Fifth grade Chinese and U.S. students’ division problem posing

A small-scale study

Abstract

This study reports a small-scale international comparative study investigating rural elementary students’ mathematical thinking on division, through analyzing the similarities and differences between division problems posed by elementary students in Inner Mongolia in China and Montana in the United States (U.S.). Bruner’s (1985) paradigmatic and narrative modes of thought served as an analytic framework in this study. The primary data source for this study was students’ responses to the open-ended prompt, “Write two different types of division problems.” Each student’s responses were coded according to the perspectives of paradigmatic and narrative modes of thought. The structures and contexts of posed problems and students’ characterization of different division problems were examined. Our findings show that most students in both countries posed problems involving partitive (i.e., group size unknown) and equal groups division. No students in either country posed array/area problems. Of the ten common structures for division problems, students in China created problems aligned with six structures while the students from the United States used only two structures. An examination of the contexts used in each problem revealed that different types of food were the most common context used by students in both countries, although with unique cultural contexts. None of the students in either group situated their story problems in a rural context.