"Approximate" Multiplicative Relationships Between Quantitative Unknowns

• In Event: 16.056 - Roundtable Session 4
  In Roundtable Session: 16.056-14 - Students' Mathematical Thinking: Grades 5-8

Abstract

In this paper we explore how middle school students represented multiplicative relationships between quantitative unknowns based on an 18-episode design experiment with 9 middle school students. Six of these students indicated that they viewed multiplicative relationships between quantitative unknowns as “approximate” or tenuous. In addition, these students had great difficulty writing equations to represent fractional relationships between two unknowns. These students were enrolled in pre-algebra classes, and they were operating with the second multiplicative concept, which means they could make three-levels-of-units structures in activity but maintain only two-levels-of-units structures in further operating. Our main account of these students’ views focuses on their efforts to simplify the units coordinations involved in representing multiplicative relationships between unknowns.

Authors

• Amy J. Hackenberg, Indiana University

• Robin Jones, Indiana University

• Ayfer Eker, Indiana University - Bloomington

• Mark Andrew Creager, Indiana University

• Ryan Timmons, Indiana University - Bloomington