Graphs of functions of two variables: results from the design of instruction

Abstract

In a series of previous studies, the authors have described specific mental constructions that students need to develop, and which help explain widely observed difficulties in their graphical analysis of functions of two variables. This new study, which applies Action-Process-Object-Schema theory and Semiotic Representation Theory, is based on semi-structured interviews with 15 students. It results in new observations on student graphical understanding of two-variable functions. The effect of research findings in designing a set of activities to help students carry out the specific constructions found to be needed is briefly discussed.

Keywords:

• functions of two variables
• APOS theory
• semiotic representation theory
• graphs
• instruction

Acknowledgements

This project was partially supported by Asociación Mexicana de Cultura AC.