...it's time to view “cramming with numbers” on the lighter side!
“I've always loved numbers and formulas! And I really thank God because since I started schooling, passing my Math exams never became a problem. I cannot remember a single test in my Math subject that is not marked with an A or is graded lower than 95%. In fact, I can confidently take my sit-in midterms and finals fresh from a 5-minute review at most 10 minutes before the test – in short, cramming with math was so cool! Others call it innate, some say it's magic. I say it's passion.”
-a Mathematics lover's point of view
“It might be possible for many to pass a Humanities test cramming the night before the exam but it becomes much more difficult to do this for math, or physical science, or an engineering course. Crammers also retain much less of anything from cramming (things which will be remembered later on when they are no longer needed).”
-a specialist
“On Mathematics... Well, for a decade of studying from kinder to high school, plus four years of taking my college math specialization, I noticed that the probability of passing an exam by studying the night before I take it is relatively higher for my math subjects than for 'philosophy' or other 'foundations of education' subjects. Is it because I'm one of those whose inclination is in Math?
On cramming? ...hmmm.. I still believe that once in a while, there is a class you can get away with doing that. Because mostly, it is the skill of memorizing which is enhanced in answering fill-in-the-blank items and questions asking for definitions by the book... Just wish that you won't be needing that knowledge again, because you'll forget it as fast as you learned it.”
-Tutor Rizza
On Cramming and Mathematics
Based on studies, cramming (or “massing”) for tests or exams reduces long-term retention. Trying to learn everything in a single session does little good, they say. A single session devoted to the study of some material should continue only long enough to ensure that mastery is achieved, as mentioned in the paper of Doug Rohrer and Hal Pashler entitled “Increasing Retention Without Increasing Study Time”.
Moreover, immediate further study of the same topic (for a particular grade level) is an inefficient use of time, if understanding of fundamental concepts was not achieved in the first place. Much worse, an attempt to “over-learn”, in the long run, will be categorized as “just a waste of time” because knowledge being read or heard but not fully-understood will just add up to the pile of misconceptions for the student. In the end, this will cause more trouble because it's like adding a new storey to a weak foundation – bound to collapse anytime --- a tragedy due to skill-gaps.
The sad part is, “most mathematics textbooks encourage over-learning and massing”. This is as reported by the Association for Psychological Science in its September 3, 2007 issue of Science Daily entitled “Back To School: Cramming Doesn't Work In The Long Term.” Students are forced to do numerous problems and to answer routinary questions of the same type in a short period of time – then abruptly moving on to something else without their efforts being processed and evaluated correctly.
What if you actually encounter challenging questions that require thinking or problem solving? And all you have reviewed are concepts and definitions memorized word for word...? Come to think of it...you're really going to be in trouble if you cram! Aside from not being able to learn the necessary concepts and skills in-depth as needed to pass the current exam, you run the risk of succumbing to skill-gaps --- the absence of required skills to handle progressive tasks, which impedes learning.
Based on experiments reported in a paper published in Instructional Science, Rohrer and Kelli Taylor recommend that practice problems in textbooks be systematically shuffled so that each practice set includes a variety of problems drawn from previous lessons.
Nonetheless, if cramming remains to be your last option, here are a few tips that may just make it work, in the short-run.
Emergency Cramming Tips for Mathematics Exams:
1. Preview the topics to be covered. Be aware of the scope of your examination.2. Be selective: skim definitions for key words only.
3. Don't read information you won't have time to review.
4. Spend the majority of your time concentrating on the example problems and take note of the pattern on how the problem was solved.
As a Mathematics educator, I always put emphasis on the fact that Mathematics is a science of patterns. It is not true that a particular drill exercise needs a unique approach which is not in any way parallel to the illustrative example being presented for the same topic. The fourth tip mentioned above is very effective in a way that it hones your computational skills and provides avenue for practice. In this manner, you will be familiar with the face and phase of the problem and, during the actual test, you'll be surprised to find out that the items “seemed to have appeared in your dreams”. Déjà vu, huh! And since you have really encountered and dealt with such questions, solving it will be as easy as 1-2-3!
Above all, Mathematics makes sense to students if they are to see it as having value to them. So take note of this more relaxed approach: attend class regularly and do what is required of you to grasp the content and right attack. Or, you can learn your lessons just the hard way... but, why prefer to acquire it the harder way?
Resources:
http://www.sciencedaily.com/releases/2007/08/070829122934.htm
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