Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond


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Definitions that Clarify Practice

Also, because general giftedness is often seen as multi- dimensional, a number of criteria have been used to place students in special school programs for the gifted.

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These include results from intelligence tests, achievement tests, creativity tests, school grades, rating scales, past accomplishments, portfolios, interviews, teacher nominations, parent nominations, peer nominations and self-reports. To determine mathematical giftedness, tests of mathematical ability are also used.

Chapter 15 discusses links between mathematical creativity, excellence in school mathematics and general giftedness using results from an empirical study of Israeli high school students, using Multiple Solutions Tasks. I was especially intrigued by Chapter 11 that describes a neuroscience study that attempted to distinguish between super mathematically gifted students, generally gifted students who excel in school mathematics, and students who excel in school mathematics but have not been identified as generally gifted.


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Three types of neuro-efficiency effects were detected in the electrical activity of the super mathematically gifted students. Technical details and topographical brain maps of electrical potentials are included in the chapter. The goal is to have students use the CPR to reflect on their own proving processes.

The rubric takes into account making connections between definitions and theorems, between representations, and between examples, as well as considering risk-taking behaviors such as flexibility, perseverance, posing questions, and explanation of proof attempts. The final chapter raises political questions associated with giftedness, but offers no easy solutions.

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Examples are: What is the relationship between education for all and mathematically gifted education? Much can be learned from the chapters in this book, although as the researchers admit, much more research on creativity, giftedness, and their relationship needs to be done. She regularly teaches graduate courses in mathematics and mathematics education. She remains active in mathematics education research and curriculum development.

Related Papers. To date, arXiv has accumulated more than one million research documents — preprints or e-prints — and currently receives submissions a month with no costs to authors. In other fields, the uptake of preprints has been relatively slower, although it is gaining momentum with the development of platforms such as bioRxiv and several newly established ones through the Center for Open Science , including engrXiv engrXiv. Manuscripts submitted to these preprint servers are typically a draft version prior to formal submission to a journal for peer review, but can also be updated to include peer reviewed versions often called post-prints.

Primary motivation here is to bypass the lengthy time taken for peer review and formal publication, which means the timing of peer review occurs subsequent to manuscripts being made public. However, sometimes these articles are not submitted anywhere else and form what some regard as grey literature Luzi, Papers on digital preprint repositories are cited on a daily basis and much research builds upon them, although they may suffer from a stigma of not having the scientific stamp of approval of peer review Adam, Some journal policies explicitly attempt to limit their citation in peer-reviewed publications e.

In spite of this, the popularity and success of preprints is testified by their citation records, with four of the top five venues in physics and maths being arXiv sub-sections scholar. The overlay journal, first described by Ginsparg and built on the concept of deconstructed journals Smith, , is a novel type of journal that operates by having peer review as an additional layer on top of collections of preprints Hettyey et al.

New overlay journals such as The Open Journal theoj. Peer review is performed easily, rapidly, and cheaply, after initial publication of the articles. A similar approach to that of overlay journals is being developed by PubPub pubpub. PubPub then provides a mechanism for creating overlay journals that can draw from and curate the content hosted on the platform itself.


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  • This model incorporates the preprint server and final article publishing into one contained system. ScienceOpen provides editorially-managed collections of articles drawn from preprints and a combination of open access and non-open venues e.

    Editors compile articles to form a collection, write an editorial, and can invite referees to peer review the articles. They are essentially equivalent to community-mediated overlay journals, but with the difference that they also draw on additional sources beyond preprints. Registered Reports represent a significant departure from conventional peer review in terms of relative timing and increased rigour Chambers et al. Here, peer review is split into two stages. Research questions and methodology i.

    Creativity in Mathematics, pt. 1 of 3, Inquiry-Based Learning (IBL) and the Moore Method

    Such a process is analogous to clinical trials registrations for medical research, the implementation of which became widespread many years before Registered Reports, and is a well-established specialised process that innovative peer review models could learn a lot from. If a protocol is found to be of sufficient quality to pass this stage, the study is then provisionally accepted for publication. Once the research has been finished and written-up, completed manuscripts are then subject to a second-stage of peer review which, in addition to affirming the soundness of the results, also confirms that data collection and analysis occurred in accordance with the originally described methodology.

    The format, originally introduced by the psychology journals Cortex and Perspectives in Psychological Science in , is now used in some form by more than 70 journals Nature Human Behaviour, see cos. Registered Reports are designed to boost research integrity by ensuring the publication of all research results, which helps reduce publication bias. A relatively new mode of named pre-publication review is that of pre-arranged and invited review, originally proposed as author-guided peer review Perakakis et al.

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    This model requires an author to solicit reviews from their peers prior to submission in order to assess the suitability of a manuscript for publication. While some might see this as a potential bias, it is worth bearing in mind that many journals already ask authors who they want to review their papers, or who they should exclude. To avoid potential pre-submission bias, reviewer identities and their endorsements are made publicly available alongside manuscripts, which also removes any possible deleterious editorial criteria from inhibiting the publication of research.

    Also, PRE has been suggested by Jan Velterop to be much cheaper, legitimate, unbiased, faster, and more efficient alternative to the traditional publisher-mediated method theparachute. In theory, depending on the state of the manuscript, this means that submissions can be published much more rapidly, as less processing is required post-submission e.

    PRE also has the potential advantage of being more useful to non-native English speaking authors by allowing them to work with editors and reviewers in their first languages. However, possible drawbacks of this process include positive bias imposed by having author-recommended reviewers, as well as the potential for abuse through suggesting fake reviewers. As such, such a system highlights the crucial role of an Editor for verification and mediation. Despite a general appeal for post-publication peer review and considerable innovation in this field, the appetite among researchers is limited, reflecting an overall lack of engagement with the process e.

    Here, a high profile but controversial paper was heavily critiqued in settings such as blogs and Twitter, constituting a form of social post-publication peer review, occurring much more rapidly than any formal responses in traditional academic venues Yeo et al. Such social debates are notable, but however have yet to become mainstream beyond rare, high-profile cases. As recently as , it was reported that relatively few platforms allowed users to evaluate manuscripts post-publication Yarkoni, Even platforms such as PLOS have a restricted scope and limited user base: analysis of publicly available usage statistics indicate that at the time of writing, PLOS articles have each received an average of 0.

    Part of this may be due to how post-publication peer review is perceived culturally, with the name itself being anathema and considered an oxymoron, as most researchers usually consider a published article to be one that has already undergone formal peer review. At the present, it is clear that while there are numerous platforms providing decoupled peer review services, these are largely non-interoperable. The result of this, especially for post-publication services, is that most evaluations are difficult to discover, lost, or rarely available in an appropriate context or platform for re-use.

    To date, it seems that little effort has been focused on aggregating the content of these services with exceptions such as Publons , which hinders its recognition as a valuable community process and for additional evaluation or assessment decisions. This is despite the fast growth of arXiv spin-offs like biorXiv , and potential layered peer review through services such as the recently launched Peer Community In peercommunityin. Combined with the generally low uptake of decoupled peer review processes, this suggests the overall reluctance of many research communities to adapt outside of the traditional coupled model.

    In this section, we have discussed a range of different arguments, variably successful platforms, and surveys and reports about peer review. Taken together, these reveal an incredible amount of friction to experimenting with peer review beyond that which is typically and incorrectly viewed as the only way of doing it.

    Much of this can be ascribed to tensions between evolving cultural practices, social norms, and the different stakeholder groups engaged with scholarly publishing. This reluctance is emphasized in recent surveys, for instance the one by Ross-Hellauer suggests that while attitudes towards the principles of OPR are rapidly becoming more positive, faith in its execution is not. We can perhaps expect this divergence due to the rapid pace of innovation, which has not led to rigorous or longitudinal evidence that these models are superior to the traditional process at either a population or system-wide level although see Kovanis et al.

    Cultural or social inertia, then, is defined by this cycle between low uptake and limited incentives and evidence. Perhaps more important is the general under-appreciation of this intimate relationship between social and technological barriers, that is undoubtedly required to overcome this cycle.

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    The proliferation of social media over the last decade provides excellent examples of how digital communities can leverage new technologies for great effect. As we have discussed in detail above, there has been considerable innovation in peer review in the last decade, which is leading to widespread critical examination of the process and scholarly publishing as a whole e. Much of this has been driven by the advent of Web 2.

    Previous work in this arena has described features of a Reddit -like model, combined with additional personalized features of other social platforms, like Stack Exchange , Netflix , and Amazon Yarkoni, Here, we develop upon this by considering additional traits of models such as Wikipedia , GitHub , and Blockchain , and discuss these in the context of the rapidly evolving socio-technological environment for the present system of peer review.

    In the following section, we discuss potential future peer review platforms and processes in the context of the following three major traits, which any future innovation would greatly benefit from consideration of:. Quality control and moderation, possibly through openness and transparency;. Certification via personalized reputation or performance metrics;. Incentive structures to motivate and encourage engagement. While discussing a number of principles that should guide the implementation of novel platforms for evaluating scientific work, Yarkoni argued that many of the problems researchers face have already been successfully addressed by a range of non-research focused social Web applications.

    One important element that will determine the success or failure of any such peer-to-peer reputation or evaluation system is a critical mass of researcher uptake. This has to be carefully balanced with the demands and uptakes of restricted scholarly communities, which have inherently different motivations and practices in peer review.

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    Creativity and Giftedness

    A remaining issue is the aforementioned cultural inertia, which can lead to low adoption of anything innovative or disruptive to traditional workflows in research. This is a perfectly natural trait for communities, where ideas out-pace technological innovation, which in turn out-paces the development of social norms. Hence, rather than proposing an entirely new platform or model of peer review, our approach here is to consider the advantages and disadvantages of existing models and innovations in social services and technologies Table 4.

    We then explore ways in which such traits can be adapted, combined, and applied to build a more effective and efficient peer review system, while potentially reducing friction to its uptake. Note that some of these are already employed, alone or in combination, by different research platforms. Reddit reddit.

    Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond
    Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond
    Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond
    Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond
    Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond
    Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond Creativity and Giftedness: Interdisciplinary perspectives from mathematics and beyond

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