Designing representations: Reasoning about functions of two variables

Research output: Contribution to journalArticlepeer-review


One major part of the effort to reform secondary school mathematics is the project of changing the goal of studying school algebra from the mastery of symbolic manipulations to the ability to reason algebraically. Another major component of these reform efforts is the creation of opportunities for students to communicate within and about mathematics. The ability to generalize, especially when the generalization requires a major breakthrough in habits of mind, is one indication of algebraic reasoning. In this article, I describe generalization activity as an opportunity to learn about seventh graders' understanding of functions. A group of students who had studied functions modeled a multivariable situation. Through individual and group work, they designed, described, and discussed various representations for functions of 2 variables. Their modeling efforts allowed them to analyze their understanding of representations of quantities, relationships among quantities, and relationships among the representations of quantities in both single- and multivariable functions.

Original languageEnglish
Pages (from-to)431-466
Number of pages36
JournalJournal for Research in Mathematics Education
Issue number4
StatePublished - Jul 1997

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Education


Dive into the research topics of 'Designing representations: Reasoning about functions of two variables'. Together they form a unique fingerprint.

Cite this