so we need other people. Davidson calls this "collaboration by difference". Through reading her book I've certainly learned a lot of things I wouldn't otherwise have learned, including but not limited to things that are artifacts of her perspective.

Davidson explains that she was diagnosed as ADHD as an adult, and it's not hard to believe. Sometimes the arguments venture far from the path you might expect them to traverse, and bookends sometimes seem to have been strapped on in editing to give a sense of coherence. Hers is a perspective different from mine, and I agree it can be valuable. It may also be what leads to broad generalizations, quick flips, and hyperbolic language that doesn't always seem to feel a need to connect closely with the truth, as with this reference to a study that Davidson does not like:

The headline-grabbing "multitaskers aren't even good at multitasking" is a nonsensical statement, when you break it down and try to think about it seriously.

If you try to think about it seriously, the study defined multitasking as the ability to focus on one task, then quickly stop, shift, and focus on a new task. They compared how well people did when they were forced to shift, and the people who naturally switch tasks a lot did worse (were slower) than people who naturally don't switch tasks a lot. This makes sense. People who tend to focus less will switch tasks more often, left to their own devices. There's no reason to expect them to focus well when you tell them to. They are less focused. It doesn't necessarily mean that less focus is always bad, and it doesn't mean that the result of the study is a nonsensical statement.

The result of that study also doesn't undermine Davidson's related claim, that switching tasks a lot might lead to better results because you end up exposed to more different ideas that you can work with flexibly. I find a lot to like in this:

We know that in dreams, as in virtual worlds and digital spaces, physical and even traditional linear narrative rules do not apply. It is possible that, during boundless wandering thinking, we open ourselves to possibilities for innovative solutions that, in more focused thinking, we might prematurely preclude as unrealistic. The Latin word for "inspiration" is inspirare, to inflame or breathe into. What if we thought of new digital ways of thinking not as multi-tasking but multi-inspiring, as potentially creative disruption of usual thought patterns. Look at the account of just about any enormous intellectual break-through and you'll find that some seemingly random connection, some associational side thought, some distraction preceded the revelation. Distraction, we may discover, is as central to innovation as, say, an apple falling on Newton's head.

I can definitely identify with the experience of being too locked in to one way of looking at something, and so missing solutions I might have seen if I stepped back, took a break with something else, talked to somebody about it, browsed the 'net for a bit, etc.

The poetic appropriateness is almost enough to convince me that Davidson was right to include the apocryphal reference to Newton, but that kind of looseness with fact grinds on me and makes it hard for me to take her seriously as a scholar in places. I think it's important to use language precisely. (Oh, that I may I not be held to that standard on my blog.)

For example: Davidson seems several times to be ending her book. One ending tells the story of her trip to Korea, when she visits 동대문시장.

In a guidebook on the plane home, I read that the Dongdaemun was founded in 1905. Its name originally meant, Market for Learning.

It's not a big deal to the general reader, I guess, and maybe it's the fault of that guidebook, but this just isn't so. I could understand "Its original name meant", since it was originally called 배우개장, but "Dongdaemun" has never meant "Market for Learning". It feels like she's sweeping too much under the rug, neglecting details that I want to know about. I happen to have some knowledge about this (and could double check with wiki), but what about all the areas where I don't know enough to fact check Davidson? If you read this book and then go around saying, "Hey, did you know Dongdaemun used to mean 'market for learning'?" you will sound like a fool, if someone knows better, and what's worse you will be spreading misinformation if they don't know better.

So how am I supposed to interpret Davidson's other claims, about research?

These key factors for educational success - rigor, relevance, and relationships - have been dubbed the new three Rs, with student-teacher ratio being particularly important. Small class size has been proved to be one of the single most significant factors in kids' staying in and succeeding in school. Twenty seems to be the magic number.

The very last book I read, The good school, took a position almost exactly opposite on class size, saying that usually parents are too worried about it, and that the body of research indicates it has only minor effects, and then only for dramatic reductions of the type you are not likely to see in practice. The reader is lucky that Davidson provides a footnote here - but it's to a 1999 summary of prior research, and doesn't seem to fully support Davidson's dramatic claim.

There are other places where Davidson seems to be just talking nonsense:

If we establish a mean, deviation from the mean is almost inevitably a decline.

This is a one-line description of the strangest statistics I have ever heard proposed. I am glad I do not inhabit this particular world of voodoo statistics. It's pretty clear how Davidson feels about mathematicians:

Is the pure abstract thinking of the mathematician really superior, cognitively, to the associational searching and reading and analyzing and interpreting and synthesizing and then focusing and narrating that are the historian's gift and trade? One could also note that it is mathematicians and statisticians, not historians, who tend to make up the statistical measures by which we judge cognitive excellence, achievement, and decline. On the other hand, it was two historians who created H-Bot, that robot who can whup most of us on standardized tests.

Yes, one certainly could note that it tends to be statisticians who "make up" statistical measures. And there could even be something to the argument, if it were made with, say, evidence of how mathematicians make IQ tests that are biased in such and such a way. Such an argument would fit well in the section of the book about standardized tests, which is approximately where, I believe, we first heard about this interesting H-Bot:

In 2006, two distinguished historians, Daniel H. Cohen and the late Roy Rosenzweig, worked with a bright high school student to create H-Bot, an online robot installed with search algorithms capable of reading test questions and then browsing the Internet for answers. When H-Bot took a National Assessment of Educational Progress (NAEP) test designed for fourth graders, it scored 82 percent, well above the national average. Given advances in this technology, a 2010 equivalent of H-Bot would most likely receive a perfect score, and not just on the fourth-grade NAEP; it would also ace the SATs and maybe even the GREs, LSATs, and MCATs too.


First, it is interesting to note that the most interesting thing I have heard about being done by historians is in fact a work of computer science. Kudos to that high school student. (And now it's clear where I stand if fight breaks out between hard and soft sciences.) Second, Davidson never actually explains that H-Bot only answers history questions, and even then, only the multiple-choice ones from NAEP (about two-thirds of the history questions, according to the original paper, a very interesting one from 2006 that I would like to look at in more depth in a later post, called No Computer Left Behind). Now, that is not really so bad - mathematicians are not offended that computers can answer math questions. The original paper seems to argue that since knowledge can be recorded, it is not worth knowing. As a student I was similarly keen on history without dates, without memorization. But there is value in having humans know these things, without having to look them up.This recent article provides an illustration: "Only about a third of American adults can name all three branches of government, and a third can't name any. Fewer than a third of eighth graders could identify the historical purpose of the Declaration of Independence." These are not things that you should have to look up - but they are things that you can test quickly and easily with multiple choice. I agree that history classes should not be limited to "memorize this list of the three branches of government", but that doesn't make it off limits on the test. Next, Davidson's claim that just half a decade after H-Bot, computers can easily ace advanced tests, tests that are computer-adaptive and, more to the point, do include essays, is pure claptrap. If she is thinking just of their multiple choice sections it may be possible, with Watson easily winning Jeopardy, showing us that the ability to answer questions is not uniquely human. (But even Watson isn't perfect.) What it doesn't mean is that now humans don't have to know anything.


Here's one more claim of Davidson's that I just don't think is based in reality:

Parents and students all know when a teacher isn't doing her job.



I think it's more complicated than that. Judging a teacher by the standardized test scores of the students is not perfect, it's an expedient, it is at least based on something objective but alone it is not perfect. Neither is relying on parents to somehow "just know". I think parents are pretty far removed, really. There is actually some evidence that student perception of teacher quality correlates with the standardized test measures. I think most folks agree that we need to use more than one measure to evaluate teachers, and there is progress in this direction.


Before leaving testing, Davidson and her sources seem to really like essay tests, suggesting that we just need to spend a little more time grading to solve all the problems of education. I have never seen a fair way of grading essays, and I have never seen a standardized grading scale or rubric that gave a score range of more than about five points. I think essays are great. Sometimes I write my own. But I don't think they are a way to fairly compare students from different classrooms or schools or states or countries. Some of the history was interesting:


That letter grade reduces the age-old practice of evaluating students' thoughts in essays - what was once a qualitative, evaluative, and narrative practice - to a grade.
The first school to adopt a system of assigning letter grades was Mount Holyoke in 1897, and from there the practice was adopted in other colleges and universities as well as in secondary schools. A few years later, the American Meat Packers Association thought it was so convenient that they adopted the system for the quality or grades, as they called it, of meats.

Davidson seems to takes such glee in trying to imply that giving students letter grades is treating them like meat. If anything, it's just the reverse! (I can't deny it's a little funny either way.)

Here's an argument against standardized testing that I think has a little bit more substance:


We don't subject a new employee to a standardized test at the end of her first year to see if she has the skills the job requires. Why in the world have we come to believe that is the right way to test our children?

Of course, some companies (EPIC, for example) actually do have new employees take standardized tests after completing training - and I think that could be a really good idea, when their job depends on skills and knowledge they may not have learned in school. But there is something to be said for people being judged in real life based on the work that they do, rather than on their test-taking skills. I think Davidson is right that project work, in which students actually do/make something meaningful, should play a bigger part in education.


But about projects: I love projects. But I don't think they can be everything, exactly because they allow and even encourage so much specialization:

That girl with the green hair would be enlisted to do the artwork. Rodney would be doing any math calculations. Someone might write and sing a theme song. Someone else would write a script. Budding performers would be tapped to narrate or even act out the parts. The computer kids would identify the software they needed and start putting this together.

There are skills that every student in a school should learn. I think it is wrong to endorse a system in which, for example, maybe two students learn to type and become the typists for the class. Everybody needs to know how to type. I think a wide range of skills are similar enough to typing in their fundamental nature that every student should be able to do them well and individually, not just in a team. I happen to think that basic programming should be one of these skills. I would have loved to see a reference to Rushkoff's Program or Be Programmed.


I do agree with Davidson that education should use technology much more effectively. But often she goes off in this direction:

If we want national standards, let's take the current funds we put into the end-of-grade testing and develop those badges and ePortfolios and adaptable challenge tests that will assist teachers in grading and assist students, too, in how they learn. Lots of online for-profit schools are developing these systems, and many of them work well. Surely they are more relevant to our children's future than the bubble tests.



Okay here's my venting about badges: Badges are dumb. They are not that motivating, and they're certainly not what an employer wants to see later. "Wow, you got the red badge? Get out of my office." I have a similar gripe about portfolios, e- or otherwise: If the point of doing something is to put it in a portfolio, it is a pointless thing. A portfolio is meant to collect work you've done. It is not an end in itself. If you are a photographer going out to do a shoot to build your portfolio, you are not a photographer. First do photography, then look at what you've done and put your best work in your portfolio. Etc. Don't write "for your portfolio" don't paint "for your portfolio" don't design "for your portfolio". A portfolio is a record of projects done, not a project itself.


In places Davidson and I completely agree on what's going on but really disagree about what it means or what to do about it:

Recently a group of educators trained in new computational methods have been confirming Gould's assertion by microprocessing data from scores earned on end-of-grade exams in tandem with GIS (geographic information systems) data. They are finding clear correlations between test scores and the income of school districts, schools, neighborhoods, and even individual households. As we are collecting increasing amounts of data on individuals, we are also accumulating empirical evidence that the most statistically meaningful "standard" measured by end-of-grade tests is standard of living, as enjoyed by the family of the child taking the exam.

To me, this is a problem because it reflects socio-economic injustice (often falling along race lines, by the way) that is alive and well in our country. It means we have to work to improve education and so-called wrap-around social services to improve educational outcomes for those that need them most. To Davidson, it seems to merely imply that standardized tests are bad. Look: kids in the south Bronx are not going to suddenly go to college and get good jobs if you just stop having them take standardized tests. I think it is not in those students' best interest to suggest that the problem is the tests.

So again, here's the part of Davidson's stuff that I agree with:

I'm not against testing. Not at all. If anything, research suggests there should be more challenges offered to students, with more variety, and they should be more casual, with less weight, and should offer more feedback to kids, helping them to see for themselves how well they are learning the material as they go along. This is called adaptive of progressive testing. Fortunately, we are close to having machine-generated, -readable, and -gradable forms of such tests, so if we want to do large-scale testing across school districts or states or even on a national level, we should soon have the means to do so, in human-assisted, machine-readable testing-learning programs with real-time assessment mechanisms that can adjust to the individual learning styles of the individual student.

Davidson is very into games, and apparently had something to do with 02M422 "Quest 2 Learn", a public school here in New York, which is built around games. They would do a lot better on the NYC progress report if they could get their ELA scores to go up. I think games can be fun, but I think relying on existing games that are made purely for entertainment to teach fundamental literacy skills is a bit of a stretch. Here in the quote he's not necessarily agreeing with me, but you could read it as indicating the thought that games can provide immersive enrichment, not necessarily replacing what you might call "the basics":

E. O. Wilson, the distinguished professor emeritus of biology at Harvard, thinks so too: "Games are the future of education. I envision visits to different ecosystems that the student could actually enter ... with an instructor. They could be a rain forest, a tundra, or a Jurassic forest."

While Nim may be a game that can be modeled mathematically, I don't think it's teaching anybody basic math. And so on. I don't think that the interactive computer systems to teach these educational building blocks yet exist. I would like to make them. I'm thinking about it.

Here are some more places where I really AGREE with Davidson:

Talking about a guy from Mozilla:

He's studying how we actually use our computers, because humans, as we know from the attention-blindness experiments, are notoriously poor at knowing how we actually do what we do.

It is darn hard to be really self-aware, really meta. Here's a quote from the head of Wikipedia:

There are so many problems to fix in the world. Why waste time having people all working on the same thing when they don't even know about it? I visit big corporations and I hear all the time about people spending a year or two on a project, and then they find out someone else is working on exactly the same thing. It makes no sense. It's a waste of valuable time. There are too many problems to solve.

I encounter this at work. I wish everybody would share more about what they're doing and collaborate when it makes sense. And it's not just me wishing that: several people have the same Dilbert cartoon up at their desks, about how Dilbert's company has two separate projects: both created to reduce redundancy.

And though categories are necessary and useful to sort through what would otherwise be chaos, we run into trouble when we start to forget that categories are arbitrary. They define what we want them to, not the other way round.

I think this reflects a really powerful understanding of the world, similar to the understanding that good scientists have that at best their "laws" are models that attempt to describe and predict the world we experience, but they are constructs of humanity.

And finally, here's a little passage that I sort of liked because it relates to how I want to make my educational technology project work. It's knit in to much with the anecdote to pull it out cleanly, and I don't like how it almost compares a basketball player to a working dog, but I think there's something to the idea about adjusting goals to maximize effort and persistence. It's related to Mihaly Csikszentmihalyi's "Creativity: Flow and the psychology of discovery and invention", which everybody in education loves to reference. This is how differentiation can work:

On some afternoons, a young star on our basketball team, a first-year student, would also be there working with Bob Bruzga and others to improve his jump by trying to snatch a small flag dangling above his head from a very long stick. As the student doggedly repeated the exercise over and over, a team of professionals analyzed his jump to make recommendations about his performance, but also recalibrated the height of the flag to his most recent successes or failures, putting it just out of reach one time, within the grasp of his fingertips the next, and then, as his back was turned, just a little too high to grasp. It is a method I've seen used to train competition-level working dogs, a marvelous psychological dance of reward and challenge, adjusted by the trainer to the trainee's desires, energy, success, or frustration, and all designed to enhance the trainee's ability to conceptualize achievement just beyond his grasp. It is also a time-honored method used by many great teachers. Set the bar too high and it is frustratingly counter-productive; set it too low and dulled expectations lead to underachievement. Dogged is the right word. That kid just would not give up. I would watch him and try again to inch my arm forward.

(Davidson was in rehab for an arm injury.)

This has gotten long, which is a testament to the richness and (possibly or) diversity of ideas in the book. I'll just add that of course Davidson is a big supporter of computer literacy, the internet, and so on, which makes it a little strange that it seems that her book is really not available online. And it's a book. I don't really see any place in Davidson's vision of the future where people read whole books. And it's not just Davidson caught in this apparent contradiction: the result of a Mozilla conference on using the web in education had as it's final product, that's right, you guessed it: a book. At least it's available as a PDF - but it blows my mind that it doesn't seem to also be available as linked HTML pages. Am I just missing it?

So there it is. Reflections on Now you see it. I will make no attempt to give the book a grade, number of stars, etc. :)

Tuesday, December 20, 2011

(link) on the non-availability of excellent prepared curricula

This post from a Washington Post (why do they have everything that resonates with me?) blog is about one particular Teach for America teacher who experienced the curricula vacuum, but I felt very much the same way when I was teaching in New York. "Hi teacher, it's your first year, make complete curricula from scratch for five classes," the system seems to say. I would love to see some better options.

New teacher decries lesson plan gap

Sunday, December 18, 2011

Thoughts on The Good School

I just finished reading The Good School by Peg Tyre. From the introduction, here's what the book sets out to do:

If you are interested in "looking under the hood," this book is for you. It will help bring you up to speed on some of the most crucial issues and controversies that are likely to affect your child's education. It will provide you with a SparkNotes version of the history of education to explain to you why things are the way they are. It will introduce you to the freshest thinking - and some of the most innovative ideas - about how to help our kids do better. But more than that, it will help you judge the value of these ideas by providing you with the most solid research available. In areas where research is not yet clear, you will meet people and hear about research that will be creating headlines - and perhaps school policy - in the years to come.

And it does it with some success. The audience is very clearly parents, and there is a good deal of pandering. Parents are the greatest! etc. And the beginning of the book is overfull of this kind of thing, including a chapter specifically for busy parents who couldn't possibly read a whole book, who just want to find a good preschool and go to sleep. So this chapter is sort of a drag, giving the recommendations without the evidence, and so on.

Chapter two on testing picks up a little bit, and there's a cogent explanation of the limitations and possible unintended consequences of standardized tests. The book might be worthwhile just for this explanation. Two interesting quotes. First, the "law" named after Donald T. Campbell:

"The more any quantitative social indicator is used for social decision-making, the more subject it will be to corruption pressures and the more apt it will be to distort and corrupt the social processes it is intended to monitore."

And some words from John Tanner, who runs Test Sense:

He draws a parallel between encouraging or even allowing teachers to teach to the test, and encouraging people to study for the eye test before they go to the DMV. "What would happen," Tanner says, "is that we'd have a lot of people passing the test but not have a clue whether they can actually see well enough to drive."

Chapter three on class size is interesting, because while acknowledging that everybody wants small class size and also that all the research seems to show smaller classes are better, if by small margins, Tyre tries to conclude that class size is not such a big deal in the domains that are usually in the field - and maybe she's right that 22 kids is not worlds better than 24, 34 not so much better than 36, and that teacher quality is more important, but I can't accept her apparent conclusion that smaller classes are not something to pursue. Never mind that nowhere is the fundamental issue of the reality of differentiation addressed: one teacher cannot do different things with different students at the same time. (Tyre does relate what I think may be an awfully common example of bad differentiation, which is simply giving a struggling, slower student less of the same stuff to do. Lowering expectations is better teaching?)

The book really picks up at chapter four, where Tyre has a strong case that there is consensus in the literature about how best to teach reading, and that too often this conclusion is ignored, to the detriment of students. To my amusement, there is a section headed "Teaching reading is rocket science," which echoes a section from a speech (given after the publication of the book) by Los Angeles superintendent John Deasy, "Teaching is rocket science". Everybody wants to talk about rocket science now. And the research-backed right way to teach reading is phonics, or as they say in the UK "systematic synthetic phonics" (because you synthesize or blend sounds together) which I happen to know because I read this section from the 2010 England Department for Education white paper "The importance of teaching", where they describe as one of their goals in the executive summary that they must:


Ensure that there is support available to every school for the teaching of systematic synthetic phonics, as the best method for teaching reading.


So it seems that people are coming around to this, but I remember even in my MAT program what I learned about how people teach reading was that there were a number of competing philosophies, and none of them necessarily had the upper hand. Phonics has the upper hand. It has the only hand. You must teach children to sound out words.

There's a chapter on math too, which I generally agree with. Tyre emphasizes the importance of carefully planned curriculum that helps students progress through conceptual understandings of carefully arranged mathematics. There's praise for Singapore math and, more indirectly, Common Core.

Tyre has support for recess. Great. Also she spends time talking about how some teachers are better than others. It's amazing that this needs to be said, but apparently it really does. The last chapter is the tale (true, she says) of how some parents got involved and helped make their local school better. Tyre supports parent involvement and system transparency, and I can only hope that things work out in general as well as they do in her story.

There are plenty of things to disagree with or be frustrated by in this book, including some little ones that are just annoying or unfortunate. Using "an octagonal" instead of just saying an octagon. Leaving the "l" out of "public". These are the most superficial. I am more concerned when I can't find a relevant endnote for a numeric claim. But the book is at its best when it goes all the way to a conclusion on a topic, provides real evidence for that conclusion, and invites the reader to engage it. Together with the outlines of educational history, I think it is a worthwhile book that can definitely help parents get started with a more informed and powerful involvement in education.