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.

Phytoseiidae mites associated with Hevea spp. from the Amazon region: a hidden diversity under the canopy of native trees

Despite the Amazon Forest being the largest tropical forest in the world, and cradle of rubber trees (Hevea brasiliensis), no studies have aimed to report the occurrence of mites associated with native trees from this ecosystem. Our survey investigates the phytoseiid mites associated with five species of native rubber trees from nine sites of the Amazon Forest, and also presents a major review of phytoseiid species from natural vegetation in Brazil. We found a total of 1305 mites, belonging to 30 species, of which seven were new to science, Amblydromalus akiri sp. nov., Amblyseius chicomendesi sp. nov., Amblyseius duckei sp. nov., Amblyseius manauara sp. nov., Iphiseiodes katukina sp. nov., Iphiseiodes raucuara sp. nov. and Typhlodromips igapo sp. nov.; beyond two new records for Brazil, Iphiseiodes kamahorae and Amblyseius martus. Our results emphasize the importance of Amazon native trees as an unexplored source of predator mites, which in turn may be further studied as biological control agents of pest mites on rubber trees. The impressive diversity, endemism and rate of new species found highlight the importance of studies on arthropod communities associated with the Amazon vegetation.

Functional and phylogenetic diversity of scattered trees in an agricultural landscape: Implications for conservation

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)

Wood and leaf anatomy of Copaifera langsdorffii dwarf trees

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Carbohydrate concentration in 'BRS Rubimel' peach trees during the annual cycle

The carbohydrate storage is necessary to support the plant growth in periods of stress, during the dormancy, in the beginning of the vegetative development and during the fruiting time. In this context, this work intended to evaluate the carbohydrate concentrations of the peach (Prunus persica (L.) Batsch) tree ‘BRS Rubimel’, cultivated under subtropical conditions. The experiment was performed at the experimental farm Lageado, of the Faculty of Agricultural Sciences of UNESP at Botucatu/SP. The evaluated peach trees were two years old and were cultivated in the spacing of 6.0 x 4.0 m. The adopted experimental delineation was in randomized blocks, making use of four plants per parcel with four repetitions. The treatments corresponded to the period of the collection of leaves and branches, during the annual cycle, corresponding to January to May and July to December 2012. The sample collection of the roots was performed in January, April, August, November and December 2012. Four fruits per plant were collected. The concentration of starch in the roots of the peach tree were superior to the ones from the branches, from August to December. The carbohydrate with the higher storage level in the peach tree ‘BRS Rubimel’ was starch.

Agronomic performance of peach trees grown in subtropical region

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