On Friday I was back at Primaria, building on
what we learned last time about colors of light. I handed out diffraction
gratings again, so they could again see how white light is composed of colors.
(I have my doubts that they really get the message that white light is
composed of colors; what they take away seems to be that the device
makes rainbows appear, which is not at all the same thing. Maybe a
dark room with a single source of light would help.) I asked them to
list the colors in order of appearance, in English and Spanish. I was
surprised to see how much trouble they had listing them in order of
appearance on the diffraction grating; they were all over the map. One
idea for the future is to have them draw what they see. But I was
even more surprised when they burst out in song "Red, orange, yellow /
Green, blue purple" when they realized that I was essentially asking
for the colors of the rainbow. They had memorized this song which
perfectly described what they were unable to describe when asked about
their observations! There must be something I can learn from this,
but I'm not sure what.
I wrote the names of the colors in this order on the board, so that
"range of colors" had a more concrete meaning. Then I asked them if
there could be anything "before" red or "after" purple (aka violet).
One boy in one group actually guessed infrared, presumably because he
had overheard me use that word to a teacher. I briefly mentioned
ultraviolet to connect it with the need for sunscreen in summer, but
the main purpose was to show the infrared camera. Things at room
temperature shine in infrared light, and the warmer they are the more
they shine, so the infrared camera is really a very different way of
looking at the world. You can walk into a kitchen, as we did, and be
blinded by the water boiling on the stove. A hand holding an ice cube
looks like a bright silhouette with a black rectangle in front of it.
People glow...you can see the glow radiating out from the openings in
their clothing, and from under their hair. You can make your way in
the dark, because everything is glowing to some extent. You can find
people hiding in the dark.
One group insisted they could see in the dark with their own eyes, so
I took them into the only room in the school which has no window: the
adult bathroom. (Linus had previously voiced this "I can see in the
dark" meme with great confidence, so I was sure it was something that
kid in the school bragged about and needed to be refuted.) I was
pretty sure that when we got in there and shut the door, most kids
would be scared and admit that they couldn't see in the dark. That
happened to one child, but several others were perfectly content with
the light coming from the gap under the door and said, see, we can see
in the dark. Preconceptions are very difficult to uproot! I
discussed this with Linus later and we agreed that he could see when
it was kind of dark, but not when it was perfectly dark. So
terminology matters. Given a way to save face, I got him to agree
with my scientific conclusion; but I had to give him a way to save
face. In any case, the little bit we could see in the mostly-dark
bathroom was nothing compared to how well we could see with the
infrared camera!
I also showed how the IR camera could see through some things which
are opaque to visible light (eg, a black plastic garbage bag, and I
mentioned but did not demonstrate smoke), and others are opaque to IR
but transparent in visible light (eg, glass windows; when I pointed
the camera at the window we saw only my reflection on the camera
display). Outside, the sky is black even during the day because the
air is relatively cold.
If all this sounds interesting, I recommend you watch this video to
get an idea of what the world looks like in the infrared. Meanwhile,
I have to make some notes for future demos: (1) it was hard for
everyone even in a group of seven to see the display. I thought I had
solved this problem by bringing a laptop and not relying on just the
camera's small screen, but you cannot imagine how seven kids have
trouble seeing the same laptop screen at once. In addition, the latop
screen was small enough that it didn't really grab their
attention. Next time, I will either bring a large LCD display, or use
a projector. (2) This activity is not very hands-on. The kids had
trouble staying tuned in. It would be good if I had the camera on a
fixed tripod out of their reach, set up a giant display with the
projector, and just let them do things and bring things in front of
the camera.
Saturday, February 4, 2012
Friday, January 27, 2012
Rainbows keep falling on my head
Yesterday Vera guided the 4-6 graders in exploring how different
colors of light mix. As you may recall, in her previous outing she
showed how light from a white bulb can be split into various colors
like a rainbow. This shows that we perceive as white is actually a
mixture of all colors, so a natural question to explore next is: What
happens if we mix different combinations of colors, like red+green,
green+blue, etc? This is a lot like mixing colors of paint, but not
exactly because many colors of paint mixed together approaches the
appearance of black, but many colors of light mixed together
approaches the appearance of white.
She directed the students to play with this computer simulation which you are free to do at home with your child. After about 5 minutes of just playing
with it, the students were guided through a set of thought-provoking
questions which made them go back and test the hypotheses they had
formed regarding light.
The concepts are similar to many I wrote about in my last visit to Primaria, so I won't belabor them here. I will remark instead on the
importance of testing students' mental models. It's one thing to say
that "white light contains all colors" but it's quite another to probe
what students really think that means in practice. If you put white
light into red glass, did the glass turn all the other colors into
red, or did it just block all the non-red colors from passing through?
The answer is the latter, but the most interesting thing is the
thought process which leads to that. How would we devise an
experiment to distinguish between these two hypotheses? By passing
the resulting red light through blue glass: if the conversion
hypothesis is true, a lot of blue light will come out, but if the
blocking hypothesis is true, basically no light will come out (because
the blue glass will block the red light). It's not enough just to
tell kids that "white light contains all colors." If you tell that to
7 kids, they will have 7 slightly different ideas about what that means
in practice. So a teacher has to find ways for students to test and
modify their mental models. Not only does this lead to a better
mental model, but it make students practice that most important skill:
using evidence to improve their model of how the world works.
colors of light mix. As you may recall, in her previous outing she
showed how light from a white bulb can be split into various colors
like a rainbow. This shows that we perceive as white is actually a
mixture of all colors, so a natural question to explore next is: What
happens if we mix different combinations of colors, like red+green,
green+blue, etc? This is a lot like mixing colors of paint, but not
exactly because many colors of paint mixed together approaches the
appearance of black, but many colors of light mixed together
approaches the appearance of white.
She directed the students to play with this computer simulation which you are free to do at home with your child. After about 5 minutes of just playing
with it, the students were guided through a set of thought-provoking
questions which made them go back and test the hypotheses they had
formed regarding light.
The concepts are similar to many I wrote about in my last visit to Primaria, so I won't belabor them here. I will remark instead on the
importance of testing students' mental models. It's one thing to say
that "white light contains all colors" but it's quite another to probe
what students really think that means in practice. If you put white
light into red glass, did the glass turn all the other colors into
red, or did it just block all the non-red colors from passing through?
The answer is the latter, but the most interesting thing is the
thought process which leads to that. How would we devise an
experiment to distinguish between these two hypotheses? By passing
the resulting red light through blue glass: if the conversion
hypothesis is true, a lot of blue light will come out, but if the
blocking hypothesis is true, basically no light will come out (because
the blue glass will block the red light). It's not enough just to
tell kids that "white light contains all colors." If you tell that to
7 kids, they will have 7 slightly different ideas about what that means
in practice. So a teacher has to find ways for students to test and
modify their mental models. Not only does this lead to a better
mental model, but it make students practice that most important skill:
using evidence to improve their model of how the world works.
Wednesday, January 11, 2012
Infrared Enlightenment
On Tuesday, Vera taught the 4-6 graders. She will be switching in more often in the next months. She's also a physicist and astronomer, and we talk constantly about teaching physics and astronomy, so we're pretty much interchangeable in terms of the experience we provide the children. We both use active learning techniques even in our college classrooms, so with these children we certainly do as much hands-on learning as possible.
Vera started by showing that white light is made of a spectrum of colors, just as I did with the Primaria class last Friday. When we separate the colors, we see a spectrum from violet to red just like in a rainbow, but there are additional "colors" (wavelengths of light) we can't see: ultraviolet (coming before violet in the spectrum) and infrared (coming after red). We have to be aware of ultraviolet because that's what gives us sunburn, but the focus Tuesday was on infrared. Last Friday, I left an infrared videocamera at the school for the children to explore with. It gives a whole new way of seeing things: it basically sees how hot things are, so for example the sky is dark (cold) and people are fairly bright (warm). Infrared light also interacts with matter differently than does visible light. For example, with the infrared camera you may not be able to see through a window which is transparent to visible light, but you may be able to see through a black plastic garbage bag. You may want to watch this short video of all these effects with your child.
I'll be doing infrared with Primaria next week, so I may post more details then. This post is brief because the video linked to above is better than anything I could write here. I definitely encourage you to watch it with your child and discuss what he/she saw and did when he/she had the camera in his/her own hands! In addition to the scientific aspects, there is some value in realizing that the whole world can be looked at in a way so completely different from the way we normally do.
Vera started by showing that white light is made of a spectrum of colors, just as I did with the Primaria class last Friday. When we separate the colors, we see a spectrum from violet to red just like in a rainbow, but there are additional "colors" (wavelengths of light) we can't see: ultraviolet (coming before violet in the spectrum) and infrared (coming after red). We have to be aware of ultraviolet because that's what gives us sunburn, but the focus Tuesday was on infrared. Last Friday, I left an infrared videocamera at the school for the children to explore with. It gives a whole new way of seeing things: it basically sees how hot things are, so for example the sky is dark (cold) and people are fairly bright (warm). Infrared light also interacts with matter differently than does visible light. For example, with the infrared camera you may not be able to see through a window which is transparent to visible light, but you may be able to see through a black plastic garbage bag. You may want to watch this short video of all these effects with your child.
I'll be doing infrared with Primaria next week, so I may post more details then. This post is brief because the video linked to above is better than anything I could write here. I definitely encourage you to watch it with your child and discuss what he/she saw and did when he/she had the camera in his/her own hands! In addition to the scientific aspects, there is some value in realizing that the whole world can be looked at in a way so completely different from the way we normally do.
Saturday, January 7, 2012
Let There Be Light! Part II
You may recall that I was disappointed with the way my light and shadow session with Primaria just before Christmas break turned out,
so I decided to cover some of the same concepts again with a different
approach, as well as add some new concepts related to light. I bought
some powerful light sources from Big 5: an LED lantern and a big
LED flashlight, and I borrowed an old slide projector just to use as a
light source. (Note to self: check eBay for used slide projectors!)
I started by showing how white light is made up of many colors. I had
them look at a compact fluorescent bulb through a special piece of
plastic (a diffraction grating) which separates the different
wavelengths of light. Different wavelengths are perceived as
different colors, so they saw this:
They described it as a rainbow, and yes, it does show that white light
is composed of colors, but it's actually even more interesting than
that. (This part in parentheses I did not go over with the kids, but
it might be useful for other audiences. If the light bulb emitted a
continuous range of wavelengths, the colors would be spread out
continuously and would just be a smear like an actual rainbow is.
This is what an incandescent bulb would look like through a diffraction grating.
But the CF bulb emits only a few specific wavelengths, so you see a
well-defined image of the bulb in one very specific shade of purple,
another well-defined image in a very specific shade of blue, etc.
This is related to how the CF bulb gets its greater energy efficiency.
The incandescent bulb emits a very broad range of wavelengths, from
the ultraviolet to the infrared, and many of these are wasted because
human eyes cannot detect them. The CF bulb by design emits only a few
specific wavelengths which are all chosen to be visible, so none of
its output is wasted. Therefore, for a given amount of visible light
output (listed in lumens on the package), it uses much less energy
(listed as watts on the package). So always buy light bulbs by
looking at the lumens, not watts! You may also see CF packages which
say "100 W equivalent", which means they give off as many lumens as a
100 W incandescent bulb, even while they drain fewer watts from the
grid. And this is also why the light from a CF bulb is sometimes
ugly: engineers have to work hard to build a set of specific
wavelengths which convincingly fake a full range of wavelengths.)
We did talk about what colors might exist beyond violet on one end of
the spectrum and beyond red on the other end. I asked, and none of
them knew that ultraviolet light from the Sun can cause sunburn, so
now they know why their parents slather on sunblock so often! I also
mentioned that next time I will bring an infrared camera so they can
see what the world looks like in that "color."
Having established that white light is composed of many colors, I
asked them about their experience mixing paints of different colors.
What do you get when you mix many colors of paint together? Some of
them knew that you get a yucky dark mess, not white. So mixing colors
is different with light than with paint! (Again, this is above their
age range, but possibly useful to readers: the difference stems from
the fact that red paint, for example, is red because it absorbs all
colors other than red, and reflects red. So if you mix that with
paint which absorbs all colors other than green and paint which
absorbs all colors other than blue, you basically have paint which
absorbs all colors! Paint basically subtracts light rather than adds
light.)
Next, I fired up the slide projector, which I has set up with a small
statute near the screen so that the statue's shadow was clearly
visible. (In practice, I had determined that using a 5-year-old as
the shadowmaker was not practical; it was difficult to keep him still
and to give directions about moving right vs left, etc. I also
darkened the room as much as I could beforehand.) I then turned on a
powerful flashlight and showed how you get two shadows with two light
sources. (This is a powerful argument against Moon-landing-hoax
conspiracy theorists, by the way, who claim that the lighting in the
astronaut's videos came from multiple studio lights; look at the video
and you will always see only one shadow from each object.) I moved
the flashlight around to different places, asking them to predict what
would happen to the shadow (where would it move? would it get taller
or shorter?) each time. This sounds very simple, but it took a few
iterations before they got it. I think this topic was right at their
level.
Next, I turned off the flashlight and put a yellow plastic film in
front of the projector. We saw that the shadow was still black,
because no light was getting there. Next, I turned on the white-light
flashlight and we saw that one shadow was yellow and the other was
white! That's because one shadow resulted from the statue blocking
the white light, and the other resulted from the statue blocking the
yellow light. Then they were eager to put another color plastic film
over the flashlight, say red to start with. I was careful to do this
in stages. I didn't mix the red flashlight light with the yellow
projector light until they had made a prediction. Then, I pointed the
flashlight somewhat away from the statue so that we saw how the light
mixed without thinking about the complication of the shadow. Then we
did the two-color shadows. Then we had a blast trying other color
combinations.
In each group, one person asked if we could put the red plastic and
the yellow plastic in front of the projector. First we discussed how
the plastic blocks all the colors in white light and only lets the
yellow through, so if I then put a piece of plastic which blocks all
colors other than red I should get what? Few of them got it, that it
would block almost all the light (the little light that did get
through appeared orange; exactly which shade depends on the details of
exactly how efficiently each film blocks each wavelength).
But that's not all! As more of a gee-whiz demo rather than teaching
principles of physical science, I had brought glow-in-the-dark paper.
I was not able to get the room very dark, so it was
unimpressive...until I whipped out a purple laser and started writing
on it with light! The laser is powerful enough that the spot where it
hits the paper really glows, and the bright glow lasts for several
seconds, so I could write a child's name and finish just as the first
letter was vanishing. This was a nice connection to other parts of
their curriculum: they were studying the deep sea and had just learned
about bioluminescence, and also they are learning their letters so
many of them could recognize their own names, and were extremely
gratified to recognize it when I wrote it.
For the groups which had a few extra minutes, I let them play with
either the slide projector and color films, or colored Christmas tree
lights, which make it easy to mix colors (warning: with the newer LED
lights the mixing is not that impressive because of the
specific-wavelength vs range-of-wavelengths issue discussed above).
In the last group, two kids stayed an extra 20 minutes while I packed
up and their peers were playing on the playground! So it seems to
have been interesting to them.
Diffraction gratings can be ordered from Edmund Scientific for about
$1 each, and I just ordered some for the school so kids can experiment
outside the very limited hours I am there. If you want to do more at
home with your child, I suggest getting a few strongish flashlights,
taping different color plastic films over them, and having fund after
the Sun sets.
so I decided to cover some of the same concepts again with a different
approach, as well as add some new concepts related to light. I bought
some powerful light sources from Big 5: an LED lantern and a big
LED flashlight, and I borrowed an old slide projector just to use as a
light source. (Note to self: check eBay for used slide projectors!)
I started by showing how white light is made up of many colors. I had
them look at a compact fluorescent bulb through a special piece of
plastic (a diffraction grating) which separates the different
wavelengths of light. Different wavelengths are perceived as
different colors, so they saw this:
 |
| The compact fluorescent bulb is at left. I stuck a diffraction grating in front of the camera lens, which separates the wavelengths (colors) of light so that we see a purple bulb, a blue bulb, a cyan bulb, a green bulb, and orange bulb, and a red bulb off to the right. This shows that what we perceive as white light is actually composed of a mixture of colors. |
They described it as a rainbow, and yes, it does show that white light
is composed of colors, but it's actually even more interesting than
that. (This part in parentheses I did not go over with the kids, but
it might be useful for other audiences. If the light bulb emitted a
continuous range of wavelengths, the colors would be spread out
continuously and would just be a smear like an actual rainbow is.
This is what an incandescent bulb would look like through a diffraction grating.
But the CF bulb emits only a few specific wavelengths, so you see a
well-defined image of the bulb in one very specific shade of purple,
another well-defined image in a very specific shade of blue, etc.
This is related to how the CF bulb gets its greater energy efficiency.
The incandescent bulb emits a very broad range of wavelengths, from
the ultraviolet to the infrared, and many of these are wasted because
human eyes cannot detect them. The CF bulb by design emits only a few
specific wavelengths which are all chosen to be visible, so none of
its output is wasted. Therefore, for a given amount of visible light
output (listed in lumens on the package), it uses much less energy
(listed as watts on the package). So always buy light bulbs by
looking at the lumens, not watts! You may also see CF packages which
say "100 W equivalent", which means they give off as many lumens as a
100 W incandescent bulb, even while they drain fewer watts from the
grid. And this is also why the light from a CF bulb is sometimes
ugly: engineers have to work hard to build a set of specific
wavelengths which convincingly fake a full range of wavelengths.)
We did talk about what colors might exist beyond violet on one end of
the spectrum and beyond red on the other end. I asked, and none of
them knew that ultraviolet light from the Sun can cause sunburn, so
now they know why their parents slather on sunblock so often! I also
mentioned that next time I will bring an infrared camera so they can
see what the world looks like in that "color."
Having established that white light is composed of many colors, I
asked them about their experience mixing paints of different colors.
What do you get when you mix many colors of paint together? Some of
them knew that you get a yucky dark mess, not white. So mixing colors
is different with light than with paint! (Again, this is above their
age range, but possibly useful to readers: the difference stems from
the fact that red paint, for example, is red because it absorbs all
colors other than red, and reflects red. So if you mix that with
paint which absorbs all colors other than green and paint which
absorbs all colors other than blue, you basically have paint which
absorbs all colors! Paint basically subtracts light rather than adds
light.)
Next, I fired up the slide projector, which I has set up with a small
statute near the screen so that the statue's shadow was clearly
visible. (In practice, I had determined that using a 5-year-old as
the shadowmaker was not practical; it was difficult to keep him still
and to give directions about moving right vs left, etc. I also
darkened the room as much as I could beforehand.) I then turned on a
powerful flashlight and showed how you get two shadows with two light
sources. (This is a powerful argument against Moon-landing-hoax
conspiracy theorists, by the way, who claim that the lighting in the
astronaut's videos came from multiple studio lights; look at the video
and you will always see only one shadow from each object.) I moved
the flashlight around to different places, asking them to predict what
would happen to the shadow (where would it move? would it get taller
or shorter?) each time. This sounds very simple, but it took a few
iterations before they got it. I think this topic was right at their
level.
Next, I turned off the flashlight and put a yellow plastic film in
front of the projector. We saw that the shadow was still black,
because no light was getting there. Next, I turned on the white-light
flashlight and we saw that one shadow was yellow and the other was
white! That's because one shadow resulted from the statue blocking
the white light, and the other resulted from the statue blocking the
yellow light. Then they were eager to put another color plastic film
over the flashlight, say red to start with. I was careful to do this
in stages. I didn't mix the red flashlight light with the yellow
projector light until they had made a prediction. Then, I pointed the
flashlight somewhat away from the statue so that we saw how the light
mixed without thinking about the complication of the shadow. Then we
did the two-color shadows. Then we had a blast trying other color
combinations.
In each group, one person asked if we could put the red plastic and
the yellow plastic in front of the projector. First we discussed how
the plastic blocks all the colors in white light and only lets the
yellow through, so if I then put a piece of plastic which blocks all
colors other than red I should get what? Few of them got it, that it
would block almost all the light (the little light that did get
through appeared orange; exactly which shade depends on the details of
exactly how efficiently each film blocks each wavelength).
But that's not all! As more of a gee-whiz demo rather than teaching
principles of physical science, I had brought glow-in-the-dark paper.
I was not able to get the room very dark, so it was
unimpressive...until I whipped out a purple laser and started writing
on it with light! The laser is powerful enough that the spot where it
hits the paper really glows, and the bright glow lasts for several
seconds, so I could write a child's name and finish just as the first
letter was vanishing. This was a nice connection to other parts of
their curriculum: they were studying the deep sea and had just learned
about bioluminescence, and also they are learning their letters so
many of them could recognize their own names, and were extremely
gratified to recognize it when I wrote it.
For the groups which had a few extra minutes, I let them play with
either the slide projector and color films, or colored Christmas tree
lights, which make it easy to mix colors (warning: with the newer LED
lights the mixing is not that impressive because of the
specific-wavelength vs range-of-wavelengths issue discussed above).
In the last group, two kids stayed an extra 20 minutes while I packed
up and their peers were playing on the playground! So it seems to
have been interesting to them.
Diffraction gratings can be ordered from Edmund Scientific for about
$1 each, and I just ordered some for the school so kids can experiment
outside the very limited hours I am there. If you want to do more at
home with your child, I suggest getting a few strongish flashlights,
taping different color plastic films over them, and having fund after
the Sun sets.
Big Study Links Good Teachers to Lasting Gain
This New York Times article discusses recent research which shows that good elementary and middle school teachers (as measured by the jump in their students' standardized test scores) have a lasting effect on their students (as measured by students' lifetime earnings, avoidance of teen pregnancy, and college enrollment). Although the difference between having an average teacher and having an excellent teacher for one year yielded only $4600 in additional lifetime earnings for each student, the cumulative effect is large: A 30-student class would yield $138,000 extra in lifetime earnings as a result of excellent teaching. (The difference between a poor and an average teacher was quoted as $266,000 in one year of teaching.) And avoidance of teen pregnancy? Priceless! Although admittedly the difference is small (8.1% vs 7.7% chance of teen pregnancy), when it happens to your family it is not a small thing.
I realize that not everything good in life can be quantified, but I think this kind of research is important because good teachers are not paid enough, and this kind of research helps us advocate for them. (And, one might argue, gives us greater motivation to get rid of poor teachers more quickly.) Many of us might think from personal experience that the effect of a good teacher is permanent, but previous studies have not supported that conclusion. Those previous studies looked only at test scores in future years, not these positive long-range life outcomes. Therefore, this more sophisticated research is an important step forward.
The study addressed fourth through eighth grade, and found that the grade in which a student encountered a good teacher did not matter. About a year and a half ago, a roughly similar study was conducted for kindergarten teachers, which concluded that good ones brought a $320,000 economic benefit to their students.
You may wish to read the New York Times column addressing the earlier research, and if you wish to dig deeper into the data you can see some slides presented by those researchers.
Update: Nicholas Kristof has written an eye-opening column about this.
I realize that not everything good in life can be quantified, but I think this kind of research is important because good teachers are not paid enough, and this kind of research helps us advocate for them. (And, one might argue, gives us greater motivation to get rid of poor teachers more quickly.) Many of us might think from personal experience that the effect of a good teacher is permanent, but previous studies have not supported that conclusion. Those previous studies looked only at test scores in future years, not these positive long-range life outcomes. Therefore, this more sophisticated research is an important step forward.
The study addressed fourth through eighth grade, and found that the grade in which a student encountered a good teacher did not matter. About a year and a half ago, a roughly similar study was conducted for kindergarten teachers, which concluded that good ones brought a $320,000 economic benefit to their students.
You may wish to read the New York Times column addressing the earlier research, and if you wish to dig deeper into the data you can see some slides presented by those researchers.
Update: Nicholas Kristof has written an eye-opening column about this.
Saturday, December 10, 2011
Let there be light!
Back to Primaria (pre-K/K) this week. The teachers asked me to
explain how lenses work, because the kids had been making toy
eyeglasses out of pipecleaners and were curious about it. I had long
wanted to do some demos with light anyway. It takes a lot of trouble
to make a room really dark (so that the light relevant to the
demonstration is more visible) during school hours, so I figured I
would go to that trouble and combine topics. Linus (my son in
Primaria) had asked just a week or so before about the Moon. He
thought the phases of the Moon were due to Earth's shadow falling on
the Moon. I pointed out that the crescent Moon appears not too far
from the Sun, so the Earth's shadow cannot be falling on it. He came
up with some crazy stuff about light bouncing back and forth, back and
forth between Earth, Sun, and Moon "like an air hockey puck." So I
had a motivation to do phases of the Moon with the kids, but first I
had to build on basic concepts of light, like the difference between
emission and reflection (the Sun emits light and is the source of
light in our solar system; the Moon reflects some fraction of the
light it receives, but not enough to illuminate the other bodies in
the solar system).
So I set up in the kids' bathroom, which is the only room with no
windows. I still had to spend a lot of time taping up the open
doorway with black plastic to prevent a lot of light coming in. In
groups of 5-6, the kids came in and we started by talking about how we
couldn't see anything without a source of light. I then turned on an
unexpected source of light: a laser pointer. We discussed how they
couldn't see the source of light directly, but they could see the
light when it reflected off the ceiling. Next, a flashlight. I
pointed it directly at them, then pointed it at the ceiling. So a
given light source can be seen directly or indirectly (reflected)
depending on your relationship to it.
Now I turned on the "Sun": a naked light bulb. Unlike a flashlight or
laser pointer, it emits in all directions. But can we always see the
Sun? We discussed various reasons for not seeing the Sun, such as
clouds. But when is it really dark? At night. And what is night?
"Clouds" were again offered as a reason, so we discussed what happens
just before night: "the Sun goes down behind the mountains." So then
we each pretended we were the Earth, and slowly turned around so that
the Sun came into and out of our field of view. [The next day, my
wife Vera offered a really good suggestion: have them extend their
arms to make a "horizon" which turns with them.] To be honest, a lot
of kids spun way too rapidly and weren't really getting it. I
repeated the whole thing with a globe. We agreed on the location of
California and looked at how California varied between bright and dark
as the Earth turned. A problem with this is that light reflecting off
the walls provides a non-negligible amount of illumination for the
back side of the Earth, and the effect is not nearly as dramatic as
you would thing. Vera suggests decoupling the day/night concept from
the light demo, just pasting up a picture of the Sun in a regular
classroom and doing the horizon thing. I think she's right about
that! Another possibility is to build a little model. If the Sun were
a Christmas-tree bulb and the Earth a nearby marble, relatively little
light would bounce off the walls of the room!
Next, we tackled phases of the Moon. I had one child volunteer to be
Earth while I took a volleyball Moon and moved it around Earth,
showing how the Earth-person sees a fully-illuminated Moon when it is
opposite the Sun, and sees (rather, does not see) an un-illuminated
Moon when it is more or less between Earth and Sun. However, this did
not work well for several reasons. Each group had a bunch of other
kids who were not the Earth and saw the whole thing from a variety of
vantage points. It was very difficult to steer the kids into seeing
what they were "supposed" to see. One girl said "now I'm the Earth"
when the Moon happened to come close to her. In one group, the
Earth-volunteer gave the wrong answer when I asked him whether the
side of the Moon he was seeing was bright or dark; I think he just
didn't know what to compare to, so I need to be more careful about
exactly how I word my questions.
Finally, the lens. The key to a good visualization is to avoid using
all three dimensions. I put a flashlight on a table so they can see
how the light spreads out by looking at the light and dark patterns on
the table. I put a comb in front of the light to give a visual
impression of light rays spreading out on the table. Then I set a
special lens on the table, which is like a slice of a lens so that it
can sit flat on the table. This shows that the light rays which go
through the lens are bent so that they converge back together rather
than continue diverging. It's quite striking if set up right. I had
a card which I pretended was a movie screen, and projected the focused
image there. We talked about movie theaters and where they would sit,
did they ever look behind them and see the bright light coming out of
the lens, and what would happen if there was no screen. For the
groups which had a bit of time left at the end, I moved the lens
around to show that if it's too close to the light, it's not powerful
enough to converge the light. It might be powerful enough to stop
further spreading of the light, though, and I showed how a second lens
could then converge that light. The idea was to show that there are
many combinations and possibilities.
I felt that the kids were more disengaged than usual, and I felt that
it was directly attributable to the "demo" rather than "hands-on"
nature of the activity. I made the "demo" decision because I felt it
would be chaos to have 4- and 5-year-olds handling flashlights and
lenses in teams of two or three. That may have been correct, but I
should have found some way to prevent the whole 20 minutes from being
all demo. One possible structure is the sandwich: an initial demo
followed by hands-on activities with a more complicated demo or
summary discussion at the end. But this didn't fit with the list of
topics I wanted to cover. I realize now that I was too much in
"professor" mode: practicing inquiry is more important than covering a
list of topics! The kids brought up (indirectly) one thing I had
thought about last year but forgotten: setting up a light so that they
can make shadows themselves. They love doing this, and if I set it up
right they can actually explore different aspects of light. For
example, I could set up two lights of different colors and they could
see how to control the color of the shadow. Or they could explore how
a given object can have differently shaped shadows depending on its
orientation to the light. I can even imagine setting up a "light
studio" which they could play with during the week before or after my
visit.
explain how lenses work, because the kids had been making toy
eyeglasses out of pipecleaners and were curious about it. I had long
wanted to do some demos with light anyway. It takes a lot of trouble
to make a room really dark (so that the light relevant to the
demonstration is more visible) during school hours, so I figured I
would go to that trouble and combine topics. Linus (my son in
Primaria) had asked just a week or so before about the Moon. He
thought the phases of the Moon were due to Earth's shadow falling on
the Moon. I pointed out that the crescent Moon appears not too far
from the Sun, so the Earth's shadow cannot be falling on it. He came
up with some crazy stuff about light bouncing back and forth, back and
forth between Earth, Sun, and Moon "like an air hockey puck." So I
had a motivation to do phases of the Moon with the kids, but first I
had to build on basic concepts of light, like the difference between
emission and reflection (the Sun emits light and is the source of
light in our solar system; the Moon reflects some fraction of the
light it receives, but not enough to illuminate the other bodies in
the solar system).
So I set up in the kids' bathroom, which is the only room with no
windows. I still had to spend a lot of time taping up the open
doorway with black plastic to prevent a lot of light coming in. In
groups of 5-6, the kids came in and we started by talking about how we
couldn't see anything without a source of light. I then turned on an
unexpected source of light: a laser pointer. We discussed how they
couldn't see the source of light directly, but they could see the
light when it reflected off the ceiling. Next, a flashlight. I
pointed it directly at them, then pointed it at the ceiling. So a
given light source can be seen directly or indirectly (reflected)
depending on your relationship to it.
Now I turned on the "Sun": a naked light bulb. Unlike a flashlight or
laser pointer, it emits in all directions. But can we always see the
Sun? We discussed various reasons for not seeing the Sun, such as
clouds. But when is it really dark? At night. And what is night?
"Clouds" were again offered as a reason, so we discussed what happens
just before night: "the Sun goes down behind the mountains." So then
we each pretended we were the Earth, and slowly turned around so that
the Sun came into and out of our field of view. [The next day, my
wife Vera offered a really good suggestion: have them extend their
arms to make a "horizon" which turns with them.] To be honest, a lot
of kids spun way too rapidly and weren't really getting it. I
repeated the whole thing with a globe. We agreed on the location of
California and looked at how California varied between bright and dark
as the Earth turned. A problem with this is that light reflecting off
the walls provides a non-negligible amount of illumination for the
back side of the Earth, and the effect is not nearly as dramatic as
you would thing. Vera suggests decoupling the day/night concept from
the light demo, just pasting up a picture of the Sun in a regular
classroom and doing the horizon thing. I think she's right about
that! Another possibility is to build a little model. If the Sun were
a Christmas-tree bulb and the Earth a nearby marble, relatively little
light would bounce off the walls of the room!
Next, we tackled phases of the Moon. I had one child volunteer to be
Earth while I took a volleyball Moon and moved it around Earth,
showing how the Earth-person sees a fully-illuminated Moon when it is
opposite the Sun, and sees (rather, does not see) an un-illuminated
Moon when it is more or less between Earth and Sun. However, this did
not work well for several reasons. Each group had a bunch of other
kids who were not the Earth and saw the whole thing from a variety of
vantage points. It was very difficult to steer the kids into seeing
what they were "supposed" to see. One girl said "now I'm the Earth"
when the Moon happened to come close to her. In one group, the
Earth-volunteer gave the wrong answer when I asked him whether the
side of the Moon he was seeing was bright or dark; I think he just
didn't know what to compare to, so I need to be more careful about
exactly how I word my questions.
Finally, the lens. The key to a good visualization is to avoid using
all three dimensions. I put a flashlight on a table so they can see
how the light spreads out by looking at the light and dark patterns on
the table. I put a comb in front of the light to give a visual
impression of light rays spreading out on the table. Then I set a
special lens on the table, which is like a slice of a lens so that it
can sit flat on the table. This shows that the light rays which go
through the lens are bent so that they converge back together rather
than continue diverging. It's quite striking if set up right. I had
a card which I pretended was a movie screen, and projected the focused
image there. We talked about movie theaters and where they would sit,
did they ever look behind them and see the bright light coming out of
the lens, and what would happen if there was no screen. For the
groups which had a bit of time left at the end, I moved the lens
around to show that if it's too close to the light, it's not powerful
enough to converge the light. It might be powerful enough to stop
further spreading of the light, though, and I showed how a second lens
could then converge that light. The idea was to show that there are
many combinations and possibilities.
I felt that the kids were more disengaged than usual, and I felt that
it was directly attributable to the "demo" rather than "hands-on"
nature of the activity. I made the "demo" decision because I felt it
would be chaos to have 4- and 5-year-olds handling flashlights and
lenses in teams of two or three. That may have been correct, but I
should have found some way to prevent the whole 20 minutes from being
all demo. One possible structure is the sandwich: an initial demo
followed by hands-on activities with a more complicated demo or
summary discussion at the end. But this didn't fit with the list of
topics I wanted to cover. I realize now that I was too much in
"professor" mode: practicing inquiry is more important than covering a
list of topics! The kids brought up (indirectly) one thing I had
thought about last year but forgotten: setting up a light so that they
can make shadows themselves. They love doing this, and if I set it up
right they can actually explore different aspects of light. For
example, I could set up two lights of different colors and they could
see how to control the color of the shadow. Or they could explore how
a given object can have differently shaped shadows depending on its
orientation to the light. I can even imagine setting up a "light
studio" which they could play with during the week before or after my
visit.
Friday, December 2, 2011
Turn! Turn! Turn!
At the elementary school, we continued our theme of learning more
about how things move, in preparation for designing the playground at
the new school site. Tomorrow, we have an optional field trip to the
Berkeley Adventure Playground to see what other kids have designed and
built. Today, we focused on spinning things.
We started with a spinnable chair. A volunteer sits in it and holds
two weights close to his/her chest while I spin up the chair. Then I
ask the volunteer to extend his/her arms as far as possible. The
chair then spins much more slowly. Arms in: the chair speeds up
again. Arms out: slows down again.
I ask the kids what else they have seen which is like this.
Surprisingly, no one said figure skating. I had to nudge them a bit
to realize it is just like the figure skater who brings her arms in to
spin rapidly. A lot of them did refer to playground equipment,
though. There is a public playground near the school (to which they
sometimes walk for lunch/PE) which has something like that, and I
think now they will have a new appreciation for it. But why does
pulling in your arms speed you up?
We had talked four weeks ago about how more massive things are more
difficult to accelerate. And to decelerate. In short, they have more
inertia. Rotational motion has an added complication. Rotational
inertia involves not only how much mass there is, but how far it is
from the center of rotation: the further from the center, the greater
the inertia. So it is much easier to spin up something whose mass is
concentrated near the center, compared to something of equal mass
whose mass is far-flung. The property of being spun up, which
physicists call angular momentum, is conserved so that a slowly
spinning far-flung object can easily be transformed into a rapidly
spinning concentrated object. Here's an analogy: I can have a certain
volume of water, but it results in a taller water level if it is put
in a skinny glass than if it is put in a wide glass. Here the volume
of water is analogous to the angular momentum (both are conserved),
and the height of the water level is analogous to the rate of
rotation.
Next, I gave them a chance to apply this new principle. I had a set
of two rods of the same size and mass, one of which secretly had most
of its mass concentrated near the middle, and the other of which
secretly had most of its mass concentrated near the ends. You grasp
the center of each rod in either hand, and rotate them back and forth.
There is a startling difference in the resistance to rotation! Once
each child had a chance to feel it, I asked them to come up with
hypotheses as to why one is easier to rotate. Surprisingly, the
connection was not instant. (I wonder how often words are a dead
giveaway. I used the word "rotation" here, but in class I just said,
"go like this." I bet if I had said "rotate the rods" something would
have clicked. But this something would not have been understanding of
physics! Asking questions with familiar terminology leads students to
"solve" problems they don't really understand, and make both teachers
and students overconfident in how much understanding has been gained.)
Many students insisted that the rods did not weigh the same, despite
my assurances. Next time, I should bring a scale to prove it!
Some students were able to guess that it had something to do with how
the weight was distributed (at least that's how I rephrased what they
said), or that something inside the hard-to-turn rod moved (which it
didn't, but I think they were on the right track in thinking that a
similar effect would be produced by some of the weight moving from the
middle toward the ends). I had to give quite a few hints, in one case
sitting on the demo chair and stretching my arms back and forth. We
finally established that we could explain the behavior by supposing
that one rod had most of its mass on the end and the other had most in
the middle. I pointed out that we had just used what we could see to
figure out something about what we couldn't see directly. That's
pretty cool, and that's what science is about.
Next, we took a bicycle wheel and I passed it around. Each student
felt that it is easy to change the orientation of the wheel (in other
words, change where its axis pointed) when the wheel is not spinning,
but quite difficult to do the same thing when the wheel is spinning.
This is another manifestation of conservation of angular momentum.
The rotating wheel seems to fight back; you have to do a lot of work
to change its direction. I asked in what real-life situations they
might have noticed the same thing. "Bicycle wheel" was a very popular
answer, but they couldn't pin down what about a bicycle wheel was
relevant. I had to hint a bit before they realized that this is why
it's easier to stay up on a bike when you're moving faster. When
you're not moving, the wheels can just fall over. When you're moving
fast, changing the axis of the wheels is not so easy, so you find it
easier to balance.
The same bicycle wheel can be used for a really neat demo. Sit on the
spinnable chair, hold the bicycle wheel so it's vertical, and have
someone spin the wheel. Now, when you turn the wheel so it is
sideways, the change in angular momentum gets transferred to the
chair, which begins to spin. Now flip the wheel over, and the chair
begins to spin the other way! This is the rotational equivalent of
two ice skaters pushing off each other and sliding off in opposite
directions.
Finally, I showed them a model of a merry-go-round, to the center of
which I had attached a spring with a small mass on the end. They
predicted that upon spinning the turntable, the mass would go toward
the outside (which it did), but they were not able to articulate
precisely why. I reminded them of the donutapult experiment four
weeks earlier: objects travel in straight lines unless acted upon by a
force. If an object is on a merry-go-round and does not hold on,
travel on a straight line means sliding off the merry-go-round. The
spring was there to prevent losing the mass, and when the turntable
slowed, the spring pulled the mass back toward the center, as the kids
predicted.
We talked about how to apply these ideas in designing a
playground. Some of the ideas were far-fetched, but that's ok! I
didn't want to discourage creativity. We also talked about space and
astronauts. Muscle and bone become very weak after extended periods
in space, and one way to provide artificial gravity to counteract this
is to spin a space station. Because everything inside "wants" to
stick to the rim of a spinning space station, the people inside will
feel like the outside edge of the station is "down", and that there is
gravity pulling things that way. And one child remarked that if you
still need some zero-g environment in the space station, you can put
it inside the axis of the spinning part. One child also asked about
stars, and I explained how some stars which are much more compact than
the Sun (neutron stars) rotate much more rapidly, as often as 30 times
per second! We know that because we can see a hot spot for a brief
period during each revolution.
about how things move, in preparation for designing the playground at
the new school site. Tomorrow, we have an optional field trip to the
Berkeley Adventure Playground to see what other kids have designed and
built. Today, we focused on spinning things.
We started with a spinnable chair. A volunteer sits in it and holds
two weights close to his/her chest while I spin up the chair. Then I
ask the volunteer to extend his/her arms as far as possible. The
chair then spins much more slowly. Arms in: the chair speeds up
again. Arms out: slows down again.
I ask the kids what else they have seen which is like this.
Surprisingly, no one said figure skating. I had to nudge them a bit
to realize it is just like the figure skater who brings her arms in to
spin rapidly. A lot of them did refer to playground equipment,
though. There is a public playground near the school (to which they
sometimes walk for lunch/PE) which has something like that, and I
think now they will have a new appreciation for it. But why does
pulling in your arms speed you up?
We had talked four weeks ago about how more massive things are more
difficult to accelerate. And to decelerate. In short, they have more
inertia. Rotational motion has an added complication. Rotational
inertia involves not only how much mass there is, but how far it is
from the center of rotation: the further from the center, the greater
the inertia. So it is much easier to spin up something whose mass is
concentrated near the center, compared to something of equal mass
whose mass is far-flung. The property of being spun up, which
physicists call angular momentum, is conserved so that a slowly
spinning far-flung object can easily be transformed into a rapidly
spinning concentrated object. Here's an analogy: I can have a certain
volume of water, but it results in a taller water level if it is put
in a skinny glass than if it is put in a wide glass. Here the volume
of water is analogous to the angular momentum (both are conserved),
and the height of the water level is analogous to the rate of
rotation.
Next, I gave them a chance to apply this new principle. I had a set
of two rods of the same size and mass, one of which secretly had most
of its mass concentrated near the middle, and the other of which
secretly had most of its mass concentrated near the ends. You grasp
the center of each rod in either hand, and rotate them back and forth.
There is a startling difference in the resistance to rotation! Once
each child had a chance to feel it, I asked them to come up with
hypotheses as to why one is easier to rotate. Surprisingly, the
connection was not instant. (I wonder how often words are a dead
giveaway. I used the word "rotation" here, but in class I just said,
"go like this." I bet if I had said "rotate the rods" something would
have clicked. But this something would not have been understanding of
physics! Asking questions with familiar terminology leads students to
"solve" problems they don't really understand, and make both teachers
and students overconfident in how much understanding has been gained.)
Many students insisted that the rods did not weigh the same, despite
my assurances. Next time, I should bring a scale to prove it!
Some students were able to guess that it had something to do with how
the weight was distributed (at least that's how I rephrased what they
said), or that something inside the hard-to-turn rod moved (which it
didn't, but I think they were on the right track in thinking that a
similar effect would be produced by some of the weight moving from the
middle toward the ends). I had to give quite a few hints, in one case
sitting on the demo chair and stretching my arms back and forth. We
finally established that we could explain the behavior by supposing
that one rod had most of its mass on the end and the other had most in
the middle. I pointed out that we had just used what we could see to
figure out something about what we couldn't see directly. That's
pretty cool, and that's what science is about.
Next, we took a bicycle wheel and I passed it around. Each student
felt that it is easy to change the orientation of the wheel (in other
words, change where its axis pointed) when the wheel is not spinning,
but quite difficult to do the same thing when the wheel is spinning.
This is another manifestation of conservation of angular momentum.
The rotating wheel seems to fight back; you have to do a lot of work
to change its direction. I asked in what real-life situations they
might have noticed the same thing. "Bicycle wheel" was a very popular
answer, but they couldn't pin down what about a bicycle wheel was
relevant. I had to hint a bit before they realized that this is why
it's easier to stay up on a bike when you're moving faster. When
you're not moving, the wheels can just fall over. When you're moving
fast, changing the axis of the wheels is not so easy, so you find it
easier to balance.
The same bicycle wheel can be used for a really neat demo. Sit on the
spinnable chair, hold the bicycle wheel so it's vertical, and have
someone spin the wheel. Now, when you turn the wheel so it is
sideways, the change in angular momentum gets transferred to the
chair, which begins to spin. Now flip the wheel over, and the chair
begins to spin the other way! This is the rotational equivalent of
two ice skaters pushing off each other and sliding off in opposite
directions.
Finally, I showed them a model of a merry-go-round, to the center of
which I had attached a spring with a small mass on the end. They
predicted that upon spinning the turntable, the mass would go toward
the outside (which it did), but they were not able to articulate
precisely why. I reminded them of the donutapult experiment four
weeks earlier: objects travel in straight lines unless acted upon by a
force. If an object is on a merry-go-round and does not hold on,
travel on a straight line means sliding off the merry-go-round. The
spring was there to prevent losing the mass, and when the turntable
slowed, the spring pulled the mass back toward the center, as the kids
predicted.
We talked about how to apply these ideas in designing a
playground. Some of the ideas were far-fetched, but that's ok! I
didn't want to discourage creativity. We also talked about space and
astronauts. Muscle and bone become very weak after extended periods
in space, and one way to provide artificial gravity to counteract this
is to spin a space station. Because everything inside "wants" to
stick to the rim of a spinning space station, the people inside will
feel like the outside edge of the station is "down", and that there is
gravity pulling things that way. And one child remarked that if you
still need some zero-g environment in the space station, you can put
it inside the axis of the spinning part. One child also asked about
stars, and I explained how some stars which are much more compact than
the Sun (neutron stars) rotate much more rapidly, as often as 30 times
per second! We know that because we can see a hot spot for a brief
period during each revolution.
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