Understanding the Concept of Mathematics and Mathematical Representation in Mathematics Teaching

Abstract

The inclusion of representation as a standard component of the process in Principles and Standards for SchoolMathematics in addition to problem solving, reasoning, communication, and connection skills is reasonable because to think mathematics and communicate mathematical ideas one needs to represent it in various forms of mathematical representation. Besides, it can not be denied that objects in mathematics are all abstract so that to learn and understand abstract ideas that would require a representation. Representation occurs through two stages, namely internal representation and external representation. Examples of external representations include: verbal, drawing and concrete objects. Thinking of a mathematical idea that allows a person's mind to work on the basis of the idea is an internal representation. A mathematical problem posed to the student and the student can solve it, so at least the student understands the problem, so that students can plan the settlement, perform the calculations appropriately, and be able to check or review what has been processed correctly. The smoothness and flexibility of students in constructing representations is largely lacking. This is evident from at least the structured algebraic form, as well as the way in which most representations are found very little. In addition, the quantitative scores of respondents in the representation are still in the low category with a moderate tendency.