Types of proportional reasoning of seventh grade junior high school students in Jombang

Abstract

This research is a descriptive qualitative research that aims to describe the type of
proportional reasoning of students. The research subjects were seventh grade students of SMP in Jombang Regency. The subject selection procedure is by purposive sampling. Data collection is done by means of tests, think aloud methods and semi-structured interviews. Data validity uses time triangulation. Data analysis techniques are carried out by: (1) grouping data in 4 categories, then reducing data not included in the 4 categories, (2) presenting data in narrative texts, and (3) concluding the type of proportional reasoning students then comparing subjects that are on the same type of proportional reasoning. Based on research conducted on 150 subjects of class VII SMP in Jombang regency, there were 62 students using cross multiplication, 30 students used additive reasoning, 45 students used multiplicative reasoning and 13 students used a mix of additive and multiplicative reasoning. Additive reasoning, the way the subject does it is to add one by one to many caterpillars associated with many leaves. In determining the missing value, the subject uses multiplicative reasoning by determining the scalar number first. Subjects with a mix of additive and multiplicative reasoning use numerical calculations and use images to reason problems. Cross multiplication, Subjects use the concept
of comparable value by specifying unknown elements with a variable. Although not all subjects use formal reasoning (cross multiplication) in completing, but the reasoning of class VII students shows that it includes relative reasoning. They don't just pair numbers with numbers. Although, there are subjects who do not fully understand invariant and covariant relationships