Patterns. Ideas. Assumptions. Deductions. Abstract as these words may seem, they can be used to illustrate important facets of human behavior and curiosity. If curiosity could be credited to killing the proverbial cat, the experience of human beings with the exploration of the unknown and the ambiguous could rarely be declared as unrewarding. The ability to think and reason (logically and analytically) separates human beings from other species on this wonderful planet. There is one branch of study, which came into being as a result of human inquisitiveness and thought, which was then modified as a tool and later, declared a branch of science. Now, many agree that this has been perfected into a form of art. Welcome to the world of Mathematics.
The origin of the word Mathematics is from Greek μαθηματικ or mathematiká, which has a root word in μθημα ormáthema, which means learning (or study or science). Since its inception, Mathematics could be considered as the subject with the widest cross-disciplinary appeal. From astronomy to advanced molecular biology and genetics, it is hard to imagine a scientific discipline without the tools provided by this vast and enlightening subject. But this wide reach among various disciplines necessitated the vast generalization of the concepts and tools of Mathematics, with the result that applications pertaining to specific disciplines often did not find their way into a math curriculum. But then, this subject was never meant to be used just as a tool. This is a subject that was born out of the same necessity to answer questions that shaped the various other disciplines of today. This is a subject that confirms the vast potential of the analytical and logical human mind. This is a subject that encourages one to form new ideas and not just to accept the existing ones. This is a subject that encourages one to think. And thinking is always critical.
Critical thinking itself is a process that involves analyzing and evaluating concepts, principles, procedures and situations in a logical and often scientific way, so that one gets the chance to understand the depth of a problem with as much clarity, credibility and precision as possible. Thinking critically bridges the gap between mathematics and other scientific disciplines or ideas, be it environmental sciences, quantum physics or global warming. Without understanding the valuable process of critical thinking, the study of pure mathematical concepts and tools could be likened to trying to row a boat in a vast ocean without an oar.
In the context of the current Summer Curriculum, the study of mathematics should be seen for what it really is: a valuable language. When used along with one's ability to think critically and reason logically, mathematics can work wonders in any scientific discipline. And in this context, there are no boundaries to thinking or learning. For the optimist, thinking is liberating. For the pessimist, thinking is enslaving. For both, thinking does something.