Spontaneous Meta-Arithmetic as the First Step Toward School Algebra

Taking as a point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following six pairs of 7th-grade students (12-13 years old) as they gradually modify their spontaneous meta-arithmetic toward the “official” algebraic form of talk. In this paper we take a look at the very beginning of this process. Preliminary analyses of data have shown, unsurprisingly, that while reflecting on arithmetic processes and relations, the uninitiated 7th graders were employing colloquial means, which could not protect them against occasional ambiguities. More unexpectedly, this spontaneous meta-arithmetic, although not supported by any previous algebraic schooling, displayed some algebra-like features, not to be normally found in everyday discourses

Constructing meaning in the service of power : an analysis of the typical modes of ideology in accounting textbooks

This paper provides an analysis of the typical modes of ideology in introductory financial accounting textbooks and training materials. Drawing on Thompson's (1990) schema concerning the typical linguistic modes through which ideology operates, this research suggests that the operation of ideology is apparent within educational accounting texts, with particular strategies being more evident than others: in particular, the strategies of universalization, narrativization, rationalization and naturalization. Given the predominantly technical nature of introductory financial accounting textbooks and training manuals, the modes of ideology identified in the texts were often quite subtle; more specifically, the ideological characteristics displayed in each of the six texts analysed were often expressions of implicit or taken-for-granted assumptions

Developing algebraic notation through number patterns

All the mathematics teachers in a Maltese secondary school were involved in setting and correcting a task involving the use of algebraic symbolization to describe number patterns in a number of their classes. A focus interview was carried out with the teachers some time after this experience. As a group, the teachers identified some very well documented difficulties that students have with the use of letters in Algebra. The work also shows that tasks of the type investigated provide teachers with contexts that they may utilize to help students make some entry points into using letters as generalized number.peer-reviewe

Spontaneous meta-arithmetic as the first step toward school algebra

Taking as a point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following six pairs of 7th-grade students (12-13 years old) as they gradually modify their spontaneous meta-arithmetic toward the “official” algebraic form of talk. In this paper we take a look at the very beginning of this process. Preliminary analyses of data have shown, unsurprisingly, that while reflecting on arithmetic processes and relations, the uninitiated 7th graders were employing colloquial means, which could not protect them against occasional ambiguities. More unexpectedly, this spontaneous meta-arithmetic, although not supported by any previous algebraic schooling, displayed some algebra-like features, not to be normally found in everyday discourses. La meta-aritmética espontánea como el primer paso hacia el álgebra escolar Tomando como punto de partida la visión del álgebra escolar como un meta-discurso formalizado de la aritmética, hemos estado siguiendo a seis pares de estudiantes de 7º curso (12-13 años) cuando modifican gradualmente su meta-aritmética espontánea hacia la forma algebraica “oficial” de hablar. En este artículo miramos el principio de este proceso. Los análisis preliminares de los datos han mostrado, como era de esperar, que mientras reflexionaban sobre los procesos y relaciones aritméticas, los alumnos no iniciados emplearon medios coloquiales que no evitaban las ambigüedades ocasionales. Más inesperadamente, esta meta-aritmética espontánea, a pesar de no apoyarse en ninguna enseñanza algebraica previa, desplegó algunas características similares al álgebra que no se encuentran normalmente en los discursos diarios.Handle: http://hdl.handle.net/10481/1831

Grade 4-6 student conceptions and utilization of informal and formal variable representations across mathematically equivalent tasks

Title from PDF of title page (University of Missouri--Columbia, viewed on October 22, 2012).The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Dissertation advisor: Dr. John LanninIncludes bibliographical references.Vita.Ph. D. University of Missouri--Columbia 2011.Dissertations, Academic -- University of Missouri--Columbia -- Curriculum and instruction."May 13, 2011"This study reports how 24 grade 4-6 students in one elementary and middle school interpreted formal (e.g., x + y = 12) and informal representations of variables (e.g., □ + ∆ = 12). While interpretations for variables represented as letters (e.g., x and y) have been well established for students in algebra classes and beyond, little research into elementary school students' initial interpretations of variables exists. The students were consistent in their meaning of various representations of variables presented in equations, but did not parallel normative algebraic solutions. For example, students treated the representation of the variables as different variables and consistently produced multiple solutions for each variable (e.g., y + y = 12; a + b = 12; and □ + ∆ = 12). Further, the common misconception that different variables can only take on different values was not a typical response for these students (Fujii, 2003). When these same tasks were presented as word problems, students treated variables in an algebraically normative way. In other words, the students were more “successful” solving the word problems (Koedinger & Nathan, 2004). Students attended to the syntactic and semantic structure of the word problems to determine meanings for the variables that were not evident in the equations

What is the object of the encapsulation of a process?

Several theories have been proposed to describe the transition from process to object in mathematical thinking. Yet, what is the nature of this ''object'' produced by the ''encapsulation'' of a process? Here, we outline the development of some of the theories (including Piaget, Dienes, Davis, Greeno, Dubinsky, Sfard, Gray, and Tall) and consider the nature of the mental objects (apparently) produced through encapsulation and their role in the wider development of mathematical thinking. Does the same developmental route occur in geometry as in arithmetic and algebra? Is the same development used in axiomatic mathematics? What is the role played by imagery

Cultural representations of mental illness in contemporary Japan

This paper presents the results of a research project aimed at studying the cultural representations of mental illness and related interventions models in contemporary Japan, and providing the basis for a comparison between Japanese and Italian mental health cultures. The research methodology is based on interviews with scholars and professionals from multiple disciplinary areas and fields of practice, in order to analyze the interactions between medical, social sciences’ and humanities’ discourse on mental illness. The results highlight the significance of home custody within the modernization of the country, between Edo and Meiji periods; the cultural frameworks of contemporary psychiatry’s action; what anti-psychiatry and the ‘critical’ reflection on mental illness represented within the academic debate; the new demands and potentialities connected to the spread of psychology within the mental health sector; remarkably new experiences of social integration with the contribution of arts

Metaphor, Objects, and Commodities

This article is a contribution to a symposium that focuses on the ideas of Margaret Jane Radin as a point of departure, and particularly on her analyses of propertization and commodification. While Radin focuses on the harms associated with commodification of the person, relying on Hegel's idea of alienation, we argue that objectification, and in particular objectification of various features of the digital environment, may have important system benefits. We present an extended critique of Radin's analysis, basing the critique in part on Gadamer's argument that meaning and application are interrelated and that meaning changes with application. Central to this interplay is the speculative form of analysis that seeks to fix meaning, contrasted with metaphorical thought that seeks to undermine some fixed meanings and create new meanings through interpretation. The result is that speculative and metaphorical forms are conjoined in an interactive process through which new adaptations emerge. Taking this critique an additional step, we use examples from contemporary intellectual property law discourse to demonstrate how an interactive approach, grounded in metaphor, can yield important insights

Deconstructing the Language of Accounting Textbooks to Make Power Relations Visible

The paper is motivated by the realization of the absent of critical engagement research problematizing the mainstream accounting worldview within accounting textbooks in the context of Indonesia. By doing so, this study uses the Thompson’s (1990) Schema of analyzing ideology to examine the content of popular introductory financial accounting (IFA) textbooks adopted by universities to reveal how, and the extent to which, the ideological status quo is reflected within these texts. This means the analysis tries to understand how ideological meaning is constructed within the textbooks. The analysis shows that the investigated textbooks portray accounting as an abstracted notion of a practical and calculative tool. Meanwhile, the ideological assumptions and socio-political and cultural background and conflict inherent in accounting are concealed and obscured. The textbooks have not scrutinized the concepts and measurement of accounting beyond employing a shareholder perspective. Consequently, the users’ attention is deflected from or glossed over the underlying ideological nature of the textbook

Review of Fredric Jameson, The Modernist Papers.

Fredric Jameson, The Modernist Papers. New York: Verso, 2007. 160 pp. ISBN 9781844670963