Representations and Reasoning Processes in Comparing and Ordering Rational Numbers in an Exploratory Approach

This study is based on a teaching unit that follows an exploratory approach, in which 5^th grade pupils (10-11 year-old) work with several representations of rational numbers, in different meanings and types of magnitudes. We seek to know if this unit contributes towards the students’ development of the capacity of comparing and ordering rational numbers leading them to use different representations and informal and formal reasoning processes. The research methodology is qualitative and interpretative, with participant observation of classes as well as the case study of a student. The results show that this student developed her understanding of sorting and comparing rational numbers, becoming more proficient both in the decimal and in the fraction representation. The study suggests that work with different representations, in an exploratory approach, allows students to learn to compare and sort rational numbers thought adequately combining formal and informal reasoning processes.

Rational Numbers; Representations; Reasoning; Comparing; Ordering