Skeptophilia (skep-to-fil-i-a) (n.) - the love of logical thought, skepticism, and thinking critically. Being an exploration of the applications of skeptical thinking to the world at large, with periodic excursions into linguistics, music, politics, cryptozoology, and why people keep seeing the face of Jesus on grilled cheese sandwiches.
Showing posts with label problem solving. Show all posts
Showing posts with label problem solving. Show all posts

Saturday, April 17, 2021

Overlooking simplicity

In the Tao Te Ching, Chinese philosopher (and founder of Taoism) Lao Tse writes, "To attain knowledge, add things every day; to attain wisdom, remove things every day."

There are a couple of interesting pieces to this concept.  First, that knowledge does not necessarily confer wisdom.  The implication is that knowledge (by itself) is less desirable than understanding, and understanding less desirable than wisdom.  If so, this definitely has some bearing on how science is taught in public schools -- often as a list of vocabulary words and definitions that do little more than scratch the surface of what's out there to learn.

Second, that doing a mental decluttering is better than trying to figure things out by jamming more stuff in.  Here, I'm reminded of what happens in my fiction writing when I'm at an impasse.  Slamming my fists against the obstacle almost never works; what frequently does is doing something else entirely, especially something stress-clearing like going for a run or playing with my dogs.  As counterintuitive as it might be, it seems like ceasing to think about the problem at all frees my brain up to figure out a solution.

How exactly that works on a neurophysiological level, I have no idea.

Lao Tse by Nicholas Roerich (1943) [Image is in the Public Domain]

As more support for Lao Tse's observation, consider the paper in Nature this week called, "People Systematically Overlook Subtractive Changes," by Gabrielle Adams, Benjamin Converse, Andrew Hales, and Leidy Klotz of the University of Virginia, which looked at another facet of this same issue -- that when approaching a solution to a complex problem, people often fail to consider solutions that require removing pieces of it or ceasing to do certain actions.  The authors write:

Improving objects, ideas or situations—whether a designer seeks to advance technology, a writer seeks to strengthen an argument or a manager seeks to encourage desired behaviour—requires a mental search for possible changes.  We investigated whether people are as likely to consider changes that subtract components from an object, idea or situation as they are to consider changes that add new components.  People typically consider a limited number of promising ideas in order to manage the cognitive burden of searching through all possible ideas, but this can lead them to accept adequate solutions without considering potentially superior alternatives.  Here we show that people systematically default to searching for additive transformations, and consequently overlook subtractive transformations.  Across eight experiments, participants were less likely to identify advantageous subtractive changes when the task did not (versus did) cue them to consider subtraction, when they had only one opportunity (versus several) to recognize the shortcomings of an additive search strategy or when they were under a higher (versus lower) cognitive load.  Defaulting to searches for additive changes may be one reason that people struggle to mitigate overburdened schedules, institutional red tape, and damaging effects on the planet.

We're so well-trained by years and years of education that the way to find a solution to a problem is to throw more stuff at it that we don't even think of looking at solutions that require simplification.

"Additive ideas come to mind quickly and easily, but subtractive ideas require more cognitive effort," study co-author Benjamin Converse said, in an interview with Science Daily.  "Because people are often moving fast and working with the first ideas that come to mind, they end up accepting additive solutions without considering subtraction at all."

Now, there's a caveat here; not all problems have simple solutions.  When I was a teacher, I used to call this the "why don't we just...?" approach.  I remember students saying, "Why don't we just use chemical reactions that absorb carbon dioxide to fix climate change?" (it's completely unfeasible to do this on a large enough scale to help), and "why don't we just pass laws protecting wilderness areas and make mass deforestation illegal?" (not only does this run afoul of private ownership and eminent domain laws, it causes problems with resource acquisition, and ignores the fact that most of the threatened wilderness in the world is outside of the United States and therefore out of our jurisdiction -- not to mention the elephant in the room of global, societally locked-in wealth inequity as the root problem).  

Complex problems rarely have simple solutions.

But the basic idea here is that the answer doesn't always lie in fixing things by doing more stuff, and the human mind doesn't tend to see those kinds of solutions as easily as ones that require further or more intense action.

So give it a try.  When you're facing a difficult problem, give a shot to a Marie-Kondo-esque simplification approach.  What could you remove (or stop doing) that might help solve the problem?  Maybe a mental decluttering would help in a lot of realms other than overcoming writers' block.

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If, like me, you love birds, I have a book for you.

It's about a bird I'd never heard of, which makes it even cooler.  Turns out that Charles Darwin, on his epic voyage around the world on the HMS Beagle, came across a species of predatory bird -- the Striated Caracara -- in the remote Falkland Islands, off the coast of Argentina.  They had some fascinating qualities; Darwin said they were "tame and inquisitive... quarrelsome and passionate," and so curious about the odd interlopers who'd showed up in their cold, windswept habitat that they kept stealing things from the ship and generally making fascinating nuisances of themselves.

In A Most Remarkable Creature: The Hidden Life and Epic Journey of the World's Smartest Birds of Prey, by Jonathan Meiberg, we find out not only about Darwin's observations of them, but observations by British naturalist William Henry Hudson, who brought some caracaras back with him to England.  His inquiries into the birds' behavior showed that they were capable of stupendous feats of problem solving, putting them up there with crows and parrots in contention for the title of World's Most Intelligent Bird.

This book is thoroughly entertaining, and in its pages we're brought through remote areas in South America that most of us will never get to visit.  Along the way we learn about some fascinating creatures that will make you reconsider ever using the epithet of "birdbrain" again.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]



Tuesday, August 21, 2018

The problem with tradition

It is a frequent source of bafflement to me that so many people don't change what they do when confronted with incontrovertible evidence that there's a better way.

Sad to say, the educational establishment is one of the worst in this regard.  For example, it's been known (or at least, strongly supported) that a person's facility for learning a second language drops off significantly after puberty since 1967, when the research of linguist and neuroscientist Eric Lenneberg showed that the brain's plasticity with regard to language more or less goes away after age 12.  So for fifty years we've been pretty certain that the way to create bilinguals is by early immersion programs -- kindergarten or (better) preschool.

But how do we do it, fifty years later?  In my school district, which is forward-thinking in a lot of respects, we start teaching foreign language in grade seven.  I.e., we wait until the point that the human brain becomes really bad at it to start doing it.

When I tell my neuroscience students about this -- that if they had been put in an immersion program at age two, they could now speak whatever language they wanted, fluently, without once memorizing a conjugation table or vocabulary list -- they are pissed.

"Then why do we still do it this way?" they ask.

Good question.  "'Cuz it's the way we've always done it," is about the best I can do.  Which has got to be the crappiest justification for anything I can think of.

So my expectation is that the recent research done by Ethan Bernstein, Jesse Shore, and David Lazer, of (respectively) Harvard, Boston University, and Northeastern University, is going to impress a lot of people and have zero cumulative effect on how we approach anything.

Their paper, released last week in the Proceedings of the National Academy of Sciences, is called "How Intermittent Breaks in Interaction Improve Collective Intelligence," and it proposes a novel approach to problem-solving: giving people a chance to work together interspersed with solitary work periods enhances the quality of solutions generated.

It's kind of counter to how we've been taught to work, isn't it?  In school, we're mostly instructed to work alone, that working together is "cheating."  The emphasis is on solitary work... except for very controlled situations of "cooperative learning" that are all too often exercises in frustration for the best students, because the individuals who are the most concerned about learning the concepts or getting good grades (or, hopefully, both) are highly motivated to do the lion's share of the work, while the less-engaged students have no particular incentive to do more than the bare minimum.  If I can think of a single teaching strategy that I have heard more students rail against than any other, it's "cooperative learning."  I can't tell you how many times I've heard kids say, "I'd rather just do it myself and get my grade rather than doing it myself and then giving my grade to five other students who sat on their asses the entire time."


But if you want true creative problem-solving, the Bernstein et al. study suggests, having people work alone isn't the best way to do it.  Neither is the throw-them-together-for-hours, let's-beat-the-problem-to-death approach.  It works best to have them work together for a while, divide up the task -- then reconvene to compare notes and integrate what each of them has accomplished, evaluate it, see what else needs to be done... and repeat as many times as needed.  The researchers write:
People influence each other when they interact to solve problems.  Such social influence introduces both benefits (higher average solution quality due to exploitation of existing answers through social learning) and costs (lower maximum solution quality due to a reduction in individual exploration for novel answers) relative to independent problem solving.  In contrast to prior work, which has focused on how the presence and network structure of social influence affect performance, here we investigate the effects of time.  We show that when social influence is intermittent it provides the benefits of constant social influence without the costs...  Groups in the intermittent social-influence treatment found... optimum solution[s] frequently (like groups without influence) but had a high mean performance (like groups with constant influence); they learned from each other, while maintaining a high level of exploration.  Solutions improved most on rounds with social influence after a period of separation.
Even before reading this study, it's the approach I've recommended for years to my AP Biology students for writing up labs.  Each of the labs we do is focused around a single question, often one that is simple to ask but not so simple to answer.  For example, our first lab approaches the question of enzyme reaction rate.  In every introductory biology class, you learn that enzymes speed up chemical reactions.  Our first AP lab asks the question, "By what factor?"  Does a typical enzyme double the rate of a reaction?  Make it go ten times faster?  A hundred times?  A thousand?

The lab procedure is designed to give the students enough data to answer the question, but getting from the raw data to a defensible answer isn't simple.  So my students work in teams, and I recommend to them that they break the task up -- one member of the team does the calculations and graphs, one writes up the procedure, one organizes the data into tables or charts, and so on.  Then they should get together, and look at what they've got, and see if they can solve the problem -- use their work to come up with an answer as a team that they can then defend.

The problem is, there's no way I can mandate this approach, and I'm afraid that some groups still end up with one or two students doing pretty much all the work, and the others going along for the ride (and because of that, not really learning much from the experience).  I simply don't have the time to have them do the lab write-ups during class, so I can't supervise them and make sure they're working on it consistently and fairly.  But I know from experience -- and the Bernstein et al. paper supports this conclusion -- that they clearly learn the most if that's how they approach the task.

And the paper also has implications for the corporate world.  In problem-solving on the job, it would improve solution quality to use a hybrid approach of teamwork and solitary work.

You have to wonder why people don't look at something like this and think, "Let's at least try this and see if it works."  But habit and laziness keep us doing the same thing over and over, even when it's been demonstrated (over and over) that what we're doing doesn't work, or at least isn't optimal.

Maybe after 31 years of teaching, I'm getting cynical.  I hope that's not true, but I have to admit my first thought on reading this was, "Wow!  Cool!  This won't change anything!"  I seriously hope I'm wrong about that.  Because there's a lot of truth to the old adage that if you always do what you've always done, you'll always get what you've always got.

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This week's Skeptophilia book recommendation is a classic, and especially for you pet owners: Konrad Lorenz's Man Meets Dog.  In this short book, the famous Austrian behavioral scientist looks at how domestic dogs interact, both with each other and with their human owners.  Some of his conjectures about dog ancestry have been superseded by recent DNA studies, but his behavioral analyses are spot-on -- and will leaving you thinking more than once, "Wow.  I've seen Rex do that, and always wondered why."

[If you purchase the book from Amazon using the image/link below, part of the proceeds goes to supporting Skeptophilia!]





Wednesday, February 14, 2018

The cure for passivity

Let me say at the outset that I enjoy and respect my students.  This is in no way intended to be a criticism of them as people.

However, I've noticed an issue with them this year that is pretty much across the board.  I know it's been there in previous years -- maybe I'm just becoming more sensitive to it, or maybe I have a disproportionate number of kids with this characteristic in this bunch of classes.

The characteristic is passivity.

They're extraordinarily well-behaved -- they're quiet, respectful, kind to each other and to me.  I think I've had to raise my voice maybe twice this year.  By and large they do their work, and any directed task I give them, they will happily dive into.

What strikes me, though, is the extent to which they want THE ANSWER.  Few of them -- there are exceptions -- will stop and try to put together what they know to figure out the response to a question, to go out on a limb and make an educated guess, or (even more seldom) to look for evidence on their own to support their answer.  They are perfectly content to have me or another student give them THE ANSWER, which they write in the blank, and forthwith stop thinking about it.

The result is that their grades on homework, labs, and problem sets are uniformly good.  Man, they have those blanks filled in like crazy, and usually with the right answers.  The problem shows up on quizzes and tests -- especially in my AP Biology class, where it's not sufficient to know the vocabulary.  To be successful in that class, you have to understand the concepts on a deep level, not just to regurgitate, but to analyze and synthesize.  If you compare the average grade on quizzes to the average grade on homework, there's a disparity that demands an explanation.

[image courtesy of the Wikimedia Commons]

And the more I've thought about this, the more I've come to the conclusion that we in the public school system have created this problem.  We've taught them all to be passive recipients of information, to sit there and take notes, merely writing down whatever the teacher tells them to, rather than questioning it, thinking about it, trying to connect it meaningfully to what they already know.  Education has become simply the memorization of lists of terms, not the opening of new worlds, the expansion of minds.

We've forgotten, I think, that the root word of education is the Latin educare -- meaning "to draw out of."  The purpose of education is to put the person in charge of their own understanding, not to make them more dependent on some authority figure to fill their brains up with factoids.

It's getting worse, not better.  We're evaluating students (and teachers, and in some cases, whole schools) on the basis of student scores on standardized, multiple-choice tests.  We discourage thinking outside the box, emphasizing that they're to find THE ANSWER, not uncover novel ways of approaching problems.  We discourage collaborative learning -- usually, it's labeled cheating, and honestly, in the context of most classrooms, that's what it's become.  In most of what we call "cooperative learning," we enable one or two students to do most of the work, and the others to ride their coat-tails, rather than true collaboration where all minds are deeply engaged.

And upon reflection, I think a lot of it is based in fear.  Fear from us teachers that if we relinquish some control in the classroom, the students will revolt, disrupt, or (at the very least) refuse to learn.  Fear that if we don't test, test, test, we won't have any way to know if the students are mastering what we're asking of them.  And the fear runs all the way up the hierarchy; teachers don't trust the students, administrators don't trust the teachers, and the state departments in charge of oversight don't trust anyone.

I think the only way to fix this is with a complete overhaul.  Vocabulary lists and rote book work have to stop being the main way students are evaluated.  At very young ages, children are natural creative problem solvers; we need to hook into that, encourage it, start modeling factual knowledge as a means to an end, not an end in and of itself.  If you want to know how a car engine works, sure, you need some vocabulary.  You're not going to get far if you don't know which part is the carburetor.  But  if all your mechanic knows is the definition of the terms, and how to recognize the parts on a diagram, it's doubtful that you'd trust him/her to repair your car.

And it's not just with auto mechanics that the fundamental goal is understanding how the pieces fit together, and how to creatively work through problems you've never seen before using the knowledge you already have.

That's the goal of all education.

After all, in this age, students have a mind-bogglingly fast access to the raw facts.  If, to solve a problem, run an experiment, understand a behavior, model a cell or organism or ecosystem, they have to learn the word mitochondria, they can do that in fifteen seconds flat.  I'd far rather they understand how energy flow through living things works and forget the terminology than the reverse.

We need classes that are based in active, project-based problem solving.  Ones where sit-down-and-listen time is occasional and of short duration.  Where students figure out what they need to know, and using us (and their technology) as resources, learn the terms and definitions in a real-world context, within which the vocabulary actually means something.  Where critical thinking and evaluation of source validity counts for more than grades on a multiple-choice test.

The transition to this model for schools would not be easy.  And such classes will demand a great deal from teachers, much more than the lecture/problems/homework/test model we've been using since the 19th century.  But walking into our classrooms this day, the second Wednesday in February, will be thirteen years' worth of students with tremendous potential, and thousands of dedicated, hard-working professionals who care deeply about education.

With that kind of talent, potential, and energy, it's eminently doable.

We just have to admit to the problems -- and commit to finding solutions.