History of mathematics in teachers' education: Motivation for and of Discussion Group 2

International audienceDiscussion Group 2 (DG 2), in a sequence of two one-hour sessions, revisits the discussion about the role of history of mathematics in teachers' education – both for pre-service teachers and currently practicing teachers. Activities of DG 2 include a discussion of examples from the literature that propose benefits for teachers and their students when history of mathematics is utilized to teach and learn mathematics. Participants will also share experiences from their own contexts. In particular, DG 2 will draw upon concrete examples from university courses, professional development programs, and projects, and when possible, the observed and/or documented benefits derived from the use of history of mathematics resulting from these examples. Finally, participants will discuss specific tasks or activities that may serve as examples for contexts that do not currently possess a strong history of mathematics dimension within mathematics teacher education programs, or which may provide new examples for those who do.

Domain-specific reasoning for method engineering based on Toulmin's argumentation theory

Methods describe and embody a broad range of relevant knowledge of enterprises. Usually they have to account for requirements stated by a multitude of various stakeholders. These are typically those that are in charge of business related actions and those that are in charge to support such actions with an IT-Infrastructure. The statement of requirements as well as the validation of methods and in particular process models with respect to those requirements relies drastically on natural language. Natural language seems to be a substantial component to explain and to give an understanding about process models or certain aspects of it. This fact requires closing the gap between the natural language and the respective modelling language. This paper proposes argumentative method engineering for purposefully depicting design decisions and convictions for method engineering through arguments. The approach is derived from Toulmin’s Argumentation Model and explicates the process of negotiating with various stakeholders. So, a model, depicting a method, specified by means of argumentative method engineering, not just includes the claims about a certain domain, it further justifies these claims by referring to already established knowledge. While it can’t be ensured that certain requirements are considered in future project, if the reasons for design decisions of method engineering are transcribed in natural language text, but the semi- formalising of arguments regarding these methods allows such an assurance. So the argumentative approach enables the sophisticated management and reuse of knowledge during the development and extension of methods. The approach is evaluated using a case study, in which a software development method was outsourced to contractors

Utilising Spontaneous Conversational Speech in HMM-Based Speech Synthesis

Spontaneous conversational speech has many characteristics that are currently not well modelled in unit selection and HMM-based speech synthesis. But in order to build synthetic voices more suitable for interaction we need data that exhibits more conversational characteristics than the generally used read aloud sentences. In this paper we will show how carefully selected utterances from a spontaneous conversation was instrumental for building an HMM-based synthetic voices with more natural sounding conversational characteristics than a voice based on carefully read aloud sentences. We also investigated a style blending technique as a solution to the inherent problem of phonetic coverage in spontaneous speech data. But the lack of an appropriate representation of spontaneous speech phenomena probably contributed to results showing that we could not yet compete with the speech quality achieved for grammatical sentences

Complex Bounds for Real Maps

In this paper we prove complex bounds, also referred to as a priori bounds for C3, and, in particular, for analytic maps of the interval. Any C3 mapping of the interval has an asymptotically holomorphic extension to a neighbourhood of the interval. We associate to such a map, a complex box mapping, which provides a kind of Markov structure for the dynamics. Moreover, we prove universal geometric bounds on the shape of the domains and on the moduli between components of the range and domain. Such bounds show that the first return maps to these domains are well controlled, and consequently such bounds form one of the corner stones in many recent results in one-dimensional dynamics, for example: renormalization theory, rigidity, density of hyperbolicity, and local connectivity of Julia sets

Quantifying the Nonclassicality of Operations

Deep insight can be gained into the nature of nonclassical correlations by studying the quantum operations that create them. Motivated by this we propose a measure of nonclassicality of a quantum operation utilizing the relative entropy to quantify its commutativity with the completely dephasing operation. We show that our measure of nonclassicality is a sum of two independent contributions, the generating power -- its ability to produce nonclassical states out of classical ones, and the distinguishing power -- its usefulness to a classical observer for distinguishing between classical and nonclassical states. Each of these effects can be exploited individually in quantum protocols. We further show that our measure leads to an interpretation of quantum discord as the difference in superdense coding capacities between a quantum state and the best classical state when both are produced at a source that makes a classical error during transmission

Quantum Nature of Plasmon-Enhanced Raman Scattering

We report plasmon-enhanced Raman scattering in graphene coupled to a single plasmonic hotspot measured as a function of laser energy. The enhancement profiles of the G peak show strong enhancement (up to $10^5$) and narrow resonances (30 meV) that are induced by the localized surface plasmon of a gold nanodimer. We observe the evolution of defect-mode scattering in a defect-free graphene lattice in resonance with the plasmon. We propose a quantum theory of plasmon-enhanced Raman scattering, where the plasmon forms an integral part of the excitation process. Quantum interferences between scattering channels explain the experimentally observed resonance profiles, in particular, the marked difference in enhancement factors for incoming and outgoing resonance and the appearance of the defect-type modes.Comment: Keywords: plasmon-enhanced Raman scattering, SERS, graphene, quantum interferences, microscopic theory of Raman scattering. Content: 22 pages including 5 figures + 11 pages supporting informatio

Introducing argumentative and discursive enterprise leading and management

Leading an enterprise requires, obviously, decision making. However, these decisions require explanations in order to make it possible for stakeholders to get an understanding about the enterprise's strategic direction. This is even more important when these stakeholders are in charge to transpose such strategic decision into their tactical or operational work. Enterprise modelling may be capable of depicting strategies per se, but it is rather a vessel of communication than of explanation. Whilst, a strategy may be accordingly modelled, those who receive such a model needs to purposeful interpret and successfully implement it. However, without any insights, justifications or references that go beyond the claim of a model, it is dificult to embrace the theory of the actual modeller. Therefore, in this paper argumentative modelling will be specifically applied to the domain of strategic management. Moreover it will be elucidated how modelled strategic arguments can be used as a basis for enterprise architecture alignment and management. As it will be shown in the paper, the application of argumentative modelling overcomes classical restrictions and makes it possible to support a discourse, which can be later on used as an explanation for the intentions of the modeller