Reflective abstraction is a mechanism of mathematical structure that allows students to build or reconstruct new knowledge to solve the problem. Process mental reconstruction every student is different, so for the formation of mathematical concepts need to be there mathematical ability is high. In other words, if someone has the ability of reconstruction good mental, it is hoped the formation of the concept is also good. The reflective abstraction mechanism can be applied to the cognitive structure of the APOS theory, namely: action, process, object and scheme to build a new mental structures. Some indicators reflective abstraction learned in these studies include: (1) action, specify veriables, (2) process, determining the mathematical model in the form of a quadratic equation, (3) object, define the set resolution of the model mathematical has been made, and (4) scheme, linking the action of objects, processes, so that form scheme and using the scheme that has developed through the action stages, processes and the object already exists in the minds of students to solve more complex problems.

Indicator

Action

Process

Object

Schema

 

Subject

High

ü

ü

ü

ü

High

ü

ü

ü

ü

 

The study employs a qualitative approach aimed at knowing reflective abstraction that students possess in reconstructing quadratic equation concepts are reviewed from the ability high mathematical. The subject in this study is 9th graders (11 female and 22 male) Junior high School 56 in Surabaya. Students have to answer two tests, both math skills test and reflective abstracation test. The subjects used were students who had mathematical skills high. Semi-structured interviews are performed individually for each subject. To two subject high ability to solve quadratic equation problems.

Figure 1. Answered Subject 1 (high ability)

 

Figure 2. Answered Subject 2 (high ability)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The results showed that reflective abstraction in both subjects was highly traceability in reconstructing quadratic equations can solve problems in different ways. On solving the quadratic equation of the subject of high mathematical ability (Figure 1) Can immediately determine the mathematical model then return to the first step in the action stage determines the variables, at the process stage can be modeled into the equation form The last quadratic at the subject stage can b resolve equations by using formula ABC, the reason the subject chose the ABC formula because the formula is easier and is felt quite quickly in resolving quadratic equations. While on the problem solving quadratic equations high ability subject (Figure 2) at the action stage can define variables, at the process stage can model into the form of quadratic equations later at the object stage can be resolving equations by using the factoring formula, selecting the factoring formula because the subject feels the formula is easy but still requires steps to simplify equations in order to be factored. Although in a different way both subject meets reflective abstraction indicators. Next to bring up the schema stage more complex, students are given an advanced question of different numbers but the operation is the same. On subjects (1 and 2) with high mathematical ability can solve the problem of advanced problems with the same answer, thus the subject (1 and 2) can be said to meet the abstraction reflective though with more complex problems.