Phenomenological perspective on mathematics education

This is a philosophical essay on a phenomenological way to understand and to work out Mathematics Education. Its philosophical grounding is the Husserlian work, focusing on its key word "going to the things themselves" in order to keep us away from the theoretical educational truth, took as the unique one. We assume the attitude of being on the life-world with the students and Mathematics as a field of research and practice that show and express themselves through lived experiences and through language. We assume to be in search of understanding of education, learning and Mathematics, as we take care, consciously, of what we are doing and saying in the same movement of saying and doing it.

Gaussian extended cubature formulae for polyharmonic functions

The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses ℳ values of linear functional (integrals over hyperspheres) and is exact for all 2ℳ-harmonic functions, and consequently, for all algebraic polynomials of n variables of degree 4ℳ - 1.

Maturity degree of composts from municipal solid wastes evaluated by differential scanning calorimetry

Differential scanning calorimetry (DSC) in association with chemical analysis was applied to assess the maturity reached by the organic fraction of Municipal Solid Wastes (MSW) subjected to composting processes with manual and fixed aeration and sampled at different composting times. Thermograms showed that the difference in the treatments, i.e., the manual aeration and the fixed aeration, had no relevant effect on the stabilization and maturation of OM in the substrates. Common thermal effects observed were: a low temperature endotherm assigned to dehydration and/or loss of peripheral polysaccharides chains; a medium temperature exotherm assigned to loss of peptidic structures, and a high temperature exotherm assigned to oxydation and polycondensation of aromatic nuclei of the molecule. Results obtained suggest that in the experimental conditions used, a shorter time of composting (about 30 d) appears adequate, in order to limit the extended mineralization of OM, whereas a prolonged composting time (up to 132 d) would produce a compost of poor quality with high ash content and low OM content.

Degree of conversion and molecular weight of one denture base and three reline resins submitted post-polymerization treatments

The effect of post-polymerization treatments (MW-microwave irradiatron and WB-water-bath) on the degree of conversion (DC) of three reline resins (Ufi Gel hard-U, Kooliner-K, and Tokuso Rebase Fast-T) and one denture base resin (Lucitone 550-L), submitted to two polymerization cycles (LS-short and LL-long), was evaluated by using FT-Raman spectroscopy (n = 5). The molecular weight (Mw) of the powder of all materials and of K polymerized specimens (control; MW; and WB; n = 3) was analyzed using GPC. DC data were analyzed using Kruskal-Wallis test (α = .05). For control specimens, there were no significant differences between U (68%) and LL (77%) and among LL, K (81%), and T (84%). LS (92%) had the highest DC (P<0.05). Only material K exhibited an increased DC after WB (P<0.05). All powders had Mw from 4.0 × 105 to 6.5 × 105 and narrow Mw distributions (2.1 to 3.6). Polymerization and post-polymerization produced K specimens with Mw similar to that of K powder.

Changes on degree of conversion of dual-cure luting light-cured with blue LED

The indirect adhesive procedures constitute recently a substantial portion of contemporary esthetic restorative treatments. The resin cements have been used to bond tooth substrate and restorative materials. Due to recently introduction of the self-bonding resin luting cement based on a new monomer, filler and initiation technology has become important to study the degree of conversion of these new materials. In the present work the polymerization reaction and the filler content of dual-cured dental resin cements were studied by means of infra-red spectroscopy (FT-IR) and thermogravimetry (TG). Twenty specimens were made in a metallic mold (8 mm diameter × 1 mm thick) from each of 2 cements, Panavia® F2.0 (Kuraray) and RelyX™ Unicem Applicap (3M/ESPE). Each specimen was cured with blue LED with power density of 500 mW/cm 2 for 30 s. Immediately after curing, 24 and 48 h, and 7 days DC was determined. For each time interval 5 specimens were pulverized, pressed with KBr and analyzed with FT-IR. The TG measurements were performed in Netzsch TG 209 under oxygen atmosphere and heating rate of 10°C/min from 25 to 700°C. A two-way ANOVA showed DC (%) mean values statistically significance differences between two cements (p < 0.05). The Tukey's test showed no significant difference only for the 24 and 48 h after light irradiation for both resin cements (p > 0.05). The Relx-Y™ Unicem mean values were significantly higher than Panavia® F 2.0. The degree of conversion means values increasing with the storage time and the filler content showed similar for both resin cements. © 2009 Pleiades Publishing, Ltd.

Potential scenarios for Internet use in the mathematics classroom

Research on the influence of multiple representations in mathematics education gained new momentum when personal computers and software started to become available in the mid-1980s. It became much easier for students who were not fond of algebraic representations to work with concepts such as function using graphs or tables. Research on how students use such software showed that they shaped the tools to their own needs, resulting in an intershaping relationship in which tools shape the way students know at the same time the students shape the tools and influence the design of the next generation of tools. This kind of research led to the theoretical perspective presented in this paper: knowledge is constructed by collectives of humans-with-media. In this paper, I will discuss how media have shaped the notions of problem and knowledge, and a parallel will be developed between the way that software has brought new possibilities to mathematics education and the changes that the Internet may bring to mathematics education. This paper is, therefore, a discussion about the future of mathematics education. Potential scenarios for the future of mathematics education, if the Internet becomes accepted in the classroom, will be discussed. © FIZ Karlsruhe 2009.

An efficient codification to solve distribution network reconfiguration for loss reduction problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)