The Invisible Link: Using State Space Representations to Investigate the Connection Between Variables and Their Referents


Courtney Pollack, Harvard Graduate School of Education, Larsen Hall G-05, Appian Way, Cambridge, MA 02138; e-mail:


The ability to represent numerical quantities in symbolic form is a necessary foundation for mathematical competence. Variables are particularly important symbolic representations for learning algebra and succeeding in higher mathematics, but the mechanisms of how students link a variable to what it represents are not well understood. Research using cognitive neuroscience methods may be able to shed light on this process by building on related work involving number symbols. Utilizing state space representations, this article presents a first effort to consider what might constitute educationally relevant stimuli for future research on student understanding of the concept of variable. Might algebra problems elicit a symbolization process that can be captured using cognitive neuroscience methods? Results suggest it depends on the role of the variable in a given problem and the structure of that problem. Suggestions for potential research avenues are also discussed.