The 'algebra as object' analogy: a view from school

Treating algebraic symbols as objects (eg. “‘a’ means ‘apple’”) is a means of introducing elementary simplification of algebra, but causes problems further on. This current school-based research included an examination of texts still in use in the mathematics department, and interviews with mathematics teachers, year 7 pupils and then year 10 pupils asking them how they would explain, “3a + 2a = 5a” to year 7 pupils. Results included the notion that the ‘algebra as object’ analogy can be found in textbooks in current usage, including those recently published. Teachers knew that they were not ‘supposed’ to use the analogy but not always clear why, nevertheless stating methods of teaching consistent with an‘algebra as object’ approach. Year 7 pupils did not explicitly refer to ‘algebra as object’, although some of their responses could be so interpreted. In the main, year 10 pupils used ‘algebra as object’ to explain simplification of algebra, with some complicated attempts to get round the limitations. Further research would look to establish whether the appearance of ‘algebra as object’ in pupils’ thinking between year 7 and 10 is consistent and, if so, where it arises. Implications also are for on-going teacher training with alternatives to introducing such simplification.

REALIZING PROFINITE REDUCED SPECIAL GROUPS

Special groups are an axiomatization of the algebraic theory of quadratic forms over fields. It is known that any finite reduced special group is the special group of some field. We show that any special group that is the projective limit of a projective system of finite reduced special groups is also the special group of some field.

Differential Habituation of Male Betta Splendens to Qualitatively Different Stimuli

Habituation is a learning mechanism that functions to decrease the amount of energy and attention focused on a certain stimuli. Male Siamese Fighting Fish, Betta splendens, are territorial animals that defend their territories using a number of aggressive displays. Male Bettas have previously shown the ability to habituate to the presence of a conspecific male when visually exposed to each other. Due to the costly nature of many of the male Betta’s displays, I hypothesized that male Bettas should differentially habituate to qualitatively different stimuli. I presented each of three groups of male Betta splendens with a different stimulus, each presenting a different level of interactivity. I predicted that the Bettas would be more likely to habituate to a less interactive stimulus than a more interactive one. No significant habituation was observed in any of the groups and no significant differences in latency to display or length of display between all three groups were observed. However, overall data trends suggest that habituation was indeed occurring and that the three different stimuli elicited different levels of display. The limited amount of visual exposure to the stimuli in this experiment might account for why results were insignificant.

Uncertainty Characterization Of A Conceptual Rainfall-Runoff Model By Using Grey Numbers

A procedure for characterizing global uncertainty of a rainfall-runoff simulation model based on using grey numbers is presented. By using the grey numbers technique the uncertainty is characterized by an interval; once the parameters of the rainfall-runoff model have been properly defined as grey numbers, by using the grey mathematics and functions it is possible to obtain simulated discharges in the form of grey numbers whose envelope defines a band which represents the vagueness/uncertainty associated with the simulated variable. The grey numbers representing the model parameters are estimated in such a way that the band obtained from the envelope of simulated grey discharges includes an assigned percentage of observed discharge values and is at the same time as narrow as possible. The approach is applied to a real case study highlighting that a rigorous application of the procedure for direct simulation through the rainfall-runoff model with grey parameters involves long computational times. However, these times can be significantly reduced using a simplified computing procedure with minimal approximations in the quantification of the grey numbers representing the simulated discharges. Relying on this simplified procedure, the conceptual rainfall-runoff grey model is thus calibrated and the uncertainty bands obtained both downstream of the calibration process and downstream of the validation process are compared with those obtained by using a well-established approach, like the GLUE approach, for characterizing uncertainty. The results of the comparison show that the proposed approach may represent a valid tool for characterizing the global uncertainty associable with the output of a rainfall-runoff simulation model.

Predição do consumo de pasto de capim-elefante (Pennisetum purpureum, Schumack) por vacas mestiças Holandês x Zebu em lactação

Foram desenvolvidas equações de predição de consumo de pasto de capim-elefante (Pennisetum purpureum, Schumack) por vacas mestiças Holandês x Zebu em lactação, utilizando-se procedimentos de stepwise em regressões múltiplas, aplicados a um banco de dados de experimentos conduzidos ao longo de três anos na Empresa Brasileira de Pesquisa Agropecuária (EMBRAPA) Gado de Leite (Coronel Pacheco, MG). As variáveis independentes disponíveis foram relacionadas a características inerentes às vacas (dias em lactação; teores de proteína, gordura e extrato seco total e produções destes componentes no leite; produção de leite in natura ou corrigida para 4% de gordura; ordem de lactação; peso vivo atual; peso vivo ao parto e grau de sangue Holandês x Zebu); ao manejo (dias de pastejo; disponibilidade de forragem e período de descanso da pastagem); ao ambiente (estação do ano e precipitação pluviométrica) e à alimentação (digestibilidade in vitro e parâmetros da composição química do pasto de capim-elefante e da cana-de-açúcar - Saccharum officinarum (L.) corrigida com 1% de uréia; consumos de suplemento volumoso (cana corrigida com uréia) e concentrado; concentrações fecais de proteína bruta e de fibras em detergente neutro e ácido). Efeitos linear e quadrático e transformações logarítmicas foram adicionalmente incluídos no banco de dados. Foram obtidas equações de predição de consumo de pasto de capim-elefante (expresso em kg/vaca/dia ou % do peso vivo) com coeficientes de determinação de 65,2 a 67,0%. As principais variáveis independentes incluídas nas equações foram o consumo do suplemento volumoso usado na estação seca do ano (cana corrigida com uréia); a digestibilidade in vitro do pasto de capim-elefante; a precipitação pluviométrica; a produção de leite corrigida para 4% de gordura; o peso vivo atual ou, em alternativa a este, o valor da pesagem realizada após o parto da vaca; além do consumo de suplemento concentrado, que evidenciou um efeito de substituição àquele do pasto de capim-elefante.

Comparação de alguns modelos matemáticos para ajuste à curva de lactação média de um rebanho da raça Caracu

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Investigação histórica nas aulas de matemática: avaliação de duas experiências

This study reflects on some procedural aspects about the development of mathematics learning from the experience with investigative activities concerning the resolution of second degree equation, which was tested a proposal for education, supported the use of texts in history of mathematics. The survey was conducted in two stages, taking the first-served basis for the second, which was carried out with a study group remainder of the first experiment. The intention was to investigate how the group participant, known as the study group, involved in the implementation of activities of research in mathematics, supported the use of the history of mathematics. Based on the results achieved during the study, it was possible to understand that the activities of research enable the development of students, range of learning mathematics and the development of skills and expertise for research as a vehicle for construction of their mathematical knowledge. This approach proposed research into the classroom is important, both for prospective teachers of mathematics and for students from elementary school, bringing a new phase for mathematical education that will come to schools

Função quadrática

In general, the study of quadratic functions is based on an excessive amount formulas, all content is approached without justification. Here is the quadratic function and its properties from problems involving quadratic equations and the technique of completing the square. Based on the definitions we will show that the graph of the quadratic function is the parabola and finished our studies finding that several properties of the function can be read from the simple observation of your chart. Thus, we built the whole matter justifying each step, abandoning the use of decorated formulas and valuing the reasoning

O intuitivo e o lógico no conhecimento matemático: análise de uma proposta pedagógica em relação a abordagens filosóficas atuais e ao contexto educacional da matemática

In this paper, we consider Meneghetti & Bicudo's proposal (2003) regarding the constitution of mathematical knowledge and analyze it with respect to the following two focuses: in relation to conceptions of mathematical knowledge following the fundamentalist crisis in mathematics; and in the educational context of mathematics. The investigation of the first focus is done analyzing new claims in mathematical philosophy. The investigation of the second focus is done firstly via a theoretical reflection followed by an examination of the implementation of the proposal in the process of development of didactic materials for teaching and learning Mathematics. Finally, we present the main results of the application of one of those materials.

A matemática nos cursos profissionalizantes de mecânica

Pós-graduação em Educação Matemática - IGCE

A atualização do projeto pedagógico nos cursos de formação de professores de matemática nos anos iniciais do ensino fundamental: licenciatura em pedagogia e licenciatura em matemática

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Matemática financeira: um enfoque da resolução de problemas como metodologia de ensino e aprendizagem

Pós-graduação em Educação Matemática - IGCE

Os Processos de visualização e de representação dos signos matemáticos no contexto didático-pedagógico

Pós-graduação em Educação Matemática - IGCE