The Connecting Quantities Process to Solve Fraction Mathematical Problems of Middle School Students

Abstract

Purpose of the study: The concept of student fraction, in general, is to understand a small part of an intact part so that students' understanding of fractions as quantities needs to be considered in the context of quantitative reasoning. This study aimed to explore and describe the reasoning of junior high school students in Bima, Indonesia, in understanding the relationship of quantities as a fraction.
 Methodology: Research was conducted with qualitative research, which was descriptive exploratory with the stages of giving the Fraction Problem Task (FPT) and task-based interviews. The subjects in this study were 4 students selected from grades 8 and grade 9, who had studied fraction material and were chosen based on the categorization shown by students on the answer sheet.
 Main Findings: The results of this study described that there were two forms of student reasoning approaches, namely the variable and the non-variable approach. In the variable approach, students used multilevel variables, namely level one and level two, whereas, in a non-variable approach, students connected quantities directly, without involving variables.
 Applications of this study: The process of connecting quantities involved quantitative reasoning with different quantitative operations, such as the quantity combination in the form of multiplication, addition, and concurrent combination of multiplication and addition.
 Novelty/Originality of this study: In the process of linking quantities, students were connecting composite units with intact units directly, and students were connecting composite units, continuous units, and then connecting to intact units.