I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or

Principles of Neural Science

Criticism and the Growth of Knowledge. Edited by I. Lakatos and A. Musgrave. Pp. viii, 282. £3·50, paperback £1. 1970. (Cambridge University Press.)

Note on Translation Introduction by Michael Holquist Response to a Question from the Novy Mir Editorial Staff The Bildungsroman and Its Significance in the History of Realism (Toward a Historical Typology of the Novel) The Problem of Speech Genres The Problem of the Text in Linguistics, Philology, and the Human Sciences: An Experiment in Philosophical Analysis From Notes Made in 1970-71 Toward a Methodology for the Human Sciences Index

Speech Genres and Other Late Essays

1. Interaction. The interactions learners have with each other build interpersonal skills, such as listening, politely interrupting, expressing ideas, raising questions, disagreeing, paraphrasing, negotiating, and asking for help. 2. Interdependence. Learners must depend on one another to accomplish a common objective. Each group member has specific tasks to complete, and successful completion of each member’s tasks results in attaining the overall group objective.

将“Cooperative Learning”融入课堂——浅谈英语素质教育

This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

To improve our understanding of novice students' production of symbolic algebraic expressions, this article contrasts students' presymbolic and symbolic procedures in generalizing activities. Although a significant amount of previous research on the learning of algebra has dealt with students' errors in the mastering of the algebraic syntax, the semiotic cultural theoretical approach presented here focuses on the role that body, discourse, and signs play when students' refer to mathematical objects. Three types of generalizations are identified: factual, contextual, and symbolic. The results suggest that the passage from presymbolic to symbolic generalizations requires a specific kind of rupture with the ostensive gestures and contextually based key linguistic terms underpinning presymbolic generalizations. This rupture means a disembodiment of the students' previous spatial temporal embodied mathematical experience.

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Gestures, Speech, and the Sprouting of Signs: A Semiotic-Cultural Approach to Students' Types of Generalization

The purpose of this article, which is part of a longitudinal classroom research about students' algebraic symbolizations, is twofold: (1) to investigate the way students use signs and endow them with meaning in their very first encounter with the algebraic gen- eralization of patterns and (2) to provide accounts about the students' emergent algebraic thinking The research draws from Vygotsky's historical-cultural school of psychology, on the one hand, and from Bakhtin and Voloshinov's theory of discourse on the other, and is grounded in a semiotic-cultural theoretical framework in which algebraic thinking is considered as a sign-mediated cognitive praxis Within this theoretical framework, the students' algebraic activity is investigated in the interaction of the individual's subjectivity and the social means of semiotic objectification An ethnographic qualitative methodology, supported by historic, epistemological research, ensured the design and interpretation of a set of teaching activities The paper focuses on the discussion held by a small group of students of which an interpretative, situated discourse analysis is provided The results shed some light on the students' production of (oral and written) signs and their meanings as they engage in the construction of expressions of mathematical generality and on the social nature of their emergent algebraic thinking

https://www.jstor.org/stable/pdfplus/3483043.pdf

Signs and meanings in students' emergent algebraic thinking: A semiotic analysis

The goal of this article is to present a sketch of what, following the German social theorist Arnold Gehlen, may be termed “sensuous cognition.” The starting point of this alternative approach to classical mental-oriented views of cognition is a multimodal “material” conception of thinking. The very texture of thinking, it is suggested, cannot be reduced to that of impalpable ideas; it is instead made up of speech, gestures, and our actual actions with cultural artifacts (signs, objects, etc.). As illustrated through an example from a Grade 10 mathematics lesson, thinking does not occur solely in the head but also in and through a sophisticated semiotic coordination of speech, body, gestures, symbols and tools.

/pdf/why-do-gestures-matter-sensuous-cognition-and-the-1574mueyxz.pdf

Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings

The aim of this paper is to investigate the progressive manner in which students gain fluency with cultural algebraic modes of reflection and action in pattern generalizing tasks. The first section contains a short discussion of some epistemological aspects of generalization. Drawing on this section, a definition of algebraic generalization of patterns is suggested. This definition is used in the subsequent sections to distinguish between algebraic and arithmetic generalizations and some elementary naive forms of induction to which students often resort to solve pattern problems. The rest of the paper discusses the implementation of a teaching sequence in a Grade 7 class and focuses on the social, sign-mediated processes of objectification through which the students reached stable forms of algebraic reflection. The semiotic analysis puts into evidence two central processes of objectification—iconicity and contraction.

/pdf/iconicity-and-contraction-a-semiotic-investigation-of-forms-2ms8nmnx5g.pdf

Iconicity and contraction: a semiotic investigation of forms of algebraic generalizations of patterns in different contexts

This chapter sketches a theory of teaching and learning that takes its inspiration from some anthropological and historico-cultural schools of knowledge—the theory of knowledge objectification. Within this theory, the problem of learning is formulated in such a way that rationalist or individualists views of cognition and social interaction are avoided. The theory of knowledge objectification posits, indeed, the problem of learning as a social process through which students become progressively conversant with cultural forms of reflection. Arising in the course of sensuous mediated cultural praxes embedded in historically formed epistemes and ontologies, learning, it is argued, is not just about knowing something but also about becoming someone. The formulation of learning as a process where knowing and being are mutually constitutive leads to a non-utilitarian conception of the classroom: entrenched in unerasable ethical concerns, the classroom appears as a space for the growth of intersubjectivity and the nurturing of what is called here the communal self. The chapter is divided into six sections. In the first section, I discuss some problematic assumptions often adopted by many contemporary theories of teaching and learning, in particular assumptions related to the learner, the content to be learned and process of learning. In Section 2, I introduce a non-mentalist, culturally embedded, concept of thinking that neither reduces the thinking subject to the mere product of discursive structures, nor posits it as a culturally-detached res cogitans. Section 3 is devoted to a discussion of the epistemological and ontological bases of the cultural theory here advocated. The concepts of learning and the mathematical classroom portrayed in this theory are presented in Sections 4 and 5, respectively. The main ideas of the previous sections are brought together in Section 6, where the educational questions surrounding the ethics of being and knowing are discussed.

http://www.luisradford.ca/pub/36_EthicsofBeing.pdf

Luis Radford

Papers

Gestures, Speech, and the Sprouting of Signs: A Semiotic-Cultural Approach to Students' Types of Generalization

Signs and meanings in students' emergent algebraic thinking: A semiotic analysis

Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings

Iconicity and contraction: a semiotic investigation of forms of algebraic generalizations of patterns in different contexts

The Ethics of Being and Knowing: Towards a Cultural Theory of Learning