eric the fruitbat » Mind/Cognition

Don’t Fear the Mistakes

erich — Wed, 01 Feb 2012 05:13:00 +0000

During teaching, there is a fascinating (and unfortunately common) problem: Students are VERY reluctant to suggest an answer, for fear that they might be wrong.

Salman Kahn, noticed this phenomenon after he started doing videos for his niece and nephew: (I’m paraphrasing) “The last thing they needed was for me to be there expecting an answer.”

Teachers at the university level are fighting a behavioral lesson that we pick up in elementary school. Although young students often have the bravery (or lack of self-awareness) that allows them to speak up in class, it’s consistently beaten out of them: There’s nothing more degrading than being laughed at by the rest of the class. The other children are so insecure themselves, that they’ll take every opportunity to pick themselves up by mocking others.

Also, even for the talented students, if they are praised about their intelligence they will end up taking fewer risks: and try fervently to be wrong less. This lesson comes from Carol Dweck’s work: Praise for Intelligence Can Undermine Children’s Motivation and Performance. [Why do some people learn faster?]

Naturally, almost everyone will leave the early public education system less excited than when they entered. University and College teachers then have the problem of rekindling the excitement and interest we were all born with. But to accomplish this, we must find ways of fighting the earlier training: we must encourage participation and the mistakes that come with exploring.

John Holt has a book, “How Children Fail”, which contains the following conclusions:

Schools promote an atmosphere of fear.
Boredom serves as another major obstacle.
‘Cookie-cutter’ education does not cultivate intrinsic interests and learning.
Mixed Signals: Parents praise curiosity and questions, school does not.
There is no single body of information that all children should learn.

So, what can be done?

Exercise Choice Theory. Recognize that you can cultivate a positive attitude, and change your response.
Fail more often, and get used to how it feels. Routinely try to go beyond your comfort zone.
Push yourself. Don’t stop at the first obstacle. Try a different approach. Don’t avoid things you dislike.
Debrief your experience. If you don’t succeed, spend time to figure out why not. Brainstorm, and loop back with any new approaches.
Also, Aligna Tugend’s book “Better By Mistake: The Unexpected Benefits of Being Wrong” contains still more lessons.

That works for oneself, but what about the students?

If they are afraid of giving the ‘wrong’ answer to a question, change the question to “tell me something that doesn’t work.”

Expert Tutors

erich — Sat, 07 Jan 2012 08:05:59 +0000

Carl Wieman (who won a Nobel for deepening our understanding of Bose-Einstein condensation) lays out some of the important findings and methodology in his talk “Science Education in the 21st Century: Using the Tools of Science to Teach Science“. In that talk he outlines some of the important responsibilies of expert tutors:

Focus on the student’s motivation. They try to provide context for the material, and pique the natural curiosity of each student. This requires understanding the student’s background knowledge, and relating material to that knowledge.
Don’t praise the person, praise the work, effort, and process. By focusing attention away from the person, we learn that effort pays off, that systematic reasoning can lead to reliable answers. We also avoid instilling a false confidence in the learner, so that they will continue to chose challenging exercises, rather than freeze up when something becomes difficult.
Provide feedback appropriate to the knowledge level of the learner in a timely manner. This takes an understanding of what students do and do not know, what amount of jargon they can handle, and what style of learning is most appropriate. By providing the feedback quickly, you can do more iterations of learning and questioning in less time.
Almost never tell the student anything. Instead, lead them through a Socratic dialog, in which the student is actively explaining, figuring, and processing the material. Especially, Don’t throw in items of knowledge that are only tangentially related with the purpose of appearing smarter than the learner.
Ask challenging questions within the student’s ability to answer.
Allow the student to make mistakes. Don’t correct early answers, instead allow the dialog to arrive at a question where the student figures out an earlier step is faulty. The student should discover their own mistake as a part of the explanatory process to later questions.
Force the student to reflect: how they learned, the process, the result, how it generalizes. Let them build and understanding by relating the new knowledge in a larger context. Let them see that progress has been made. Reinforce the success with self-reflection.
Probe for the students knowledge and state. Most incorrect answers are due to an incorrect conceptual model of the problem. The tutor has to find the fault, and lead the student to uncover through their own effort by a sequence of questions.
Force students to work their brain. Don’t let the off the hook with one question correctly answered. Continue the challenge, reinforce the knowledge. Explore the ways in which in applies.

The idea is to guide the novice into expert-like thinking patterns.

In addition, Wieman says that experts have the ability to “monitor their own thinking” in their area of expertise. They have the ability to ask themselves, “Do I really understand this, is this a sensible way to be solving this problem, how can I check my understanding?”
“Experts can do that. Novices can’t,” says Wieman.
…
In the end, there really is no such thing as teaching. There is just learning. Teachers can help you learn by pushing you and prodding you and guiding you along the way. But they can’t hand you knowledge, the way a traditional lecture is designed to do.

Novice	Expert
Content is made of isolated pieces of information to be memorized.	Content is a coherent structure of interrelated concepts.
Knowledge is handed down by an authority and has little to do with real life.	Knowledge describes nature and is established by experiment.
Problem solving is pattern matching memorized recipes to given problem.	Problem solving is using systematic, concept-based strategies that have wide applicability.

Further References:
NAS Press “How People Learn“
Redish, “Teaching Physics” (Phys. Ed. Res.)
Handelsman, et al. “Scientific Teaching”
Wieman, (this talk) Change Magazine – Oct. 07

Using Science to Teach Science

erich — Sat, 07 Jan 2012 07:02:19 +0000

I’ve recently absorbed American RadioWorks feature on “Tomorrow’s College“. Especially interesting was the program “Don’t Lecture Me, where the story of some physicists gathered data about the learning and understand of their students, only to discover that the traditional lecture model of a knowledgeable expert disseminating information to a passive audience is ineffective.

Research conducted over the past few decades shows it’s impossible for students to take in and process all the information presented during a typical lecture, and yet this is one of the primary ways college students are taught, particularly in introductory courses.
…
[Joe] Redish [,a professor of physics at the University of Maryland,] wanted to reach the students who weren’t teaching themselves. So he began trying to better understand how people learn.

There is a Problem with Lecturing:

Even though, Eric Mazur, a Harvard physicist, made his lectures fun and full of attention grabbing demos which regularly recieved great evaluations from students, they still didn’t improve on a conceptual test of physics principles.

David Hestenes, a physics professor at Arizona State, wrote a series of articles developed a conceptual test of physics, and observes: “Students have to be active in developing their knowledge, They can’t passively assimilate it. If you look at what’s happening in the introductory classes, even at the best schools, the classes only seem to be really working for about 10 percent of the students, and I think all the evidence indicates that these 10 percent are the 10 percent of students that would learn it even without the instructor. They essentially learn it on their own.”

There’s even a few techniques which can be used. Eric Mazur, likes to quiz the students with conceptual questions (using clickers to get audience answers on the board) and then lets them discuss it among themselves: a process called peer instruction. During discussion, any student who has the right answer, is more likely to convince others, than vice versa. Not only that, but that student is also more likely to convince other students than the professor, because she can relate more closely to the conceptual difficulties (having only just learned the concept) than the professor, who has so internalized the idea that he cannot understand the conceptual challenges.

That’s the irony of becoming an expert in your field, Mazur says. “It becomes not easier to teach, it becomes harder to teach because you’re unaware of the conceptual difficulties of a beginning learner.
…

To make sure his students are prepared, Mazur has set up a web-based monitoring system where everyone has to submit answers to questions about the reading prior to coming to class. The last question asks students to tell Mazur what confused them. He uses their answers to prepare a set of multiple-choice questions he uses during class.

Mazur begins class by giving a brief explanation of a concept he wants students to understand. Then he asks one of the multiple-choice questions. Students get a minute to think about the question on their own and then answer it using a mobile device that sends their answers to Mazur’s laptop.

Next, he asks the students to turn to the person sitting next to them and talk about the question. The class typically erupts in a cacophony of voices, as it did that first time he told students to talk to each other because he couldn’t figure out what else to do.

Once the students have discussed the question for a few minutes, Mazur instructs them to answer the question again.

The uptake has been slow among college’s: “Your research matters,” Redish says. “Your teaching you can get by with.” This occurs for two reasons: 1. The risk of being denied tenure, because “good teaching comes by neglecting research”. 2. Professors are not given any formal assistance to prepare classes, nor is there a requirement on teaching ability; So most mimic the system they grew up with, and become traditional lecturers.

“It’s kind of ironic that we as professors don’t have any type of training in any way, shape or form,” says Andy Petzold. “It’s the only teaching degree that you don’t need to go through any actual training in teaching to do.”

The University of Minnesota Rochester has taken these ideas to radical new lengths. No lecture halls, no frats, not library (everything is online), campus is actually the top two floors of a mall, all classroom furniture has wheels.

To see this philosophy in action, I visit a biology class. It starts with an assignment. The students have to write a multiple choice question based on the material they’ve been learning.

“You know you understand something when you can teach somebody else,” says the professor, Kesley Metzger. “So if a student can’t write a question, then it gives them an idea that they don’t fully understand the material.”

It’s not that they’re expected to understand everything they’ve read, [says Metzger], “but we expect them to have looked over the material so that when they come to class we can use that time not just to introduce the terminology but to actually engage at a deeper level so that they can explore what those things mean [and] they can think critically about ideas.”

The fact that people learn better when they’re actively engaged is one of the central findings of cognitive research conducted over the past few decades. Another finding, one that may seem obvious, is that people learn when they’re motivated to learn.
…
[Lehmkuhle, Chancellor at UMR,] thinks colleges need to start thinking about education not as the pursuit of knowledge in distinct disciplines, but as the acquisition of skills necessary to succeed in a world where knowledge is constantly changing. “You really have to teach them how to learn.”

eXtreme Education: Cognitive programming

erich — Mon, 17 Oct 2011 10:26:02 +0000

I read a few articles that I’d like to pull together and place under the growing umbrella of what might probably become my personal teaching philosophy. First, when you look at eXtreme Programming, it consists of a collection of reinforcing practices. I’m not going to review them here because I just want to highlight the interconnectedness of the method (image taken from the book, Extreme Programming Explained: Embrace Change, by Kent Beck).

With that visual in mind, I want to project the idea of self-reinforcement and process improvement into education. Education is about personal growth, and continuous learning. It’s about having a supportive environment in which you can safely experiment, without fear of reprisal or long-term consequence. You need the opportunity to fail, so that you can analyze what doesn’t work.

But, for too long in America, we have been afraid to let our kids taste the bitterness of failure. As a consequence, they are mediocre in ability, but feel confident. This confidence is artificial, and cannot survive the harsh realities of the working environment that lies beyond the sandbox of public school. Yet, in a worthwhile education, it’s not failure that’s a problem! It’s the approach and mindset, that you use to reflect on the experience.

In three articles, Why Do Some People Learn Faster[1], How Not to Talk to Your Kids[2], and What if the Secret to Success Is Failure?[3] I read this weekend, I learned a couple of valuable lessons that can definitely improve the effectiveness of a teacher.

Lesson 1. Praise work, and don’t hint at natural ability.

There’s a long standing myth that top performers in a field are naturally gifted. When in reality, they are more obsessed, more focused in their practice and training, and just plain out-work everyone else. We should communicate this sentiment to our inheritors.

[psychologist Carol Dweck] Randomly divided [New York 5th graders] into groups, some were praised for their intelligence. They were told, “You must be smart at this.” Other students were praised for their effort: “You must have worked really hard.”

Then the students were given a choice of test for the second round. One choice was a test that would be more difficult than the first, but the researchers told the kids that they’d learn a lot from attempting the puzzles. The other choice, Dweck’s team explained, was an easy test, just like the first. Of those praised for their effort, 90 percent chose the harder set of puzzles. Of those praised for their intelligence, a majority chose the easy test. The “smart” kids took the cop-out.

Why did this happen? “When we praise children for their intelligence,” Dweck wrote in her study summary, “we tell them that this is the name of the game: Look smart, don’t risk making mistakes.” And that’s what the fifth-graders had done: They’d chosen to look smart and avoid the risk of being embarrassed.[1]

By praising work, the students will choose the opportunity to fail! because those are opportunities for learning.

Lesson 2. By failing in the right frame of mind, they will learn faster.

Dweck distinguishes between people with a fixed mindset — they tend to agree with statements such as “You have a certain amount of intelligence and cannot do much to change it” — and those with a growth mindset, who believe that we can get better at almost anything, provided we invest the necessary time and energy. While people with a fixed mindset see mistakes as a dismal failure — a sign that we aren’t talented enough for the task in question — those with a growth mindset see mistakes as an essential precursor of knowledge, the engine of education.

It turned out that those subjects with a growth mindset were significantly better at learning from their mistakes. As a result, they showed a spike in accuracy immediately following an error. Most interesting, though, was the EEG data, which demonstrated that those with a growth mindset generated a much larger Pe signal, indicating increased attention to their mistakes. (While those with an extremely fixed mindset generated a Pe amplitude around five, those with a growth mindset were closer to fifteen.) What’s more, this increased Pe signal was nicely correlated with improvement after error, implying that the extra awareness was paying dividends in performance. Because the subjects were thinking about what they got wrong, they learned how to get it right.[2]

Lesson 3. It’s up to the schools to provide an environment that encourages the productive frame of mind.

The final article, [3], was about the KIPP program, and the institution of a status card, about a child’s developing character.

[Duckworth] and her team of researchers gave middle-school students at Riverdale and KIPP a variety of psychological and I.Q. tests. They found that at both schools, I.Q. was the better predictor of scores on statewide achievement tests, but measures of self-control were more reliable indicators of report-card grades.[3]

By encouraging students to regularly reflect on their own behavior, analyze and explain what the feel and why they acted the way they did, progress is made rapidly and steadily. And, often, the learner doesn’t know.

Though the seven character strengths aren’t included in every lesson at KIPP, they do make it into most conversations about discipline. One day last winter, I was speaking with Sayuri Stabrowski, a 30-year-old seventh-and-eighth-grade reading teacher at KIPP Infinity, and she mentioned that she caught a girl chewing gum in her class earlier that day. “She denied it,” Stabrowski told me. “She said, ‘No, I’m not, I’m chewing my tongue.’ ” Stabrowski rolled her eyes as she told me the story. “I said, ‘O.K. fine.’ Then later in the class, I saw her chewing again, and I said: ‘You’re chewing gum! I see you.’ She said, ‘No, I’m not, see?’ and she moved the gum over in her mouth in this really obvious way, and we all saw what she was doing. Now, a couple of years ago, I probably would have blown my top and screamed. But this time, I was able to say: ‘Gosh, not only were you chewing gum, which is kind of minor, but you lied to me twice. That’s a real disappointment. What does that say about your character?’ And she was just devastated.”

Stabrowski was worried that the girl, who often struggled with her behavior, might have a mini-meltdown — a “baby attack,” in KIPP jargon — in the middle of the class, but in fact, the girl spit out her gum and sat through the rest of the class and then afterward came up to her teacher with tears in her eyes. “We had a long conversation,” Stabrowski told me. “She said: ‘I’m trying so hard to just grow up. But nothing ever changes!’ And I said: ‘Do you know what does change? You didn’t have a baby attack in front of the other kids, and two weeks ago, you would have.’ ”[3]

This steady focus on character building, isn’t just a metaphor that used to rate each other’s conduct, it’s a valuable and prolonged exercise in cognitive behavioral therapy. Practicing the self-reflection leads to better performance. Because the learner can build the mental models that them (a) know when they aren’t achieving what they want, (b) feel confident that they can exercise some amount of self control and direction, and (c) monitor their own effectiveness to (d) experiment with different approaches.

How does this relate to eXtreme Programming again?

Fundamentally, this process of self-monitoring underpins the eXtreme Programming methodology. Programming isn’t about writing clean, correct code the first time. Likewise, education isn’t about memorizing facts and computing answers. At it’s core, education is about communicating self-directed development.

We should focus on learning the tools and techniques to discover approaches that work by analyzing the faults in attempts that didn’t work. We should practice this in everyday life as well as on our homework. Repeatedly applying those tools until they really sink in, and we all become better, more flexible, more understanding, more capable people.

Minds from Agents

erich — Mon, 27 Sep 2010 18:15:27 +0000

Recently, I came across this SEED article, Divide Midns, Specious Souls; which has this deliciously anti-religious, pro-science quote:

Within the wide range of works arranged along the axis of soulism, from Life After Death: The Evidence, by Dinesh D’Souza, to Absence of Mind, by Marilynne Robinson, it is clear there is very little understanding of the brain. In fact, to advance their ideas, these authors have to be almost completely unaware of neurology and neuroscience.

I don’t know nearly as much cognitive science as I should, mostly because the school system completely avoids the edifying motto “Know Thyself”. What I have learned has been purely motivated by my own curiosity and experience. To that end I’d like to elucidate why I think this article’s above quote is spot-on.

One of my friends has been diagnosed with Schizophrenia. Which is, despite it’s outward manifestations, is a brain disorder, not a psychological one. I strongly suspect that the disorder arises from a breakdown of one (or more) of the mental agents responsible for maintaining the illusion of a unified mind.

I conjecture that a normally functioning brain is still composed of many different opinions, desires, wishes and goals, all in a trade-off war for satisfaction. If the agent responsible for weighing these differences breaks down, then the illusion of a unified mind can also break down. This is exactly the behavior that you’d expect if the brain were the hardware that runs a ‘Society of Mind‘.

For those that are willing to look, there is a mountain of evidence from behavioral psychology and cognitive science that supports the view that I have from studying computer science: The brain is hardware that runs the software of the mind. The mind (what some wish to promote to a soul) simply doesn’t survive damage to the hardware of the brain. And if you think otherwise, you are deluding yourself. You are, in fact, a self-referencing software loop.

Building Linguistic Structure

erich — Thu, 04 Jun 2009 07:54:10 +0000

Yesterday, I had an interesting thought. My advisor once made the cultural observation that many people in Computer Science invent their own language and then immediately write a self-hosting compiler. I agree that a compiler is quite a feat of engineering and serves as a nice test case to demonstrate that the language you’ve invented is powerful enough that it can handle real-world complexity. Unfortunately, this test fails in a few important ways.

First, It doesn’t actually show as much as you think it might. There is a very strong filter on failed languages. By using this test the author runs the risk of re-designing the language, specifically to insert constructs that help them build the compiler. Now, this isn’t necessarily a bad thing, except that compiler writing is now a fairly mature field. There are standard abstractions (esp. in the lexing and parsing) that a new language will probably not experiment with. So, the author will usually just build these existing and well-understood abstractions into the new language. Rather than encouraging language experimentation we get more of the same, but with different syntax.

Second, Not all useful languages even have their own compiler. I’m specifically thinking of the domain specific languages (DSL). Nobody would write an awk interpreter in awk; or a mail engine using sendmail (even if it is Turing Complete). These are languages designed to do a specific task, many of them are quite essential to their respective fields, but none of them are self-hosting. Nor should we expect them to be.

My argument here is that the cultural practice of writing a self-hosting compiler is a big distraction. New languages should be for experimenting with new linguistic constructs. We should be looking toward the DSLs, and incorporating their innovations into our more main-stream languages. Right now, we seem to be optimizing our languages for compiler construction.

I’d rather see our languages evolve in a different direction. I’m really eager to witness the birth of an AI. For this to happen though, we need languages for expressing patterns of thought, not patterns of bits. We need the ability to cohesively and flexibly assemble the stuff of thought. I’m thinking Society of Mind stuff here. We need languages that allow for statistical fuzziness, sloppy associativity, and the ability to construct metaphor.

The linguistic tools that we find useful for building compilers are not necessarily the same tools that will help us build a mind.

Thinking about Thinking

erich — Sun, 29 Jun 2008 22:36:29 +0000

So far, in my reading of Minsky’s Society of Mind, his hypothesis, that the mind is an agglomeration of specialized agents working in conjunction with each other completely meshes with observations of my own behavior. In particular, I’ve noticed that when I get stuck thinking about a problem, I’ll endlessly repeat, in my head, the knowledge and reasons surrounding the problem until the solution/new path/new thought occurs to me. It’s not me that’s doing the thinking here, rather It’s me that the thought occurs to, which explains the phrase, “It occurred to me that…”). So our Ego has the mistaken opinion that it’s the originator of all the thought in the mind, while all the time it’s more the receiver of the thoughts which occur in the brain.

But if this is true, then what is it that makes one person smarter than another? It must be that more thoughts (maybe of different character) occur to the smarter person. But then how does one make themselves smarter? One probable method would be to do daily exercises in logic puzzles and brain teasers, on the presumption that it will exercise and stimulate some parts of the brain from latent dormancy into activity, and that this sort of change in brain activity will be of general use in life’s daily problems. I’m not a psychologist, and have no data on the efficacy of this approach, but it seems plausible. More helpful, would be a correlation between specific types of problems and wether experience in solving particular instances of that type will extend to an increased ability to solve all problems in that class.

Yet the revered smarts of Einstein and Leibniz isn’t that they were particularly good at solving instances of know problems, computers can do that better than any human, it’s that they saw connections and aspects of unsolved problems that then allowed those problems to be solved. What brain calisthenics would help you to answer the currently unanswered questions? Here I draw a blank and even have a difficult time speculating. History is replete with anecdotes about flashes of insight that answer the prepared mind (penicillin was found in dirty dishes, structure of benzene revealed in a dream of snakes, gravity with the fall of an apple, etc). But beyond extended concentration on a given problem to prepare the mind, none of these tales suggest a general approach for encouraging the frothy bubbling of thoughts that the brain must present to the consciousness trying to solve the problem. Intelligence then will vary as a result of the computational structure in underlying medium (neural brain) that supports thought.

I’m at a loss when I try to conjure up a method by which we can transform my brain’s architecture so that it can better do my thinking for me. If Minsky is right (and I really think he is) then the solution must lie in the study of multi-agent systems and emergent behavior. Unfortunately, we are still developing the non-linear methods and mathematical tools that will help an understanding of such systems. But the research will be useful for much more than the study of thought, it applies to a very wide range of things found in nature (Economic behavior, Environment/Ecosystems, Evolution + Game Theory, etc.) and cuts across so many fields that it’s likely everyone has a roughly equal chance of contributing, wether they realize it or not. This really is the age of the multi-disciplined researcher.

Update: a Reasonable Deviations post about the Creativity Machine, which incorporates an apropos feedback mechanism, that readily models the difference between the consciousness which experiences thought and the separate generative mechanism of thought.

Some Wisdom from Minsky

erich — Mon, 16 Jun 2008 02:24:58 +0000

I was briefly reading Minsky’s Society of Mind and found these passages memorable.

The secret of what anything means to us depends on how we’ve connected it to all the other things we know. That’s why it’s almost always wrong to seek “the real meaning” of anything. A thing with just one meaning has scarcely any meaning at all.

The smaller two languages are the harder it will be to translate between them. This is not because there are too many meanings, but because there are too few. The fewer things an agent does, the less likely that what another agent does will correspond to any of those things. And if two agents have nothing in common, no translation is conceivable.

Graph of the English Language

erich — Sat, 31 May 2008 00:43:14 +0000

Dictionaries are really great tools, but they can only go so far. The really good ones (The OED) will give the user a really good ‘feel’ for the word, a sense of the connotations that go beyond the straightforward definition. A thesaurus can also be really useful, especially when you’re searching for a specific word, but can only remember associated words. But both of these tools lack visualization. Here is where technology can help out and create a more immersive, exploratory environment for our words. The thesaurus, through it’s simple listing of words related to other words, has some really interesting features, specifically that of directionality. Sometimes you find wordA in the listing for wordB but not vice-versa. Using these listings, we could build one giant directed graph of the English language. But what would we expect to find?

The graph is probably not acyclic.
High probability that it’s not planar, and therefore will be hard to draw.
There will be clusterings of words (probably short words) around certain concepts
These clusterings will probably center around descriptive features of our world (such as the mythical Eskimo words for snow)
It will reveal interesting conceptual connections between words, (sounds, cheese and knifes can all be ‘sharp’)
Those connections probably relate to our internal models of the world (synethesia).
Emphasis of these connections probably varies by culture (but anyone familiar with idioms from more than one languages already knows this)
There will be gaps and holes in the language, that will show up as empty areas between conceptual clusterings.

I’m primarily interested in seeing how this type of visualization can help us to understand the tangled relationship between language and cognition. It’s been a combination of laziness and that 2^nd item that’s prevented me from writing this kind of software (which would be a great exercise to try out graph visualization techniques). But then again, others have forseen my vision (as usual).