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Re: [Phys-l] What are your answers for this teacher?

Proportional reasoning involves a lot of things. It involves seeing
proportionality. It involves understanding that when two things are
proportional that if one increases 10% the other will also increase 10%, so
if one is multiplied by 1.1 the other is likewise multiplied by 1.1. It
involves understanding when to multiply or divide. So if you have the
distance and the speed, the proportional reasoner will figure out that you
divice the distance by the speed. And to a large extent it is an obvious
piece of reasoning. The non proportional reasoner will have to have a
memorized equation and then manipulate it. But they often memorize it
backwards or upside down.

The teeter totter analogy is an example of compensation reasoning.

Just analogies handed to people do not work that well, and telling them is
not very productive. The experience of Thinkin Science is that the person
has to physically see the principle in action and try to figure it out. In
other words the learning cycle is necessary. Watch the Doors video to see
the problem with college students. I gave the URL in a previous post.

If you want to find this out for yourself, try teaching proportional
reasoning, and use either the Lawson Test or Jerry Epstein's test of
proportional reasoning pre and post. Also look at the correlation between
proportional reasoning and other skills.

Analogies are much better used after an exploration of this type of
reasoning. The student has to be convinced by evidence that their current
type of reasoning is not working, or they will not change it. People who
already think at a high level see the reasoning as obvious and think they
can just explain it to others. But this does not work. It is like the
farside cartoon showing the master and the dog. The master is saying
things, and the dog is hearing "blah, blah, blah...". What you have to do
to improve thinking is definitely not obvious. It has been found using
research, and generally it does not involve explaining but a learning cycle
approach. There may be better ways to do it, but at present this seems to
be the best way. We also do not know why some people seem to immediately
acquire higher level thining and others never do. But we do know that 85%
of elementary teachers can acquire formal operational reasoning, but seldom
do.

I have raised proportional reasoning from about 40% to 60% in a short summer
school course, and I think it would be difficult to do much better in that
time period. There was some telling involved, always after the exploration.

To begin to really understand what is known about cognitive enhancement
actively read "Really Raising Standards" by Shayer & Adey, and "Science
Teaching and the Development of Thinking" by Lawson. Both are accessible
and scholarly.

John M. Clement
Houston, TX


Maybe I'm being dense, but I do not see how algebraically
manipulating
a three variable equation is proportional reasoning. Yes, one can do
mindless operations to accomplish the algebra, and we need to help
students understand the process. I completely agree with your optics
example below. But understanding basic algebraic manipulation is not
the same as proportional reasoning. I have no problem using
analogies
to help students and teachers understand proportional
reasoning. With
V = IR, I use a teeter totter with V on one side and IR on the other
side. If you keep R constant and decrease V, what happens to
I? Well,
decreasing V makes the teeter totter go down on the right side. THe
only way to balance it is to reduce I. This analogy is very
useful for
learners. The triangle, however, does not fit into the same
category.
It helps people avoid thinking rather than assists thinking.

When you say that Shayer and Adey say that 3 variable equations are
not understandable unless you have proportional reasoning, are they
talking about the teeter totter reasoning above or are they talking
about the algebraic manipulation? My bet is it's the former.

So again, maybe I'm missing something. Can you explain how
going from
V=IR to I=V/R involves proportional reasoning?

Bill


On Apr 10, 2011, at 1:41 PM, John Clement wrote:

Simple algebraic manipulation is truly understandable if you have
proportional reasoning. According to Shayer and Adey, 3 variable
equations
are not understandable unless you have proportional reasoning.
Students can
get by learning the rules, but deeper understanding will be lacking.
Basically the equations covered by the triangle rule are 3 variable
equations. Of course it does not work with 4 variable equations.
It does
not work or if they are given a=F/m.

So getting students to think at higher levels is the
ultimate key.
The
triangle rule is just a notch below in desirability getting
them to
memorize
the algebraic manipulations to isolate a variable. Both can be just
mindless manipulation.

My favorite example of how lack of proportional reasoning makes
physics hard
is the hi/ho=di/do equation for magnificaiton in optics. The
students are
just looking at similar triangles and using proportions.
But I can
remember
how there were students who seriously could not remember this
equation so
they memorized hihodido as the jingle for the equation. I can
remember how
I thought that was stupid. Now I know that the students who did
this lacked
proportional reasoning, so this was their only way to remember such
equations.

Algebra to most of the students is just a memorized set of rules,
some of
which make absolutely no sense. Similarly division by
fractions is a
memorized rule, so even college students when asked to
divide 1/2 by
2 will
often get 1 as the answer. I have seen this too many times to
consider it a
random error. They don't visualize than think about what is going
on. But
once you have the higer reasoning skills such as proportional, two
variable,
and compensation reasoning algebra is often vary obvious.

So again, what you do to keep your job may be very different from
what you
do to really help the students. If you don't have the time to
improve the
thinking, you may have to resort to cheating by pumping the
students
up with
rules that they will temporarily use. My reaction to the triangle
rule is
that if the student can explain why it works, I will let them use
it. But
any trick which is inexplicable, may not be used.

John M. Clement
Houston, TX


So are you saying that one cannot help students understand
this simple
algebraic process in, say, half a year's time, so they can do
well on
an exam? While proportional reasoning might take longer than
this, the
process underlying the triangle does not.


_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l