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Circles disturbed
Circles Disturbedbrings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier--\"Don't disturb my circles\"--words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds--stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities.
A book unlike any other,Circles Disturbeddelves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of \"myths of origins\" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more.
In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.
eBook
Experienced teachers talking about their mathematics teaching with linguistically disadvantaged learners
Learners of mathematics who are linguistically disadvantaged for a variety of reasons, including impoverished socioeconomic status, continue to be educationally disadvantaged and at considerable risk of school failure and early dropout. This is the case in many parts of the world. While much has been researched on linguistically disadvantaged learners in the fields of sociology and general pedagogy, little is known about the classroom teaching of mathematical content in language-responsive ways for all learners in school. Experienced mathematics teachers draw on a wealth of knowledge of content teaching in language-responsive ways developed through their practices working with linguistically disadvantaged learners in their classrooms. In this paper we report on interviews with some of these experienced mathematics teachers from seven educational contexts focusing on teaching probability in language-responsive ways. We focus on what we can learn from these teachers that could inform our practice as mathematics teacher educators and our research. We identify three challenges and three practices that add nuance and depth to theoretical research findings and recommendations on language in mathematics teaching, which can potentially develop these findings in more practical and accurate ways.
Journal Article
Investigating and promoting teachers’ expertise for language-responsive mathematics teaching
In spite of the widely accepted need for language-responsive subject-matter teaching, few teachers are prepared for this challenge due to the lack of empirically founded subject-specific professional development (PD) programs for language-responsive classrooms. The design research study presented in this article pursues the dual aim of (a) promoting teachers’ expertise in language-responsive mathematics teaching using PD courses and (b) investigating teachers’ developing expertise in qualitative case studies. Both aims are pursued based on a conceptual framework for teacher expertise in language-responsive mathematics teaching, starting from typical situational demands that teachers face in language-responsive mathematics teaching and the orientations, categories, and pedagogical tools they need to cope with these situational demands, especially the demand to identify mathematically relevant language demands. For language-responsive teaching, the interplay of categories for mathematical goals and language goals turns out to be of high relevance.
Journal Article
Math for English majors : a human take on the universal language
\"This helpful, humorous handbook for the mathematically challenged uses author Ben Orlin's empathy, humor, and \"bad drawings\" to unravel the secrets behind the world's most confounding language\"-- Provided by publisher.
Book
Mathematical Discourse
This book examines mathematical discourse from the perspective of Michael Halliday's social semiotic theory. In this approach, mathematics is conceptualized as a multisemiotic discourse involving language, visual images and symbolism. The book discusses the evolution of the semiotics of mathematical discourse, and then, proceeds to examine the grammar of mathematical symbolism, the grammar of mathematical visual images, intersemiosis between language, visual images and symbolism and the subsequent ways in which mathematics orders reality. The focus of this investigation is written mathematical texts. The aims of the book are to understand the semantic realm of mathematics and to appreciate the metaphorical expansions and simultaneous limitations of meaning in mathematical discourse. The book is intended for linguists, semioticians, social scientists and those interested in mathematics and science education. In addition, the close study of the multisemiotic mature of mathematics has implications for other studies adopting a social semiotic approach to multimodality.
eBook
A functional start to computing with Python / Ted Herman
\"Open source and easy to use, Python offers the availability of exciting libraries of software, application programming interfaces, and even connections to web services. This textbook uses Python as a working environment to teach the basics of computing for students with no prior programming experience. Unlike similar texts, it organizes topics based on a functional first approach to teaching programming. The book includes case studies of practical problems as well as homework and interactive tools online, such as flashcards\"-- Provided by publisher.
Book
Can mathematics assessments be considered valid if learners fail to access what is asked of them?
Background: The underperformance of South African learners in literacy and numeracy is a source of concern, especially when learners move from Grade 3 to Grade 4. Aim: This article reflects on the reading and comprehension challenges of English language learners (ELLs) in the Grade 4 2013 mathematics Annual National Assessments (ANAs). Setting: The study took place in two primary schools that served relatively less affluent sectors of the community in the Eastern Cape. Learners were IsiXhosa speakers learning mathematics in English. Methods: A sample of 26 out of 106 isiXhosa-speaking Grade 4 learners in the two schools participated in task-based interviews (focused on ANA questions) in which reading and linguistic mediation was provided. While the broader study (from which this article derives) revealed learners’ challenges in reading, comprehension, transformation and process skills, here the focus is on findings related to reading and comprehension skills, which are foundational to accessing written assessment items. Results: Interview excerpts show the negative influence poor English reading and comprehension skills had on learner access to questions and their subsequent performance in the ANA. Conclusion: The article challenges the validity of assessing ELLs’ mathematical competence in English ANAs and draws implications for strengthening ELLs’ language and mathematical proficiency in the Foundation Phase.
Journal Article