The correlation between reading and mathematics ability at age twelve has a substantial genetic component

Dissecting how genetic and environmental influences impact on learning is helpful for maximizing numeracy and literacy. Here we show, using twin and genome-wide analysis, that there is a substantial genetic component to children’s ability in reading and mathematics, and estimate that around one half of the observed correlation in these traits is due to shared genetic effects (so-called Generalist Genes). Thus, our results highlight the potential role of the learning environment in contributing to differences in a child’s cognitive abilities at age twelve.

Interrupting the child/adult dichotomy: A genealogy of genius as an administrative object in educational discourse

Part of a special issue on childhood and cultural studies. The writer provides a genealogy of genius that interrupt the child/adult dichotomy and disrupts the notion of child as subject. Tracing the evolution of the notion of “genius,” she notes that although conceptualizations of genius have changed considerably over the years, it has continually been a concept that distinguishes the haves from the have-nots. The writer maintains that the idea of genius consistently invokes images of both maleness and whiteness and marginalizes the experiences of women and other groups.

William James, Sciences of Mind, and Anti-imperial Discourse

In the past few decades, the humanities and social sciences have developed new methods of reorienting their conceptual frameworks in a “world without frontiers.” In this book, Bernadette M. Baker offers an innovative approach to rethinking sciences of mind as they formed at the turn of the twentieth century, via the concerns that have emerged at the turn of the twenty-first. The less-visited texts of Harvard philosopher and psychologist William James provide a window into contemporary debates over principles of toleration, anti-imperial discourse, and the nature of ethics. Baker revisits Jamesian approaches to the formation of scientific objects including the child mind, exceptional mental states, and the ghost to explore the possibilities and limits of social scientific thought dedicated to mind development and discipline formation around the construct of the West.

Given and News : Media discourse and the construction of community on national days

National anniversaries such as independence days demand precise coordination in order to make citizens change their routines to forego work and spend the day at rest or at festivities that provide social focus and spectacle. The complex social construction of national days is taken for granted and operates as a given in the news media, which are the main agents responsible for coordinating these planned disruptions of normal routines. This study examines the language used in the news to construct the rather unnatural idea of national days and to align people in observing them. The data for the study consist of news stories about the Fourth of July in the New York Times, sampled over 150 years and are supplemented by material from other sources and other countries. The study is multidimensional, applying concepts from pragmatics (speech acts, politeness, information structure), systemic functional linguistics (the interpersonal metafunction and the Appraisal framework) and cognitive linguistics (frames, metaphor) as well as journalism and communications to arrive at an interdisciplinary understanding of how resources for meaning are used by writers and readers of the news stories. The analysis shows that on national anniversaries, nations tend to be metaphorized as persons having birthdays, to whom politeness should be shown. The face of the nation is to be respected in the sense of identifying the nation's interests as one's own (positive face) and speaking of citizen responsibilities rather than rights (negative face). Resources are available for both positive and negative evaluations of events and participants and the newspaper deftly changes footings (Goffman 1981) to demonstrate the required politeness while also heteroglossically allowing for a certain amount of disattention and even protest - within limits, for state holidays are almost never construed as Bakhtinian festivals, as they tend to reaffirm the hierarchy rather than invert it. Celebrations are evaluated mainly for impressiveness, and for the essentially contested quality of appropriateness, which covers norms of predictability, size, audience response, aesthetics, and explicit reference to the past. Events may also be negatively evaluated as dull ("banal") or inauthentic ("hoopla"). Audiences are evaluated chiefly in terms of their enthusiasm, or production of appropriate displays for emotional response, for national days are supposed to be occasions of flooding-out of nationalistic feeling. By making these evaluations, the newspaper reinforces its powerful position as an independent critic, while at the same time playing an active role in the construction and reproduction of emotional order embodied in "the nation's birthday." As an occasion for mobilization and demonstrations of power, national days may be seen to stand to war in the relation of play to fighting (Bateson 1955). Evidence from the newspaper's coverage of recent conflicts is adduced to support this analysis. In the course of the investigation, methods are developed for analyzing large collections of newspaper content, particularly topical soft news and feature materials that have hitherto been considered less influential and worthy of study than so-called hard news. In his work on evaluation in newspaper stories, White (1998) proposed that the classic hard news story is focused on an event that threatens the social order, but news of holidays and celebrations in general does not fit this pattern, in fact its central event is a reproduction of the social order. Thus in the system of news values (Galtung and Ruge 1965), national holiday news draws on "ground" news values such as continuity and predictability rather than "figure" news values such as negativity and surprise. It is argued that this ground helps form a necessary space for hard news to be seen as important, similar to the way in which the information structure of language is seen to rely on the regular alternation of given and new information (Chafe 1994).

Logic as the Universal Science : Bertrand Russell's Early Conception of Logic and Its Philosophical Context

Bertrand Russell (1872 1970) introduced the English-speaking philosophical world to modern, mathematical logic and foundational study of mathematics. The present study concerns the conception of logic that underlies his early logicist philosophy of mathematics, formulated in The Principles of Mathematics (1903). In 1967, Jean van Heijenoort published a paper, Logic as Language and Logic as Calculus, in which he argued that the early development of modern logic (roughly the period 1879 1930) can be understood, when considered in the light of a distinction between two essentially different perspectives on logic. According to the view of logic as language, logic constitutes the general framework for all rational discourse, or meaningful use of language, whereas the conception of logic as calculus regards logic more as a symbolism which is subject to reinterpretation. The calculus-view paves the way for systematic metatheory, where logic itself becomes a subject of mathematical study (model-theory). Several scholars have interpreted Russell s views on logic with the help of the interpretative tool introduced by van Heijenoort,. They have commonly argued that Russell s is a clear-cut case of the view of logic as language. In the present study a detailed reconstruction of the view and its implications is provided, and it is argued that the interpretation is seriously misleading as to what he really thought about logic. I argue that Russell s conception is best understood by setting it in its proper philosophical context. This is constituted by Immanuel Kant s theory of mathematics. Kant had argued that purely conceptual thought basically, the logical forms recognised in Aristotelian logic cannot capture the content of mathematical judgments and reasonings. Mathematical cognition is not grounded in logic but in space and time as the pure forms of intuition. As against this view, Russell argued that once logic is developed into a proper tool which can be applied to mathematical theories, Kant s views turn out to be completely wrong. In the present work the view is defended that Russell s logicist philosophy of mathematics, or the view that mathematics is really only logic, is based on what I term the Bolzanian account of logic . According to this conception, (i) the distinction between form and content is not explanatory in logic; (ii) the propositions of logic have genuine content; (iii) this content is conferred upon them by special entities, logical constants . The Bolzanian account, it is argued, is both historically important and throws genuine light on Russell s conception of logic.

Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

Investigating the effectiveness of an ecological approach to learning design in a first year mathematics for engineering unit

This is presentation of the refereed paper accepted for the Conferences' proceedings. The presentation was given on Tuesday, 1 December 2015.

Mathematics, programming, and STEM

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10-week teaching experiment, mathematical meaning-making was enriched when primary students wrote Logo programs to create 3D virtual worlds. The analysis of results found deep learning in mathematics, as well as in technology and engineering areas. This prompted a rethinking about the nature of learning mathematics and a need to employ and examine a more holistic learning approach for the learning in science, technology, engineering, and mathematics (STEM) areas.

Applying pure mathematics: mathematics in the natural sciences

The book of nature is written in the language of mathematics. This quotation, attributed to Galileo, seemed to hold to an unreasonable1 extent in the era of quantum mechanics.

Becoming a teacher: emerging teacher identity in mathematics teacher education

This research examines three aspects of becoming a teacher, teacher identity formation in mathematics teacher education: the cognitive and affective aspect, the image of an ideal teacher directing the developmental process, and as an on-going process. The formation of emerging teacher identity was approached in a social psychological framework, in which individual development takes place in social interaction with the context through various experiences. Formation of teacher identity is seen as a dynamic, on-going developmental process, in which an individual intentionally aspires after the ideal image of being a teacher by developing his/her own competence as a teacher. The starting-point was that it is possible to examine formation of teacher identity through conceptualisation of observations that the individual and others have about teacher identity in different situations. The research uses the qualitative case study approach to formation of emerging teacher identity, the individual developmental process and the socially constructed image of an ideal mathematics teacher. Two student cases, John and Mary, and the collective case of teacher educators representing socially shared views of becoming and being a mathematics teacher are presented. The development of each student was examined based on three semi-structured interviews supplemented with written products. The data-gathering took place during the 2005 2006 academic year. The collective case about the ideal image provided during the programme was composed of separate case displays of each teacher educator, which were mainly based on semi-structured interviews in spring term 2006. The intentions and aims set for students were of special interest in the interviews with teacher educators. The interview data was analysed following the modified idea of analytic induction. The formation of teacher identity is elaborated through three themes emerging from theoretical considerations and the cases. First, the profile of one s present state as a teacher may be scrutinised through separate affective and cognitive aspects associated with the teaching profession. The differences between individuals arise through dif-ferent emphasis on these aspects. Similarly, the socially constructed image of an ideal teacher may be profiled through a combination of aspects associated with the teaching profession. Second, the ideal image directing the individual developmental process is the level at which individual and social processes meet. Third, formation of teacher identity is about becoming a teacher both in the eyes of the individual self as well as of others in the context. It is a challenge in academic mathematics teacher education to support the various cognitive and affective aspects associated with being a teacher in a way that being a professional and further development could have a coherent starting-point that an individual can internalise.

Modeling dynamic demand response using Monte Carlo simulation and interval mathematics for boundary estimation

With the rapid development of various technologies and applications in smart grid implementation, demand response has attracted growing research interests because of its potentials in enhancing power grid reliability with reduced system operation costs. This paper presents a new demand response model with elastic economic dispatch in a locational marginal pricing market. It models system economic dispatch as a feedback control process, and introduces a flexible and adjustable load cost as a controlled signal to adjust demand response. Compared with the conventional “one time use” static load dispatch model, this dynamic feedback demand response model may adjust the load to a desired level in a finite number of time steps and a proof of convergence is provided. In addition, Monte Carlo simulation and boundary calculation using interval mathematics are applied for describing uncertainty of end-user's response to an independent system operator's expected dispatch. A numerical analysis based on the modified Pennsylvania-Jersey-Maryland power pool five-bus system is introduced for simulation and the results verify the effectiveness of the proposed model. System operators may use the proposed model to obtain insights in demand response processes for their decision-making regarding system load levels and operation conditions.