Exam Preparation (for students)

Preparing for an exam, particularly for the first few exams upon entering university, can be very challenging. I would like to summarize a few tips, which have helped me during my studies. Of course, practice habits can vary and different strategies can succeed.

1) Start early: Particularly if exams tend to come in bunches at your university (final exam period, yearly exam period, end of semester, or similar phases), then having a bit of extra time can be worth many grades. Therefore, if you give yourself, say, 20% more time than usual can often lead to substantial improvements. Another possible advantage is that this extra preparation period can mitigate unforseen circumstances (e.g. a flu).

Another key advantage of starting early is that you are going to learn the subject more thoroughly. At least for me, and as far as I have talked to others, spreading out the material and learning it in smaller bits and more slowly seems to transfer it better to long-term memory. Of course, this approach does mean that it is going to take more time to prepare in total. Or does it? In the short run, the answer is indeed affirmative. In the long run, the situation is less clear. If certain knowledge ‘leaks out’ then it might be necessary to try to put it back in for future exams. This can take considerable time!

2) Stick to a system: In the beginning of university studies, it usually takes a few trial-and-error attempts to find a working system for preparation. Personally, I have worked through the lecture notes first. During this process, I tried to condense the definitions, results and examples to an absolute minimum. This led to a survey of around 5-10 pages per course of essentials. This ‘summary sheet’ was then used during the entire learning phase and  I went through it again frequently. Then I considered exercises assigned during the course. The last step was to try to grasp more of the available literature and try to see, whether my knowledge would hold up in different contexts (new exercises, other books or lectures, trying to extend parts of the lecture notes myself, etc.)

The system at least guaranteed that I had the basics available to pass a course. Depending upon the time and effort, those basics would then scale to a level to completely master the material. However, this system is by no means perfect (can you see the flaws?). Nevertheless, having these standard steps, I always knew roughly, where I was in the process and I also had some confidence that the effort would pay off. Hence, if you have found a strategy that works for you, my personal advice would be to just stick to it for a considerable time frame (say multiple exams and semesters).

3) Examples vs theory: Most exams, at least those testing material beyond multiple choice, require some more theoretical aspects as well as practical ones. For example, you may need to know facts, results, definitions and so on. Practical and more open-ended aspects include new calculations, creative writing, etc. Preparing for both aspects of an exam simultaneously can be very challenging. However, this problem can be actually used to one’s advantage.

Just studying an endless string of facts can be quite boring and may not be motivating. Similarly, just playing around with simple examples, reading certain parts superficially and trying to do exercises by trial-and-error without any background knowledge is often equally frustrating. Therefore, one advice is simply to switch if one aspect becomes repetitive or dull, i.e., to change from more creative practice to learning facts and vice versa.

Of course, if an exam just requires a large number of facts via multiple choice, then the most important aspect is to develop a strategy to avoid frustration while studying. Once you found one, which works for you, just stick to it (see 2).

4) Be aware of risks: Exams may have many different formats and regulations. This may include, what you can bring to the exam (e.g. some exams may allow a single page of notes while others are closed book). The duration of exams may differ drastically, some professors may structure exams differently than others, or parts of the material may not be exam relevant (usually distrust this statement, if it is in the notes, just learn it). There are many other changes and variations, which you may encounter for the first time at university.

The key issue in this regard is to be aware of the most problematic aspects already during the preparation phase. Suppose you have identified that the highest risk regarding a bad grade and/or even failing, is the limited time available. However, the material is not too difficult. Then it does not help much to repeat simple theoretical facts multiple times in the last few days but it would be more helpful to practice time-demanding questions. As an example, suppose you have to solve a certain class of equations in the exam as an auxiliary task. If solving this problem is easy but takes you a very long time in practice, just doing the calculations several times on different examples should increase the speed quite naturally. Similar remarks apply for other high-risk issues as there is usually some aspect in the preparation process to reduce the risk considerably.

5) Reach out: If you really feel stuck while studying and simply cannot comprehend several aspects, don’t despair. First, try to learn all those aspects well, which you can grasp. In breaks from learning these parts, reach out to others. Probably the most natural place to start is not the academic staff in the first place. The far more natural starting point is the discussion with your fellow students. Usually, the skills and perceptions are somewhat complementary and this can clear up already 90% of the difficulties via discussions, and be it only 10 minute exchanges at lunch. Furthermore, this helps you to isolate the really difficult aspects from those, where just you have managed to be quite stubborn or were misled somehow.

In the second step it is then crucial to approach the academic staff with the remaining aspects, where most of the class is stuck. This is tremendously helpful for both sides as it makes it a lot clearer for professors and teaching assistants, where the difficulties really lie and how to improve the material. Furthermore, as students the process to sort the challenging from the straightforward aspects should have already produced a tremendous practice effect.

6) Take it seriously: Although this may sound obvious to most of you, it may be the most important aspect in the preparation for an exam. Do take the preparation for an exam seriously, i.e., really view it as an important task or a critical job that needs to get done thoroughly and accurately. The moment you try to reduce the exam to a nuisance or minor matter, this is the moment, when you have already failed. It is worth remembering that in the vast majority of cases, failure in an exam is not caused by ‘having a bad day on the day of the exam’. It is simply caused by lackluster preparation. Therefore, you should think of the preparation phase as the real exam, the day of the exam is there to actually give a condensed survey, how your preparation went.


Disclaimer: As with all my previous posts, the discussion above is certainly not exhaustive. Please feel encouraged to comment, criticize and propose other helpful strategies.

 

Transdisciplinary Courses

Transdisciplinary courses are probably among the most difficult to plan, implement and teach. A first natural question is whether one needs such courses at all? Modern science, and complex global life, pose challenges that may be difficult to address with classical techniques from just one particular field. Indeed, if individual fields would be enough, there would be a lot less (open) problems. The need to branch out, combine, connect and intertwine as a problem solving-strategy has already produced tremendous results, e.g., modern medicine would be impossible without heavy input via tools and approaches from chemistry and physics. It seems quite likely that the next generations of students could benefit from learning how to bridge disciplines. A key question is when students should branch out: immediately when starting at university, in the intermediate part of their studies, or just when needed in doctoral studies or even via continuing education? This question is already a tricky one. The standard answer is: it depends! However, it seems that a balanced approach is to be called for, i.e., starting far too early, might mean that the basics suffer while starting too late, or never, could lead to missing out on a potentially promising approach. It seems reasonable to roughly spend six semesters really focusing mostly on technical groundwork. it should be noted that this does not necessarily mean to just take courses from one particular area. Many classical established combinations of subjects have been proven to be successful roads. From my personal experience, this has been the interface between mathematics and physics as well as to computer science. Learning fundamental mathematical tools is necessary for physics and computer science. Being able to program and to understand algorithms is a key skill for mathematics and physics, while basic physical intuition and core problems motivate many parts of mathematical thinking and computing. Hence, there is literally no reason why, say a mathematics major, should not aim to maybe take a minor in physics, computer science or a related discipline. Once major technical skills have been acquired during the first few years, there is opportunity in the curriculum to expand horizons if students continue at university; if not, training on-the-job in an industrial setup is a suitable broadening of horizons anyhow. On the university level, continuing to a master-level or doctoral degree should give students at least some flexibility. In this situation expanding to new areas can easily be accomplished. Students are now prepared with a toolkit from their core discipline, which allows them to start out on firm ground. Practical issues are mostly sorted as having a first degree usually implies familiarity with studying and learning principles at university. Even though there may be no real consensus on the timing, let us suppose now that one wants to offer a few transdisciplinary courses around the time of semesters 7-10 to supplement master-level or beginning doctoral studies. Then one has to decide how to practically implement a course. Administrative hurdles do arise: which department is responsible, what amount of credit to give, and whether the course should be co-taught by two faculty members, are just the tip of the iceberg of questions. In fact, the ‘underwater’ part of the iceberg might be even more dangerous as we all known. I would argue that the university should just provide a broad skeleton and leave the precise decisions to individual departments. On the departmental level, a simple rule could be to implement an equal contribution principle. This means that each department contributes equally in all regards: faculty support, credit points, topical contributions, and so on. This would ensure that not too much additional strain is placed on the existing curricula. To guarantee flexibility, the courses should be oriented towards challenges that are recent and of general interest. For example, it is clearly a mathematical challenge how to analyze the dynamical processes of and on complex networks while the impetus and implications for this class of problems can easily be found in the stability of financial markets or in the sustainability of ecological diversity. An advantage in this context is that students would adapt and learn new methods from distant subjects on the fly. To pick up the last example, agent-based and game-theoretic models from economics or foodweb modeling and structure could be picked up in a course on economic or ecological network dynamics. These tools are also important from theoretical standpoint in mathematics per se. They are frequently not part of the undergraduate curriculum so a transdisciplinary course is an excellent opportunity to introduce them. Overall, I would argue that if a transdisciplinary course is well-prepared, it can open up new horizons for students after some technical groundwork. After all, leading students to the edge of knowledge and new research horizons is also one of the goals of university education.