The concentration in K-12 education on higher-order thinking has diminished the importance of math fact automaticity, which is the ability to deliver a correct answer immediately from long-term memory without impeding the working memory. This quantitative study investigated the influence of automaticity of high school students on their Missouri…

Felix Klein's Erlangen program classifies geometries based on the kinds of geometric transformations that preserve key properties of their figures, rather than focusing on the geometric figures themselves. This shift in perspective, from figurative to operative, fits Piaget's characterization of mathematical development. This paper considers how…

During professional development, the authors learned about strings--a powerful instructional routine used in elementary classrooms to elicit students' mental mathematics strategies and use those strategies to build conceptual understanding. Strings provided the authors with a way to make relatively small changes to guided notes in algebra 1,…

This study explored the mental constructions displayed by pre-service mathematics teachers (PMTs) when applying Cramer's rule. The aim was to reveal the character of mental constructions made around the nature of the solution set of equations and the role of parameters in the solution of equations with parametric coefficients. These mental…

The focus of the current proposal is to examine the effect of two dynamic simulations on the participants' conceptions of rate of change. Conceptions of rate of change were measured according to Carlson et al.'s (2002) Mental Actions framework and how the participants related the physical simulations to the graphical representations (Heid, et al.,…