Analogical Scaffolding of Abstract Ideas in Physics
Introduction
Making sense of very abstract physics concepts can be difficult for
students. The electromagnetic wave is a very abstract concept
bearing little resemblance to anything we experience in the real
world.
Research question: How can students make sense of very abstract
concepts in physics?
Hypothesis: There are varying levels of abstraction. Simpler levels
can be used to scaffold understanding of higher levels.
This poster explores a model of learning where students begin by
making simple analogies with low levels of abstraction. Simple
analogies form an analogical scaffolding that students use to build
more complex analogies.
This model is based on a cognitive theory of analogy1.
Noah Podolefsky, Wendy Adams, Noah Finkelstein
University of Colorado - Boulder
contact: [email protected]
We conducted interviews with students using the PhET computer
simulations to provide grounding for our model.
1. The inspiration for our model is Lakoff & Nunez cognitive theory of the layering of conceptual metaphor - see
Lakoff & Nunez (2000) Where Mathematics Comes From - How the Embodied Mind Brings Mathematics into Being.
The PhET Computer Simulations
For the other two students, the order was reversed (R S).
The representation of sound in the Sound Waves simulation
resembles ripples in water.
The picture in the center bridges the water wave to the concept of
pressure.
Water goes up
Crest of wave
Water goes
down
Trough of wave
Karen (S R) interpreted the dark and light areas in the wave as
peaks and troughs.
"The amplitude is, uh, how loud it is…oh I see. And it's just, I think
that's how, how big the waves are, or a little amplitude is little
waves . Yeah, you can barely see 'em. These are really really big,
like really deep and really…high."
Gary* (S R) described a water waves to pressure analogy:
"Like, it's not just a wave. At least, I remember from playing with
the simulation, the air pressure changes the whole way and I guess
it would make sense, if you think, talking about the whole, like,
disturbance I guess. As, like, a wave like in the ocean, 'cause it does
come down and up, but you have to think of it differently. It's the
pressure that's taking those highs and lows, instead of actually a
wave."
Wave represents pressure
phet.colorado.edu
Peaks and Troughs in Sound Waves
Water Waves - Pressure Analogy
Target - Sound
Air particles
Higher pressure
compressed
Air particles
Lower pressure
rarefied
Wave represents displacement
Think aloud interviews were conducted with five students using
PhET simulations.
Three students used Sound Waves preceding Radio Waves (S R).
Mapping Sound Waves to Water Waves
Source - Water
Student Interviews
Mapping Sound Waves to Radio Waves
* Students' names have been changed.
The Sound Waves simulation becomes the source of an analogical
mapping to Radio Waves.
Sound Waves
Sound - Radio Waves Analogy
Concepts that are understood for sound map to concepts for radio.
Radio Waves
Karen (S>R) describing radio waves:
"They act the same as sound waves, just you can't hear them
because the frequency is too low, or the radio waves...I think."
The Physics Education Technology (PhET) project is a suite of
over 35 computer simulations of physical phenomena.
Designed to be fun, interactive, and help students connect physics
to the real world.
Example of Analogical Mapping:
The Planetary Model of the Atom
Source - Sound Waves
Target - Radio Waves
Distance between crests is
Distance between crests is
wavelength
wavelength
Number of crests passing a point in Number of crests passing a point in
1 second is frequency
1 second is frequency
Wave represents pressure
Wave represents electric field
A Jump Rope Analogy
The Ordering of Analogies
Source - Solar System
Planet
Sun
Sun is yellow
Sun is massive
Planets orbit sun
Sun attracts planets
Planets attract planets
Target - Atom
Electron
Nucleus
??
Nucleus is massive
Electrons orbit nucleus
Nucleus attracts electrons
Electrons repel electrons
Adapted from Gentner D, Gentner DR (1983).Flowing Waters or Teeming Crowds: Mental Models of Electricity. In
Gentner, D. & Stevens, A.L. (Eds.), Mental Models, Hillsdale,New Jersey: Lawrence Erlbaum, 99-129.
An analogical mapping can be thought of mathematically as a
mapping M from a source domain S to a target domain T:
M: S
T
Mathematical form of analogical mapping
Analogical mappings are not isomorphic:
The sun is yellow, but the nucleus does not have any color.
Planets attract, but electrons repel.
If one were to map the attractive quality of planets directly to the
atom, one would conclude that electrons attract.
Below is a pictorial representation how analogies are linked together.
Analogical links are indicated by arrows.
Some students used a jump rope analogy for Radio Waves.
The jump rope analogy led to wrong ideas about sound (indicated by
broken links, see next section on student interviews).
Sound Waves precedes Radio Waves
1 - Sound Waves references water waves
2 - Water is analogy for Sound Waves
3 - Radio references Sound Waves
4 - Sound Waves is analogy for Radio
2
4
1
3
Radio Waves precedes Sound Waves
1 - Radio Waves references jump rope
2 - Jump rope is analogy for Radio Waves
3 - Sound Waves references jump rope
4 - Jump rope is analogy for Sound Waves
4
3
2
Analogical Scaffolding
After using the Radio Waves simulation, Karen was asked how
sound was related to radio waves:
"Well, it's not really moving air. I think of compression of air when I
think of sound waves, but here I just think of, like things like
electrons moving through the air...but that doesn't make any sense
because...since electrons are creating it, it can't be electrons."
Susan (R>S) used Radio Waves before Sound Waves. She makes
use of a jump rope analogy.
"The amplitude stays the same right on this half but at the
beginning it's varied. And I'm, kind of, not real sure why that is.
Just because, unless it needs, like, kind of a high beginning
amplitude or something…like when you do with a jump rope or
something, you need, like, a big shock to start off the wave."
Susan also used the jump rope analogy to explain how one
electron's motion related to the other electron in Radio Waves.
"I guess it makes it look like this electron and this one are a little bit
more related because they're, they're on the same line that's, kind
of...like they're connected to the same jump rope."
ken
Bro
k
Lin
2
Broken Link 4
Source - Jump Rope
Jump rope carries the wave
Wave represents jump rope position
Points on the jump rope move because
they are part of the string
Target - Radio Waves
Electrons carry the wave
Wave represents electron position
Electrons move because they are
part of the wave
When the Susan used Sound Waves, she borrowed the jump rope
analogy over from Radio Waves.
"Um…just…it's not really moving back and forth. I think the
speaker kinda maybe makes it look that way, like it's sucking some
back in, but I don't really think that's what it's actually doing. It's
just like, uh, like you push it once and then the wave goes across
and then you push it again and the wave goes across. Um, I guess,
1
In our model of learning, students progress from a low level of
abstraction to a more abstract level.
This forms a scaffolding, helping the student to build understanding of a
concept requiring a high level of abstraction.
Low level
Representation
Phenomenon
Concrete
Concrete
Water wave
Conclusions
High level
Abstract
Concrete
Sound wave
Abstract
Abstract
Radio wave
This work supported by:
The Kavli Operating Institute
The National Science Foundation.
We have developed a model of student learning where simple,
concrete analogies are used to scaffold understanding of more
complex, abstract analogies.
This model is based on a cognitive theory of analogy, and also on
student interviews.
Student interviews provided evidence in support of our model.