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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
Enacting multilingual learner core practices: a PST’s approximations of practice of mathematics language routines
This study considered a preservice teacher’s (PST’s) attention to multilingual learner core practices within her approximations of practice of mathematics language routines during a secondary mathematics methods course. We used a framework of approximations of practice to understand how a PST enacted and developed an understanding of multilingual learner core practices. To provide a vision for what multilingual learner core practices can look like in nontraditional instructional contexts, we qualitatively analyzed four approximations of practice of mathematics language routines from a single PST during a single semester of a methods course. We share how she navigated the remote teaching context and engaged sample students in all of the multilingual learner core practices despite the challenges of the COVID-19 pandemic, providing an example of what these practices may look like in remote instruction. We also discuss how these multilingual learner core practices interact and complement one another. We consider possible implications, limitations, and future research directions.
Journal Article
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
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
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
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
Pentagon or “Five-Angle Shape”? Exploring the Effects of Shape Names on Young Children’s Geometric Shape Knowledge
The present study compared Japanese and U.S. preschool children’s knowledge of geometric shapes. The main goal was to explore if differences in shape-naming conventions in Japanese and English could explain differences in children’s understanding of geometric shapes. In ancient Chinese-based languages (e.g., Japanese), all standard 2D shapes (except for the rectangle) take the form of “[the number of angles]-angle-shape” (e.g., “five-angle shape” for pentagon). Not only are the shape labels relatively easy to construct, each label includes a description of a defining property within its name (i.e., the number of angles). In contrast, English shape names are relatively more complex and do not readily suggest defining shape characteristics. A language in which shape names are relatively easy to construct and communicate defining shape properties should boost children’s shape knowledge. Participants were 33 Japanese (
M
age
= 54.24 months,
SD
= 7.33 months) and 26 U.S. children (
M
age
= 55.58 months,
SD
= 8.03 months) between 42 and 68 months old. Children were asked to determine the validity of shape stimuli in a Shape Identification Task. They were also given a mental rotation task to control for spatial reasoning. Findings indicated that language-group membership and age, but not spatial reasoning, significantly predicted shape knowledge. As expected, Japanese children outperformed U.S. children in identifying geometric shapes. The findings suggest that labeling and describing geometric shapes using their defining properties could support children’s shape learning.
Journal Article