APPLICATION OF COGNITIVE CONDENSATION
AND OF THE POWER LAW OF PERFORMANCE
The following summary page on "studying successfully" is based on direct implications of cognitive condensation, the power law of performance, and of the intrinsic structure of knowledge (see the causal, functional and logical relations).
Learning is a cumulative process, where new knowledge and skills are integrated into existing ones that are modified, extended, or reorganized.
Years of practice have shown that most of the difficulties of students in a given class can be traced to (a) their academic background, (b) the intrinsic structure of the subject matter, and (c) their study skills or methods.
In particular, the hierarchical structure of mathematical and scientific theories is not respected by many students. As a result, they encounter serious difficulties -- not because of any lack of intellect -- but rather because of the implacable structure of the subject. This point is best illustrated by the example of introductory and calculus -based physics. A true mastery of the lessons on units and on vectors - a mastery demonstrated through extensive exercises and problem solving - coupled with a working knowledge of basic calculus leads to an enjoyable and challenging journey through this introductory course. Some students, however, fail to study immediately and master the lesson on vectors. This leads to great difficulties throughout the semester for any student.