A Descriptive qualitative analysis of junior high school students' ability to understand mathematical concepts in fractional materials

Source abstract

The focus of this research is to examine junior high school (Grade VII) students' ability to understand mathematical concepts when solving fraction problems, using a qualitative, descriptive design. The analysis focuses on three abilities: restating concepts, presenting concepts in different forms of mathematical representation, and applying concepts or algorithms to obtain solutions. The novelty of this study lies in combining tiered categorization (high, medium, low) with an in-depth qualitative description of each ability group, enabling identification of students' achievement characteristics on each indicator in greater detail than in previous similar studies. The research was conducted at a public junior high school in Metro City, based on pre-survey results showing a low completion rate among students in solving fraction problems. Six of the 26 students in Class VII A were selected through purposive sampling, taking into account variation in pre-survey scores to ensure proportional representation of the high-, medium-, and low-ability groups. Data were obtained through a written test on fraction material that mathematics teachers and lecturers had validated, then analyzed through the stages of data reduction, data presentation, and conclusion drawing. The results place students' concept understanding in the medium category, with an average score of 52 and an average ability percentage of 61.1%. Students in the high group were able to meet all three indicators; the medium group was able to use mathematical representations and problem-solving algorithms, but was not yet consistent in restating concepts; while the low group had not shown achievement on any of the three indicators. These findings are specific to the research subjects and are not intended to be generalized broadly. This study provides a diagnostic picture of students' patterns of understanding of fraction concepts that can inform teachers in designing instruction that places greater emphasis on the meaning of concepts before students move on to related material, such as ratio and proportion, with the limitation that the subjects were drawn from a single school.