In this modern world, it gets tougher and tougher to figure out if someone is a Jim or a Jane. Whatever happened to the easy era of codpieces and corsets? Without those to fall back on, here’s a bit of physics you can use to figure it out in a pinch.

Have the person in question fold a small piece of paper into a little tent. Kneel on the floor and put the paper between their fingers, as in prayer, with their hands at their forehead. Have them bend forward at the waist and place the paper in front of them on the floor, and sit back up. Now, they should put their hands behind their back, and lean forward and try to touch the paper with their nose, while keeping their balance.

If they fall forward, it’s a man. If they keep their balance, it’s a woman. (Note, this doesn’t always work, choose your test subjects carefully).

What’s going on? Women have a lower center of gravity, we’ve got short torsos, long legs, and those nice wide hips. So if you were able to balance a woman lengthwise on your arm, her balance point would be somewhere around her belly. Men, on the other hand, have long torsos and a lot of weight in their chests. So when he tries to lean forward to touch the paper, he can’t do it because it brings his center of mass too far forward in front of his knees and he falls over.

Another way to see this biological difference between men and woman is this. Find a man and woman of equal height and have them stand next to each other. Her legs will be longer than his, and his torso will be longer than hers It’s quite striking. Or, find a man who’s a bit taller than a woman. Chances are their legs will be of equal length!

And an insightful addendum from Swans on Tea

Add “Can I balance you lengthwise on my arm” to the list of “things likely to get me slapped”

I am a science education and communications consultant -- view my website for my full range of services.

Any of you Second-Lifers out there, who are also crazy enough to stay up all night to watch an eclipse, come to one of many locations in Second Life the night of July 30/August 1. Totality is at 4:09 am Linden Time, but the party starts earlier than that. Put it on your calendars! Should be a real fun time — co-hosted by my old boss Paul Doherty (funnest boss on the planet & a great science communicator). I’ll be there. I’m DrSteph Scanlan in SL — look me up!

Here is the Exploratorium’s website on the eclipse

and here is their blog from the crew in China.

And here’s more on the Exploratorium in Second Life

I am a science education and communications consultant -- view my website for my full range of services.

[[AAPT Millikan Lecture: Eric Mazur]]

Eric Mazur (Harvard) was awarded the Millikan prize this year, and this blog post is a detailed account of the marvelous keynote lecture he gave for the occasion. You can download the entire presentation on his website, and I recommend that you do so, because, well, it was marvelous!

The AAPT Press release on the award has this to say:

“Professor Eric Mazur’s Peer Instruction technique has altered the landscape of physics teaching. Numerous teachers have adopted Peer Instruction, enlivening their classes by turning passive students into active learners. AAPT’s Robert A. Millikan Medal recognizes Eric Mazur’s outstanding scholarly contributions to physics education,” says Harvey S. Leff, Chair, AAPT Awards Chair, as well as the 2008 AAPT Past President, and Professor Emeritus of Physics, California State Polytechnic University.

Here’s the content of the lecture.

He opened up with this poem from the “Dear Professor” collection of poems based on emails sent to a real live physics professor and compiled by his wife.

Dear Professor,
I still don’t believe heavy
and light things fall at the same speed.
A feather and a stone, for example.
You kept saying I’d get it
if I lived in a vacuum.
Do you live in a vacuum?

One stark moment in Mazur’s career came when one of his students, taking a concept quiz about force and motion, asked him,

“How should I answer these questions? According to what you taught me? Or according to the way I usually think about these things?”

Why is there this difference, asks Mazur, between the world of physics and the real world? He wanted to know, so he went to Harvard square and undertook to find out. He asked people there who hadn’t taken a physics course whether physics had anything to do with the regular world. Their response?

“Yeah”

“Sort of”

“I’m sure in some way it does”

“Yes, definitely. I’m just not sure it applies to what I do everyday.”

So, while there was some hesitation, generally people were pretty positive about the connection between physics and real life. But studies have shown that generally after taking introductory physics, students believe physics is less relevant to the real world than they did when they entered the class! There is something about the way we’re teaching physics that is divorcing it, in students’ minds, from the stuff of everyday experience.

Why?

Mazur’s answer is that “spherical cows endanger physics.”

(Don’t know what a spherical cow is? From Wikipedia:

Spherical cow is a metaphor for highly simplified scientific models of reality. The phrase comes from a joke about theoretical physicists:

Milk production at a dairy farm was low so the farmer wrote to the local university, asking help from academia. A multidisciplinary team of professors was assembled, headed by a theoretical physicist, and two weeks of intensive on-site investigation took place. The scholars then returned to the university, notebooks crammed with data, where the task of writing the report was left to the team leader. Shortly thereafter the farmer received the write-up, and opened it to read on the first line: “Consider a spherical cow. . .

Mazur argues that — mostly through our textbooks — we paint a picture of physics that is

• Really weird
• Different from the real world
• Truly confusing

Physics is Weird

You’re an introductory physics student. You buy your big fat tome of a physics textbook and crack it open to see what this stuff is all about. What do you see? Really weird pictures, says Mazur. Elephants sitting on tables (with the force of gravity clearly labeled), a tightrope walker walking a rope slung between two capacitor plates, a huge wrench trying to lever the earth (to illustrate torque), a catapult set up to slingshot stones at a sunbather. “I wish I was making this stuff up,” he said, as he showed us one hilarious image after another — monkeys pulling themselves up a pulley, a periscope allowing a penguin to look underwater, a man standing in a box floating in the ocean (Be sure to download the whole presentation if you want more examples — I don’t want to pirate his presentation any more than necessary to make the point).

These textbook pictures are meant to make the content interesting or funny or engaging for students, but they just come across as strange and silly. They certainly don’t suggest that physics has anything to do with the real world. Silly art makes us look weird, he says.

Physics is Different

Image from M. McCloskey, Intuitive Physics, Scientific American 248 (1983), pp. 122-130

Think about the above image for a moment. Which path is right? If you’re a physics teacher or know something about physics, chances are you chose the parabolic path — path C. That’s what all Mazur’s Harvard colleagues chose — he showed us videotape of them.

But what about when he asked the everypeople out on Harvard square? They all chose path B. Why? Things fall straight down. When he asked them what they’d say if he told them that most physicists chose path C, they said

“I’d take their word for it, but I’d want to know why”

“I’d have to see it.”

“I’d be concerned for the world of physics.”

“I wouldn’t believe you.”

“I’m sure you know what you’re talking about, but why would it go so far forward if you weren’t throwing it?”

He then showed us a video of someone running while they drop a ball. And would you believe it? Path B is the closest to what really happens! The runner would have to be running at 25 miles per hour in order to have the ball drop to the ground where his foot falls at the end of his stride. Or, he’s running on some tiny planet where g is 1/100th that on earth. But as physics folk, we choose the path that fits our model, even if the representation of that model is wrong! None of the professional physicists he asked mentioned that the picture was exaggerated — they were even a little offended that he asked them the question! When he asked them what they would say if he said that path B was actually the most correct, they asked him, “In what sense?” The model overrides our personal experience. No wonder people feel physics doesn’t represent the real world. Illustrations like this are really problematic. They look realistic, but the trajectory of the ball is unrealistic. So there is this unrealistic image projected on a realistic background. How confusing! He showed us about 5 pictures just like this one, taken from physics textbooks.

To make matters worse, in an attempt to make pictures interesting and “real world” textbook artists put all sorts of distracting elements in pictures: hikers, baseball players, bridges, trees. He showed us, for instance, one picture of a boy throwing a ball from a bridge, with trees in the background. The parabolic path of the ball was marked on the diagram. He then showed us results from an eye-tracking study of that image, showing what parts of the picture people looked at. Where did they look? The boy, the ball, the trees, the text showing the height of the bridge. Do they look at the parabolic trajectory at all — the whole point of the diagram? Not really.

These realistic renderings of images are a distraction, he argues, not a help. These are unnecessary elements.

Physics is Confusing

In this part of the talk, he pointed out errors in textbooks, including his own. He asked us, first, are the components of a vector (eg., the x and y components) themselves vectors? There was some disagreement in the audience. There appears to be some disagreement in the textbooks too, as he showed us pages within the same textbook that first showed the components to be vectors, and then scalars, and then vectors again. In his own textbook, he found he was using confusing language to talk about whether “momentum was conserved” versus “the total momentum is constant”. He argued that because we know what we mean when we say something, we’re unconscious of the errors. We’ve become blind to what is actually written because we know what we intend to say. To the physicist it all makes sense, but the students are confused.

To Sum it all up:

Mazur summed up his main points thusly:

Silly art makes us look weird

Misplaced realism makes physics different

Lack of precision confuses

We need to be more careful in our representations, he says.

An audience member asked him what he thought the simplest concept in physics was. He thought for a while but finally answered that no concept is simple. “Sometimes I’m surprised at how we manage to learn,” he said. No wonder these things are difficult, we’ve taken thousands of years to develop our discipline.

Another interesting story, for those familiar with peer instruction. This illustrates just how much faculty can be set in their ways. He gave a talk to faculty and gave them a challenging question that he knew would be a struggle. Their responses showed that there was not a consensus on the right answer. He asked them to turn to their neighbor and discuss the answer. Generally in his classes, this results in an in lively discussion which results in most students choosing the correct answer because they are able to understand the answer as argued by a neighbor. With the faculty, fistfights almost broke out, they argued so vehemently. When he asked them to revote, the results were exactly the same — nobody changed their mind!
Thank you Dr. Mazur for such a wonderful talk!

I am a science education and communications consultant -- view my website for my full range of services.

I’ve just posted a new episode of my Science Teaching Tips podcast — Which is Closest?

Which is farthest away from the earth, the stars or Pluto? The answer may be obvious to you, but a lot of people get this wrong.  Here’s the task — arrange these in the order from closest to furthest from the earth:  moon, sun, Pluto, stars, and clouds.  Think about it first, and then listen… listen carefully!  It can be easy to miss the mistakes that people make.

We went out and harassed the employees at the Exploratorium with this little survey.  I was astounded by what we found.  Many teachers are.  Linda explains why people (even highly educated people!) answer as they do, and what this means for teaching about science.

I am a science education and communications consultant -- view my website for my full range of services.

[[AAPT Session: Transforming University Physics Departments]]

This (VERY LONG) post is primarily for college teachers.

Many of us are questioning whether the way we teach science at the university level is the best way to do it. Do we really want to perpetuate the current system, which rewards students who can perform abstract calculations with aplomb, but can’t answer basic conceptual questions about the same topics? Those who want to urge a different way of teaching at the college level, however, face the sluggish inertia of our country’s venerable institutions of scholarship and learning. Universities change slowly, and with good reason – academia is our culture’s knowledge factory, and so it should be conservative. The nature of what we produce in academic science – evidence-based knowledge – requires a conservative and skeptical faculty. We don’t take every scientific fad that comes along, the scientific establishment is slow to change. But we’re much slower to change the way we teach science at the university level than we are to change our scientific models.

Part of the problem is that faculty don’t often apply the same scientifically rigorous approach to their teaching as they do to their scientific scholarship – ie., methods based on empirically-based repeatable experiments. Faculty generally use teaching methods based on personal beliefs, don’t assess the results of their teaching, and pay more attention to the anecdotes of their neighbor than the peer-reviewed literature. They don’t read the education research literature (not surprising) and doubt its generality. Now, I must say, I personally don’t believe that education research has the same level of “truthiness” as does research in the natural sciences. It’s psychological research, essentially, which is inherently limited in its validity. But, there are still some common themes that have been shown over and over again to increase student learning of the material (such as the effectiveness of peer instruction). There are things that we know about how to best educate our students.

These are all questions that we’re wrestling with at Colorado – if anybody has any thoughts, please add them in the comments. I’ll be publishing something for university faculty on this subject, so the more input I have, the better.

This session at AAPT examined how several universities have changed the culture of how physics is taught in their department. These may serve as lessons for the rest of us.

Note that there’s a brand new wiki starting up at http://stemreform.org/ to establish the content for a User’s Guide to change in STEM education. If you’ve got experience in this area, get involved with the wiki!

How have others transformed their departments?

John Belcher – TEAL at MIT

Technology-enabled active learning (TEAL) uses a system of lecture, followed by students predicting the outcome of an experiment. The experiment is done and then followed by a computer visualization of the experiment to highlight its salient features. They use a version of SCALE-UP (students in small groups at tables working together with instructor at the middle) along with Eric Mazur’s Peer Instruction, with the added emphasis on visualizations. You can download their great visualizations for electricity & magnetism here.

University of Illinois – Tim Stelzer
They changed their introductory physics course to use peer instruction and online homework. They used a team-teaching approach, where two or three faculty were responsible for planning and implementing all aspects of the course (ie., they were all responsible for lecture, rather than having one in charge of lecture and one in charge of recitations). They adapted and built on work created by others. You don’t need to recreate the wheel, he said, but you do need to adapt existing materials to your own situation.

Why change?

At MIT, they changed the way physics was taught in part due to strong pressure: There was a high failure rate in the department, and a board member actively complained that something had to change. Students also didn’t attend the lectures – which is apparently part of the student culture at MIT. John Belcher told his own story – he was an extremely popular lecturer, he worked hard and students rated him very well, but still, nobody came to class and he failed a large portion of students. His average attendance rate was just 50%!

At the University of Illinois, they were also facing serious critiques of their course which sparked change – in fact, the engineering department was no longer going to require the introductory course anymore.

If it ain’t broke, don’t fix it. But what if there’s no crisis? How do we justify the need for change? This was the topic of Laurie McNeil’s talk. She’s written a delightful (but long!) Physics Manifesto summarizing the rationale and road to change. Definitely take a look if you’re interested in this, they’ve got a wealth of experience).

Opportunities to change

While there are reasons to change, what sorts of things let a department change? At MIT, first of all, they got a bunch of money. They also had a pariah senior faculty willing to devote the 80 hrs per week to lead the changes. Dr. Belcher admitted that it burned him out took him a few years to recover.

The University of Illinois didn’t want any such superman to lead the forms – rather, they gathered a small group of faculty who were interested in supporting the reforms. This was supported by the administration, who gave the faculty teaching release time in order to develop the new course. Having transformed a single course myself, I can attest that this is absolutely necessary – you can’t transform a course while attending to all the regular duties that a faculty member is responsible for.

So, some of the key ideas of what helped these departments change were:

• external funding
• important people who supported the change
• data showing that traditional methods weren’t working
• Friendly competition between faculty – if Dr. XXX was successful in teaching this way, so can I!
• Having a group of committed individuals
• Having one committed individual

Faculty training was particularly important, as it was important for instructors to be familiar with the content of the new course. This can take a lot of time.

Barriers to change

The common themes for what made change difficult were:

• Faculty lacking knowledge or experience about teaching methods
• Faculty resisting change
• TA’s resisting change
• Students resisting change
• Only a few individuals supporting change
• Lack of resources (such as classroom space or money)

Many of these are situational, not just about certain “curmudgeonly” individuals! So, change to university courses requires attacking some of the situational constraints.

It is also important to adapt a curriculum to your particular institution. For instance, if you have a small faculty:student ratio, perhaps having a large number of student groups won’t work, or maybe you have to add some undergraduate learning assistants to help with managing student discussion in the groups. In the same vein, in order to transfer curricular materials to another institution, it’s important to provide a list of all the resources necessary to teach that course, so the new instructors are prepared.

Reactions to change

At MIT, students reacted really positively to the pilot test of the new course, but when they ran the full blown course, the students actually petitioned against the changes. What went wrong? For one, the students at MIT just didn’t want to come to lecture! That was not part of the student culture at the institution. They found that having professionals assess that students were learning more, even though they didn’t like it, was critical in convincing the department to keep the changes. They now have 80% attendance, compared to a typical 50% attendance for most general requirement courses at MIT. Another thing they found was that it was critical to train the faculty properly in how to run the new course in order to have it go smoothly.

What about the faculty? They certainly agree that it’s a good thing to have students coming to class, as well as to have more resources going into the freshman courses. There is still faculty resistance, however – they want to lecture more and are worried students aren’t synthesizing the material without their explanations. Others, though, think that teaching this way gives students a more intellectually deep understanding of the material. In general, he’s found, the younger faculty are the most enthusiastic about the changes. Laurie McNeil also said that physicists have pretty healthy egos and don’t really take direction well. And after all, why change? They get rewarded in the current structure with teaching awards. It’s easier to change newer teachers whose teaching methods are less well-established and who don’t stand to lose face by trying something new.

At UNC, similarly, Laurie McNeil found that faculty didn’t really change their teaching style that much, and TA’s were even more conservative (after all, they don’t have a lot of power in the department). The students, however, were the ones who were most resistant. This is a common theme. Denis Rancourt from U. of Ottawa told us that his students told him that they couldn’t learn unless they he forced them to.

At U. Illinois, on the other hand, they found that both students and TA’s were quite happy with the reforms, and the student ratings of their TA’s increased.

In a different session, a faculty member mentioned the “Jerry Lewis effect” of curricular reform — you may be more popular elsewhere than you are at home. In other words, it maybe harder to get someone local who shares your vision of how the materials that you’ve created will be used, whereas someone at another institution may buy-in much more easily.

How to keep change going

(sustainability!)

There was some disagreement on the panel whether it’s important to have someone in charge of the reforms – a pariah instructor dedicated to the effort – or whether that was actually harmful in terms of sustainability.

The University of Illinois said that now that the work has been done to make the changes part of the course, it has a certain inertia, it will keep going like a massive aircraft carrier. However, one audience member asked him if this is a frictionless aircraft carrier? He pointed out that education reform efforts tend to devolve, you have to keep putting energy into it to keep it going.

Many agreed that it helps to have data showing the effectiveness of the reforms (like increased student learning and attendance), as well as to have people at other institutions doing the same thing. Both validate the kind of work you are doing.

The other problem of sustainability relates to the perspective of individual faculty. The university culture is that a particular person “owns” a course, and so when someone else teaches the course then they don’t necessarily use the other person’s materials. University faculty are incredibly independent beasts – they were hired, after all, for their intellectual merit. So, it wouldn’t be appropriate to expect an instructor to adopt course materials wholesale – that is counter to the university culture. Faculty need to have creativity and power in their own classroom, so that they’re excited about teaching the course and feel that they own it and understand why things are being done in a particular way in the course. How can we create our mateials so that this is the case?

I am a science education and communications consultant -- view my website for my full range of services.

So, we’re almost to the end of my spate of posts from the AAPT (American Association of Physics Teachers) conference (and yes, I promise I’ll get back to more general-interest stuff).  I just have to say that this last conference was one of the most stimulating I’ve ever been to.  Best conference ever!  Also the most poorly organized, but you can’t have everything.

There were so many sessions that interested me, from using art to communicate science, to how students think about math, to the effect of the type of questions TA’s ask of students.  And I could understand them.  I’m used to going to huge conferences (like the American Physical Society or Material Research Society), where you only understand the first 2 minutes of the talk (if you’re lucky).  Those conferences are always a tease — you read the abstract and get excited about learning something cool about, say, superconductors, and then you go to the talk, quickly lost, and you feel that if you just knew more you might learn something new.  So you sit in these unsatisfying sessions, paying half-attention and perusing the program looking for something to make you happy, wandering from talk to talk and never quite finding what you’re looking for.  Hmm, sounds like dating…

This conference, on the other hand was – interesting – understandable – and friendly!  People in the physics education community are, well, so nice.  They’re in the field because they care for people and their world.  Wonderful bunch.  I made friends at this conference, which has never happened to me at a conference.  In part, it’s a smaller conference than the huge physics conferences (you have NO idea if you haven’t been to one — at any one moment there are generally about 20+ talks happening simultaneously.  Thousands of physicists.  Geekfest.)

So, a big thanks to everyone in the physics education community for being so cool and doing such excellent work.  And for being fun.

Now, once I finish nursing this hangover, I’ll finish up those blog posts on the conference.  <grin>

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[[PERC Talk, Fostering science learning in diverse urban settings, Kenneth Tobin, CUNY]]
Dr.Tobin told us the story of when he plunged into a challenging experiment – to teach high school physics in urban Philadelphia. It was, needless to say, a challenge. He was an older white Australian, in a classroom with at-risk African American youth. We were both speaking English, he says, but we had no idea what the other was saying. He just didn’t understand the culture and language of urban black youth, and they didn’t understand or trust this older white man.

The solution he came up with, when working later with a class in the Bronx, was co-generational dialogues. Let’s just talk to one another, he suggested. So, they discussed with students in groups, how we might best teach you? They came up with ideas such as having the students teach one another. The teacher might be speaking, but another student would be simultaneously working with the students near him or her to teach them. They found this to be very effective, and gave the students a lot of power to take control of their own learning. The students liked learning from their peers because they were better able to understand one another because they shared a common culture and language. The students also began to have more self-confidence and those who were on the verge of dropping out ended up going on to college. He showed a powerful video clip of one of the students explaining how the class had been run to the new teacher who would be teaching the class the next semester. The teacher was skeptical of doing this peer instruction in the class, but the student was adamant about why this method was best.

This kind of teaching method, of course, requires the teacher to let go of some of the power and control they hold in the classroom. This is particularly difficult in high school where the measure of the success of a teacher is how much control they have over their class. This is even a struggle in college. For instance, the SCALE-UP curriculum restructures the classroom into small groups working together on a task with an instructor circulating as a guide, rather than all students on the same task as defined by the instructor who is in complete control. This is difficult for many faculty, and the classroom does look quite chaotic.

I think that making these kinds of changes can be very difficult – it requires a lot of soul-searching and the strong desire to see some changes in the outcomes of teaching. If you’re trying this sort of thing, be easy on yourself.

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[[AAPT Session:  Performance in large lecture courses, Brian Jones, Colorado State]]

If you’ve got a large lecture class (or, really, any size class) — like it or not, you’re a performer.  In this session, one lecturer gave several of his tips for injecting some theater into his classes in order to engage students and pique their interest.  By viewing your lecture as a bit of theater, you can take control of many aspects of the students experience.  Don’t allow the tone of your lecture to be accidental — you can explicitly frame it to accomplish what you want it to accomplish.

Theme music

Dr. Jones plays music at the beginning and end of class, which is related to the topic for that days’ course.  Students love it, and he asks them to “DJ” the class by submitting songs for him to play (they’re told the topics in advance).  He found this particularly good for starting class — he always chooses music that has a fade at the end.  This serves as a cue to the students (who are talking to neighbors, talking on their cell phone, checking their email) that class is starting, and they quiet down and pay attention.

Costume

He uses his clothes to act as a cue to students, to frame what that day is going to be like.  He can dress up, for example, for a more formal lecture day, or wear a tie dye shirt when it’s going to be a wacky day of demos.  This cues the students as to what they can expect that day.

Voice

As always, you can use your voice to paint the hues of the lecture, to emphasize, pause, or add drama.

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[[AAPT Sesson:  Text editing, problem posing, and jeopardy tasks in introductory physics, Fran Mateycik]]

I heard a couple neat ideas at a talk on some different ways to pose physics questions.

Jeopardy

Students are given a part of a problem and then asked to come up with the problem statement.  For example, F = m(hull)*g – rho(water)*V(submerged)*g.  What problem would this be part of the solution to?  She found that most students were able to recognize the individual terms and what they represented but seemed to struggle with putting this together into a coherent statement of the actual problem to be posed.

Text editing

In this task, students are given a problem and asked to determine if there is missing information or information that’s not relevant?  For example, in some random question perhaps the length of the rod isn’t relevant information.  She found that most students could identify information that was missing but had a lot of trouble identifying information that wasn’t relevant.

You can find the researchers’ website here.

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[[AAPT Session:  Easing the transition to upper level E&M, Corinne Manogue and Improving the Teaching and Learning of Upper-Division E&M, Chandralekeh Singh]]

This post is primarily of interest for college faculty.

There have been a wealth of good discussions at this conference about how to work on making changes to upper-division or middle-division college courses.  We’ve made so many great changes at the introductory level, so what are the issues facing our physics majors at the upper division?  Dr. Manogue had several thoughts based on her many years teaching a radically transformed program at Oregon State called Paradigms.  Here are some of them, below.

Vector Fields

In junior E&M, the idea of having a vector at every point in space (which is the basic idea of a vector field) is quite new to students, and they struggle with it.  One way to deal with this is to represent vector fields in multiple ways (like using color to represent the 3rd dimension).

Chunking & Cognitive Overload

I thought this was the most valuable idea mentioned in these discussions.  Our working memory has only about 7 “slots” to put information in while we’re actively learning or thiking about that information.  That’s why phone numbers are 7 digits long.  We can increase the amount of information we can stick in our working memory by grouping ideas together in some way.  For instance, which sequence of numbers is easier to memorize, 9749-6589 or 2001-1945?  The second two are both easily-recalled years, whereas the first two are random sets of numbers.  We can use chunking to help students process more information by using sets of knowledge they already have in order to teach a topic.  For example, in E&M, you can build an understanding of potential, use their current understanding of forces, and then put those “chunks” together.  In addition, just being aware of cognitive overload as you’re teaching these difficult topics is important.  There are many concepts that we are already facile with, but students are thinking about them a bit more slowly.  For instance, if you’re lecturing about the B field of a current carrying wire and use the term “theta-hat” and continue talking… if your students are still stuck on “theta-hat” they’re going to miss the rest of your brilliant explanation.

Mathematics and physics

There is a real mismatch between how the math department teaches math and how the physics department teaches math.  One thing we can do in physics is to emphasize geometry and use a variety of ways of showing the math (like graphs, words, and pictures).  We can also emphasize that math is about symbols and physics is about things. We need to separate our symbolic knowledge from the physics represented by that knowledge.  That distinction is often not clear to students, who see the math in a symbolic for that looks very different when they leave math courses and enter physics courses.

In addition, the struggle to understand the mathematics at this level can cause a cognitive overload that makes it difficult for students to attend to the actual physics behind the math.

Chandrelekeh Singh (from Penn State) also gave a talk on some similar concepts.  She added the following

Functional (conceptual) understanding

What we want students to be able to do, Dr. SIngh argues, is to be able to apply the concepts they learn to new situations  In other words, if they learn about the general theory of conductors, they should then be able to do a problem in the real world that applies that knowledge.  But this is very difficult for students to do.  She found that graduate students had great math skills, but often lacked what she calls “functional understanding” — they had difficulty in answering conceptual questions.  She thinks this is due to poor training at the undergraduate level.

Abstract concepts

Many of the concepts at this level are very abstract, and as instructors we need to help guide students in making the connection from the concrete situation to the abstract formalism (“scaffold” in ed speak).   As instructors, we have much more experience with these abstract concepts an they seem quite obvious to us.  We have an intuition about these abstractions which makes it difficult for us to empathize with students struggle.  For example, she’s noticed that students continue to be uncomfortable with polar coordinates, and will often transfer a problem to cartesian coordinates even when it’s easier to do in polar.

Systemic change

The way the educational system is currently structured, those students who thrive in a system where you learn by lecture, not learning deep concepts and able to perform calculations without understanding are rewarded (through admission to graduate school).  We, as instructors, make that system.  If we want to reward a different type of student understanding, the onus is on us.

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