Mobilizing histories in mathematics teacher education: memories, social practices, and discursive games

In the first part of this paper, we share and elucidate the way we mobilize histories in some disciplines that are part of the undergraduate courses in mathematics teacher education offered by State University of Campinas and Federal University of Rio Grande do Norte in Brazil. This way of mobilization can be featured as a set of collective indisciplinary problematizations occurring in a series of student investigations. Mobilizing practices of mathematics culture are the object of these investigations. These practices are performed by different communities both constituted by and constituent of different human activities. In the second part of this paper, we will discuss our way of mobilizing histories, contrasting it with the theoretical perspective of expansive learning, just as it has been defended by Yrjö Engeström, in his article Non scolae sed vitae discimus—towards overcoming the encapsulation of school learning. We will also attempt to highlight the role which this researcher has attributed to history in his model of expansive learning, a perspective based on the current research on activity theory.     

The use of anhydrous CeCl3 as a catalyst for the synthesis of 3-sulfenyl indoles

Anhydrous CeCl₃ was successfully used as a catalyst for the synthesis of several 3-sulfenyl indoles in good to excellent yields through the reaction of indole with N-(alkylthio) and N-(arylthio)phthalimides in DMF.     

Rational Surfaces with Many Nodes

We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain n b ₂ –2 disjoint smooth rational curves with self-intersection –2, where b ₂ is the second Betti number. In the last section this is applied to the study of minimal complex surfaces of general type with p _g = 0 and K² = 8, 9 which admit an automorphism of order 2.     

Formal fusion of a pyrrole ring onto 2-pyridyl and 2-pyrimidyl cations: one-step gas-phase synthesis of indolizine and its derivatives

Two ortho-hetarynium ions, the 2-pyridyl and 2-pyrimidyl cations, react promptly with 1,3-dienes in the gas phase by annulation, formally by fusion, onto the ions of a pyrrole ring. This novel reaction proceeds through an initial polar [4 + 2+] cycloaddition across the C[triple bond]N+ bond, followed by fast ring opening, a [1,4-H] shift, and finally a recyclization that results in a contraction of a six- to a five-membered ring and dissociation by the loss of a methyl radical. For the 2-pyridyl cation, this reaction yields ionized indolizines (pyrrolo[1,2-a]pyridines), while for the 2-pyrimidyl cation, it gives ionized pyrrolo[1,2-a]pyrimidines. The annulation reaction, performed in the rf-only collision quadrupole of a pentaquadrupole (QqQqQ) mass spectrometer, occurs readily with both 1,3-butadiene and isoprene, and is thermodynamically and kinetically favored as predicted by ab initio calculations. Ortho-hetarynium ions and 1,3-dienes provide, therefore, the two building blocks for the efficient one-step gas-phase synthesis of ionized bicyclic pyrrolo[1,2-a]pyridine (indolizine) and pyrrolo[1,2-a]pyrimidine, as well as their analogues and derivatives.     

Substituent Effects on Hydrogen Bonding in Watson–Crick Base Pairs. A Theoretical Study

We have theoretically analyzed Watson–Crick AT and GC base pairs in which purine C8 and/or pyrimidine C6 positions carry a substituent X = H, F, Cl or Br, using the generalized gradient approximation (GGA) of density functional theory at BP86/TZ2P. The purpose is to study the effects on structure and hydrogen bond strength if X = H is substituted by a halogen atom. Furthermore, we wish to explore the relative importance of electrostatic attraction versus orbital interaction in the above multiply hydrogen-bonded systems, using a quantitative bond energy decomposition scheme. We find that replacing X = H by a halogen atom has relatively small yet characteristic effects on hydrogen bond lengths, strengths and bonding mechanism. In general, it reduces the hydrogen-bond-accepting- and increases the hydrogen-bond-donating capabilities of a DNA base. The orbital interaction component in these hydrogen bonds is found for all substituents (X = H, F, Cl, and Br) to contribute about 41% of the attractive interactions and is thus of the same order of magnitude as the electrostatic component, which provides the remaining 59% of the attraction.     

Influence of cobalt complex on thermal properties of poly(ethylene terephthalate)/polycarbonate blend

The effects of processing time and concentration of cobalt acetylacetonate III complex in poly(ethylene terephthalate)/polycarbonate reactive blending were investigated. The blend was prepared in an internal mixer at 270°C, 60 rpm, at different processing times (5–20 min) and catalyst concentration (0.00625–0.075 mass%). The reaction product was evaluated by differential scanning calorimetry (DSC), thermogravimetry (TG) and wide angle X-rays scattering (WAXS). In general, the DSC curves showed two glass transition temperatures (T _g’s) close to each homopolymer, independent of the processing time and complex’s concentration, suggesting the presence of two phases: one rich in PET and other one rich in PC. In all cases, melting temperature (T _m), cold crystallization temperature (T _cc) and crystallinity degree (X _c) were progressively reduced with blending conditions. The TG curves presented two decays. The first one represented the PET rich phase and the other one was related to the PC phase. The WAXS diffractograms showed that the Bragg’s angle and interplanar spacing of PET remaining practically unchanged.     

Hydrogenation of oleic acid over sol-gel ruthernium catalysts

The hydrogenation of oleic acid to oleyl alcohol over Ru-alumina and Ru−Sn-alumina sol-gel catalysts has been studied. It was found that, besides its hydrogenation activity, the Ru−Sn-alumina catalyst promotes thecis-trans isomerization of the unsaturated acid. This effect is used to explain some kinetic features of the system, like the high induction time observed in the formation of alcohols, and to re-examine the role of tin.     

New crystals in the lithium sulfate family

The preparation and structures of caesium lithium sulfate, Cs_1.15Li_2.85(SO₄)₂, and caesium lithium rubidium sulfate, Cs_0.90Li_2.88Rb_0.22(SO₄)₂, are described and discussed in the context of simple and double sulfate polymorphism. The latter structure is related to the former through the substitution of Rb for Cs. In both crystals, the sulfate ions occupy two non‐equivalent sites, but the ions are disordered in Cs_1.15Li_2.85(SO₄)₂.     

Platinum(II) complexes of 2-, 3-, and 4-formyl-pyridine thiosemicarbazone and 2-, 3- and 4-acetyl-pyridine thiosemicarbazone

Seven platinum(II) complexes isolated from thiosemicarbazones derived from 2-, 3- and 4-formylpyridine and 2-, 3-, and 4-acetylpyridine have been characterised by microanalyses, molar conductivities and by their i.r. and ¹H-n.m.r. spectra.