Wholes, parts and quotients: Investigating children's reasoning on tasks involving fractions and fractional numbers

Rational numbers and operations with rational numbers, including fractional numbers, are a critical component of mathematics K-12 curriculum. Common Core State Standards in Mathematic suggest formal introduction of fractional numbers in Third Grade. There are different positions which form essentially two camps of educators and researchers who debate when fractional numbers should be formally introduced to school students. While the importance of the concept of fractional numbers in school curriculum has been widely documented, there is very limited research focused on elementary students' formal learning of fractions and fractional numbers and development of their reasoning while using multiple representations and solving problems involved fractional numbers.;This study investigated the reasoning methods that Third Grade students developed during their first formal study to the concepts of fraction and fraction number and classified these methods using Bloom's (1956) Taxonomy and Kieren's (1993) levels of mathematical knowledge. The study focused on two Third Grade classrooms in a large urban public school district. Several sources of data included total 32 interviews with eight (N=8) strategically selected students four in each class, teacher interviews, lesson observations, and student written work. Eight case studies and a cross case analysis have been developed and described.;The study confirmed results of earlier research showing that reasoning about fractional numbers using number line is challenging and that the instructional language used in the classroom greatly affects students' comprehension of fractional numbers.;The findings of this study suggest that students must have a systematic exposure to the number line representation of numbers before learning about fractional numbers. It is.