In this information age, the capacity to perceive structure in data, model that structure, and make decisions regarding its implications is rapidly becoming the most important of the quantitative literacy skills. We build on Kaputa's belief in a Science of Need to motivate and direct the development of tasks and tools for engaging students in…

The nature of mathematical reference fields has substantially evolved with the advent of new types of digital technologies enabling students greater access to understanding the use and application of mathematical ideas and procedures. We analyze the evolution of symbolic thinking over time, from static notations to dynamic inscriptions in new…

Jim Kaput lived a full life in mathematics education and we have many reasons to be grateful to him, not only for his vision of the use of technology in mathematics, but also for his fundamental humanity. This paper considers the origins of his "big ideas" as he lived through the most amazing innovations in technology that have changed our lives…

We explore some key constructs and research themes initiated by Jim Kaput, and attempt to illuminate them further with reference to our own research. These "design principles" focus on the evolution of digital representations since the early 1990s, and we attempt to take forward our collective understanding of the cognitive and cultural…

This research focuses on some of the affordances provided by SimCalc software, suggesting that its use can have important consequences for students' mathematical affect and motivation. We describe an episode in an inner-city SimCalc environment illustrating our approach to the study of affect in the mathematics classroom. We infer students'…

One of the great strengths of Jim Kaput's research program was his relentless drive towards scaling up his innovative approach to teaching the mathematics of change and variation. The SimCalc mission, "democratizing access to the mathematics of change," was enacted by deliberate efforts to reach an increasing number of teachers and students each…

Wireless networks are fast becoming ubiquitous in all aspects of society and the world economy. We describe a method for studying the impacts of combining such technology with dynamic, representationally-rich mathematics software, particularly on participation, expression and projection of identity from a local to a public, shared workspace. We…

In this paper we examine the possibility of differentiating between two types of nonexamples. The first type, "intuitive nonexamples," consists of nonexamples which are intuitively accepted as such. That is, children immediately identify them as nonexamples. The second type, "non-intuitive nonexamples," consists of nonexamples that bear a…

This article probes how philosophical structures are immanent in empirical work and how philosophy might be understood when it is within the precincts of science. My interest is in both opening philosophy to disruption by a science that knows itself as inside history and opening science to the costs of its inability to tolerate the necessary lack…

Since Pakistan's inception in 1947, the government has made continuous efforts to provide free, universal, basic education to its citizens. This is evidenced by educational plans, policies, and five-year education sector reforms, including partnerships with international agencies and developed countries. However, these efforts have not yielded any…

This article examines the pervasive influence of progressive education and travel on a public school kindergarten teacher's professional life. In a statement included in her handwritten list of goals for the children in her classroom, she echoed John Dewey, noting that a kindergarten child should "....live life fully and well because this is a…

This article focuses on the ways that one individual child, Christina, experienced urban life in and outside of a diversely populated elementary school with a multicultural curriculum. Labeled by the school and her parents as white, Christina identified as Latina, and used specific spaces in the city to support this claim. Drawing on data from a…

Americans in U.S. Society find themselves at a historical juncture where schools are implementing zero tolerance policies and--at the same time--also trying to promote tolerance, typically across differences such as race, class, culture, ability, and religion. Both these efforts respond to deeply held and serious concerns. But depending on the…

A serious problem in Botswana is the large number of girls and young women who drop out of school. Just over half of the female population attends secondary schools, and the percentage of school-enrolled females has fallen in recent years. Few researchers have studied the dropout problem in Botswana. Twenty-four individuals selected for this study…

This article examines the life of education reformer Flora White, who both represented and deviated from the stereotypical new woman portrayed in popular literature of the late nineteenth and early twentieth century. White's decision to reject marriage and children in favor of a career resulted in greater financial insecurity and an unmet desire…