‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation

In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence—namely, in Toulmin’s sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument relates to, proposed a classification of warrants (a priori, empirical, institutional and evaluative). Our approach to analysing teacher arguments proposes an adaptation of Freeman’s classification that distinguishes between: epistemological and pedagogical a priori warrants, professional and personal empirical warrants, epistemological and curricular institutional warrants, and evaluative warrants. Our proposition emerged from analyses conducted in the course of a written response and interview study that engages secondary mathematics teachers with classroom scenarios from the mathematical areas of analysis and algebra. The scenarios are hypothetical, grounded on seminal learning and teaching issues, and likely to occur in actual practice. To illustrate our proposed approach to analysing teacher arguments here, we draw on the data we collected through the use of one such scenario, the Tangent Task. We demonstrate how teacher arguments, not analysed for their mathematical accuracy only, can be reconsidered, arguably more productively, in the light of other teacher considerations and priorities: pedagogical, curricular, professional and personal

Some Properties of Vector Measures taking Values in A Topological Vector Space

In this paper we study some properties of vector measures with values in various topological vector spaces. As a matter of fact, we give a necessary condition implying the Pettis integrability of a function /: S-0 E, where S is a set and E a locally convex space. Furthermore, we prove an iff condition under which (Q, E) has the Pettis property, for an algebra Q and a sequentially complete topological vector space E. An approximating theorem concerning vector measures taking values in a Frechet space is also given. © 1987, Australian Mathematical Society. All rights reserved

Some types of vector measures

Let x be a metrizable locally convex space with a Schauder basis and let B(T) be a σ-ring generated by the compact subsets of a locally compact Hausdorff space T. We prove that any vector measure μ:B(T)→X which has an antiregular relative is antimonogenic (Theorem 16) and that μ can be uniquely decomposable, μ = μ1 + μ2, where μ1 is monogenic and μ2 has an antiregular relative (Theorem 19). These results are due to R. A. Johnshon [6] for the case where X is the real line. © 1993 Akadémiai Kiadó, Budapest

Studying teachers' mathematical argumentation in the context of refuting students' invalid claims

This study investigates teachers' argumentation aiming to convince students about the invalidity of their mathematical claims in the context of calculus. 18 secondary school mathematics teachers were given three hypothetical scenarios of a student's proof that included an invalid algebraic claim. The teachers were asked to identify possible mistakes and explain how they would refute the student's invalid claims. Two of them were also interviewed. The data were analysed in terms of the content and structure of argumentation and the types of counterexamples the teachers generated. The findings show that teachers used two main approaches to refute students' invalid claims, the use of theory and the use of counterexamples. The role of these approaches in the argumentation process was analysed by Toulmin's model and three types of reasoning emerged that indicate the structure of argumentation in the case of refutation. Concerning the counterexamples, the study shows that few teachers use them in their argumentation and in general they underestimate their value as a proof method. © 2010 Elsevier Inc

Computational Chemistry for the Identification of Lead Compounds for Radiotracer Development

The use of computer-aided drug design (CADD) for the identification of lead compounds in radiotracer development is steadily increasing. Traditional CADD methods, such as structure-based and ligand-based virtual screening and optimization, have been successfully utilized in many drug discovery programs and are highlighted throughout this review. First, we discuss the use of virtual screening for hit identification at the beginning of drug discovery programs. This is followed by an analysis of how the hits derived from virtual screening can be filtered and culled to highly probable candidates to test in in vitro assays. We then illustrate how CADD can be used to optimize the potency of experimentally validated hit compounds from virtual screening for use in positron emission tomography (PET). Finally, we conclude with a survey of the newest techniques in CADD employing machine learning (ML)

Identification of a nanomolar affinity a-synuclein fibril imaging probe by ultra-high throughput: In silico screening

Small molecules that bind with high affinity and specificity to fibrils of the a-synuclein (aS) protein have the potential to serve as positron emission tomography (PET) imaging probes to aid in the diagnosis of Parkinson's disease and related synucleinopathies. To identify such molecules, we employed an ultra-high throughput in silico screening strategy using idealized pseudo-ligands termed exemplars to identify compounds for experimental binding studies. For the top hit from this screen, we used photo-crosslinking to confirm its binding site and studied the structure-activity relationship of its analogs to develop multiple molecules with nanomolar affinity for aS fibrils and moderate specificity for aS over Aß fibrils. Lastly, we demonstrated the potential of the lead analog as an imaging probe by measuring binding to aS-enriched homogenates from mouse brain tissue using a radiolabeled analog of the identified molecule. This study demonstrates the validity of our powerful new approach to the discovery of PET probes for challenging molecular targets