I was lousy at word problems. As soon as I saw the paragraph on the page I got nervous, and by the time I got to ” Johnny had twelve apples.” I was almost in a panic.
Later someone told me some tricks to convert sentences into equations. I learned to write “+” every time I saw the word “and” and “=” whenever I saw the word “is”. This made it easier, but I never quite got the hang of it in elementary school, and I got my worst grades in that part of my math class.
My husband on the other hand loved word problems. Not only were they simple to do, but the math in them was often easier. My husband went on to get a degree in astronomy which requires lots of physics, while I studied Biology. Recently, however, I began to take physics classes, and I discovered that physics is taught differently than other subjects, and this difference may be the reason why some people find physics easy, and others find it hard.
Physics is quantitative. This is the heart of the subject, and the heart of how it is taught. If a physicist can write an equation to describe something, then he understands it. Thus to a physicist, the world is one big word problem, and when he learns how to state the equation, then he’ll understand everything about it.
Some physicists probably see the symbol”+” when someone says the word “and” automatically. For them the thought of having fifteen ways of describing a concept would simply be confusing, for how could it be more precise to use the words “combine”, “annex”, or “compound” when the symbol “+” says it with so much less fuss? These physicists probably had comments on their English papers telling them to use a thesaurus.
Writing and Physics have different meanings for precise. To a writer, the word that most precisely describes a concept depends on factors such as its past usage and the connotations that it invokes. To a physicist a concept is most precisely described by terms that will always get you the right numerical answer.
I discovered this difference when I was taking a physics test, and I needed to remember the definition of “work”.
Websters dictionary defines “work” as “Exertion of strength or faculties; physical or intellectual effort directed to an end; industrial activity; toil; employment; sometimes, specifically, physical labor.” This definition works fine in the arts, but it is way too wishy-washy for the sciences, because it can’t be stated as an equation.
When I looked up the definition of work in my old chemistry book, I found this equation for it.
Work = Force X Distance
What this means is that if my car breaks down and I have to push it back to my house, I’ve done some work as you will surely agree.
The definition in my physics book, however, is different. It states that Work is the Force parallel to the s direction times the displacement, or F cosine theta s.
Ya got that?
So, why do physicists feel the need to insert trigonometry into a simple definition like this? Because if the point is to write an equation to describe something, this is the more precise description. What this statement says is that work is only done in the direction that you are going. If your little kid tries to help by pushing the car sideways so that the car rocks, or heaven forbid they try to push it in the opposite direction, they aren’t doing work, and you will soon chase them off to stop their unproductive activity.
The trigonometry terms make it easier, because they state precisely what you need to plug into your calculator to get the right number. So what is easy to a physicist is not necessarily what is easy to a chemist or a journalist. A physicist needs to be able to quantify a concept. To come up with one clear way of describing a it with numbers.
I was confused because the numerical description of work was listed before someone told me what it was. I found the physics definition harder to remember and harder initially to understand. And what this reveals is something that all teachers must face eventually. That there is more than one way to describe the same problem, and different people will find some descriptions easier to understand than others.
I think that the reason there is so little overlap between students of biology and students of physics is because this difference in thinking about the world, which is mirrored in how these subjects are taught.
Let me give you another example:Thermodynamics.
What is thermodynamics? The word is derived from the Latin root “thermo” which means heat, and “dynamics” which means movement, and this is exactly what it is about, the movement of heat from one thing to another. This is a concept that you must understand whenever you boil an egg. One thing that I wondered about is why chemists thought that thermodynamics was easy, and physicists thought that it was hard.
In chemistry and biology, the first law of thermodynamics is often called the conservation of energy. It says that “Energy is neither created nor destroyed, it only passes from one form to another.” To go back to the egg example, If you want to boil your egg, you have to add energy to it, but you can’t just snap your fingers and make the egg suddenly hard boiled, you have to add energy to it by putting it in the pot of water and putting it on the stove. You turn on the heat, and the pot heats up the water, which boils the egg.
This is an easy concept for chemists who include it in all first year chemistry texts. Biologists modify the description to emphasize that this has to do with Energy and not just heat because biologists are concerned with people eating food and using it to do work. But this concept is not easily put into an equation. Because of this, this concept is harder for physicist to describe.
In fact, a physics book doesn’t start with the first law. They first insert another law of thermodynamics called the zeroth law of thermodynamics which states:
A statement that needs to be said before a physicist will trust the thermometer that she has stuck into her turkey. Then the physicist states the first law of thermodynamics as follows:
Delta U = delta Q – delta W
Where U is the heat added to a system. Q is the internal energy, and W is the work.
Delta means a change.
Which definition do you find easier to understand?
This equation in words says that the change in heat of a system equals the change in the internal energy of a system minus the external work done by this system. You have to believe that this equation describes the entire situation in order to get the concept that energy is neither created nor destroyed. You take for granted that someone isn’t going to come in latter and add new terms to the equation.
An egg won’t spontaneously become hard boiled because that would be work and that can’t happen until you add heat to the egg (U).
To boil an egg, the hot plate changes by warming up (the delta U). This changes the heat in the pot of water with the egg in it (delta Q), and does work on the egg cooking it (delta W).
This is a hard concept on many levels for physicist. Take the last term, W. This is work. Remember work? Work is the “F cos theta s” or the force times the distance in the direction that does the work. How do you translate that into an egg going from a soggy mess to a firm solid?
This isn’t the same as pushing a car down the street. It isn’t even the same as a “change in state” of matter like going from ice to water. Hard boiling an egg is a complicated change in the physical structure of biological chemicals. It’s got too many molecules, and too many atoms, and too many changes going on at once. Thermodynamics is hard for a physicist. Keep this in mind when you teach a subject to students with different backgrounds.
A physics student may see boiling an egg differently than a cooking student. Given the problem:
How long do I need to keep my egg in boiling water before it becomes hard-boiled?
A cook expects to learn by experience. They might buy an egg timer to help calculate it, learning by testing that it tastes better to them if they turn the timer twice before removing the egg.
The physicist doesn’t want to have to experiment to get the answer. He should be able to figure out the answer by considering how many joules of heat your hot plate puts out, and exactly how much energy is getting into the egg to do the work of cooking. Somewhere in there must be a rate in seconds that will allow him to plug in the numbers and with the proper conversion factor give a precise time in minutes for the egg to cook.
Because students of different backgrounds will try to solve the same problem differently, a teacher should remember to describe how people in the field they are teaching think about a problem. They should give both qualitative and quantitative examples, and not assume that one or the other is easier to understand. Being sensitive to differences in world-view should help a teacher to teach physics to biologists, or even to teach creative writing to physicists.
How you describe the world determines how you understand the world; and if you can describe the world in a way that your student understands, then it will make the subject easier for them.