Units coordination, defined by Steffe (1992) as the mental distribution of one composite unit (i.e., a unit of units) "over the elements of another composite unit" (p. 264) is a powerful tool for modeling students' mathematical thinking in the context of whole number and fractional reasoning. This paper proposes extending the idea of a…

This paper provides evidence on how elementary school students from a Mexican public school move from using an operational sense, expressed in computational strategies, to a kind of relational thinking based on structure sense ideas and expressed by number decomposition. Even though the results are somewhat preliminary, they illustrate how…

This paper presents strategies identified in Mexican rural school students in seeking structure on equivalence tasks that involve the equal sign and tasks that do not. The results arise from the pilot study of a research project on the structure of numbers and numerical operations -- a key aspect of early algebraic thinking. [For the complete…

This paper addresses how secondary students might reason about amounts of change in covarying quantities. Two empirically based forms of covariational reasoning are distinguished. The first form-- reasoning about quantities as varying simultaneously and independently--supports tandem comparison of amounts of change. The second form--coordination…

A Mathematics course for elementary school teachers (MFET) is required in North America in most teacher education programs. Our study investigates the perceptions of prospective elementary school teachers with respect to the contributions of such a course to their teaching. The results show that acquiring an understanding of concepts from the…