A teaching experiment-using Mathematica to investigate the convergence of sequence of functions visually as a sequence of objects (graphs) converging onto a fixed object (the graph of the limit function)-is here used to analyze how the approach can support the dynamic blending of visual and symbolic representations that has the potential to lead…

In this article I present some results from a 5-year longitudinal investigation with young students about the genesis of embodied, non-symbolic algebraic thinking and its progressive transition to culturally evolved forms of symbolic thinking. The investigation draws on a cultural-historical theory of teaching and learning--the theory of…

This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written…

Music education is often advocated as having "extra-musical effects" contributing to the development of the whole child. The pedagogy teachers employ to deliver music programs could affect the significance of such benefits. This paper will review literature documenting how children benefit from receiving music education delivered using…

National standards and funds have helped ensure that technology access is no longer as problematic as it once was in education, but some questions remain about how effectively educational technologies are being utilized prepare students with 21st century skills that include higher-order thinking skills. For this reason, scholars have emphasized…