$P$ Problem as a means to encourage students' conceptualization of fractions

Ieva Kiliene

Students connect fractions with pie-charts as they are taught in 3rd grade in Lithuania, but they do not have a deeper understanding of the concept. Word problems could be a tool to find misunderstandings and conceptions of fractions students have. In this study, we use word problems where fractions are shown as a numerical magnitude of a level of liquid in a glass (as an analogy to a number line) and check them with students. Each additional drop of liquid gives a new fraction. This way we raise the discussion in class and find out in which phase of the conception of fractions the students are and what misunderstandings and correct ideas they have about fractions. We did design-based research, conducted the teaching experiment, and analyzed qualitative data. We suggest a lesson plan including word problems that teachers can use to raise a discussion.