Mastery of the Concept of Percentage and Its Representations in Finnish Comprehensive School Grades 7–9

Abstract

This research was conducted in 2019 in collaboration with Japanese colleagues, with the research tasks translated from the original Japanese. In Finland, a total of 1112 students from grades 7–9 in primary school participated in the study. In our article, we examine Finnish students’ mastery of the concept of percentages and how they express their mathematical thinking about percentages in a multimodal way. A multimodal expression of mathematical thinking can typically take the form of natural language, written mathematics, pictorial representations, mathematical symbolic language, or combinations of these, which can be used to manage information, such as through tables. Our focus is on Finnish primary-school students’ mastery of the concept of percentages, and we then narrow our analysis to tasks where students have used a multimodal approach. We analyze the representations of the concept of percentages and the related thought processes. The concept of percentages was best mastered in grade 9 and weakest in grade 7. Students mostly used a combination of pictorial language, natural language, and mathematical symbolic language to describe their solution processes. However, describing their thinking in different ways did not necessarily highlight possible errors in their reasoning.