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A fundamental question in early childhood mathematics concerns the relationship between young children's own informal signs and the formal abstract symbolic language of mathematics. This study presents research investigating the genesis of mathematical semiosis from a Vygotskian cultural-historical (social-semiotic) perspective. In this study we look at the premature stages of dealing with quantity and their relationships. Our aim is to reveal the interweaving of young children's sign-use and to consider the role of intertextuality in mathematisation. Longitudinal, ethnographic data were gathered from case studies of seven children aged 3–4 years in an inner-city nursery school in England, documenting observations of their spontaneous pretend play. The data are interrogated through interpretive analysis and show that some graphical signs moved between individuals' texts, also borrowed from others including the teacher, and woven together. Children's progressive understandings of mathematical sign-use appear to be attained in part through intertextual exchanges in social and culturally meaningful contexts, such as pretend play. [ABSTRACT FROM AUTHOR]

Numbers and measurements enable transactions and communication in translation in ways that are helpful and indisputably necessary. However, as deployment of quantification and mathematisation has become more complex and opaque, it is important to interrogate the validity of measures and predictions, especially if they are to be used as a basis for action. This article takes a critical look at the various types of quantification and mathematisation used in translation and considers the effects of these on translators working in highly technologized workflows. It introduces the concept of algorithmic norms, whereby translators feel pressured to reverse engineer and conform to the demands of algorithmic management. [ABSTRACT FROM AUTHOR]

Copyright of Revue d'Orthopédie Dento-Faciale is the property of Parresia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Mathematisation ability of prospective teachers that was low in solving mathematical literacy problems needs serious attention. Therefore, to help prospective teachers do mathematization, they were employed by giving mathematical literacy problems. This study aims to produce mathematical literacy problems that were valid, practical, and have potential effects on the mathematization ability of prospective teacher students. The study was conducted using a design research type development study. Thirty students of prospective teachers in a private university in Sidoarjo became the subjects. Mathematical literacy problems’ qualities from this research should support prospective mathematics teachers in categorizing horizontal and verticalization activities. In addition, the problems were designed using the Program for International Student Assessment (PISA) framework with the Indonesian context. The results suggested that the developed mathematical literacy problems could be categorized valid based on validators’ evaluation, practically based on the small group phase results, and have the potential effects were assessed from the results of student tests handed in field test phase using mathematical literacy problems. The test results showed that 78% of prospective mathematics teachers were in the good category of mathematization ability after using the developed problems. The developed mathematical literacy problem has a potential effect so that it can be used as an alternative question in lecturing higher education activities to support the mathematics of prospective teacher students.

In mathematics education, there is general agreement regarding the significance of mathematical literacy (also quantitative literacy or numeracy) for informed citizenship, which often requires evaluating the use of numbers in public policy discourse. We hold that such an evaluation must accommodate the necessarily fragile relation between the information that numbers are taken to carry and the policy decisions they are meant to support. In doing so, attention needs to be paid to differences in how that relation is formed. With this in mind, we investigated a public discourse that heavily relied on numbers in the context of introducing, maintaining, and easing the rules and regulations directed to contain the spread of the virus SARS-CoV-2 during the first epidemic wave of COVID-19 in Germany with its peak in early April 2020. We used a public-service broadcasting outlet as data. Our theoretical stance is affiliated with post-structuralist discourse theory. As an outcome, we identified four major related strategies of using numbers, which we named rationalisation, contrast, association and recharging. In our view explicit attention to these strategies as well as identifying new ones can aid the task of furthering critical mathematical literacy. [ABSTRACT FROM AUTHOR]

Introduction. The paper deals with the philosophical problems of the mathematisation of nature in modern science.Methodology and sources. The analysis is based on the issues in modern science viewed through the prism of the critique of the mathematisation of nature in phenomenological philosophy.Results and discussion. It is argued that the radical mathematisation of nature devoid of any references to the source of its contingent facticity in humanity, leads to the diminution of humanity and concealment of the primary medium of existence, that is the life world. Phenomenology shows how the life-word can be articulated through contrasting it to “nature” constructed scientifically. It is the analysis of the scientific universe as mental creation that can help to uncover the life-world when “nature” (as scientifically constructed and abstracted from the life-world), is itself subjected to a kind of deconstruction which leads us back to the life-world of the next, so to speak, reflected order.Conclusion. The life-world is articulated under the conditions that there exists a scientific explicability of nature. The life-world as it is articulated in theology does require some alternative explication of nature, but, contrary to science, it never leads to the concealment of the life-world. What is common to these life-worlds is exactly that which cannot be explicated by science, namely the underlying personhood.

The seventeenth century can be viewed as an era of (closely related) innovation in the formal and natural sciences and of paradigmatic diversity in philosophy (due to the coexistence of at least the humanist, the late scholastic, and the early modern tradition). Within this environment, the present study focuses on scholastic logic and, in particular, syllogistic. In seventeenth-century scholastic logic two different approaches to logic can be identified, one represented by the Dominicans Báñez, Poinsot, and Comas del Brugar, the other represented by the Jesuits Hurtado, Arriaga, Oviedo, and Compton. These two groups of authors can be contrasted in three prominent features. First, in the role of the theory of validity, which is either a common basis for all particular theories (in this case, sentential logic and syllogistic), or a set of observations regarding a particular theory (in this case, syllogistic). Second, in the view of syllogistic, which is either an implication of a general theory of validity and a semantics of terms, or an algebra of structured objects. Third, in the role of the scholastic analysis of language in terms of suppositio, which either is a semantic underpinning of syllogistic, or it is replaced by a semantics of propositions. [ABSTRACT FROM AUTHOR]

Learners have difficulties applying mathematics in the real world. This design–action research explored the heuristics of the Realistic Mathematics Education (RME) approach for learning calculus. Ten in-service student-teachers completed a questionnaire with open-ended and closed-ended items on their experiences in applying Calculus in both decontextualised and contextualised settings. They also completed two assessment worksheets. The data were analysed for themes, and statistical paired t-test for comparison. The findings indicate that the teachers had positive learning experiences, even though there was no statistically significant difference in their performance. This suggests that the RME approach can be effectively used in the mathematics classroom to create an interactive learning environment, and to facilitate students in solving real-world problems. [ABSTRACT FROM AUTHOR]

Some mathematics educational reform policies indicate that mathematics education should be connected to learners‟ cultures. However, teaching in schools rarely brings the interconnection between mathematics and culture in pedagogically informed ways. Connections are often done superficially; the curriculum in schools lacks content and specific strategies that enable the making of the connections explicit in the context of teaching. The qualitative study from which this paper emerges worked with three mathematics teachers in an attempt to teach mathematics in ways that connect key concepts with culture. Through mathematizing culturally-based activities performed at a cultural village2, two Grade 9 mathematics topics in the South African curriculum were indigenised. A teaching unit on the indigenised topics was designed and implemented in five Grade 9 classes at the same school. The paper demonstrates that the experience of designing, implementing, and reflecting on the intervention study had some positive contribution to the participating teachers‟ pedagogical repertoire. Teachers saw the possibility of using cultural villages as instructional resources for connecting mathematics education to learners‟ cultures in the South African curriculum. I argue that cultural villages can be used as contexts for mediating culture and mathematics education.

This article explores 6th-grade students’ modelling with data in generating models for selecting an Australian swimming team for the (then) forthcoming 2016 Olympics, using data on swimmers’ times at various previous events. We propose a modelling framework comprising four components: working in shared problem spaces between mathematics and statistics; interpreting and reinterpreting problem contexts and questions; interpreting, organising and operating on data in model construction; and drawing informal inferences. In studying students’ model generation, consideration is given to how they interpreted, organised, and operated on the problem data in constructing and documenting their models, and how they engaged in informal inferential reasoning. Students’ responses included applying mathematical and statistical operations and reasoning to selected variables, identifying how variation and trends in swimmers’ performances inform model construction, recognising limitations in using only one performance variable, and acknowledging uncertainty in model creation and model application due to chance variation. [ABSTRACT FROM AUTHOR]

The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that “enable” year 10/11 students to successfully begin the modelling process, that is, formulate and mathematise a real world problem. The 3-year study will take a design research approach in working intensively with six schools across two educational jurisdictions. It is anticipated that this research will generate new theoretical and practical insights into the role of “enablers” within the process of mathematisation, leading to the development of principles for the design and implementation for tasks that support students’ development as modellers. [ABSTRACT FROM AUTHOR]

In this essay I offer some reflections on the field of mathematics education, and particularly the sociopolitical analysis of mathematics education that has emerged in contemporary scholarship. Here I attempt to do two things. First of all I respond to a recent book on "disorder" in mathematics education, identifying some themes and problematics that I find intriguing and generative from my perspective outside the field. Here I reflect on the way that mathematics is positioned in educational discourse generally as a proxy for human capital and general intelligence. Next I relate stories from my life and practice as a primary school teacher in which mathematics, as I understood it, bumped productively against problems in everyday life. Finally, I conclude with a reflection on the productive tension between naïve place-based mathematical understandings and abstract context-bridging mathematical knowledge forms. [ABSTRACT FROM AUTHOR]

Mathematics and determinism may seem two very different topics, especially when mathematics is associated with the social sciences and economics. Nonetheless, this has not always been the case. In 1873 a curious debate took place in Paris between a young Léon Walras and Pierre Emile Levasseur concerning the compatibility of mathematics, economics, and free will. It was the consequence of a Laplacian view of mathematics that Walras inherited from physics, a view that associated mathematics with a peculiar philosophical conception. We reconstruct the historical context of the debate, the particular view of mathematics that lead to it, and then analyse the attitudes of Cournot, Walras, and Levasseur on the issue. We show that the mathematisation of economics was deeply influenced by how physicists understood mathematics. [ABSTRACT FROM PUBLISHER]

Copyright of Ekonomia XXI Wieku is the property of Uniwersytet Ekonomiczny we Wroclawiu and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we analyse the relation as a mathematical concept. We discuss the following properties of relations: reflexivity, symmetry, antisimmetry and transitivity and define equivalence relations and order relations . We give a methodical approach to the forming of a mathematical relation in preschool children such as relations position, size relations, temporal relations, inclusion and relations of numbers. On specific examples, through series of games and activities, we do mathematisation of relations, i. e. we pay attention to their basic characteristics.

En este documento describo las principales componentes del marco teórico del proyecto PISA/OCDE analizando para ello la noción de alfabetización matemática, las diferentes variables que componen el dominio, las variables que organizan los instrumentos de evaluación, y los diferentes significados del término competencia.In this work I describe the PISA/OECD project framework main components. For this purpose, I analyze the notion of mathematical literacy, the different variables of the domain, the variables of the assessment instruments, and the different meanings of competency.

This paper introduces the notion of “financial Logos ”, defined as a structuring discourse embedded in management tools and beliefs of financial practices. I hypothesize that this discourse contains a specific representation of risk mathematically modelled by probability measures. Next I use a performativity based approach to describe the concrete action of the financial Logos on financial practices: the framing of financial decision-making by mathematical modelling. I argue that it is not possible to think of a given financial practice without epistemologically and sociologically thinking of the contribution of the mathematical modelling to this practice. I conclude with consequences for ethics of finance: extending ethics of action to epistemic ethics, I suggest that, in finance, any preference in mathematical modelling is also a preference in ethics. [ABSTRACT FROM AUTHOR]

Narratives that capture children's learning as they go about their day-to-day activities are promoted as a powerful assessment tool within early childhood settings. However, in the New Zealand context, there is increasing concern that learning stories-the preferred form of narrative assessment-currently downplay domain knowledge. In this paper, we draw on data from 13 teacher interviews and samples of 18 children's learning stories to examine how mathematics is made visible within learning stories. Despite appreciating that mathematics is embedded in a range of everyday activities within the centres, we found that the nature of a particular activity appeared to influence 'how' and 'what' the teachers chose to document as mathematics learning. Many of the teachers expressed a preference to document and analyse mathematics learning that occurred within explicit mathematics activities rather than within play that involves mathematics. Our concern is that this restricted documentation of mathematical activity could potentially limit opportunities for mathematics learning both in the centre and home settings. [ABSTRACT FROM AUTHOR]

Data from open modelling sessions for year 10 and 11 students at an extracurricular modelling event and from a year 9 class participating in a programme of structured modelling of real situations were analysed for evidence of Niss's theoretical construct, implemented anticipation, during mathematisation. Evidence was found for all three proposed aspects. With respect to Niss' s enablers of ideal mathematisation explaining unsuccessful mathematisations, flaws in the modelling of the year 10-11 students were related to the required mathematics being beyond the knowledge of the group members or poor choice of the particular mathematics to use in the modelling context; whilst unsuccessful attempts at mathematisations in the year 9 class were related to inability to use relevant mathematical knowledge in the modelling context. The necessity of these enablers as requisites for modelling, particularly in a classroom context, needs further investigation. [ABSTRACT FROM AUTHOR]

Copyright of Socialinių Mokslų Studijos is the property of Mykolas Romeris University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract Ben Fine and Dimitris Milonakis have done political economy a great service by drawing attention to the insights lost in the twists, turns and reductions in the transition from political economy to economics. These two volumes constitute a solid foundation upon which a new generation can build a political economy for the future. This review presses some of their meta-theoretical arguments a little further than they actually do in an attempt to 'toughen-up' the new political economy and make it more able to carry the fight to economics. [ABSTRACT FROM AUTHOR]

In the Quattrocento and Cinquecento the rise of linear perspective caused many polemics which opposed the supporters of an artificial geometrisation of sight to those who were praising the qualities of the drawing according to nature, or were invoking some arguments on a physiological basis. These debates can be grouped according to the four alternatives that form their central concerns: restricted vs. broad field of vision; ocular immobility vs. mobility; curvilinear vs. planar picture; monocular vs. binocular vision. By retaining the first terms of these four alternatives, the history of perspective eliminated many heterodox constructions. From the viewpoint of mathematisation the interest of these debates is that they succeeded, rather than preceded, the adoption of a perspective system defined by the intersection of the visual pyramid. Thus the history of linear perspective constitutes a genuine case of a posteriori justification, or, put differently, it gives us a case of upside down mathematisation. [ABSTRACT FROM AUTHOR]

In this article, the work on mesospace embodiments of mathematics is further developed by exploring the teaching and learning of vector concepts through climbing activities. The relevance and connection between climbing and vector algebra notions is illustrated via embedded digital videos. [ABSTRACT FROM AUTHOR]

In this innovative teaching experiment, the context of climbing is used to induce the teaching and learning of angle concepts. This article reports on the outcomes of a three day teaching and climbing experiment and the impact of this experience on the teacher's understanding of meso and micro embodiments of mathematics, angle representations, as well as shifts in their attitudes about teaching/learning geometry. [ABSTRACT FROM AUTHOR]

The paper argues that the Nash Equilibrium Refinement Programme was less successful than its competitor, the Epistemic Programme (Interactive Epistemology). The prime criterion of success is the extent to which the programmes were able to reach the key objective guiding non-cooperative game theory for much of the twentieth century, namely, to develop a complete characterisation of the strategic rationality of economic agents in the form of the ultimate solution concept for any normal form and extensive game. The paper explains this in terms of unjustified degrees of mathematisation in Nash Equilibrium Refinement Programme. While this programme’s mathematical models were often inspired by purely mathematical concerns rather than the economic phenomena they were intended to model, the Epistemic Programme’s models were developed with a keen eye to the role beliefs and desires play in strategic interaction between rational economic agents playing games; that is, their interactive epistemology. The Epistemic Programme succeeded in developing mathematical models formalising aspects of strategic interaction that remained implicit in the Nash Equilibrium Refinement Programme (NERP) owing to an unjustified degree of mathematisation. As a result, the Epistemic Programme is the more successful theory. [Copyright &y& Elsevier]

In this work I describe the PISA/OECD project framework main components. For this purpose, I analyze the notion of mathematical literacy, the different variables of the domain, the variables of the assessment instruments, and the different meanings of competency. [ABSTRACT FROM AUTHOR]