The Use of Visualization in Solving Mathematical Problems
An effective and efficient strategy to illustrate math problems is visualization. Visual representation of a mathematical problem in one’s mind or on a piece of paper shows the links among several segments of the problem. It is called schematic representation. Students who are poor in solving math problems make immature and improper representations that are more pictorial and less schematic.
The use of visual representation in solving math problems is beyond the knowledge of many students. Some students apply the power of visualization inappropriately and ineffectively. It is also true about many teachers. They rely on mere math problem solving guidebooks to teach students how to solve mathematical problems.
Strategies Of Solving Mathematical Problems
Reading, understanding and paraphrasing mathematical problems for successful math problem solving are other cognitive strategies. Students should be taught to hypothesize a plan, assess the process and estimate an outcome of their attempts to solve problems. The process in which math problem solving is done involves not only cognitive strategies such as estimation and visualization but some self-regulation strategies as well.
Good math problems solvers go for different strategies to work out problems. They read to understand and represent to solve them. On the basis of their understanding they translate the numerical and linguistical information in the problems into mathematical notations. They go through the problems again and again to get to the bottom of them. Then they meditate on the process of solving them.
Students with inefficiency in solving mathematical problems do not find the underlying cause of problem. They lack the resources, which are essential for execution of this complex cerebral activity. Attempts made by such students generally lack self-regulation process or metacognitive. So their endeavors to comprehend, analyze and solve problems go into water. To learn and teach cognitive strategies and metacognitive processes is the maker of a good problem solver.
Math problem solving is both a good mental exercise as well as brain booster. It makes the mind inventive and the brain fertile. Practicing it regularly nourishes students’ logical bent of mind. The curriculum of math problem solving is one of the most essentials part of education.