Alternative Theoretical Frameworks for Mathematics Education Research by Elizabeth de Freitas download in ePub, pdf, iPad
Lesh has suggested that manipulative materials can be effectively used as an intermediary between the real world and the mathematical world. Dienes's theory of mathematics learning has four basic components or principles. The report generally concludes that manipulatives are effective in promoting student achievement but emphasizes the need for additional research.
This has led Suydam and Higgins to conclude that across a variety of mathematical topics, studies at every grade level support the importance of the use of manipulative materials. Bruner states that learning the structure of knowledge facilitates comprehension, memory, and transfer of learning.
The work of these two men lends additional support to this point of view. Researchers in mathematics education are in the process of accumulating a persuasive body of evidence that supports the use of manipulative materials in the mathematics classroom. The unifying theme of these four principles is undoubtedly that of stressing the importance of learning mathematics by means of direct interaction with the environment. The newly defined learning environment would create new demands for additional sources of information and direction.
This position, misunderstood by many, has been the focus of considerable controversy. Each suggests that the learning of large conceptual structures is more important than the mastery of large collections of isolated bits of information. Piaget regards intelligence as effective adaptation to one's environment. It is a refreshing thought.
The class lesson would be greatly de-emphasized in order to accommodate individual differences in ability, and interests. Learning is thought to be intrinsic and, therefore, intensely personal in nature. Such involvement routinely involves the use of a vast amount of concrete material. Given the sheer number of studies undertaken, it is perplexing to note that more is not known about the precise way in which manipulative materials affect the development of mathematical concepts.
For example, the regrouping procedures used in the process of adding two numbers is independent of the type of materials used. This, of course, includes other people. Emphasis is placed, therefore, on the interrelationships between parts as well as the relationship between parts and whole. Used by inexperienced teachers who are weak in math, they say, the curriculum can be murky. The role of students would be expanded to include the assumption of greater degree of responsibility for their own education.
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