Experiencing Manipulative Material for the Teaching and Learning of Mathematics

This paper presents some outcomes from research based on classroom experiences. The main themes are the use of mirrors, kaleidoscopes, dynamic geometry software, and manipulative material considering their possibilities for the teaching and learning of Euclidean and non-Euclidean geometries.

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)

Organic material decomposition and nutrient dynamics in a mulch system enriched with leguminous trees in the Amazon

As novas técnicas propostas para a agricultura na Amazônia incluem sistema de rotação de capoeira enriquecido com árvores leguminosas e transformando a queima da biomassa em cobertura morta sobre o solo. A decomposição e a liberação de nutrientes da cobertura morta foram estudadas usando sacos de liteira com malha fina que continham cinco tratamentos com diferentes espécies de leguminosas em comparação a um tratamento-controle com vegetação natural. As amostras para cada tratamento foram analisadas para conteúdos de C total, N, P, K, Ca, Mg, lignina, celulose e polifenóis solúveis em diferentes tempos de amostragem durante um ano. A razão constante de decomposição variou com a espécie e com o tempo. A perda de massa nos sacos de decomposição foi de 30,1 % para Acacia angustissima, de 32,7 % para Sclerolobium paniculatum, de 33,9 % para Inga edulis e para a vegetação secundária, de 45,2 % para Acacia mangium e de 63,6 % para Clitoria racemosa. Foi observada imobilização de N e P em todos os tratamentos, sendo a mineralização do N negativamente correlacionada com o fenol, razão C/N, razão (lignina + fenol)/N, razão fenol/P e o conteúdo de N nos sacos de liteira. Depois de 362 dias de incubação no campo, 3,3 % de K, 32,2 % de Ca e 22,4 % de Mg permaneceram no material em decomposição. Os resultados evidenciaram que a baixa qualidade mineral e a alta quantidade de carbono orgânico e aplicado como cobertura morta podem limitar a quantidade de energia disponível para os microrganismos resultando em uma competição por nutrientes com as plantas agrícolas.

Creating Meaningful Homework and Implementing Homework Presentations to Aid in Mathematics Instruction

In this action research study of sixth grade mathematics, I investigated the use of meaningful homework and the implementation of presentations and its effect on students’ comprehension of mathematical concepts. I collected data to determine whether the creating of meaningful homework and the implementation of homework presentations would have a positive impact on the students’ understanding of the concepts being taught in class and the reasoning behind assigning homework. The homework was based on the lesson taught during class time. It was grade-level appropriate and contained problems similar to those students completed in class. A pre-research and post-research survey based on homework perceptions and my teaching practices was given, student interviews were conducted throughout the research period, weekly teacher journals were kept that pertained to my teaching practices and the involvement of the students that particular week, and homework assignments were collected to gauge the students’ understanding of the mathematics lessons. Most students’ perceptions on homework were positive and most understood the reasoning for homework assignments.

Improving Communication about Mathematics through Vocabulary and Writing

In this action research study, where the subjects were my 6th grade mathematics students, I investigated the impact of direct vocabulary instruction on their communication and achievement. I strategically implemented the addition of vocabulary study into each lesson over a four-month time period. The students practiced using vocabulary in verbal discussions, review activities, and in mathematical problem explanations. I discovered that a majority of students improved their overall understanding of mathematical concepts based on an analysis of the data I collected. I also found that in general, students felt that knowing the definition of mathematical words was important and that it increased their achievement when they understood the words. In addition, students were more exact in their communication after receiving vocabulary instruction. As a result of this research, I plan to continue to implement vocabulary into daily lessons and keep vocabulary and communication as a focus of my 6th grade mathematics class.