One of the things that’s puzzling to anyone, and especially us logic-oriented scientists, is how people can look at strong evidence and seemingly ignore it.  They go with their gut, or what they think they know, instead of the data staring them in the face.

This is the basis of a huge amount of work in what is called behavioral economics — or, the psychology of why we make the economic decisions that we do.  There’s a great article and radio piece on NPR about Daniel Kahneman’s work in economics, which won him the Nobel Prize in 2002.  For instance, we have the illusion of validity (we have too much confidence in our own judgment), or the anchoring effect (we’re unduly influenced by numbers that we’re exposed to, such as a “compare to” price on an item).

Here are some classic examples, as written in an email from Nathan Lasry:

1- A group is given the price of an object they must buy. The same object can be purchased 5$ cheaper across town (remember this is 5$ in the late 70s early 80s, so was worth much more than today’s 5$). The question: Would you drive across town to get the object?

Most people said YES to driving across town IF they were saving 5$ on a 15$ calculator.
Most people said NO to driving across town IF they were saving 5$ on a 125$ coat.

The trouble? When you walk into the grocery store to spend that 5$, it really doesn’t matter where it came from…
This result does not fit at all with classical economic theory that portrays humans as ’spock-like’ rational agents that would place an absolute value on driving across town.

2- In another interesting example, people were asked:
Do you prefer getting $1000 with 100% certainty or getting a 50% chance of receiving $2500. Most will choose the certain $1000, although the expectation value of the second option is higher 1250$.  This is ok from a strictly rational perspective because these folks are willing to pay 250$ as ‘insurance’. So you can call them ‘Risk aversive’.
BUT
The same people are then asked what they would choose between a certain loss of $1000 versus a 50% chance of either loosing nothing or loosing $2500.  Most will choose the riskier 50% alternative. So the SAME ‘risk averse’ people in the first example become ‘risk seeking’ in the second.

These, and all sorts of other biases, are outlined in a great book I’m listening to right now, How We Decide.  A lot of the themes from this book keep cropping up in my favorite podcast, Radio Lab, especially their recent episode on Choice. If you find this stuff interesting, check out the work of Baba Shiv, who sticks his subjects into MRI machines to see the hardwiring underlying how emotions affect our decisions.  He was the one who did the famous study showing that people not only rated the same wine more highly when told it was expensive, but actually had a better subjective experience of the wine based on their expectations.  And here is a TED talk by Dan Ariely on how our irrationality is predictable, and we can be encouraged or discouraged from cheating with some simple manipulations, like being reminded of an honor code, or replacing cokes with dollars.  He calls this our “buggy moral code.”

Another book that comes highly recommended is  Kluge: The Haphazard Construction of the Human Mind
Here’s some stuff covered in that book (as written in an email from Bill Goffe):

- halo effect: attractive people are seen as better teachers, they earn more, etc. (presumably halos from non-people have an impact too)

- priming: what is in your mind when a second topic comes up is likely to color how you view or judge the second. Marcus gives this example: you ask undergrads how happy they are and how many dates they had last month. If the happiness question is asked first, there is no correlation between the answers. If if you first ask about dates, there is a correlation between the answers.

- anchoring and adjustment (a variation on priming): a number that people have in mind influences their estimate of something entirely different. One example: add 400 to the last three digits of your phone
number. Then, when did Attila the Hun’s rampage end? If the phone answer was less than 600, the median guess was A.D. 629, if the sum was between 1,200 and 1,399, the median year was A.D. 979.

- mere familiarity: people prefer what they know. Marcus reports one study (now done in 12 languages) that people prefer letters in their own names. One study told half the participants that feeding alley cats were legal and the other half were told it was illegal. Yet, most favored the current policy, whichever it might be.

- threat: the more we are threatened, the more we cling to our beliefs. I could imagine that this comes up in the physics classroom when beliefs about mechanics are challenged.

- confirmation bias: we tend to be place more weight on evidence that supports our beliefs than evidence that doesn’t (I think this one is widely known); the flip side is “motivated reasoning.”

This examination of the irrationality of people’s economic behavior was apparently pretty controversial stuff in economics, whose models assumed that humans are essentially rational and logical decision makers who will make the choices that benefit them the most.

But there’s probably another reason for economists’ resistance. An imperfectly rational human being challenges a really important idea: the notion that markets work well because individuals can be counted on to make the best choice for themselves.

“Merely accepting the fact that people do not necessarily make the best decisions for themselves is politically very explosive. The moment that you admit that, you have to start protecting people,” Kahneman says.

In other words, if the human brain is hard-wired to make serious errors, that implies all kinds of things about the need for regulation and protection.

In our own work in educational research and reform, this has many implications as well.  After all, we’re often presenting faculty with data and information at how students learn best, and meeting great resistance.

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I’ve got a new podcast posted, this one with my esteemed colleague Valerie Otero of the University of Colorado at Boulder.  She tells us why she thinks that the idea of student “misconceptions” is very dangerous — and gives us a new way to think about student ideas in the classroom, and some activities to address them.  This is in the Beyond Penguins and Polar Bears episode on Keeping Warm, and targets common student ideas about heat.  Still, the general message about misconceptions is, I think, one that every teacher should hear.

Listen to Warm Blankets and Cold Breezes (10 minutes)

You can also read this month’s content article on heat (what is it?  How do people and animals keep warm?) written by moi.

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We think of taking tests as something to assess whether we learned something, but there is a fascinating set of literature that shows that it does more than that.  Tests can be learning events in their own right.  It makes sense when you think about it.  How is it that we learn things?  By making neuronal connections, or strenthening neuronal connections, in the brain.  Each time we take a test and are asked to recall information, that neuronal path gets strengthened.  That’s why flash cards are useful.  One of the seminal papers on this topic is The critical importance of retrieval for learning by Karpicke and Roediger.

• When someone recalls something from memory, they’re more likely to be able to recall it again later — much more so than when that information is just presented to the person.
• People forget information more slowly when tested on it
• Asking people questions whose answers involve numbers increase people’s retention of numbers presented in text (by directing their attention to the type of information important to learn for the test)
• Questions asked before a task can activate prior knowledge and focus students on the relevant material

Robert Bjork of UCLA, who studies learning and forgetting, has written extensively on this topic, especially given that students don’t really know how it is that they learn, and their study habits don’t make the most effective use of what we know about our cognitive function.  His “how to succeed in college” paper is a nice summary of this research.

But, you might ask, what if you take a test and get the wrong answer?  Doesn’t that then cement the wrong answer in your brain? So isn’t there a danger to testing ourselves when we might get the wrong answer stuck in our head?  Some research suggests that testing could distort knowledge in this way:  When you get the wrong answer on a multiple choice test, you’re more likely to make that same mistake on a later test.

Giving someone feedback on their performance on a test can reduce memory distortions, but this is sometimes not feasible (especially in today’s climate of standardized testing).   Luckily, new research shows that, no, making mistakes still helps us learn.  A set of two articles authored and co-authored by Nate Kornell sheds some light on these questions:

• When they tested students before they studied a text, students did better on a test after having studied the text, even though they got most of the questions wrong.  This appeared to be due to the testing itself, rather than focusing students’ attention on the important aspects of the text, because students learned better when tested than when key information in the text was bolded.  (Note the implications for students’ exuberant highlighting of texts!)
• This kind of testing also reduced forgetting after a one week delay.
• This kind of testing was also more effective than reading the same question and trying to memorize the words of the question itself (without trying to retrieve the answer).
• In another study, where students were doomed to fail (being tested on word association pairs that most people get wrong), they found the following:  Trying (and failing) to answer a question, and then studying it, produces better learning than studying it (for a longer time) without first trying to answer it.

Thus, give your students pre-tests!  The act of trying (unsuccessfully) to retrieve an answer helps you do better on a later test (and not just because the pre-test gave you a clue as to what would be on the final test).  Pre-processing is very important!

It’s crucial, however, that students be given a chance to restudy the tested material.

Scientific American article

Nate Kornell’s website with links to his publications.  (Gosh, he’s cute!)

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If you’re a teacher — of physics, or any other physical science — and haven’t yet picked up a copy of Edward Redish’s Teaching Physics with the Physics Suite , I’m making a bid right now that you do so.

I finally read it — really read it — instead of just browsing through a chapter that I needed to reference for a paper.  For a slim volume, it is a surprisingly powerful compilation of effective teaching techniques based on research, and what you as an instructor need to do in order to implement them to their maximum power.

First he goes through a wonderfully succinct summary of what cognitive research can tell us about teaching — the book is worth buying just for these 30 clear pages.

He goes on to discuss exams and homework — the goals of assessment and different types of questions.  He has a resource CD with a bunch of research based surveys, like the Force Concept Inventory, or different attitude surveys.  He then gives a quick look at some of the major research-based teaching methods, like Peer Instruction (PI), Interactive Lecture Demonstrations (ILDs), Tutorials, and Just In Time Teaching (JiTT).  It’s certainly more useful for teachers of physics (at any level) but I think that most people teaching the physical sciences will come away with something useful from the book.

Here’s a gem.

I had been teaching for 20 years before I realized that when students asked me questions, I was responding as a student rather than as a teacher.  Having been a student for 20 years, having been rewarded for giving good answers to teachers’ questions, and having been successful at getting those rewards, I had a very strong tendency to try to give the best answer I could to any question posed.  Once I realized (embarassingly late in my teaching career) that the point was not getting the question answered correctly but getting the student to learn and understand, I shifted my strategy.

Now, insted of answering students’ questions directly, I try to diagnose their real problem.  What do they know that they can build an understanding on?  What are they confused or wrong about that is going to cause them trouble?  As a result, instead of answering a question right off, I ask some questions back.  Often, I discover that students are trying to hide a confusion by creating questions that sound as if they know what they are talking about.  Helping them to find resources within themselves that they can bring to bear often makes all the difference.

Redish, “Teaching Physics with the Physics Suite,” (2003), p. 190.

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Below I am reposting a rather long piece taken verbatim from the website of Steve Detweiler who just says that it’s an “amusing anecdote from a friend of mine.”  So, I’m not sure of the veracity of the story, and some claim that it’s an urban legend.  It may well be.  But it opened up some deep discussion on the PHYSLRNR email list, which I attempt to summarize below.

HEAVY BOOTS

About 6-7 years ago, I was in a philosophy class at the University of Wisconsin, Madison (good science/engineering school) and the teaching assistant was explaining Descartes.

He was trying to show how things don’t always happen the way we think they will and explained that, while a pen always falls when you drop it on Earth, it would just float away if you let go of it on the Moon. My jaw dropped a little. I blurted “What?!” Looking around the room, I saw that only my friend Mark and one other student looked confused by the TA’s statement. The other 17 people just looked at me like “What’s your problem?” “But a pen would fall if you dropped it on the Moon, just more slowly.” I protested.

“No it wouldn’t.” the TA explained calmly, “because you’re too far away from the Earth’s gravity.” Think. Think. Aha! “You saw the APOLLO astronauts walking around on the Moon, didn’t you?”

I countered, “why didn’t they float away?”

“Because they were wearing heavy boots.” he responded, as if this made perfect sense (remember, this is a Philosophy TA who’s had plenty of logic classes). By then I realized that we were each living in totally different worlds, and did not speak each others language, so I gave up.

As we left the room, my friend Mark was raging. “My God! How can all those people be so stupid?” I tried to be understanding. “Mark, they knew this stuff at one time, but it’s not part of their basic view of the world, so they’ve forgotten it. Most people could probably make the same mistake.”

To prove my point, we went back to our dorm room and began randomly selecting names from the campus phone book. We called about 30 people and asked each this question:

1. If you’re standing on the Moon holding a pen, and you let go, will it
a) float away,
b) float where it is,
or c) fall to the ground?

About 47 percent got this question correct. Of the ones who got it wrong, we asked the obvious follow-up question:

2. You’ve seen films of the APOLLO astronauts walking around on the Moon, why didn’t they fall off?

About 20 percent of the people changed their answer to the first question when they heard this one! But the most amazing part was that about half of them confidently answered, “Because they were wearing heavy boots.”

MORE ON THE BURNING QUESTION OF HEAVY BOOTS

I decided to settle this question once and for all. Therefore, I put two multiple choice questions on my Physics 111 test, after the study of elementary mechanics and gravity.

13. If you are standing on the Moon, and holding a rock, and you let it go, it will:
(a) float away
(b) float where it is
(c) move sideways
(d) fall to the ground
(e) none of the above

25. When the Apollo astronauts were on the Moon, they did not fall off because:
(a) the Earth’s gravity extends to the Moon
(b) the Moon has gravity
(c) they wore heavy boots
(d) they had safety ropes
(e) they had spiked shoes

The response showed some interesting patterns! The first question was generally of average difficulty, compared with the rest of the test: 57% got it right. The second question was easier: 73% got it right. So, we need more research to explain the people who got #25 right but did not get #13 right!

The second interesting point is that these questions proved to be excellent discriminators: that is, success on these two questions proved to be an extremely good predictor of overall success on the test. On the first question, 92% of those in the upper quarter of the test score got it right; only 20% of those in the bottom quarter did. They generally chose answers (a) or (b). On the second question, 97% in the upper quarter got it right and 33% in the lower quarter did. The big popular choice of this group was (c)…33% chose heavy boots, followed closely by safety ropes at 27%.

A telling comment on the issue of fairness in teaching elementary physics: Two students asked if I was going to continue asking them about things they had never studied in the class.

———————————

First off, here’s the physics.  Earth is not the only thing with gravity.  The moon exerts a gravitational force on things, but it just exerts less force, mostly because it’s just got less stuff.  Stuff attracts stuff, and so less stuff will attract other stuff less strongly.  If you drop a pen, it will fall slowly, because the acceleration due to gravity is weaker.  Earth is far away, but that doesn’t really matter — when you are on the surface of the moon, the gravitational attraction of the moon is stronger than that of the earth.  That’s why the astronauts could jump very high on the moon.  You would weigh less on the moon than you do on the earth.  If the astronauts jumped really really really hard, they could float away from the moon.  The same is true on the earth (but to jump that hard, you need rockets, and that’s what the space shuttle does).

So, here’s the discussion.  One instructor said that she had used similar questions in her class, and gotten similar results.  Many students thought the pen would float away.  One year, she asked them instead about a crescent wrench instead of the “apocryphal pen.”  They all answered that question correctly!  Another instructor, however, gave a similar set of questions to his class, and most of them answered correctly.  What’s he doing differently?

What’s the problem?  This question forces students to challenge a preconception that they had walking in the door — perhaps that “things float in space” or “heavy things get weighed down.”  Apparently the misconception that the moon has no gravitational attraction persists through most physics courses.  Even though they might be able to state that the moon has gravity (as evidenced by correct answering of the second question, as to why the astronauts stayed on the moon), they have trouble transferring that understanding to the “what happens when you drop a pen on the moon” question.  They are thinking, argued one instructor, in terms of the surface features of the problem (we’re on the moon!) rather than the underlying features (all chunks of matter have gravity).  Students transfer more when they’re interactively engaged in the material, says the research (e.g., Cognitive Development, 6, 449-468 (1991), Learning and Transfer: Instructional Conditions and Conceptual Change, Michelle Perry).

John Clement gave a few ideas for ways to address this misconception in class:

Given enough time you could propose a number of what-if questions which might help the TA understand what is going on.  Why did the rocket have to fire its engines to prevent a crash?  Why don’t rocks fly away from the moon?  What force pulled Apollo 13 around the Moon?  Whey when the astronaut dropped a feather and hammer did they both fall to the surface of the Moon? This last one has no heavy boots!!!

Another really important question is to ask why they think there is no gravitational attraction on the Moon.  A number of students will reply “because there is no air”.  The common misconception is think that “gravity” is due to the air pressing you down.  Or they may say because the Moon does not rotate, as this is another common misconception.  These are explained in the teachers manual for Minds on Physics, and students are asked questions
to bring out these misconceptions while building a coherent model of gravitational attraction.

So rather than attacking the “heavy boots” conception, the student has to internalize the model that there is (at least in classical mechanics) no threshold to the action of forces, and that unbalanced forces cause acceleration.  Then they have to apply it to a variety of cases, of course, along the way.  It helps to have them apply these conceptions to objects on other planets.  So blocks of wood in a water filled bowl all float at the same level on the Moon and the Earth, but springs supporting masses are stretched less on the Moon.

So the “heavy boots” is not the primary concern.  The concept of forces and acceleration are the primary concern.  Once the students have a firm model of forces, and of NTNs general gravitational law, the idea that things can float on the Moon will go away.

A few more comments that I liked:

Can the boots be heavy if the astronaut is not?  Are the boots heavier than the astronaut?  If not, do the boots weigh down the astronaut or does the astronaut way down the boots?  I think a few questions like this can make the logical inconsistency evident. (Jerry Touger)

But, countered Dave Van Domelen:

Actually, it goes along with ideas like blankets being intrinsically warm.  Qualities as properties of things, rather than the result of interactions.

And from John Clement, an idea I’d never heard before:

This comes from the concept that “gravity” exhibits a threshold effect.  You have to have enough of it to be pulled down, otherwise you float.

Which, pointed out a discussant, suggests that students are using buoyancy as an analogy — if you’re heavy enough you sink, if you’re light enough you float.  Or, perhaps, friction is the correct model — there is a threshold at which the force becomes effective.

Of course, trying to address these misconceptions as “problems” to be plucked out of the students minds won’t work.  They’re using these ideas because they fit with their experience of the world.  Trying to understand their underlying conceptions (without perjoratively labeling them as misconceptions) and working from there, will be most productive.  Dewey Dykstra has written quite a bit about this, and you can see my previous post on that.

Other resources:

• Minds on Physics (vol 4) has a good section on moon/earth comparisons
• An entire thesis was written on the “heavy boots” problem
• Chapter 4 (p 44-46) of another thesis also deals with this problem
• David Hammer, More Than Misconceptions” published in AJP in 1996.

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No, of course not.  But to hear us education folks prattle on, you’d think that an instructor who lectures to their students is doing them a grave disservice.

Well, if all they’re doing is lecture, then their students could be getting more bang for their buck.  But lecturing is perhaps an indispensable part of class, especially in large college courses.  I’m reading a great article right now on how to make lectures more effective — here are some tidbits from that article (P.A. deWinstanley and R. A. Bjork, “Successful Lecturing:  Presenting Information in Ways that Engage Effective Processing,” in Applying the Science of Learning to University Teaching and Beyond).

Firstly, people need to be active in order to learn.

Toward achieving the goal of having students actually learn during lectures, it is important to remind ourselves of some fundamental properties of humans as learners. Learning does not happen, for example, through some kind of literal recording process. Rather, learning is an interpretive process: new information is stored by relating it to, or linking it up with, what is already known.

So, in lecture, we need to be able to spark the kinds of cognitive processes that actually help people learn.  For one, students’ attention can’t be divided if they’re to fully process what we’re trying to teach.  But Powerpoint and other tools require students to both attend to something visual (the screen) while they process something auditory (what we’re saying).  The end result seems to be that students think they understand, but can’t actually recall the material on the test  (Note the implications for students’ tendency to multitask during class!)  That’s horrible — students leave with the impression that they don’t need to study because they know the material, but they really don’t.

It’s also important that students, once their attention is directed, have a chance to interpret and elaborate upon what is presented in lecture.  New information has to be fit in with what a student already knows.  A graph, for example, isn’t easily memorized.  But once a student has determined what that visual information represents, and used it to answer a question, he will more likely recall the graphic or its message.

In order to remember information, it’s also important that students be given a chance to generate and retrieve that information.  The act of recall strengthens neuronal connections, creating learning.  That’s why it’s helpful to test oneself when studying for a test (and this is useful even if you aren’t given the answers about whether you’re right or not, though feedback is more helpful).  Producing information helps us learn more than being presented with that information.  Even something as simple as having to fill in missing blanks in a word (eg., “try to incorporate g-n-r-t-ng into your lecture”) results in better learning than reading that same word in bold (eg., “try to incorporate generating into your lecture.”)  Of course, the use of personal response systems (“clickers”) fulfills this end very nicely.

A few presentation tips from the article:

Space repetitions of information across lectures.  Long term recall is improved when information is spread out over time.  That’s why it’s better to study over several days, rather than cram the night before the test.

Show key concepts in several different ways. This is termed “encoding variability,” and gives students a chance to learn the material in more than one way, which helps them generalize what they’ve learned.

Provide structure. This is the goal of the ubiquitous outline we see in talks, lectures, syllabi, etc.  Some studies have found that students learn a lot from filling in an instructor-prepared outline of lecture notes (eg., headings and subheadings), rather than taking lecture notes on a blank piece of paper.  Concept maps are also useful ways of helping students see the big picture.

Use visuals and mnemonics. This is another way of increasing encoding variability, or the different ways in which students process the information that’s being presented.  Vivid examples and analogies can help, as can graphs, figures, or having students produce their own diagrams.  Enthusiasm and humor, well-placed, can also serve as a mnemonic.

Ask students questions. Ask students questions in class, and require them to give the reasons behind their answers.  Again, clicker questions are a great way to do this, and to make sure every student has a chance to explain their reasoning (at least to their peers).  To get the real benefit here, the questions have to be genuine questions, not rhetorical.  So many instructors ask a question, and then answer it themselves, lulling students into a certain passivity.

So, there are many ways to make lecture an extremely positive learning experience for our students.  But simple enthusiasm and clear explanations aren’t enough.

Here is the original chapter if you’d like to read it.

(P.A. deWinstanley and R. A. Bjork, “Successful Lecturing:  Presenting Information in Ways that Engage Effective Processing,” in Applying the Science of Learning to University Teaching and Beyond).

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This PERC talk was from Anna Sfard about how we construct meaning socially

How we talk about things, says Sfard, matters.  How we talk about things changes what we see, and also what we do.

How do we talk about math or physics?  How do we talk about learning math and physics?

We need more than one way of talking.

For example, she showed a clip of a teacher discussing negative numbers with her class.  She had students re-invent the rules for adding and subtracting signed numbers.  SHe expected that students would have a hard time with “minus times minus” but instead the first problem was about “plus plus minus”.  What is 2 times (-5)?  One student gave the answer that 2 times -5 is -10 because “5 is the bigger number”.  The class followed this student, citing that rule for the answer for several other problems.  When the teacher presented her argument, the children were skeptical and openly disbelieved her.

What went wrong?

We can see learning as acquisitionist and participationist.

If learning is change, what is is that changes when a person learns math/physics?

Acquisitionist.  Piaget would say “one’s concepts/mental schemas change.  One constructs and acquires those new constructs.”  Learning depends on our cognitive makeup.

Participationist. Vygotsky wuld say one’s participation in an activity, form or practice changes.  The form of activity or way of performing a task changes.  Learning depends on human agency.

Acquisitionist and participationist are not incompatible.  Both are useful.  You can choose which one to use depending on what you’re looking at.

What about school learning?

School learning means a change in thinking.   But what is thinking?

People develop skills by doing things together.  These activities are communicated by communication.  So “commognition=communication + cognition”.  Learning, says, Sfard, is a form of communication.

What is math or physics?

Math is a way of thinking.  It’s a discourse. We communicate about math through keywords, symbols, descriptions, and processes (like proofs).  But is communication all there is to math (or physics)?  What is number?  It’s an idea we made up to communicate something about the world.  Apart from people, number (or force) doesn’t really exist. We can’t describe “force” without using the word force!?

Let’s go back to the example of the math class and negative numbers.  That class created new rules together, though not the ones the teacher wanted them to arrive at.  What they arrived at wasn’t consistent or contingent on other things that they knew (or would eventually know).  The teacher has knowledge that the students didn’t have.  She was an expert and needed to have an active role in that conversation.  However, she was likely to use words in a different way, with different rules, than the students would. So, the class needed to agree about who gets the final say if people don’t agree.  Invention isn’t enough!  The teacher didn’t make it explicit how she goes about talking about ideas, and she renounced her leadership.  So, the students invented their own rule, a rule that wasn’t that great, and the teacher’s leadership was difficult to regain because they hadn’t formed an agreement on the role of teachers and students.

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This is the from PERC (Physics Education Research Conference). This talk was by Andrea diSessa (Berkeley), who developed the theory of phenomenological primitives (or p-prims).

diSessa’s recent work is looking at how students’ intuitive ideas help them construct meaning.  For example,  Newton’s Law of cooling says that the rate of change of temperature of something is proportional to the difference in temperature between the thing and its surrounding.  That means that liquids cool off quickly at first.  One of the students in the high school class that he studied explained that “so when one is way off they kind of freak out” and then they “calm down” when they get closer to equilibrium.

Going back to 1993, in his writings on p-prims he developed some ideas of ideas that people bring to problems such as these.  Eg., “more effort begets more result”, a p-prim of “agency.” “Abstract balance” is a p-prim indicating that in certain situations things must balance out.  Abstract imbalance is the idea that things can be “out of balance.”  Equilibration is a “return to balance” that can involve either overshooting equlibration or slowing equlibration.

“I think that the liquids like to be in equilibrium [abstract balance], so when one is way off they sort of freak out and work harder to reach equilibration [abstract balance, where "agency" is defined as "freaking out" and "working harder"] and when it’s closer to equilibrium they’re more calm [lower agency].  So they sort of drift slowly [lower effort begets lower rate of change].

So, this person has introduced agency (“freaking out”) in an area that is usually not seen as having agency.  The amount of agency is controlled by the temperature differency, and “more effot begets more change” is invoked to explain the rate of heating and cooling. The net result is that the student has created a causal chain in his understanding of heating and cooling.  These are very useful ideas! Temperature difference is what drives the rate of heating and cooling in this student’s mind, which is exactly right!

What about how the glass reaches equilibration…. does it slow down and approach equlibration, or does it “overshoot” it and then come back?   Here is one student explanation:  “The hot water is like shocked.. but the colder water that you put it into… causes it to cool down really quickly.  but once it’s at a lesser temperature, it starts to slow down as it reaches equilibrium.”  Like the word “freaking out”, “shocked” invokes an idea of agency.  “Once the really cold water gets put into the much warmer water, it experiences like a shock because they’re so drastically different.  So it gets closer to that temperature faster in the beginning and stops freaking out and calms down as it approaches equilibrium.”  Again, this student is bringing up the idea of temperature difference being important.

Eventually, though the students start translating their ideas into math.  A few days later, a student asks why the cooling graph for a hot object is steeper than that for acold object the student says “because the hot one is further away from equilibrium than the cold one.”  She’s dropped the anthropomorphism and ideas of agency.

So, these intuitive ideas help students make sense of something, and move towards a more abstract formal understanding.  Note that this is like the ideas in one of my first posts this week, where we discussed how to use students’ informal understanding of some event to build up a more mathematical description.

He emphasized that social interaction, like how these kids figured out their ideas of heating and cooling, is an important part of how we know.

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This is the beginning of the PERC (Physics Education Research Conference).  This talk was by Michael Posner, about how brain science informs us about effective classroom learning.

Brain research gives us insight into the process of how people learn and understand, including techniques like fMRI.  Neuroimaging contributes to our understanding of how we should teach. In language, for example, skilled readers don’t have to concentrate on the details of reading — such as the organizaiton of letters into a unit or a word.  But children who are still in the process of doing this, or who have reading difficulties, can have trouble extracting the meaning of their reading because they’re still concentrated on this process of reading, which makes it difficult to focus on the meaning behind the words that they’re reading (or, even, to enjoy it).  Studies on people with brain injury shows us which areas of the brain are relevant for these different tasks.

Infants, even at 7 months, have some primitive ability to count.  For example, when infants are shown two puppets, which are covered by a screen, and then a 3rd puppet is added, they will look longer when there is 1 puppet left when the screen is taken away than if the addition is correct.  When we look at the brain activity in the relevant area (the anterior singulate, which is active in error correction), these infants show activity in the same area as do adults (albeit a few milliseconds later).

Attention and self regulation is a large area of his study. This is what, he tells us, lets us stay seated in this room despite our desire to go out for cocktails.  The ability to concentrate and control oneself is very important for kids in school, who need to sit still in class, not leave, and deal with their fear about school.

Expertise.  We’re trying to build particular skills in college.  An expert chess player, exposed to 5 seconds of a master game, can reproduce the entire board.   A novice can only do the usual memory span of 5 or 6 pieces.  The expert can chunk the board into portions.  We chunk letters into words when we read, and we chunk portions of faces together to let us recognize them.  There is a particular part of the brain that works on this chunking operation, and another part of the brain that then remembers if we know that person.  An expert in birds see birds in a different way — the visual part of their brain reacts differently to birds than a non-expert.  It performs automatically and delivers the information to other parts of the brain.  What about physics experts.  Do they see the world differently?   He showed us a standard textbook picture of a spool being pulled.  It’s likely, he says, that our posterior visual system reacts differently to this picture, due to our training, in relation with other aspects of the brain.

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Today’s session is all about using diagnosis, or assessment, in your teaching (“Designing a Diagnostic Learning Environment in the Pre-College Classroom”; Lezlie DeWater, Eleanor Close, and Hunter Close).

In the last post I talked about one way to elicit students ideas, using a video and brainstorm.  This time, they gave us a bunch of pull-back cars to play with — cars that you pull backwards (storing up some energy) and then move forward when you let them go.  It’s amazing how easy it is to get physics teachers to play around!

Pull back car from Arbor Scientific

Then we went, as groups, to flip-chart paper, and were asked to “make a representation of what you notice about the car and how it moves.”  We spent a while doing that, drawing arrows and pictures and words, and instructor circulated asking quesitons like “what does that line mean?” or “why is there a smiley face there?”  We then did a “gallery walk” to see what other groups had drawn.

• Many people noticed that a small backwards pull gave the car a lot of forward motion, and some people tried to measure how far forward it would move for a certain amount of pull-back.
• Some noted that there were different kinds of energy (eg., KE, U, and work) and gave some some of pie chart or graph showing the different amounts.
• Some showed the motion of the cars going straight or curved
• Some pictures were more artistic and had pictures, some had graphs or data, some drew vectors and representations of the motion.

How does this help students and instuctors?

• It gives students feedback, as the instructors asked them questions about what they’d drawn
• It gives students feedback, as they see what others have drawn and how it’s similar or different from what they drew
• It reinforces your ideas to see other students notice the same thing you did
• It gives students a broader view of the phenomenon to see what other students drew that they didn’t key into
• As an instructor, you can listen to how students are explaining their drawings to each other during the gallery walk and get an idea of what they’re thinking.

One concern is — will students think that it’s a contest to get the “better” poster, and try to figure out which poster is the best?  Students have a lot of ego competitiveness.

Some strategies to avoid this kind of thinking is to set this up as “what are some of the things you liked in different posters?”  Or, highlight the “smart” elements that are present in the poster that they might see as the “idiot” poster.  Students and teachers can have different ideas about what constitutes “science-like” representations — this is a chance to try to make your ideas about “what is science” explicit.

How does this fit into a broader framework of “how we teach?”  We were given a handout about the Algebra Project (see “Radical Equations” by Robert Moses, 2000, p. 120).

1.  Students start with a physical event – a trip or some other event.  For us, we played with cars.  Another example is taking a trip on the metro.

2.  Student gives a pictorial representation, giving an abstract representation of that event.  For us, it was writing on posters about the cars and giving some sort of picture.  For the metro trip, it could be making a picture of that trip.

3.  Students use “people talk” to discuss pictures. When we discussed the posters in general casual language, we told our stories of our drawings in “normal” language.  This gives teachers and students a window into student ideas.

4.  Students move towards more structured language. The event is translated into more physics talk, using words like start, finish, energy, direction, distance.  We get students to develop physics or math models for important features of the event.  This is a particularly deliberate process in the class.  In this activity, for example, we could identify “giver of energy,” “receiver of energy,” forms of energy,” “evidence for energy.”  The class then made new representations showing these different aspects of the car over time.

5.  Symbolic representation. After the first four steps have happened, then students can start to make some sort of symbolic representation that makes sense to them.  These are personal representations, but then students move towards some representation that everyone can understand, so everyone in the class can communicate.

This process helps students make sense of abstract symbols that, too often for students, are devoid of meaning.  A game that they are unable to play.  Students create their own mathematical and physical truths through their own direct experience.

Diagnoser

On a side note — they’ve developed a very nice online tool called Diagnoser which lets you assign question sets to students, and their answers give information to teachers about just what difficulties students are struggling with.  For example, if they look at a graph and give a particular answer for the speed at a point, they may be confusing position and speed.  Diagnoser will give you summary information for your class (as well as for each student) about common difficulties in your class. There are also several elicitation activities included in the site and example lessons for addressing these difficulties.

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