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In this study, we investigated the literacy practices of undergraduate calculus students and non-mathematics STEM faculty members as they read excerpts from a calculus textbook. We found several differences in their practices that appeared to be tied to the didactical nature of the excerpts and the participants' identities and power relationships with the textbook. We use these differences to explore the concept of "didactical disciplinary literacy" to examine the ways readers approach the process of learning from a mathematics textbook and how their practices are related to their positionality with respect to the text. We also explore the development of the readers' thinking about the mathematical concepts and suggest connections between this development and their literacy practices. The study results have implications for the ways that mathematics textbooks can be used as resources for learning the content and literacy practices of the field.

Textbooks have been the subject of research within and across disciplines, but have not yet been widely studied from a disciplinary literacy perspective. Readerly agency is also understudied in disciplinary literacy. The present paper aims to illuminate both of these areas by examining facets of agency that readers demonstrated during think-aloud interviews with a college calculus textbook, thus exploring the disciplinary literacies that are involved in reading this didactical text. Authors have drawn on the recently forwarded theory of "didactical disciplinary literacy," as well as definitions of agency in both literacy and math fields, to reveal how agency was enacted by readers using the textbook to negotiate unknowns in calculus. Findings show participants exhibiting agency in a range of ways, but not always in direct relationship to themselves as agents within the field of mathematics. This study invites college instructors and secondary teachers to consider ways they might foster didactical disciplinary literacy skills to support student learners in mathematics, and other disciplines.

Textbooks are a standard component of undergraduate mathematics courses, but research shows that students often do not view textbooks as productive resources to support learning. This article seeks to understand the factors affecting how individuals engage in reading a calculus textbook excerpt and what they learn from reading. To better understand the separate roles of background knowledge and other reading practices, we compare 2 readers: a 2nd-semester calculus student and a nonmathematics STEM professor. We employ the concepts of "sense making" and the "implied reader" to analyze each reader's experience and a disciplinary literacy perspective to explain the similarities and differences we find between the 2 readers. We propose the concept of "didactical disciplinary literacy"--an adaptation of disciplinary literacy applied to didactical texts--to describe the ways that the professor drew on his identity as a teacher to shape his reading practices.

Although lecture is the traditional method of university mathematics instruction, there has been little empirical research that describes the general structure of lectures. In this paper, we adapt ideas from narrative analysis and apply them to an upper-level mathematics lecture. We develop a framework that enables us to conceptualize the lecture as consisting of collections of narratives to identify connections between the narratives and to use the narrative structure to identify key features of the lecture. In particular, we use the idea of framing and embedded narratives to identify central ideas in the lecture and to understand how examples, diagrams, and smaller claims contribute to the development of those ideas. Additionally, we create a graph structure for the lecture using the repetition of mathematical ideas across embedded narratives, and we employ graph-theoretic analysis to support our identification of framing narratives and to highlight particular roles of embedded narratives.

Researchers have increasingly focused on how gestures in mathematics aid in thinking and communication. This paper builds on Arzarello's (2006) idea of a "semiotic bundle" and several frameworks for describing individual gestures and applies these ideas to a case study of an instructor's gestures in an undergraduate abstract algebra class. We describe the role that the semiotic bundle plays in shaping the potential meanings of gestures; the ways gestural sets create complex relationships between gestures; and the role played by polysemy and abstraction. These results highlight the complex ways in which mathematical meanings--both specific and general--are expressed in gesture, and to highlight the integrated nature of elements of the semiotic bundle.

Textbooks play an important role in undergraduate mathematics courses and have the potential to impact student learning. However, there have been few studies that describe students' textbook use in detail. In this study, 1156 undergraduate students in introductory mathematics classes were surveyed, and asked to describe how they used their textbook. The results indicate that students tend to use examples, instead of the expository text, to build their mathematical understanding, which instructors may view as problematic. This way of using the textbook may be the result of the textbook structure itself, as well as students' beliefs about reading and the nature of mathematics. Although many instructors may not clearly convey how they want their students to use the textbook, students do report using it more productively when they believe they are asked to do so. This suggests that instructors should carefully choose text materials to promote mathematical reasoning, and actively encourage their students to read the text in a way that supports the development of this reasoning. (Contains 1 figure and 12 tables.)

Textbooks have the potential to be powerful tools to help students develop an understanding of mathematics. However, many students are unable to use their textbooks effectively as learning tools. This paper presents a framework that can be used to analyze factors that impact the ways students read textbooks. It adapts ideas from reader-oriented theory and applies them to the domain of mathematics textbooks. In reader-oriented theory, the reader is viewed as actively constructing meaning from a text through the reading process; this endeavor is shaped and constrained by the intentions of the author, the beliefs of the reader, and the qualities the text requires the reader to possess. This paper also discusses how reading mathematics textbooks is further constrained by the authority and closed structure of these textbooks. After describing the framework, the paper discusses recommendations for future avenues of research and pedagogy, highlighting the importance of teachers' roles in mediating their students' use of textbooks.

Inferential reasoning is a central component of statistics. Researchers have suggested that students should develop an informal understanding of the ideas that underlie inference before learning the concepts formally. This paper presents a hands-on activity that is designed to help students in an introductory statistics course draw informal inferences about a bag of bingo chips and connect these ideas to the formal T-test and confidence interval. This activity is analyzed using a framework and recommendations drawn from the research literature. (Contains 3 figures and 3 footnotes.)

The team discovery of nuclear fission in Germany in 1938 and the lack of recognition given to Fritz Strassmann and Lise Meitner, physicist, are discussed. Otto Hahn, a chemist, received the Nobel Prize, awarded in 1945 for 1944, for the discovery of fission. Because she was female and one-quarter Jewish, Meitner was discriminated against in various ways, among them that she was not an experimentalist, having done theoretical work with Otto R. Frisch, her nephew. They were nominated for the Novel Prize in Physics for contributions to the discovery of fission. Various distortions in reporting, including slights of Hahn in the US, are discussed.

In the 1990s, in work of Le Bruyn and Smith and in work of Le Bruyn and Van den Bergh, it was proved that point modules and line modules over the homogenization of the universal enveloping algebra of a finite-dimensional Lie algebra describe useful data associated to the Lie algebra. In particular, in the case of the Lie algebra sl2(C), there is a correspondence between Verma modules and certain line modules that associates a pair (h, φ), where h is a 2-dimensional Lie subalgebra of sl2(C) and φ ∊ h* satisfies φ([h, h]) = 0, to a particular type of line module. In this article, we prove analogous results for the Lie superalgebra sl(1|1) and for a color Lie algebra associated to the Lie algebra sl2. [ABSTRACT FROM AUTHOR]