"They are the same" is a phrase that teachers often hear from their students in arithmetic and algebra. But what do students mean when they say this? The present paper researches the notion of sameness within algebraic thinking in the context of generating equivalent numerical equalities. A group of Grade 6 Mexican students (10- to…

Flexibility in transforming algebraic expressions is recognized as fundamental for a rich procedural knowledge. Here, flexibility in-depth is proposed as the ability to apply one strategy to a wide range of unfamiliar expressions. In this study, design experiments with four groups of students were conducted to support students' flexibility…

This research explored students' views of geometric objects through the implementation of a curriculum module that allowed them to explore the relationships between transformational geometry and linear algebra. The majority of the students were middle and secondary mathematics education majors enrolled in a one-semester geometry course that is…

This article describes a technology-based approach for dealing with a misconception that some students hold concerning the equivalency of geometric transformations. Students can begin to conceptualize transformations in terms of the relationship between preimage and image figures rather than focus on the motion of a figure. (Contains 7 figures.)