A study of fourth-grade students' explorations into comparing fractions

The purpose of this study is to examine the growth of mathematical understanding in a class of twenty-five students in a suburban New Jersey school. The students worked on challenging mathematical tasks using Cuisenaire Rods(TM) to explore the differences in pairs of fractions in a supportive classroom environment that encouraged students to expand on their ideas.; Data comes from videotapes of six classroom sessions, recorded by multiple cameras; students' written work; and researcher field notes. The videotapes of both group work and class discussion were analyzed. The research questions focused on how the posing and resolution of student conjectures leads to the development of mathematical reasoning.; The findings suggest that the process of learners justifying their own conjectures is an important factor in the growth of understanding. Students used each other's thinking to build upon their own ideas and to make generalizations. They expanded their understanding of the concept of unit, proportions and inverse relationships.; This research provides evidence of how engaging mathematical tasks and a classroom environment where collaboration and thinking deeply about ideas are valued can lead to unexpected results without students relying on the memorization of standard algorithms. The findings appear to indicate that engaging mathematical tasks and classroom environment are two important factors that should be considered when designing curriculum that stresses on conceptual understanding.