Unitizing, a cognitive support for number sense, describes how students conceptualize quantities in terms of units. Given the importance of this skill, a formative assessment tool was developed for array multiplication problems, including arrays that model the distributive property found in typical classroom curricula. Video of 77 fourth grade…

Review of the history of trigonometry content and pedagogy indicates the necessity and importance of trigonometry in the school curriculum (e.g., van Brummelen, 2009; van Sickel, 2011). For example, understanding trigonometric functions is a requirement for understanding some other areas of science, such as Newtonian physics, architecture,…

Although proof has long been viewed as a cornerstone of mathematical activity, incorporating the mathematical practice of proving into classrooms is not a simple matter. In this dissertation I aim to advance research on proof by addressing this issue. In particular, I explore the role proof might play in promoting the learning of mathematics in…

The purpose of this study is to examine the nature of what students notice about symbols and use as they solve unfamiliar algebra problems based on familiar algebra concepts and involving symbolic inscriptions. The researcher conducted a study of students at three levels of algebra exposure: (a) students enrolled in a high school pre-calculus…

Recent reform efforts in mathematics education call for the development of early algebraic reasoning, and for the provision of rich mathematical experiences for all students. In spite of such emphasis, many elementary school students, especially those with mathematical learning disabilities (MLD), often experience great difficulty in early algebra…

In an era of new standards and emerging accountability systems, an understanding of the supports needed to aid teachers and students in making necessary transitions in mathematics teaching and learning is critical. Given the established research base demonstrating the importance of justification and reasoning in students' mathematics learning and…