teaching and using critical thinking

So frustrating!  

 

I was reading the transcript of an interview of the chief environmental officer of one of America's largest companies.  Their efforts appeared to be real rather than the normal corporate environmental green washing so many use.  Then she spoke about energy, but used units of power (watts)  rather than energy (watt-hours) .  Three times and a huge difference.   It may have just been a misspeak, but it stuck with me.  I frequently see science and engineering mistakes all the time in major newspapers ..  many might be simple editing errors.   There's a simple technique  that only takes high school science to understand what's going on.  It is a  quick way to do a bit of high level critical thinking.

 

Dimensional analysis involves looking at the dimensions of a quantity.  Velocity is the distance that can be traveled in some unit of time - or length divided by time (miles per hour): L/t.  Acceleration is the rate of change of velocity or velocity/time: L/t² . Area has the dimensions of length times length: L².  Volume is the cube: L³.  Force is mass times acceleration: m*L/t².  Energy is: m*L²/t² and so on.  

 

You can use this for simple tasks like changing units   60 minutes/hour * 60 seconds/minute = 3600 seconds/hour.¹   It can be a powerful way to quickly check an answer.  If you do a calculation and come up with E = mc³ you instantly know it's wrong as the units of energy are mL²/t² and not mL³/t³.  Mistakes like this or calling energy power cause you suspect the article in the New York Times or the Wall Street Journal.  Was it a bad writer or bad editor - or was it garbage in the first place?

 

In physics you do a lot of conjecture building.  A lot of this involves simple models to get rough answers.  The trick is to be correct enough to get a sense that it's a path worth looking into or just trashing.  It's also a very powerful way to estimate an answer when the physics involved is complex and you don't have enough information.   A few years ago I did a quick calculation to determine the energy cost of having a coxswain in competitive rowing.  [warning: Follow the link if you're curious about the power of the approach and are comfortable with high school level algebra and physics.  It starts after a bit of Olympic history.] I was able to quickly find a useful relationship between number of rowers and boat speed.  It surprised me at first, but fits with Olympic records.  From there you can  estimate the speed penalty of the coxswain as a dead weight.  Doing it properly would involve serious fluid dynamics and/or experimental measurements.²  Once you have the estimate you can do another simple calculation to estimate the energy cost of fighting the wiggle waggle of an un-coxed boat at the oars.  (the cox has other advantages, but that gets into human physiology and psychology).

 

Techniques like this are the tools of curiosity.  Being curious about something is the basis ...  this line of thought came while watching some rowing on the Olympics and being led to an obvious question -- why is there a cox in some events?   Then other questions present themselves and you follow. 

 

 It isn't difficult to teach thinking like this. Rather than the standard path of math courses - they're mostly aimed at 19^th and 20^th century tasks anyway -  I'd like to see some shortened or even eliminated and replaced by a statistics and probability course.  Logic and numeracy could come in almost anywhere.  Perhaps through multiple paths - science, history, computing skills and even art and sports.  All of this comes under the banner of critical thinking .. something everyone aspires to and most avoid as it causes too much questioning of the standard order.  

 

One of my favorite teachers in high school was a history teacher - Mr Wolff.  A master teacher, he taught a course in comparative religion and held an after-school philosophy group for interested students (that's where I first encountered and came to love Kierkegaard).  Somewhat after my time he was put on probation by the school board for putting religions on equal footing .. specifically for not teaching Christianity as the true religion. It wasn't proper for students to decide on their own one way or the other.  So much for critical thinking in the day.  

 

I'm not a trained educator and can't claim to know much about technique.  I do have a few ideas for information literacy as do many others.  It's time to experiment and see what works.  We're up against computational filters and conscious and unconscious biases of those who build them and the code underneath and a blizzard of purposely misleading highly targeted (some would say weaponized) information.  Creating unbiased information is extremely difficult - that's the hardest part of doing science.  Approaching the task like a scientist - being critical at all steps - is something that can be taught at simple levels.  Perhaps more important is recognizing that most information systems are built with such robustness and teacher the end user how to sort out what is fishy.  A subject for long discussion and perhaps a serious of posts on them and some critical ideas about STEM education.  

 

I'll end with part of a talk Richard Feynman gave in 1966 on the difference between knowing the name for something (how K12 history and science are usually taught)  and beginning to understand it.

 

So we went alone for our walk in the woods. But mothers were very powerful in those day's as they are now, and they convinced the other fathers that they had to take their own sons out for walks in the woods. So all fathers took all sons out for walks in the woods one Sunday afternoon. The next day, Monday, we were playing in the fields and this boy said to me, "See that bird standing on the stump there? What's the name of it?"

I said, "I haven't got the slightest idea."
He said, 'It’s a brown-throated thrush. Your father doesn't teach you much about science."

I smiled to myself, because my father had already taught me that [the name] doesn't tell me anything about the bird. He taught me "See that bird? It's a brown-throated thrush, but in Germany it's called a halsenflugel, and in Chinese they call it a chung ling and even if you know all those names for it, you still know nothing about the bird--you only know something about people; what they call that bird. Now that thrush sings, and teaches its young to fly, and flies so many miles away during the summer across the country, and nobody knows how it finds its way," and so forth. There is a difference between the name of the thing and what goes on.

The result of this is that I cannot remember anybody's name, and when people discuss physics with me they often are exasperated when they say "the Fitz-Cronin effect," and I ask "What is the effect?" and I can't remember the name.

I would like to say a word or two--may I interrupt my little tale--about words and definitions, because it is necessary to learn the words.

...

There is a first grade science book which, in the first lesson of the first grade, begins in an unfortunate manner to teach science, because it starts off an the wrong idea of what science is. There is a picture of a dog--a windable toy dog--and a hand comes to the winder, and then the dog is able to move. Under the last picture, it says "What makes it move?" Later on, there is a picture of a real dog and the question, "What makes it move?" Then there is a picture of a motorbike and the question, "What makes it move?" and so on.

I thought at first they were getting ready to tell what science was going to be about-- physics, biology, chemistry--but that wasn't it. The answer was in the teacher's edition of the book: the answer I was trying to learn is that "energy makes it move."

Now, energy is a very subtle concept. It is very, very difficult to get right. What I meant is that it is not easy to understand energy well enough to use it right, so that you can deduce something correctly using the energy idea--it is beyond the first grade. It would be equally well to say that "God makes it move," or "spirit makes it move," or "movability makes it move." (In fact, one could equally well say "energy makes it stop.")

Look at it this way: that’s only the definition of energy; it should be reversed. We might say when something can move that it has energy in it, but not what makes it move is energy. This is a very subtle difference. It's the same with this inertia proposition.

Perhaps I can make the difference a little clearer this way: If you ask a child what makes the toy dog move, you should think about what an ordinary human being would answer. The answer is that you wound up the spring; it tries to unwind and pushes the gear around.

What a good way to begin a science course! Take apart the toy; see how it works. See the cleverness of the gears; see the ratchets. Learn something about the toy, the way the toy is put together, the ingenuity of people devising the ratchets and other things. That's good. The question is fine. The answer is a little unfortunate, because what they were trying to do is teach a definition of what is energy. But nothing whatever is learned.

Suppose a student would say, "I don't think energy makes it move." Where does the discussion go from there?

I finally figured out a way to test whether you have taught an idea or you have only taught a definition.

Test it this way: you say, "Without using the new word which you have just learned, try to rephrase what you have just learned in your own language." Without using the word "energy," tell me what you know now about the dog's motion." You cannot. So you learned nothing about science. That may be all right. You may not want to learn something about science right away. You have to learn definitions. But for the very first lesson, is that not possibly destructive?

...

So much more to talk about...

__________

¹ As an exercise convince yourself that if you express a gallon as a volume, miles per gallon can be expressed in terms of  inverse acres.

² With a bit of other information I performed a simple calculation for the astonishing two hour marathon attempt and believe it would have been about 2:02 without car pacing - there is a serious aerodynamic advantage.  Record attempts should not allow pacing - or at least they should indicate where it is used and print and estimate of the advantage.  

Nike, of course, has a more accurate estimate of the advantage's size.  But simple calculations combined with some quick experiments may be enough to suggest pacing shouldn't be allowed if the record is to be considered pure.

 

Comments

[Jheri]

Pick me! ;)

1 mpg is 1.72 billion inverse acres

right?

[steve]

you win Jheri