The primary goals of interactive learning environments (ILEs) are to improve student engagement and learning outcomes. In this paper, we examine different tablet-based user interaction strategies within the domain of analytical geometry (i.e., the intersection of algebra and geometry) that supports active learning for math problem solving. From a learning technology view, we ground our work usi...

We define a class of generic CR submanifolds of Cn of real codimension d, 1 ≤ d ≤ n, called the Bloom-Grahammodel graphs, whose graphing functions are partially decoupled in their dependence on the variables in the real directions. We prove a global version of the Baouendi-Treves CR approximation theorem for Bloom-Graham model graphs with a polynomial growth assumption on their graphing functions.

We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a limit graphing. The spectral measure of the Laplacian on the limit graphing is the weak limit of the spectral measures of the Laplacians of the finite graphs. AMS Subject Classifications: 05C80

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Graph-related practices are central to scientific endeavors and graphing has long been hailed as one of the core “general process skills” that set scientists apart. One research question that has not received much attention is, “Are scientists generally competent readers of graphs, or are graphs indissolubly tied to practices and understandings of their everyday workplace?” This study was desig...

Abstract Graphing is an important practice for scientists and in K-16 science curricula. Graphs can be constructed using array of software packages as well by hand, with pen-and-paper. However, we have incomplete understanding how students’ graphing vary environment; differences could affect best to teach assess graphing. Here explore the role two environments practice. We studied 43 undergradu...