Mathematics has made it possible for great advances in science and technology. It has become so important to so many fields, including those as diverse as Psychology, Economics, Medicine, Linguistics, and even History. Mathematics was invented by the Babylonians around four thousand years ago. Knowing mathematics means being able to use it in a purposeful way. To learn mathematics, students must be engaged in exploring, conjecturing and thinking rather than only in routine learning procedures.
Students construct personal knowledge that derives from meaningful experiences. Therefore, they are much more likely to retain and use what they have learned. Teachers need to understand ways to engage students actively in learning mathematics. Psychology contains several major propositions and is of value to the mathematics educator. It suggests many general principles of teaching. Mathematics has been influenced by psychology over the years. The methods of teaching have changed as a result of psychology.
The Psychology of mathematics is focusing directly on the processes of mathematical thinking and on the ways in which people come to understand the structures. Mathematics is used in empirical science like psychology. A very important step in general movement with all its push toward more potent rational and creative powers, has been the strong focus on identifying the broad understanding, concepts and generalizations which permeate a given discipline. Mathematics was considered useful in developing powers of logical reasoning, and it has become the major justification for teaching it.
Human mental ability is developed, through experience that has developed in human intellect of certain cognitive structures. School has become meaningful because the school of learning takes place only to the degree that a new learning is related to existing cognitive structure. New learning can b attached to the new idea if it is incorporated into the learner’s cognitive structure by attaching it to some existing structure and modifying it to accommodate the new idea.
Teachers must carefully evaluate children’s concepts and intuitive notions so that the new learning can be extension of existing ideas. Teachers will probably find that one point of view is more successful than another. Teachers can produce the best results by teaching in a way in which they will believe will be comfortable of them and the students. It is important for the teacher to use correct strategy. A good method is more important than the topic itself. Teachers do not need to apologize for the way they teach mathematics.
The test of quality of their teaching is a result. The area of cognitive psychology has a great impact on elementary school and mathematics instruction. It gives an indication of how children are thinking during different periods of mental development. The mental development of a child involves a phenomenon that occurs in similar stages. Children could attain these stages at different ages, but the important point is that every child goes through each stage. Cognitive development takes place through the mechanism of equilibration.
When it is presented with a new idea, the cognitive equilibrium of a child is disturbed. In other words, a child could learn through a process that would him or her expands his or her ability in different situations. This is when the state of disequilibrum and cognitive development in learning takes place. There are two concepts of equilibration; Assimilation and accommodation. Assimilation is the cognitive activity through which a new idea is brought into a person’s cognitive structure by applying existing cognitive structure to an unfamiliar situation.
Accommodation requires the development of schemata. The schemata are developed after a child develops and prepares himself to assimilate a new problem and solution into the cognitive structure. Knowledge of the stages of development is important to understanding. This gives us more indication of how the child is thinking in a given stage. Teachers must be concerned about the way in which they introduce a new area of study. Teachers need to improve their pedagogical skills. They have to reveal an understanding of how learning takes place.
Conceptual development involves intrinsic human needs and behavior may be used to motivate advantage. Teachers should be more concerned with how children learn than they are with how they teach. Learning mathematics involves much more than an active intellectual process that has become typically the case today. Learning must be meaningful, which means that the learner must be ready to learn. The teacher has the responsibility to build reading, motivate the learner and constantly encourage the effort of each and every student.