Linguistics

Traditionally, it has been assumed that the Greek alphabetic numerals were independently invented in the sixth century BC. However, the author finds a remarkable structural similarity between this system and the Egyptian demotic numerals. He proposes that trade between Asia Minor and Egypt provided the context in which the Greek numerals were adopted from Egyptian models.

This study analyzes a cultural model for greatness at the Math Corps, an enrichment mathematics program of primarily African American students from public schools in Detroit, Michigan. Corpus analysis of staff addresses reveals eight interrelated conceptual relationships about greatness, conceptualized as a resource inside individuals motivating success. Compared to contemporary and historical American English corpora, this cultural model differs systematically from general understandings of greatness. Aspects of these conceptual relationships are then elaborated through gestural and graphic modalities. This cultural model produces a framework for decision and action, motivating student success in a challenging educational environment. This study integrates ethnography, corpus linguistics, and discourse analysis in understanding conceptual metaphor and cultural models, both in educational settings and other discourse communities.

Mathematical prescriptivism is a language ideology found in school mathematics that uses a discourse of rationality to prescribe language forms perceived as illogical or inefficient. The present study is based on a three-year ethnographic investigation of the Math Corps, a community of practice in Detroit, Michigan, in which prescriptive language in the classroom is used both to highlight beneficial algorithms and to build social solidarity. Although motivated by the analogy with English orthographic reform, prescriptivism at Math Corps avoids potentially harmful criticism of community members of the sort often experienced by African American students. A playful linguistic frame, the prescriptive melodrama, highlights valued prescriptions, thereby enculturating students into the locally preferred register, the ‘Math Corps way’, which encompasses social, moral, linguistic, and mathematical practices and norms. A sociolinguistic and anthropological perspective on prescriptivism within communities of practice highlights positive alternatives to the universalizing prescriptions found in other English contexts.

Across multiple disciplines, written numerical notation is a topic of keen interest, yet several unresolved issues in its analysis are either elided or taken as settled. Numerical notation is a complex phenomenon with multiple independent histories—more than 100 distinct systems used over the past 5,500 years, interweaving with, rather than strictly paralleling, the histories of writing systems. Social, semiotic, and cognitive approaches are brought to bear on six incompletely answered questions about numeration in relation to the earliest writing. Is numerical notation a necessary precursor to writing? Does the earliest numerical notation initially serve a bookkeeping function for early states? What is the relationship between tallying and numerical notation? Does the use of numerical notation change human cognition about the domain of number? How does the emergence of numerical notation relate to linguistic representations of number? Finally, among all domains of knowledge, why is number so widely represented using graphic notations? Recognizing that these issues are not resolved, and identifying different possible resolutions, must be preliminary to fully integrating numerical notation within the broader history of writing.

The world’s diverse written numeral systems are affected by human cognition; in turn, written numeral systems affect mathematical cognition in social environments. The present study investigates the constraints on graphic numerical notation, treating it neither as a byproduct of lexical numeration, nor a mere adjunct to writing, but as a specific written modality with its own cognitive properties.
Constraints do not refute the notion of infinite cultural variability; rather, they recognize the infinity of variability within defined limits, thus transcending the universalist / particularist dichotomy. In place of strictly innatist perspectives on mathematical cognition, a model is proposed that invokes domain-specific and notationally-specific constraints to explain patterns in numerical notations. The analysis of exceptions to cross-cultural generalizations makes the study of near-universals highly productive theoretically. The cross-cultural study of patterns in written numbers thus provides a rich complement to the cognitive analysis of writing systems.