A blog about physics from a well caffeinated grad student.
I’ll write a more interesting post soon, but for now, I present Lawrence Krauss. Here he gives, what I’ve decided to be, the best one hour overview of cosmology I’ve ever seen. (via richarddawkins.net)
What do you all think about his suggestion that getting a universe from nothing is natural?
So, in case you don’t know by now, it’s Blog Action Day 2009… ( or at least, it will be for another half hour. I’m a bit behind the times.)
Blog Action Day is an annual event held every October 15 that unites the world’s bloggers in posting about the same issue on the same day with the aim of sparking discussion around an issue of global importance. Blog Action Day 2009 will be one of the largest-ever social change events on the web.
The topic of choice for this year is: Climate Change. Yes, that scary thing.
I puzzled a while trying to think of something physicsy to tell you about climate change. I could tell you that same story about how CO2 in the atmosphere traps heat causing an increase in average global temperatures. I could tell you that this is exactly the reason why the planet Venus (with a CO2 rich atmosphere), although it is further than the sun from Mercury, is hotter by a long shot. But I decided against repeating those same old stories, because I figure you’ve probably heard them many times and are probably getting numb. Instead I’m going to go outside my comfort zone and plunge into the depths of Limnology and tell you about some current issues involving climate change in the convective currents of holimictic lakes.
…what’s a holimictic lake, you ask?
Good question. I’m not much for fancy names; I prefer concepts. So, let’s start with the basics. Firstly, you must have heard that hot air rises. But why does it do that? Well, air that is hotter than the air surrounding it is also less dense than that air. This means that a volume of hot air weighs less than the same volume of colder air. The colder air will be pulled towards the earth more than hot air and so hotter air will be pushed out of the way (upwards) by colder air.
The same is true for water, but only to a certain degree; 4°C to be exact. Water, unlike air, is densest at 4°C, so in a tub of 5°C water, a 7°C blob of water will tend to rise to the top. On the other hand, in a tub of 1°C water, a 3°C blob of water will tend to sink because even though it’s warmer it is more dense.
Now, consider a lake in the four seasons. During the Summer the lake water is generally above 4°C, so the sun will warm the top layers of the lake and that water (being warmer and less dense) will stay on top and the cooler water will stay deeper down.
When Fall comes around the top part of the lake will be cooled. Eventually that top part of the lake will cool to the same temperature as the bottom part. Winds can cause some turbulence and the bottom parts and top parts of the lake will get mixed up.
When Winter comes along the top part of the lake will be colder than the bottom part which can happen when the lake is lower than 4°C. The top layer of the lake may freeze over and the lake will again get separated into layers of different temperature — this is called stratification.
The lake gets mixed up again when Spring comes around. The top of the lake will be heated again and when the lake water at the top reaches 4°C it will sink to the bottom and mix up the lake.
A lake that undergoes this kind of mixing is called a holimictic lake and if it does it twice a year (as described above) it’s called a dimictic lake.
…what does this have to do with climate change, you ask?
Well, nutrients from the lakebed seep into the lower parts of the lake while it’s stratified (Summer and Winter for a dimictic lake). When the lake mixes, these nutrients get mixed into the whole lake. If you are aquatic life which has adapted to depend on those nutrients, this mixing is a very good thing. Without it, many species of fish would not be able to survive in that lake.
Climate change threatens to put a damper on that mixing process for some lakes. As average global temperatures increase, unusually warm Winters become more likely. What would happen to a dimictic lake during one of these unusually warm Winters? Well, the lake won’t cool very much during the Fall, and might even stay above that 4°C mark. This would cause less mixing during the Fall. To make matters worse, because of the warm Winter, there will be less mixing during the Spring as well. To make matters worse still, those salts that are dissolved in the deep parts of the lake make those deep layers more dense. Less mixing during a certain Fall or Spring means more salts stay built up in the deep layers of the lake making it even more difficult to mix the upper and lower layers in future seasons. This is a runaway process and it can lead to a nutrient deficient lake, and very unhappy fish.
The take away message? Climate change isn’t just about things getting warmer and sweating more during the summer. Climate change is a direct threat to whole ecosystems. By tipping ecosystems out of balance it endangers many species of animals, including the animals causing the tipping (us). It’s high time that you start sweating over this situation. Please think about ways to cut your greenhouse gas emissions. If you need some suggestions, here are two good ones.
So, I’ve never heard this myth before, but a friend asked me about it a while ago. The myth states that running in the rain will make you wetter when you arrive at your destination than if you had walked. This was on my mind recently because it was actually a bonus question in the physics lab I’m TAing for this year.
Apparently Mythbusters showed that running is a better option for staying dry, but only after they corrected for a false result they’d obtained in a previous show. So how could you figure this out without going through the hassle (or fun) of running through some rain yourself?
Well, what we could do is set up an idealized situation. Imagine there are 5000 drops of rain falling in every cubic meter above you. Let’s say they fall at 5 m/s straight downwards. To simplify things even further, let’s suppose we ignore the structure of our bodies and just consider a blocky person to have a set width, depth and height. Let’s make up a name for this person; Sponge Bob Square Pants (Bob for short). So, let’s say Bob is 0.25m thick, 0.5m wide, and 1m tall.
If Bob stands in the rain, all of the rain will hit his head. The number of drops hitting him per second is equal to the density of the rain times his width times his height thickness times the velocity of the rain in the downwards direction;
5000 drops/m^3 x 0.25m x 0.5m x 5m/s = 3125 drops/s
If he moves (walks or runs) this amount won’t change because the downward velocity of the rain won’t change with respect to him. But, on the other hand, if Bob walks or runs in the rain, the rain will have a horizontal velocity with respect to him, so the rain will start to hit him in the front. We can find the number of drops hitting his front by the same method.
5000 drops/m^3 x 0.5m x 1m x V = 2500 drops/m x V
I’ve just called Bob’s walking/running speed V. I’ll leave it like that and plug in his speed at the end. If Bob needs to run to his house which is 20m away, a total number of drops of rain will hit him in front and back for the trip which we can calculate. We just need to multiply the above results by the time it takes him to get there and then add them together. That’s just the distance to his house divided by his walking/running speed.
time = 20m/V
But here something funny happens. For the rain hitting his front:
(2500 drops/m x V) x (20m /V) = 2500 drops
Hey! It doesn’t depend on how fast he runs! So it really comes down to the rain hitting his head:
(3125 drops/s) x ( time to get home )…
The faster he runs, the less time it takes him to get home. So to minimize the number of rain drops hitting his head, the faster he needs to run.
… but hey! I’m not the same shape as Sponge Bob, and rain doesn’t always fall straight down, you say?
Well, for those of you who want a more complex analysis, here’s a link to an online running-in-the-rain-wetness calculator. Check it out, it’s fun!
So maybe you’re a non-physicist, who wonders how physicists think. Maybe you aren’t really sure how those crazy physicists come up with all of these equations and theories seemingly from thin air. Maybe you’re getting a bit bored of F=ma posts. Well, I’m going to try my best to give you a bit of an inside look at some of the conceptual tools commonly used by physicists in a little series called: The Physicist’s Toolbox.
This week: Thought Experiments
When someone mentions the term “thought experiment”, the first person that probably comes to mind is Einstein and his daydream about trying to chase a beam of light — an image of which even non-physicists will be familiar. This is because thought experiments tend to be very memorable and accessible because they usually involve simple math or no math at all. Despite their mathematical simplicity, however, they still manage to shed light on puzzling aspects of nature.
Physics is an empirical science which means that you can do all the thinking and theorising you want, but at the end of the day, if it doesn’t match the real world experimental results, it’s wrong. This fact might make the term “thought experiment” seem like a bit of an oxymoron. It’s true, a thought experiment won’t serve to prove anything in the same way a real experiment would, but it still has tremendous value. Thought experiments serve to collect one’s thoughts and attempt to make certain concepts in physics more intuitive. Occasionally they can shed new light on how the world works.
Here’s a really neat example. Remember Galileo? Remember the story of him dropping a cannon ball and a musket ball from the leaning tower to show that they fell at the same rate? Well, it’s unlikely that Galileo actually did this. It’s more likely that this was a well crafted thought experiment. Imagine starting with the assumption that heavier objects fall faster. What happens now if you attach a lighter object to a heavy object? The light object would want to fall slower than the heavy one, and would almost act like a parachute for the heavy one. But if you consider the compound object, it is heavier than both objects alone. So shouldn’t it fall faster? This thought experiment demonstrates that the assumption that heavier objects fall faster leads to a contradiction. An obvious resolution to the contradiction is to declare that all objects, regardless of their weight, fall at the same rate. If one did this experiment in real life would probably not see the objects fall at the same rate because of air friction. The power of the thought experiment is in its simplicity. It serves to demonstrate how nature should behave under certain assumptions and signals that something more is needed to be understood if nature doesn’t behave like this.
Newton’s cannon ball is another great example of an enlightening thought experiment. Really, just the simple picture of a few trajectories of a cannon ball being shot with greater and greater force demonstrates how things like the moon can orbit the earth. Good thought experiments like this tend to give the thinker an “aha!” moment; that moment of realization.
I’ve blogged about a few thought experiments here on Morning Coffee Physics. Some fun ones include Einstein’s elevator experiment, and the Rope and Wood riddle.
There’s one more thought experiment I really like. Imagine placing a chain (constant mass per unit length) on an obtuse triangular block. On one side, there is less chain, but a steeper slope. On the other side, there is more of the chain, but the slope is not too steep. Which way will the chain slide?
Sure, you could work out the forces and angles and all that jazz. But there is a very simple way to see the answer. Think about it for a few seconds.
…
Done? Okay.
Just connect another chain below and let it hang off of the ends of the previous chain, like so. Have you felt that “aha!” moment yet?
The hanging chain is symmetric so it should pull on each side of the top chain equally, which cancels its effect out. But if the top chain slid to one side or the other, for every link that fell off the block, another would replace it on the other side (coming from the hanging chain). Meaning the two (now linked) chains would spontaneously spin around the block! This is a ridiculous notion and a violation of the laws of conservation of energy. Therefore, the chain in the previous picture must remain at rest. No math necessary!
Anyone else have a favorite thought experiment?
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A great reference: Brown, J. R., “Thought Experiments”.
So maybe you’re a non-physicist, who wonders how physicists think. Maybe you aren’t really sure how those crazy physicists come up with all of these equations and theories seemingly from thin air. Maybe you’re getting a bit bored of F=ma posts1. Well, I’m going to try my best to give you a bit of an inside look at some of the conceptual tools commonly used by physicists in a little series called: The Physicist’s Toolbox.
This week: Symmetry
Physicists are obsessed with symmetry, perhaps even more than people with an OCD. It’s human nature to look at something symmetric and call it beautiful. Even physicists call their theories and equations beautiful if they contain some kind of symmetry. The aesthetic attraction humans have towards symmetric things is not a surprise to me; the laws of the universe are founded on symmetry. It’s only natural that the things we see every day in our world reflect this symmetric undertone of the universe and we call these things beautiful.
…so what is symmetry, you ask?
You probably have a good idea of what symmetry is by just looking around your everyday life. You probably look in the mirror every morning and notice that our bodies are symmetric. If one draws a vertical line down the center of the human body, the right side is approximately the mirror reflection of the left side. This is called reflectional symmetry but it is one of many types of symmetry.
You can make the idea of symmetry more general by roughly saying that something is symmetric if you do something to it and it stays the same. The “doing something” part, physicists like to call an operation. This could mean anything; reflection, rotation, translation, magnification, etc. So to be more specific, physicists say that some “thing” is symmetric under a specified operation.
Look at that picture of the square up above, for example. Ignore the colorful dots and just concentrate on the shape. If I rotate the square by any multiple of 90 degrees, it will look exactly the same as if I hadn’t done anything. So you could say that the square has rotational symmetry. The operation here is a rotation by an angle which is a multiple of 90 degrees. So an even better thing to say is that the square is symmetric under rotations by angles of multiples of 90 degrees.
…okay, but what does this have to do with physics, you ask?
This is the cool part. In physics, instead of looking at shapes of things and studying how the shape of something is symmetric under an operation, we go a bit further. We study how the rules of nature stay the same under a certain operation. Let’s look at a concrete example. Let’s say I do a little experiment: drop a ball from some height and time how long it takes to hit the ground. Then I take myself, the ball and the entire earth and move it ten feet to the left (in other words, I preform a translation on the system). Now I redo the same experiment. The ball should take exactly the same time to hit the ground if dropped from the same height. So, the rules of nature are symmetric under translation in space.
Since so many people have heard about Einstein’s Special Relativity, let’s use that as an example too. Einstein postulated that the speed of light is constant for all “inertial” observers. This is a statement of symmetry. It’s saying that if you preform an operation on an observer, the speed of light should stay the same for that observer. The profound insight was that this was even true for operations that changed the speed of the observer. These operations are called Boosts. (Note: I don’t mean acceleration. It’s not the same thing as a boost. I mean this as a mathematical concept.) So, if you consider two different observers, with different (constant) velocities, the speed of a light ray will be the same for each of them. Noticing that the constancy of the speed of light is symmetric under boosts leads to crazy results which you probably already know about (time dilation, length contraction, etc).
In fact, when physicists notice (or impose) types of symmetry in their theories, different laws of physics just fall out of the equations. Some of these are:
Symmetry is has become such a useful tool that physicists have come to assume that physics theories should abide by some standard symmetries. This is partly the reason you hear crazy ideas like the world having ten dimensions. String theory starts with the assumption that there are “strings”, it then imposes symmetry arguments and what falls out is: the world has ten dimensions.
But what happens when symmetry breaks and the laws of nature become a bit lopsided? Hey it happens! Nature isn’t a perfectly spherical cow.
That’s when things get even more interesting…
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Update: An interesting TED talk on Symmetry.
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1. I shouldn’t even bother with F=ma posts anymore. Rhett at Dot Physics is totally owning everyone with his super interesting classical mechanics posts.
Well now. That was a long lasting spontaneous blog hiatus…
Sorry. It’s not that I’ve run out of ideas, it’s mainly lack of time… well, since time is relative, maybe it’s just that I perceive myself as having less time than I actually do. But enough excuses… let’s get back to the physics.
I saw a really neat (3 page!) article on arXiv today called “Google Earth Physics“. I love google, and I love physics, so naturally I had to check it out. The abstract reads,
Google Earth photographs often show ships and their wakes in great detail. We discuss how the images can be used to calculate the velocity of these ships.
Did someone say, do-it-yourself-physics? I knew I had to post this. Naturally, ZapperZ beat me to it… but I’ll go one step further and actually try it out.
The actual article is only three pages long and is very easy to read, so if you want more details I’ll direct you straight to the source. But the main suggestion of the article is that using a very simple formula and making two measurements, you can get a rough estimate of the velocity of a boat. The formula is simply,
boat velocity = 1.25 * Sqrt(wl)/Sin(ang)
; wl is wavelength of wake in meters,
ang is angle between wake and boat direction of motion
The 1.25 comes from some dimensionful constants in front involving Pi and g, but if you use standard units (meters) for the wavelength of the wake, those factors just become 1.25. (The fine print also says this assumes the boat is in deep water. In shallow water this equation isn’t accurate.) You can check out the article for the real formula. To make the measurements you just need to measure an angle and the wavelength shown in the picture up at the top. You can use a protractor for the angle and a ruler for the wavelength and then use the scale given in google maps to convert between your “image length” and the actual length.
I found a boat in my area (toronto) on google maps here. Then I used gimp to measure the wavelength and angle of the wake. I then converted my image length to a real length by measuring the image length of the google scale and a simple ratio:
real distance = wavelength * real length of gscale/img length of gscale
= 76px * 10m / 93px
= 8.17m
And I measured an angle of around 35 degrees. Plugging that into the equation I get:
boat velocity = 6.23 m/s = 22.4 km/h
I’d say that’s a fair velocity for a boat… but what do I know about boats. Try it for yourself and see if you get the same answer!
Okay. So, I have another riddle for you. This one is not really physics based, but still it can be solved with logic alone (no math). I’ll give it to you in storybook form just for fun.
Once upon a time there was a forest, and in this forest there lived a sufficiently large number of gnomes (the exact number of gnomes doesn’t matter). They were extremely logical beings and valued the needs of the group far above their own individual needs, so much so that no mirrors existed in their village, so as to keep the focus of their attention away from themselves. They valued homogeneity, which was just as well since all of them were identical… well, except for one thing: their hats. For some inexplicable reason, while most of the gnomes had red hats, there were a certain number of them (say “N”) who had blue hats. These blue hatted gnomes didn’t themselves know that they had blue hats (for lack of mirrors, you see) and it was a taboo subject of the highest degree. No gnome would EVER give any indication — verbal or otherwise — as to the color of another gnome’s hat.
One day, at one of the gnome village meetings, where all the gnomes gathered to discuss serious matters, they decided as a group that because they valued homogeneity so much, it would be better for the village if all of the blue hatted gnomes left and lived elsewhere. Nothing more was discussed. No gnomes were singled out as having blue hats. The blue hatted gnomes were simply expected to leave as soon as they knew they had blue hats.
How many village meetings passed before all of the blue hatted gnomes left?
This is a really tricky riddle. Just remember, the solution has nothing to do with the gnomes using sign language to tell other gnomes about their hats, or using spoons as mirrors to see themselves. It’s a much more elegant and logical solution. If you haven’t heard it before, feel free to bounce ideas back and forth in the comments.
(Here are Part 1, Part 2 and Part 3 in case you missed them).
Well… I don’t think my students have this much conceptual difficulty, but I thought I’d start this post off with a bit of comedic relief.
Anyways, a week has passed since the last practical but I’m not behind in posting because this is the undergraduate reading week. My mind has been bubbling with ideas since then; most of which are the result of a TA brainstorming session we had on Friday. A group of enthusiastic learning assistants (lured partly by free pizza) gathered to share their ideas, concerns and advice with a representative from the undergraduate education department (or something of that sort). It looks like there are a lot of problems with this new physics curriculum (IE: the “practical sessions”). We conveyed a lot of worries and put forth a lot of suggestions which I will try to summarize here.
What I should first mention is that I am not alone in my difficulties. Almost all of the other learning assistants are, like me, having difficulties. Here are, in my opinion, the top three problems that we and the students are having with this course:
So. Problem 1 (The biggest):
Students need feedback on their work so that they can narrow down what it is they don’t understand. I think one of the hardest things about learning (in a student’s reference frame) is figuring out what it is you don’t know. But students are not given any feedback on their lab book (aside from an initial trial grading of the first activity). The reason for this is that not all activities in their lab books will get graded, and the choice of which ones will be graded is kept secret until midterm. The problem is that the TAs haven’t been told either… so we can’t go through on a weekly basis and put comments in the lab books because we haven’t been assigned enough hours to do that much “correcting”. Hopefully this will be easily taken care of by simply telling the TAs to grade a subset of the week’s activities on a regular basis.
Students need meaningful feedback when feedback is given to them. It’s quite deceiving when a computer tells a student that they’ve gotten the question 100% right when the truth of the matter is there are many things they still don’t understand. But this is what is happening. Each week the students are expected to complete an online assignment hosted by the Mastering Physics website. The problem with these assignments, I think, is best conveyed using the analogy of — and I apologize to the students for this analogy — trying to teach a donkey the way into town by leading it with a carrot on a stick, then expecting it to be able to make the journey on its own. The questions on the Mastering Physics assignments are good questions BUT they are asked in such a way that holds the students hands and practically gives them the answers to each step. This severely reduces the effectiveness of the questions. When I asked one of the students if she had trouble with the Mastering Physics questions she replied, “Well, I got the question right … but I still don’t understand what I did“. Other TAs and even past students have told me similar stories about these assignments.
… but perhaps these assignments are intended to be more useful as feedback for the TAs, you say?
If this were the case, then at least their existence would have some merit. The fact that the vast majority of the students in my section get above 90% on every question should illustrate that this is not very helpful as feedback for us. Apparently this Mastering Physics site has been used for years, much before the recent curriculum change. I think it was part of an effort to recycle old bits of curriculum that is falling short.
It also looks like a good example of an over-reliance on technology to improve education. Computers don’t teach people; people teach people. Fancy gadgets, clickers and advanced quizzing systems are a great idea, but they themselves are not enough. They need to be used effectively. I think this curriculum is still in its early stages of metamorphosis and everyone is still trying to figure out more effective ways of using the new technology and new teaching methods.
Possible solution to all three problems:
One fantastic solution to this problem came together as a melange of a few suggestions in the TA brainstorming session. The organizers of this course got rid of the formal tutorial sessions because they deemed them ineffective and thought it would be more effective to work that kind of material into the practicals. The way we are currently doing this is not working. Instead, what would be more helpful is to have “theoretical” questions as part of the lab activities. There are several benefits to this if it is conducted well.
Firstly, it would encourage the students to work out questions as groups inside the practical sessions. They could get immediate feedback from the TA, and if they worked out the question on their fancy new whiteboards (which I found to be an effective method when I tried it last week) the TA could immediately gather feedback from them in terms of conceptual difficulties and so forth. The questions could be made more difficult without the “hand holding” formulation because if they truly got stuck, they could ask the TA who would be able to gauge what hints were just enough to get the group back on track.
Secondly, the questions could be directly related to the lab activities they would do immediately after. This could solidify their understanding and also make it more interesting. They would be able to see the physics happen on paper, and then in real life. From a purely personal perspective, I frequently found the classroom material to be detached from “real life” physics when I was an undergraduate. It would be nice for the students to see a strong connection between the two through the curriculum.
Thirdly, and most importantly, it would give the students a taste of real science. IE: using a model to derive a prediction (hypothesis) and test it out in the lab. This would also mean that students could be expected to come up with their own experiment (perhaps with the TA’s help) in order to test their prediction. This would eliminate the mundanity of following lab activity instructions step-by-step with no real thought behind it (as was very common for me in my undergraduate days).
In all, I think it’s been a productive week for me as a learning assistant. I’ve pretty much given up on addressing them as a class in an attempt to gather conceptual difficulties. Instead what I found more useful was to visit each workstation individually. They are much less shy when I do that. That, in conjunction with having them work out a tricky problem on their whiteboards, will hopefully generate a better feedback loop between us.
I’d love to see more of these TA brainstorming sessions for other courses. I think much can be gained from a diverse group of minds and some free pizza.
Quantum mechanics is weird. It gets even weirder when you try to interpret what the theory is telling you about “reality”. In fact, I’m taking a course at the moment called: Interpretations of Quantum Mechanics. I’m hoping eventually I’ll get some blogable material out of it.
For now, I have a question for you all. It will be a purely subjective question (not like last time). I’ve blogged about the random nature of the quantum world before, and I’ve also given an account of an experiment that demonstrated the requirement (under certain assumptions) for an inherently random world, but the nature of reality is still a hotly debated topic in the world of physics. Some physicists reject the notion of a world that is fundamentally random and instead consider the possibility that we’re not seeing the whole picture. They come up with, so called, hidden variable theories that attempt to explain away the randomness by postulating some hidden property in the small world that we can’t directly measure. I’ve also recently come across a paper that hypothesises that the (random) quantum mechanical nature of the very very small could be an emergent phenomenon; that is to say (in pedestrian terms) we aren’t squinting hard enough to see all of the information about a quantum system and this lack of information results in seemingly random behaviour.
I wish I understood these things well enough to explain them here… but I don’t. Instead I’d like to know what your personal preference is for reality and why.
Which description of reality are you (secretly?) cheering for? Are you more comfortable with the completely non-random deterministic view of the world, or are you instead enjoying the idea of a world built on random behaviour? AND WHY?
(Here is Part 1 and Part 2, in case you missed them).
Sorry for the silence this week… you know how it is.
Before I begin, looks like the MIT physics department is having a few troubles of its own with the new physics curriculum. And, don’t forget to check out the First Excited State for Week 2 of the teaching journal.
I need your help. The practicals are becoming slightly tricky in terms of grabbing students’ attention for tutorial-like situation. As I mentioned last week, the students are vastly more motivated to do the activities than ask tutorial questions because they will be getting graded on the activities. We have the ability to create quiz questions on their workstation computers and we’ve tried creating a quiz question to try to draw out questions from the students. What actually happened was they spent a little while on the question, guessed if necessary (since it wasn’t worth any grades) and then didn’t ask any questions (probably for fear of not having enough time to do the lab activity).
I’ve been toying with a few ideas to try to get their participation in asking questions. The first is instead of asking the whole class a question and going over the solution, to instead go around and ask each workstation one at a time. It would take up the same amount of time for the students. The upside is that they will be much less shy and almost certainly reveal any gaps they have in their understanding. The downside is that any enlightening bit of information will be confined to that table.
In order for the whole class to benefit, I’d have to somehow engage the whole class in problem solving. One general idea I’ve had in that respect is to do away with a multiple choice quiz type question (and eliminate half hazard guesses) and instead ask an involved/conceptual problem. They could then write their answers/ideas on their whiteboards and share their ideas with the rest of the class. Alternately, if they are too shy to speak up, I could go around the class while they are working on the activities and look at the ideas on their whiteboards and discuss with them.
I think the problem here is shyness and time constraints. I’m wondering if any of you have ideas to get students to participate in sharing their conceptual difficulties with the class. Also, I’m wondering if any of you have any ideas for relatively short, interesting questions on the subject of static electricity.
Neat things to read…
