THE MATHEMATICAL PROFIENCY OF ELEMENTARY STUDENT WINNING THE NATIONAL OLYMPIAD MEDALS IN SCIENCE IN MAKING EQUATION

Abstract

The importance of a skill in making equation was highly considered by the researcher while giving arithmetical tasks “…- 79 = 412” to 86 fifth graders. They were asked to fill the blank. It was found that there were 85 pupils answered the tasks incorrectly. If the pupils’ abilities in making equation are well-applied, then they would be able to determine what they should fill in the blank, because the pupils will probably think that the equivalent equation could be made is“… = 412 + 79”. Thus, an ability of making equation should be considered since early stage. On the other hand, there is particular factor supporting pupils in solving the tasks which is pupils’ mathematical proficiency, including (1) conceptual understanding; (2) procedural fluency; (3) strategic competence; (4) adaptive reasoning; and (5) productive disposition. Then, this mathematical proficiency will optimize the pupils’ ability in constructing equation. Therefore this study aims to describe pupils’ mathematical proficiency in making equation. The subject of this study is the student winning the National Olympiad medals in science, as he is the national assets that should be well-preserved, concerned, and used as role-models for his peers. This study is qualitative by using test and interview as the methods. The test conducted contains an initial equation, 18 + d = 16. The subject is then asked to make as many as equations equivalent to the initial one. The result is analyzed based on particular indicator of mathematical proficiency in making equation. The result shows that; for conceptual understanding, the subject has made 37 equations equivalent to the initial one with different concepts such as square, square roots, and fraction. For procedural fluency and strategic competence, he has made particular equations as many as 12 strategies. One of interesting strategies is by squaring the both sides of the initial equation although the square roots haven’t been taught in elementary grades. For adaptive reasoning, he argues that there is a relationship between an initial equation and the new one because both equations have similar d value. And for productive disposition, he has fluently made such 37 new equations by various ways or strategies through well-procedures in about 30 minutes. This study concludes that the elementary grade students’ mathematical proficiency winning the National Olympiad medals of science has been well-applied in making equation.