Thursday, May 31, 2012

Wrapping up Five Minds for the Future

Five minds for the future
by Howard Gardner (yes the multiple intelligences guy)

I started this book, stopped, wrote up some interesting selections in another post, then finished reading the book. It's an okay book. I think I initially got it because I had Gardner confused with someone I like more. But Gardner's not bad. I like a lot of the things he has to say in this book.

Here are selections that I comment on:

"Teachers ought to illustrate the several ways in which a particular math problem can properly be solved or a literary passage can be interpreted; ..."

Maybe this is an important difference between math and literature. In math, there can be many ways to solve a problem, but after a solution is reached it is either correct or incorrect. Of course there are cases where perhaps only one of several solutions is found, and then this all does get more complicated at advanced levels when we are concerned with proving theorems and, more to the point, first finding theorems to prove - but correctness is in some sense fundamentally verifiable. In literature, it seems the focus is often on multiple equally viable interpretations. Perhaps I am wrong here, but at the very least it does seem that the experience of reading and benefiting from literature varies much more and depends much more on uniquely personal interactions between reader and text in ways that are different from the experience and benefits of doing math.

"A truly respectful individual offers the benefit of the doubt to all human beings. As much as possible, she avoids thinking in group terms. She reserves censure for those who truly deserve it. She remains open to the possibility that her judgment may have been wrong. And she is on the alert for a change in behavior that will in turn reinstate a feeling of respect toward that other individual.

"In my view, respect should not entail a complete suspension of judgement. When a person consistently acts disrespectfully toward others, that person should be called to account. And should disrespect persist, and deteriorate into frankly antisocial behavior, that person should be ostracized from society. (On rare occasions, an entire group may forfeit its right to be respected.) Mahatma Gandhi kept reaching out to Hitler; the Indian leader wrote a letter to Hitler, addressed Dear friend,' calling on him to change his tactics and promising him forgiveness in return. In turn, Hitler remarked, 'Shoot Gandhi, and if that does not suffice to reduce them to submission, shoot a dozen leading members of Congress [Gandhi's political party].' When unconditional respect inadvertently encourages antihuman responses, it is counterproductive."

This is interesting for two reasons. First, I had never heard that story of Gandhi and Hitler, and it's an interesting story. Second, this is one of several places where Gardner recommends ostracizing some people. Maybe this is the only reasonable choice when faced with true sociopaths - but it is still troublesome, seemingly inconsistent with virtue, and certainly not an option open to, for example, a teacher in a classroom faced with a sociopath student.

"Particularly valuable evidence comes from studies of rescuers - inhabitants of Nazi-occupied Europe who, at considerable risk to themselves, elected to hid Jews or other hunted individuals. According to Samuel Oliner, rescuers appeared quite ordinary on the surface; they resembled many others who were bystanders and even some who actively aided the Gestapo. Closer study revealed telltale differences. Rescuers were marked by a childhood during which their parents avoided physical punishment, opting instead for lucid explanations of rules and practices. The rescuers stood out from their fellow citizens in the strong values - often but not invariably religious - that they absorbed from their parents; a constructive and optimistic stance that they assumed toward life; feelings of connectedness to others, even those from a different group; and above all, an intuitive (indeed instinctive) reaction that what was being done to the innocent was wrong and that they themselves were capable agents who ought to (indeed, who must) take corrective action.

This is really interesting. I think it speaks to the importance of ideas about the nature of the universe that are formed (and perhaps largely influenced by external environment rather than genetics) at an early age based on the family setting.

"In what kind of a world would we like to live if we knew neither our standing nor our resources in advance?"

I really liked this question, used in introducing ethics.

Here are selections that I like, without comment:

"Syntheses are put forth all the time - for example, most textbooks and many trade books (including this one!) are frank efforts to synthesize knowledge about a possibly unwieldy topic so that it can be assimilated by a target audience. Determining what constitutes an adequate synthesis is not possible; as with the proverbial question "Does a string stretch across a room?" the answer must be contextualized. It turns out that arriving at an adequate synthesis is challenging, and anticipating the criteria for a judgement even more so."

"Individuals differ significantly in their predisposition to metaphorize, and in their capacity or inclination to transfer lessons from one class or discipline to another. Aristotle deemed the capacity to create apt metaphors as a sign of genius."

"Secondary-school students cannot be expected to be scientific or historical disciplinarians."

"Until recently, creativity has been seen by psychologists as a trait of certain individuals; as such it should be measurable through paper-and-pencil tests; and an individual deemed "creative" should be able to evince that trait across various performance domains. In the prototypical item on a creativity test, subjects are asked to think of as many uses as possible for a paper clip, or to give an imaginative title to a squiggle, or to choose the target that can be associated with two supplied words (mouse-cottage: both can be linked to cheese). The final tally received on such a measure is believed to reflect creative potential in any domain of knowledge."

"A wit said of Camille Saint-Saƫns, an aging musical prodigy who never fully realized his early promise: 'He has everything but he lacks inexperience.'

"The creator stands out in terms of temperament, personality, and stance. She is perennially dissatisfied with current work, current standards, current questions, current answers. She strikes out in unfamiliar directions and enjoys - or at least accepts - being different from the pack. When an anomaly arises (an unfamiliar musical chord, an unexpected experimental result, a spike or dip in the sale of goods in an unfamiliar territory), she does not shrink from that unexpected wrinkle: indeed, she wants to understand it and to determine whether it constitutes a trivial error, an unrepeatable fluke, or an important but hitherto unknown truth. She is tough skinned and robust. There is a reason why so many famous creators hated or dropped out of school - they did not like marching to someone else's tune (and, in turn, the authorities disliked their idiosyncratic marching patterns).

"All of us fail, and - because they are bold and ambitious - creators fail the most frequently and, often, the most dramatically. Only a person who is willing to pick herself up and 'try and try again' is likely to forge creative achievements. And even when an achievement has been endorsed by the field, the prototypical creator rarely rests on her laurels; instead, she proceeds along a new, untested path, fully ready to risk failure time and again in return for the opportunity to make another, different mark. Creative activity harbors more than its share of heartaches; but the "flow" that accompanies a fresh insight, a break-through work, or a genuine invention can be addictive."

"Executives realize at a deep level that creativity is a chancy undertaking that can never be guaranteed- only fostered or thwarted."

"Undisciplined creativity is creativity undermined."

"Turning to specific disciplines, I do not believe that science and mathematics ought to be inflected as a means of honoring group differences. As universal languages, these ought to be construed and taught similarly around the globe."

"In the long run, rule by fist, fiat, fear, and fury is destined to fail."

"'A person who is determined to do something constructive with his life needs to come to terms with the fact that not everyone is going to love him." (Barenboim)

"They asked, in effect, what kinds of citizens do we want to produce?"

"Perhaps, indeed, there are no truly universal ethics: or to put it more precisely, the ways in which ethical principles are interpreted will inevitably differ across cultures and eras. Yet, these differences arise chiefly at the margins. All known societies embrace the virtues of truthfulness, integrity, loyalty, fairness; none explicitly endorses falsehood, dishonesty, disloyalty, gross inequity."

"An education centered on good work

"Until the third decade of life, young persons spend more time in school than in any other institution. They are in the presence of teachers more than in the company of parents; they are surrounded by schoolmates more than by siblings or children in the neighborhood. Formal educational institutions play a key role in determining whether an individual is proceeding on the road to good work and active citizenship."

(endnote) "Benjamin Bloom, Taxonomy of Educational Objectives (New York: Long-mans, Green, and Co., 1956)."

"(An aside on literacy: the first cognitive assignment for all schools is mastery of the basic literacies of reading, writing, and calculation. Because this point is an has long been uncontroversial, I need not elaborate on it here.)"

"In any event, creativity goes hand in glove with disciplinary thinking. In the absence of relevant disciplines, it is not possible to be genuinely creative."

Sunday, May 27, 2012

Indirect arithmetic for more engaging practice

This article is interesting in and of itself, on the psychology and reality of cheating, but I also very much like the task they had people do in some of the experiments.

In this grid, find the two numbers that add to ten.

Problems like this are very different from typical arithmetic exercises like "what is 5.82 + 6.36?" For one thing, it is a bit more of a puzzle rather than a question, which makes it seem more fun to me. For another, it rewards highly skills like estimation and working logically to break down the problem. In this example, you might first see that the 1.69 and 1.82 can't possibly be involved, since there is no other number greater than 8. Then one might start looking for reasonable pairs with final digits that add to ten, and so on. Compared to a more traditional approach of the form "estimate 5.82 + 6.36" which seems pointless because it lacks a context that makes the estimating appropriate, problems of this grid type provide a real context, even if only in the context of the game.

I have seen similar examples, such as the card games I played with middle school students in an after school math program, in which students are never asked to do arithmetic for its own sake, but are asked to play games that require doing arithmetic for success. It makes for much more engaging practice.

Wednesday, May 23, 2012

Lectures vs. Videos

Can a video replace a lecture? I'm not sure.

I go to lectures I would never watch a video of because a lecture can be an enjoyable experience. It's an event. You go, you sit, you meet people, you experience the whole thing with no scrubbing through to find a more interesting bit. It may be more memorable because of this immersion in a novel environment, because it can encourage more engagement.

I think research could shed light on whether video can be as effective as a non-interactive lecture. Test students after a non-interactive live lecture that is recorded. Have other students watch the recording and test them. There may be some positive effect of being live. Maybe some research like this has been done - I'd like to see it.

Lectures also happen to me spontaneously when someone figures out that I would benefit from hearing something at a particular moment. Teachers are often good at figuring out what you need to hear.

I think there is some room for computer adaptive systems to get better at figuring out what you need to hear and when. I don't know that they'll be as good as a good teacher any time soon, but they may be better than a bad teacher rather quickly.

Tuesday, May 22, 2012

Quotes from Rework

by Jason Fried and David Heinemeier Hansson

This book is largely the same as Getting Real, which you can read for free online. Both are pretty good, and pretty quotable. Here are some quotes I like, from Rework:

"Instead of describing what something looks like, draw it. Instead of explaining what something sounds like, hum it. Do everything you can to remove layers of abstraction.

"The problem with abstractions (like reports and documents) is that they create illusions of agreement. A hundred people can read the same words, but in their heads, they're imagining a hundred different things."

"Maybe it's because of the copy-and-paste world we live in these days. You can steal someone's words, images, or code instantly. And that means it's tempting to try to build a business by being a copycat.

"That's a formula for failure, though. The problem with this sort of copying is it skips understanding - and understanding is how you grow. You have to understand why something works or why something is the way it is. When you just copy and paste, you miss that. You just repurpose the last layer instead of understanding all the layers underneath.

"So much of the work an original creator puts into something is invisible. It's buried beneath the surface."

"Businesses are usually paranoid and secretive. They think they have proprietary this and competitive advantage that. Maybe a rare few do, but most don't. And those that don't should stop acting like those that do. Don't be afraid of sharing."

"There are plenty of companies out there who have educational requirements. They'll only hire people with a college degree (sometimes in a specific field) or an advanced degree or a certain GPA or certification of some sort or some other requirement.

"Come on. There are plenty of intelligent people who don't excel in the classroom. Don't fall into the trap of thinking you need someone from one of the "best" schools in order to get results. Ninety percent of CEOs currently heading the top five hundred American companies did not receive undergraduate degrees from Ivy League colleges. In fact, more received their undergraduate degrees from the University of Wisconsin than from Harvard (the most heavily represented Ivy school, with nine CEOs).

"Too much time in academia can actually do you harm. Take writing, for example. When you get out of school, you have to unlearn so much of the way they teach you to write there. Some of the misguided lessons you learn in academia:

  • "The longer a document is, the more it matters.
  • "Stiff, formal tone is better than being conversational.
  • "Using big words is impressive.
  • "You need to write a certain number of words or pages to make a point.
  • "The format matters as much (or more) than the content of what you write.

"It's no wonder so much business writing winds up dry, wordy, and dripping with nonsense. People are just continuing continuing the bad habits they picked up in school. It's not just academic writing, either. There are a lot of skills that are useful in academia that aren't worth much outside of it.

"Bottom line: The pool of great candidates is far bigger than just the people who completed college with a stellar GPA. Consider dropouts, people who had low GPAs, community-college students, and even those who just went to high school."

"If you are trying to decide among a few people to fill a position, hire the best writer. It doesn't matter if that person is a marketer, salesperson, designer, programmer, or whatever; their writing skills will pay off.

"That's because being a good writer is about more than writing. Clear writing is a sign of clear thinking. Great writers know how to communicate. They make things easy to understand. They can put themselves in someone else's shoes. They know what to omit. And those are qualities you want in any candidate.

"You can't hide anymore. These days, someone else will call you on it if you don't do it yourself. They'll post about it online and everyone will know. There are no more secrets."

"Instant cultures are artificial cultures. They're big bangs made of mission statements, declarations, and rules. They are obvious, ugly, and plastic. Artificial culture is paint. Real culture is patina.

"You don't create a culture. It happens. This is why new companies don't have a culture. Culture is the byproduct of consistent behavior. If you encourage people to share, then sharing will be built into your culture. If you reward trust, then trust will be built in. If you treat customers right, then treating customers right becomes your culture.

Culture isn't a foosball table or trust falls. It isn't policy. It isn't the Christmas party or the company picnic. Those are objects and events, not culture. And it's not a slogan, either. Culture is action, not words."

"A lot of companies post help-wanted ads seeking "rock stars" or "ninjas." Lame. Unless your workplace is filled with groupies and throwing stars, these words have nothing to do with your business.

"Instead of thinking about how you can land a roomful of rock stars, think about the room instead. We're all capable of bad, average, and great work. The environment has a lot more to do with great work than most people realize.

"That's not to say we're all created equal and you'll unlock star power in anyone with a rock star environment. But there's a ton of untapped potential trapped under lame policies, poor direction, and stifling bureaucracies. Cut the crap and you'll find that people are waiting to do great work. They just need to be given the chance.

"This isn't about casual Fridays or bring-your-dog-to-work day. (If those are such good things, they why aren't you doing them every day of the week?)

"Rockstar environments develop out of trust, autonomy, and responsibility. They're a result of giving people the privacy, workspace, and tools they deserve. Great environments show respect for the people who do the work and how they do it."

"Write to be read, don't write just to write. Whenever you write something, read it out loud. Does it sound the way it would if you were actually talking to someone? If not, how can you make it more conversational?"

Sunday, May 20, 2012

Bits from the beginning of Five Minds for the Future

Five minds for the future
Howard Gardner

This guy keeps going with his multiple intelligences thing. I haven't finished the book, but here are some selections I wanted to remember:

"In the long run, it is not possible for parts of the world to thrive while others remain desperately poor and deeply frustrated."

"In a world where we are all interlinked, intolerance or disrespect is no longer a viable option."

"'Education is inherently and inevitably an issue of human goals and human values.' I wish that this statement were mounted prominently above the desk of every policymaker. One cannot even begin to develop an educational system unless one has in mind the knowledge and skills that one values, and the kind of individuals one hopes will emerge at the end of the day. Strangely enough, however, many policymakers act as if the aims of education are self-evident; and as a consequence, when pressed, these policymakers often emerge as inarticulate, contradictory, or unbelievably prosaic. How often my eyes have glazed over as I have read vacuous proclamations about 'using the mind well' or 'closing the achievement gap' or 'helping individuals realize their potential' or 'appreciating our cultural heritage' or 'having the skills to compete.' Recently, in speaking to ministers of education, I've discovered a particularly Sisyphean goal: 'leading the world in international comparisons of test scores.' Obviously, on this criterion, only one country at a time can succeed. To state educational goals in this day and age is no easy undertaking; indeed, one purpose of this book is to posit several more gritty goals for the future.

"A first caveat: science can never constitute a sufficient education. Science can never tell you what to do in class or at work. Why? What you do as a teacher or manager has to be determined by your own value system - and neither science nor technology has a builtin value system. Consider the following example. Let's say that you accept the scientific claim that it is difficult to raise psychometric intelligence (IQ). From this claim one can draw two diametrically opposite conclusions: (1) don't bother to try; (2) devote all your efforts to trying. Possibly you will succeed, and perhaps far more easily than you had anticipated. Same scientific finding: opposite pedagogical conclusions."

"To the extent that personal service or personal touch continue to be valued, these disciplines will provide a good livelihood for those who have mastered them. But my focus here falls chiefly on the scholarly disciplines that one should acquire by the end of adolescence, and the one or more professional disciplines needed to be a productive worker in society."

"Most important, set up 'performances of understanding' and give students ample opportunities to perform their understandings under a variety of conditions. We customarily think of understanding as something that occurs within the mind or brain - and of course, in a literal sense, it does. Yet neither the student nor the teacher, neither the apprentice nor the master, can ascertain whether the understanding is genuine, let alone robust, unless the student is able to mobilize that putative understanding publicly to illuminate some hitherto unfamiliar example. Both teacher and students ought to strive to perform their current understandings; much of training should consist of formative exercises, with detailed feedback on where the performance is adequate, where it falls short, why it falls short, what can be done to fine-tune the performance.

"Why talk about performances of understanding? So long as we examine individuals only on problems to which they have already been exposed, we simply cannot ascertain whether they have truly understood. They might have understood, but it is just as likely that they are simply relying on a good memory. The only reliable way to determine whether understanding has truly been achieved is to pose a new question or puzzle - one on which individuals could not have been coached - and to see how they fare."

"When critics deride business schools as being too academic, they usually mean that the ultimate uses of the purveyed knowledge are not evident; students are not forced to flex their text or lecture- or discussion-obtained knowledge. Here, in brief, is why most standardized measures of learning are of little use; they do not reveal whether the student can actually make use of the classroom material - the subject matter - once she steps outside the door. And here is why traditional training in the crafts requires a culminating masterpiece before the journeyman can rise to the level of master."

"As Plato remarked so many years ago, 'Through education we need to help students find pleasure in what they have to learn.'"

Friday, May 18, 2012

Quotes from Frederick W. Kantor

One of the most interesting things to come out of teaching a New York Academy of Sciences after-school math program at Ronald Edmonds middle school in Brooklyn was quite entirely unexpected.

As I was introduced to people on the first day of the program, some pride was shown by the administrator when she indicated a heavily bearded, wizened old man sitting next to a girl having trouble with fractions or some such thing. Doctor Kantor, she said, who had all those things published in the journals.


The very same Dr. Frederick W. Kantor of Columbia University, famous in some circles for originating the field of Information Mechanics. (The wiki page is now called Digital Physics; I don't think Dr. Kantor would approve.) The astonishingly low chance of running into an innovative physicist at a New York City public middle school, and then one whose work I find so interesting, was enough to make me think the universe was having a laugh with me.

I don't always follow everything Dr. Kantor says, but just yesterday after the last of this after-school program's sessions we chatted for a bit and it was really quite enjoyable. Here are two quotes, the second of which is him quoting Chien-Shiung Wu:

"A theory that tries to explain its assumptions is a tautology."
- Fred Kantor

"They forget that mass is an assumption."
Madame Wu to Fred Kantor

Dr. Kantor also spoke of some newer work of his, especially that relating information mechanics and the foundations of mathematics, which I really hope he publishes soon. I'm no expert, but I think information mechanics is a candidate for being a Really Good Idea that people have been neglecting.

Thursday, May 17, 2012

Brief thoughts on Simulacron-3

Daniel F. Galouye

I finally FINALLY got a chance to read Simulacron-3 after my request went through. It only took a few years!

This book is the basis for, among other things, the movie The Thirteenth Floor. It's arguably also the inspiration for The Matrix and a lot of related thinking. I'd be curious to know if there are proper antecedents to Simulacron-3, beyond abstract philosophers.

It's interesting reading a book from 1964. The basic idea of simulating a whole world is pretty interesting and modern-feeling, but the gender roles are archaic and computers are basically imagined as bigger versions of that era's, with physical components that you change like a lightbulb and programming basically by wire. And of course there are moving sidewalks everywhere, because that's what we do in the future.

Two quotes to pull out:

"You can hardly stuff people into a machine without starting to wonder about the basic nature of both machines and people." (p. 24, and repeated again later)

"For self-awareness is the only true measure of existence!" (p. 140)

Interesting that the characters care so little for the people in the simulation within a simulation, when they're so concerned about the people in the first simulation... But I am glad I finally encountered this book in person.

Monday, May 7, 2012

Reinvent standardized tests for openness

Identical tests kept secret until administration should be replaced by large open banks of test questions an appropriate sampling of which are faced by individual test takers. The only secrecy that should remain is in the particular combination of questions that the individual test taker faces when taking the exam.

It is always possible for test content secrecy to be compromised. There seem to be such problems now in California. It is claimed that breaches in security "could lead to invalidating test scores for entire schools or prevent the state from using certain tests." A system in which this can happen is not a robust system, and it is always possible for this to happen in a system that relies on test content secrecy. Perfect test content secrecy is not possible.

Limiting access to test materials before administering exams, especially when this means limiting it to companies motivated to produce tests at the lowest possible expense, does not effectively prevent  problems with the exams. And since there is only one version of the exams, problems affect every test taker. This has been the case with English and math tests recently in New York.

A far better solution to testing is to curate large banks of questions accessible to the public at large. This would allow many eyes to identify problems with questions, and give every student a fair chance to prepare for the kinds of questions that will appear on their exam.

The number of questions should be large enough that the probability of a test taker encountering a previously viewed question is fairly small. A test taker, especially one who prepares voraciously, may recognize a question during an examination, but this can also happen with secret content tests, and in any event it is the result of the test taker's learning.

If the banks of questions are sufficiently large and rich, this method may ameliorate the problems of "teaching to the test". It should become clearly more efficient to learn general principles and problem-solving skills, rather than simply reciting every existing question. Of course some practice with questions from the banks for practice is not necessarily bad, but by itself such an approach is unlikely to yield optimal results.

Since taking the test does not yield any new information about the test anyone else will face, it becomes possible for test takers to take and retake exams at any time with no new costs in exam development. This eliminates problems of exam-day sickness and the like.

Appropriate scoring of exams may be more difficult since test takers do not face the same questions. An intelligent and open system of evaluating question difficulty should be developed and marking should be aligned with the purpose of the exam. It may not be that the goal of the exam is to perfectly rank every test taker, and it may be easier to determine if a test taker has demonstrated competency and is ready to move on.

The modern world is advancing where transparency increases, and so should it be with testing.