Children’s Number Sense and Arithmetic Ability in Various Models of Fraction: Focused on the Area Model and the Vertical Line Model

Abstract

This study aimed to identify learners' level of number sense and arithmetic ability in solving fractional problems using area and vertical line models, and to derive specific implications for teaching fraction. We analyzed responses from 227 sixth-graders attending 11 elementary schools in each of the 11 education support offices in Seoul to the number sense and arithmetic ability test paper developed based on the three-fraction representations of area models, structured vertical-line models, and empty vertical-line models. The results confirmed that the mean and incorrect answers by question, errors which habitually mistook the entire model for 1, without checking the entire given model in a range larger than 1, occurred frequently. Additionally, there were cases of problems being solved mechanically without using models. The meaning and use of the fractional model should be explicitly presented in teaching and learning situations, and opportunities to access fractional representation in various forms and ranges should be provided. It is also necessary to offer learners opportunities to implement problem-solving strategies on their own, based on representations, so as to promote their number sense and arithmetic abilities.