Using Student Written Work to Investigate Stages in Sixth-Grade Students' Ways of Operating With Numbers

• In Event: Roundtable Session 2
  In Roundtable Session: Children's Development of Mathematical Concept Knowledge

Abstract

In this study, we investigate the frequency of various stages of students’ numerical development utilizing 93 sixth-grade students’ written responses from an assessment containing whole number and fraction tasks using both continuous and discrete quantities. We found a large percentage of students who are able to understand whole numbers as made up of groups of smaller numbers, such as 35 being made of 7 groups of 5, and yet lacked the ability to develop advanced fraction schemes or coordinate complex quantitative situations without figurative material. Our findings bring attention to the importance of better understanding the affordances and constraints of such students and help document how written responses of these students might differ from more or less mathematically sophisticated students.

Authors

• Catherine Ulrich, Virginia Polytechnic Institute and State University

• Jesse L.M. Wilkins, Virginia Polytechnic Institute and State University