Layers of Conceptual Understanding of Fractions among Elementary Student

Volume 12 Issue 3 November - January 2019

Research Paper

Layers of Conceptual Understanding of Fractions among Elementary Student

Sri Rahayuningsih* , Cholis Sa’dijah **, Sukoriyanto***, Abadyo****

*Graduate Program, State University of Malang, Indonesia

** Professor, Department of Mathematics Education, State University of Malang, Indonesia

***_**** Lecturer, Department of Mathematics Education, State University of Malang, Indonesia

Rahayuningsih, S., Sa’dijah , C., Sukoriyanto, & Abadyois. (2019). Layers of Conceptual Understanding of Fractions among Elementary Student. i-manager’s Journal on Educational Psychology, 12(3), 13-23. https://doi.org/10.26634/jpsy.12.3.15241

Abstract

Pirie & Kieren (1994b) states that conceptual understanding in human beings is divided into eight levels. This qualitative and descriptive research study aims to identify the layers of conceptual understanding of fractions through three representations, namely of circles, rectangles, and number lines. The subjects of this research are three sixth-grade students from SD Batu Malang. The instruments of this research are an essay test consisting of 12 questions and a semistructured interview. The essay test is adopted from Tunç-Pekkan (2015) and test the fractional analysis of a circle representation, rectangle-representation, and number line representation with four questions provided for each representation. The data analysis of this research uses the resource triangulation technique. Based on the work done by the students, the results show that in terms of layers of conceptual understanding, Subject 1 demonstrated understanding layers from Primitive Knowing (Pk) through Property Noticing (Pn), Subject 2 demonstrated understanding layers from Image Making (Im) through Property Noticing (Pn); and Subject 3 demonstrated understanding layers from Image Making (Im) through Formalizing (F).