Stages of Preparation for an Exam
The traditional science exam follows a predictable formula of how students will prepare in order to do well in an exam. Every class will have a mixture of every kind of student, but their are still general patterns.
Stage One: Announcement
About two or three weeks before the exam is written, the teacher will announce that a test is coming up. When this happens, some students will not even pay attention, figuring that there is plenty of time between now and the exam. Others will flip open their school planners and pencil the date in, organized much more than the average student.
Generally, the announcement of the exam generates a bit of buzz in the class, but not too much (since the threat is so far away).
Stage Two: One Week Out
As the exam looms nearer, review sessions are common. This is where people begin to really think about the exam (not just in abstract terms). During these times, the students will start to ask questions about concepts they aren’t familiar with. They will have plenty of practice for the exam, but if they are anything like me, they are still waiting to start most of the problems, because there is a bunch of time left before that exam.
An alternative: the beginning of panic. Depending on the actual content of the exam, panic can begin to blossom at this time. For some classes, the sheer amount of material becomes almost overwhelming. Personally, I’ve experienced this sensation for my mathematics class, where the amount of formulas and procedures we had to memorize and know how to use was a bit nuts.
Still, with one week left, the student will generally feel good about his or her chances on the test.
Stage Three: T-Minus Three Days
At this point in time, full panic has either set in, or the student knows exactly what they are doing. With only a few days left until the exam, students are in an awkward position in class. The exam is soon, but the teacher does not want to waste time reviewing old material (since that had already happened), so he or she moves on to new material. Therefore, the students have to try and absorb new material while simultaneously thinking about their upcoming exam. Evidently, what usually happens is that the new material is only somewhat understood and not contemplated for very long.
It’s at this stage in the game that I personally crack down on studying. Usually, this means going over the topics for the tests, and redoing any assignments that are part of the exam. I choose to do this three days and less before the exam because I feel like it gives my mind the “muscle memory” to know what to do when I encounter a similar question on an exam.
This strategy can somewhat backfire if there is a lot of material on the exam, because it means I’ll have to go through an extraordinary amount of work in only a few days. Consequently, the days leading up to the exam are quite stressful, and it is difficult to think about anything other than the exam.
Stage Four: One Day Until the Exam
As the penultimate day draws near, I have two possible reactions: confidence that I know the material well, or utter panic that I won’t be able to do as well as I would like on the exam. With so little time until the exam, those are the basic mindsets I have. If there are problems I try that day that aren’t making sense to me, it’s probably enough to send me down in a funk, certain I will do terrible on the test (usually, I don’t do horribly).
For others, it’s a day of making sure to read over the notes and testing one’s knowledge of the subject. I do this too, but I find it more useful in science exams to be practicing problems instead of theory (though both are indeed important).
Stage Five: Moments Before the Exam
As the hour draws near, many are beginning to get trapped in a mental panic. Questions are shot back and forth between students, as if they are part of a tennis rally. Answers are recited in textbook-like form, and procedures are gone over. For a few unlucky students, questions about concepts are still posed, which implies that there are still uncertain subjects left to the student.
When there are only ten minutes or so left before the exam, many students adopt a military-like approach. For one of my more difficult classes (not for me, but in general), my friend would say something to the effect: “Well boys, let’s get ready for war. See you on the other side.”
The stages of preparation for an exam follow this pattern pretty well, to the point that I know the routine to follow for each one. I always feel like it’s an endeavour that must one cross, like a huge hill that one has no choice to climb. As the climb approaches, I don’t necessarily want to climb it, but I resign myself to the fact that I must. Then, once I reach the top, I feel a huge sense of relief that it is all over.
An important thing to note is that these are the stages of a science exam when there’s only one coming up. At the end of the semester, the situation is a bit different. For one, the exams are all distributed at around the same time. Secondly, the exams are comprehensive, which means there is much more material than on an exam during the semester.
This means it is very difficult to wait until a few days before the exam to begin studying. It’s possible, but I definitely don’t recommend it (actually, I barely recommend any of my procedure). To deal with this, I try to begin studying sooner, and I try to address the most pressing exam first. It’s not the best strategy, but it’s the one that I use.
As you can see, the stages of an exam are filled with one thing: stress, which is why it feels so amazingly good to finish one of them.
I used to hate reading a text when someone would write with qualifying language (this was also prevalent in how many people I looked up to spoke). Why couldn’t they just go ahead and say the thing that they wanted to say? Why did their have to be language such as “this suggests” or “I can’t say for sure”? It would drive me insane because I believed that writing that made an impact doesn’t need this extra baggage surrounding statements.
Before then, I was reading a lot of material on domains such as design, writing, and generally creating some type of art. What this meant was that the goal was to connect with the audience, and this was best done in direct language. There was no need to say things in a roundabout way. Instead, the artist could take a direct stab at the issue and touch the person viewing the piece.
This is the mindset I brought with me when I started to read more material by scientists, and that’s where I started seeing all this qualifying language. Like I said, it did not make sense. Why wouldn’t they just communicate without putting clauses on all of their statements?
Slowly, I found the answer: scientists are trying really, really hard not to fool themselves. In a nutshell, a good way to explain the scientific process is that we are trying to look for ways that we are fooling ourselves. Throughout history, we’ve seen over and over that humans can be easily fooled into thinking something is true when there is actually a much larger picture. I highly doubt our ancestors thought there was anything other than what they could see with their eyes (except for perhaps a god). Then we smashed this perception in the 19th century by discovering that light is a wave and can have wavelengths that we cannot perceive.
In particle physics, we’ve seen a complete makeover in regards to what we think the universe “truly” is like. We went from just seeing matter to thinking about the atom to breaking that apart into fundamental particles. Finally, we pushed that even further by saying that these fundamental particles are part of a wave function. In the end, we’ve gone from what we can see to having the entirety of the universe being composed of wave functions.
Obviously, this is a radical change with respect to our first thoughts about the universe. Therefore, what we’ve found is that the scientific process has shown us just how wrong we are. As such, I believe most scientists have a certain fraction of skepticism in their minds when approaching any kind of phenomenon. It’s not personal, it’s that history has shown us that it is the safe bet to make.
The truth is that a scientist should be willing to believe anything, as long as the requisite proof is supplied. If a scientist won’t believe a statement after sufficient proof is given, then there is a problem, but that tends to not happen when someone says a comment like this.
What I find fascinating is that, if the person really believed in what they said and could say that it makes sense to anyone, there shouldn’t be a problem with supplying good evidence. If not, there should be at least an explanation as to why evidence is hard to come by.
Remember, lack of evidence doesn’t mean a statement is false, but it sure won’t convince me to believe in it.
Unfortunately, I get into many situations in which those claiming extraordinary things cannot bring any proof, and then they get upset that I won’t believe them. However, I couldn’t do anything better. It’s difficult to accept a proposition on the basis of someone just telling you so. As a science student, I’ve learned that this is a terrible way to go about finding knowledge about our universe. Trusting the human senses because they feel right might seem okay intuitively, but that’s the problem. Humans don’t have an intuition that is good for some of the deepest questions about the universe, since they are happening at a realm that is basically invisible to us. Therefore, we must safeguard against any attempt to “reason things out” without actually using tests and logic and theory. Without the scientific method, we would still believe that the world is only made up of components we can see.
So what does this have to do with qualifying language?
It means that scientists are careful about what they say. It’s fun to say something with certainty, but that technically never happens with science. Science is a process in which we can give ourselves a “good idea” (and sometimes a great idea) about the world, but we can never be one hundred percent certain. This is what makes science what it is. Consequently, the responsible scientist will use qualifying language because they know it’s good to be as specific as possible about what we know. Apart from perhaps a few minutes of fame, there’s absolutely no long-term reason that would make it a good idea to oversell a scientific achievement. It will always catch up to you, and so it’s not worth it. Therefore, scientists are fond of using qualifying language in order to remind us that they don’t have all the answers.
Now, I always shake my head when I see someone write without qualifying language, particularly because it’s not completely honest. The truth is almost never absolutely declarative, and I believe we’d do much better to remember this.
Qualifying language isn’t a sign of weak communication or “not believing in one’s message”. It’s about being honest about what you know and what you don’t.
When a scientific topic is covered in the media or talked about extensively, words like “proven” are often used. This word is often accompanied by a grandiose claim that seeks to impress people. Either this miraculous medicine is proven to work, or this diet is proven to be more effective. Everywhere we look in science communication, the word “proven” is there.
Unfortunately, while scientists and those who are familiar with the scientific process understand what we implicitly mean by the word “proven”, it is a completely different reality for those who are merely passive receptors to scientific information from the world at large. To them, the word “proven” means certainty, as in 100% certainty. When a scientist or science communicator says that something is “proven”, the idea they get is that the scientific concept or hypothesis has been validated and will be correct forever.
This is at odds with the enterprise of science. As every student in a scientific discipline finds out during their education, science is self-correcting and always updating its beliefs through experimentation. No idea is set in stone, except for perhaps the idea of how science should be conducted (as mentioned above). Everything else is fair game for updating, improving, or renovating.
However, it’s inconvenient for scientists to talk with all these uncertainties surrounding their experiments. Therefore, the more colloquial language of hypotheses being “proven” is used, simply because it’s easier. Make no mistake though: the implicit assumption is always there. Science as a principle cannot know that something is 100% true. We can be very, very, very certain of it, but never fully.
If you were fully certain something had been proved, then there would be no way to change your mind about the topic. Therefore, no more experimentation would be needed, and the information would never be updated. Your view on this particular topic would be static, never changing. As such, the scientific process would be useless. Incidentally, the information you believe would basically become the stuff of religious beliefs.
This is why I dislike the term “proven”. Despite what some people may believe, science is not the same thing as mathematics, and only the latter can definitively prove something. The former always has a certain degree of uncertainty surrounding it.
Consequently, I favour a different way of looking at which scientific theories are accepted and beat out competing ones. Instead of thinking about a scientific hypothesis as the best fit for the data, I like to think of it as a game of survivor. There are a bunch of candidates looking to explain a certain phenomenon, and the first thing that occurs is that the data invalidates certain hypotheses. As the data is analyzed further, more hypotheses are crossed off the list because they don’t adhere to the data until only one remains. This final hypothesis isn’t necessarily proven. Instead, it simply hasn’t been disproven. Therefore, it becomes the survivor and the accepted theory.
This process much better illustrates the process of science. It’s about constantly pruning out hypotheses that don’t fit the data, and keeping the one that survives the trimming. By thinking about the process in this way, we can get a better idea of what a scientist really means when they say an idea is “proven”.
A Sense of Play
In mathematics, there’s a sense of play that must be achieved if one wants to really understand what is going on in mathematics. Contrary to what people might think, this sense of play and “just getting” mathematics is not some sort of genetic feature (or at the very least, not only genetic). It’s the result of immersing oneself in mathematics and freely playing with the concepts. After a long time, this play translates into what people call “intuition”.
Have you ever opened up a graphing calculator program and tried out different functions? Have you looked at their features and thought, “this is interesting”? Have you ever opened up your mathematics book and simply read it of your own accord to see if there were cool things you had missed?
That is what it means to have a sense of play.
Having a knack for mathematics is not so different from being good at a sport, or a musical instrument. Sure, having the right technical skills is important, but being really good at something requires one to experiment and refine one’s process. In this sense, trying new things and playing with numbers, functions, and other mathematical concepts is key to improving one’s “skill” in mathematics.
This sort of aptitude doesn’t necessarily translate to solving more complex problems or suddenly learning new concepts faster. What it does do is give one a better way to “see” a concept, making it more approachable and familiar instead of challenging because one does not know how to proceed.
Develop a sense of play in mathematics and test things. Take out a piece of paper and try some equations out just for the fun of it, and you may surprise yourself by the relationships and patterns you find.