Onmatu- General Math Learning Article
Years of tutoring math and studies of cognitive psychology and philosophy had led me to distinguishing major students’ motivations towards education. Practically most interesting are motivations for learning, which lay between total absence of motivation, and pure motivation of true scientist or mathematician. Total absence of motivation for studying a subject is no mere dramatic, but may be a sign of taking a wrong direction in education. It may be better to reach some basic level of mastering the subject, and concentrate on more favoring disciplines. Sincere scientific motivation is very rare, and usually needs a little extra tuition of best experts in the field. As observed, most students have different kinds of intermediate motivations. Deep understanding of the kind of motivation, which is actual to the given student, empowers the tutor with versatile psychological tools to increase this motivation. What is more important, understanding the fact that existing motivation of the student is intermediate, enables the tutor to gradually transform this motivation towards a more sincere one of the true scientist. If the tutor succeeds, the student can continue studies almost without any extra tuition.
So what are these different kinds of intermediate motivation of the student? Depending on culture and mentality, most of them are of four types:
• Quickly benefit from fundamental knowledge. This is most widespread motivation issue in the culture of market relations. False benefit comes in forms of esteems and marks, which are relative, and hardly express the depth of real-world applied understanding of the subject. The most destructive side of this sort of motivation is it’s limitation of one;s plans with a very short-term perspective. For example, studying calculus empowers student to think in terms of modern science, which makes him less naïve and less manipulated by the mysterious British scientists from BBC. However, she or he will have chance to appreciate this gift of math only a decade or two from now. Therefore, there is no straightforward benefit of calculus, except for college and university grades, which have little to do with real-life esteem. The constructive side of this motivation is that the student makes much more effort in the perspective of feasible revenue, which maybe: money and gifts from parents or grateful classmates, whom the student can help with math and thus become truly important to his or her society.
• Prove to anyone her or his intellectual superiority. The evident reason is to make parents and teachers proud and to establish higher standards. The covert reason for being superior is to despise those who are less smart. Difficulty, which accompanies this motivation, is the fear of making mistakes. Pride is extremely vulnerable even to the smallest mistakes. But without extracting experience of one’s own mistakes, one can never succeed. In cases like this tutor has to balance between intimidation and praise, to make student’s pride work for the educational success.
• Become wonderful, for admiration and envy of others (preferably in the miraculous way - easily, like in a fairy tale). This is probably the least problematic motivation for future artists, and in the same time the most difficult one for such a complex and unrepresentative discipline like math. Miraculous life view makes the surrounding world not transparent to the laws of cause and effect, which are formulated mathematically. Everything in such miraculous world happens by chance, which of course has nothing to do with the probability theory. If this is the case, many vivid examples are the only means to make the cause-effect relations feasible enough to break through this magic shield of mental laziness.
• Study exhaustingly just to please parents or teacher, without any personal pleasure. Such an attitude towards education originates from an attitude towards the whole life, which is “life is suffering”, like in Buddhism. This situation is less common in our prosperous world, however sometimes this is the case. Personal satisfaction, pleasure and joy of education are substituted with the sense of guilt. Student feels guilty for each pleasing moment in the education process. This feeling is aimed towards those who are his or her surrounding, which is also supposed to suffer. While teachers show reprehension and disapproval of small pleasures which the student has, he or she would shift towards dull and unproductive way of studies. The only good thing about this suffering attitude is that it makes one quite persistent, but at the cost of creativity.
Dealing with these intermediate motivations, and gradual transition of the student to a more complex way of thinking using the language of mathematics is the essence of my teaching approach. Main thing is to reveal the original potential of the student, and implement it in the learning process considering student’s intermediate motivation. The more complicated role the student has to play in life, the more he or she will need mathematically sharp mind. Vice versa, the more complexly the person thinks – the more ambitious role he or she will play.