Exploring students’ proportional reasoning in solving guided-unguided area conservation problem: A case of Indonesian students

Abstract

Proportional reasoning has been greatly influencing the development of students’ mathematical abilities. Along with the area conservation ability, it helps elementary students comprehend area measurement. This exploratory study aimed to produce qualitative-descriptive data on elementary students’ proportional reasoning in solving the conservation of plane figures. The study used guided-unguided area conservation problems using a proportional reasoning level as the analysis framework. Data were collected from 4 primary school students in Sidoarjo, Indonesia, who were in fifth-grade class. The students' strategies used were identified to analyze the students' proportional reasoning in solving area conservation. Results show that the level of proportional reasoning varies from zero to two. Regarding the students' proportional reasoning levels, most of the students' strategies use visual clues and cute paste strategies. Only one student can reach the level of quantitative reasoning by using a formula to compare both area measurements. Interestingly, the problem of the conservation of plane figures failed to reveal students' formal proportional reasoning due to their insufficient knowledge of fractions, division, multiplication, and decimals. Some implications regarding students' proportional reasoning and interventions in the area conservation problem are discussed.

Keywords

• area conservation
• guided-unguided problems
• part-whole relation
• proportional reasoning