Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

Online distance mathematics education in Brazil: research, practice and policy

In this article, we address online distance mathematics education research and practice in Brazil, which are relative newcomers to the educational scene. We present the national context of education in Brazil, highlighting the organization of the educational system, and also a summary of national legislation on distance education and an overview of digital inclusion in the country. We outline the potential and relevance of distance education for the Brazilian educational system and show how it could intervene in the system. With respect to research and practice in online mathematics education, we present support for research, examples of studies and highlight different aspects being addressed, including its essential components. In addition, we discuss the synergy between distance education and teacher education, and mathematics distance education and modeling, as well as other initiatives in the national scenario.

Identificação de Neutrophil Extracellular Traps em lesões tegumentares de pacientes com Paracoccidiodomicose e análise da formação de NETs in vitro por neutrófilos humanos desafiados com Paracoccidioides brasiliensis

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Initial growth of bauhinia variegata trees under different colored shade nets and light conditions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Neutrophil extracellular traps identification in tegumentary lesions of patients with paracoccidioidomycosis and different patterns of NETs generation in vitro

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Participation of dectin-1 receptor on NETs release against Paracoccidioides brasiliensis: role on extracellular killing

Paracoccidioides brasiliensis is a dimorphic fungus from the Paracoccidioides genus, which is the causative agent of paracoccidioidomycosis, a chronic, subacute or acute mycosis, with visceral and cutaneous involvement. This disease that is acquired through inhalation primarily attacks the lungs but, can spread to other organs. Phagocytic cells as neutrophils play an important role during innate immune response against this fungus, but studies on antifungal activities of these cells are scarce. In addition to their ability to eliminate pathogens by phagocytosis and antimicrobial secretions, neutrophils can trap and kill microorganisms by release of extracellular structures composed by DNA and antimicrobial proteins, called neutrophil extracellular traps (NETs). Here, we provide evidence that P. brasiliensis virulent strain (P. brasiliensis 18) induces NETs release. These structures were well evidenced by scanning electron microscopy, and specific NETs compounds such as histone, elastase and DNA were shown by confocal microscopy. In addition, we have shown that dectin-1 receptor is the main PRR to which fungus binds to induce NETS release. Fungi were ensnared by NETs, denoting the role of these structures in confining the fungus, avoiding dissemination. NETs were also shown to be involved in fungus killing, since fungicidal activity detected before and mainly after neutrophils activation with TNF-α, IFN-γ and GM-CSF was significantly inhibited by cocultures treatment with DNAse.

Husserl's two notions of completeness: husserl and hilbert on completeness and imaginary elements in mathematics

In this paper I discuss Husserl's solution of the problem of imaginary elements in mathematics as presented in the drafts for two lectures he gave in Göttingen in 1901 and other related texts of the same period, a problem that had occupied Husserl since the beginning of 1890, when he was planning a never published sequel to Philosophie der Arithmetik (1891). In order to solve the problem of imaginary entities Husserl introduced, independently of Hilbert, two notions of completeness (definiteness in Husserl's terminology) for a formal axiomatic system. I present and discuss these notions here, establishing also parallels between Husserl's and Hilbert's notions of completeness. © 2000 Kluwer Academic Publishers.