Published on *SelfGrowth.com* (http://www.selfgrowth.com)

By *Ajay Seshadri*

On *June 04, 2012*

There is a great deal of work at large in getting learners to think correctly. The real test lies in being able to approach new problems with the right frame of mind. Such a frame of mind is not acquired by merely following instructions. There is a certain subtlety in the way Mathematical problems are framed. The challenge lies in finding the missing links and the begging questions. Once the missing links are identified, the task of understanding the questions that the problem leaves behind is to a greater or lesser extent a challenge. The objective of problems especially in geometry seems to be to make minds sharper when in reality they are just problems to be solved. If the student looks at them merely as problems to be solved to acquire high grades then invariably that does not lead to the right frame of mind needed to solve problems in Mathematics.

There is an irony in this scenario for on the one hand a frame of mind that has little to do with the problem is needed while on the other the problem has to be solved regardless of the frame of mind. This presents a dilemma in students which is largely of a psychological nature. In fact this is by itself a rider. Having the thinking skills developed depends on developing the right frame of mind and the confidence that the dilemma can be addressed by students. Once the learner obtains the facts of knowledge he/she has to apply the thinking skills to throw light on the revelations of what he/she has learnt. In Geometry visualization runs parallel to the logical ability to construct diagrams that have reasons for their dimensions. The properties of a right angle triangle give it its dimensions that are logical constructs derived from axioms.

One aspect of reasoning that is more often undermined in the process of solving problems is the tendency to jump to conclusions. In part the correct approach to solving problems lies in maintaining a distance from the need to draw conclusions. Although conclusions are necessary they are a natural occurrence of the revelation process and not compulsive acts that have more to do with demand. If the psychological aspect is divorced from the Mathematical aspect then students are in a better position to approach the problems correctly and solve them. This is what **online tutoring** sets to achieve in learners.

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