Background:
Students' difficulty in learning and suitably understanding the concept of the algebraic variable has been studied with a number of tools and documented for several populations. Little research has been conducted, however, using the same tool to explore understanding of the notion among populations from different countries in an attempt to establish similarities and differences in levels of achievement and difficulties.

Materials and methods:
A questionnaire designed to explore the understanding of the algebraic variable and its different uses (as specific unknown, as general number, in functional relationship) was administered to 184 ninth-year students, 92 in Spain and 92 in Mexico, and 82 Mexican and 85 Spanish eleventh-year students, all from medium-lower income families and attending public schools.

Results:
The results obtained analyzing a questionnaire are presented.

Conclusions:
The results obtained revealed similarities and differences among the groups, providing evidence of the strengths and weaknesses of the education system of each country. The 3UV Model offers an appropriate answer to algebraic problems and three uses of the variable and the aspects that characterize each one of them.