By Richard E. Bleil
Many years ago, my thermodynamics professor would often tout his favorite line, “use your brain and save your pencil.” That may be dated, since I’m guessing that kids may not even know what a pencil is anymore
Okay, that’s an exaggeration. But the concept is the same. Currently, I am working with an online tutorial service in chemistry. I have many students confused by the concept of the “limiting reagent”, which is simply the chemical that runs out first, but because the rates they are used means it may not necessarily be the chemical that is in the lesser amount.
Here is the analogy that I have been using. Suppose you are making bicycles, with one frame and two tires each. If you have 50 frames, and 80 tires, how many bicycles will you be able to make?
The solution is quite simple. We need twice as many tires as frames, so from the tires we can make 80/2, or 40, bicycles. It doesn’t matter that we have 50 frames; once we run out of tires, we’re done. We’ve made as many bicycles as possible. We’ll have 40 bicycles, and 10 leftover bicycle frames.
In chemistry, we need to convert to a unit called “moles”, then take into account “stoichiometric coefficients” to account for the rate at which the reactants are used. But, that’s not germane to this post. The point that I am making is that I will ask students the question regarding bicycles, and when I ask which one will run out first. they’ll say “frames” because there are fewer. I’ll reply no, because we use tires twice as fast. So, I will ask to reinforce the question, I’ll repeat, so which one will run out first.
Then a silence.
If we manage to get to the correct answer (tires will run out first), then I’ll ask how many bicycles we can make. And they’ll say “two”? Well, no, we have 80 tires, so how many bicycles. They’ll reply, “80?” (and remember, we just covered that we need two tires per bicycle).
The problem isn’t that the students are somehow lacking in mental faculties. They can do it, and they’re smart enough to be able to figure it out, but I believe that the problem is that they don’t want to figure it out. They’re blurting out numbers, words, anything they’ve heard recently. They are not thinking about the question or the parameters of the problem.
So why is this? Okay, they may be tired (or stoned or drunk) since often I am helping students in the late hours of the night (or early hours of the morning). There’s a good chance that they are also distracted, because if I am helping them. then they are clearly on a computing device of some type connected to the internet, so they very well may be chatting with friends, playing a game, or on a social media site. But there are more insidious possibilities. The students may believe that they are not smart enough, or will not, understand the answer. Or they may just not want to learn (for example, if they only want answers to put on the homework answer key or software).
Whatever the reason, it breaks my heart. Solving problems like this are so much fun for me. It’s like figuring out a puzzle, or a solution on a video game that has been troublesome. The easy video encounters are not nearly as much fun as the “boss”, and to beat the “boss”, you have to figure it out. In this analogy, the “boss”, then, is the author of the question. Am I smart enough to beat the expert who wrote the question at their own game? Can I find the pathway, process, secrets to finding the answer.
The other day, I had a student taking a junior or senior level engineering thermodynamics course. My degree is in thermodynamics, but not engineering. The difference is application, details, and terminology. For example, the two questions were related to solar heating in a home, and a hydroelectric plant, and the engineers like to use Watts, which is energy per second, rather than just energy as chemists use. This was a stretch for me; in principle, I knew the formulas to use, I knew the principles involved, but it was applying what I already knew to a new situation, and I have to tell you, while it was a stretch for my old worn-out brain, it sure was satisfying to find the solutions.
Homework is no different. A teacher will not give a question if the student lacks the background and preparation to answer it. Nobody would not ask the student to solve a division if the student doesn’t now how to add. That means that any question the student faces, they already have the background to solve it. To actually find the answer is just, well, synthesis. Finding the pathway to defeating the boss. Blurting out nonsensical answers only makes things worse. It adds time, and frustration, to finding the actual answer.
When I was in college, like most of us, tried to answer questions quickly. If a professor stopped me in the hallway with a question for me, I would try to blurt out an answer quickly. There is nothing new in pointing out that this means I wasn’t listening to understand the question, but to answer it. Here’s a trick I started to use: I made it a conscious effort to draw a breathe before answering any question.
This might seem odd, but it did two things for me. It allowed me to let the professor finish, and listen to what is being asked, because I knew I would have to draw the breathe anyway. The other thing is that it gave me time to formulate my thoughts. The brain works quickly, and drawing a breathe goes a long way in formulating a coherent answer. And, frankly, I believe it made me look more thoughtful and analytical as well since I didn’t give out knee-jerk answers.
You are more intelligent than you realize. Think. It’s amazing what you can do. I was watching a movie today with a friend of mine set in the 18th century. One of the characters mentioned a creature that can travel a thousand miles in a day. It can get you from one end of this (well-known) city to the other in the same day. This struck me as odd, and it literally took me about five more lines in the movie while I processed the statement. I turned to my friend and said, “did that person just say that the city has a thousand mile diameter?” She caught it too.
Must be why we’re friends.