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Some errors in the learning of algebra suggest that students might have difficulties giving meaning to algebraic symbolism. In this paper, we use problem posing to analyze the students' capacity to assign meaning to algebraic symbolism and the difficulties that students encounter in this process, depending on the characteristics of the algebraic statements given. We designed a written questionnaire composed of eight closed algebraic statements expressed symbolically, which was administered to 55 students who had finished their compulsory education and who had some previous experience in problem-posing. In our analysis of the data, we examine both syntactic and semantic structures of the problem posed. We note that in most cases students posed problems with syntactic structures different to those given. They did not include computations within variables, and changed the kinds of relationships connecting variables. Students easily posed problems for statements with additive structures. Other differences in the type of problems posed depend on the characteristics of the given statements.

The cleft palate presented by transforming growth factor-β3 (Tgf-β3) null mutant mice is caused by altered palatal shelf adhesion, cell proliferation, epithelial-to-mesenchymal transformation and cell death. The expression of epidermal growth factor (EGF), transforming growth factor-β1 (Tgf-β1) and muscle segment homeobox-1 (Msx-1) is modified in the palates of these knockout mice, and the cell proliferation defect is caused by the change in EGF expression. In this study, we aimed to determine whether this change in EGF expression has any effect on the other mechanisms altered in Tgf-β3 knockout mouse palates. We tested the effect of inhibiting EGF activity in vitro in the knockout palates via the addition of Tyrphostin AG 1478. We also investigated possible interactions between EGF, Tgf-β1 and Msx-1 in Tgf-β3 null mouse palate cultures. The results show that the inhibition of EGF activity in Tgf-β3 null mouse palate cultures improves palatal shelf adhesion and fusion, with a particular effect on cell death, and restores the normal distribution pattern of Msx-1 in the palatal mesenchyme. Inhibition of TGF-β1 does not affect either EGF or Msx-1 expression. © 2014 S. Karger AG, Basel [ABSTRACT FROM AUTHOR]

Folic acid (FA) is essential for numerous bodily functions. Its decrease during pregnancy has been associated with an increased risk of congenital malformations in the progeny. The relationship between FA deficiency and the appearance of cleft palate (CP) is controversial, and little information exists on a possible effect of FA on palate development. We investigated the effect of a 2-8 weeks' induced FA deficiency in female mice on the development of CP in their progeny as well as the mechanisms leading to palatal fusion, i.e. cell proliferation, cell death, and palatal-shelf adhesion and fusion. We showed that an 8 weeks' maternal FA deficiency caused complete CP in the fetuses although a 2 weeks' maternal FA deficiency was enough to alter all the mechanisms analyzed. Since transforming growth factor-β3 (TGF-β3) is crucial for palatal fusion and since most of the mechanisms impaired by FA deficiency were also observed in the palates of Tgf-β3null mutant mice, we investigated the presence of TGF-β3 mRNA, its protein and phospho-SMAD2 in FA-deficient (FAD) mouse palates. Our results evidenced a large reduction in Tgf-β3 expression in palates of embryos of dams fed an FAD diet for 8 weeks; Tgf-β3 expression was less reduced in palates of embryos of dams fed an FAD diet for 2 weeks. Addition of TGF-β3 to palatal-shelf cultures of embryos of dams fed an FAD diet for 2 weeks normalized all the altered mechanisms. Thus, an insufficient folate status may be a risk factor for the development of CP in mice, and exogenous TGF-β3 compensates this deficit in vitro. Copyright © 2011 S. Karger AG, Basel [ABSTRACT FROM AUTHOR]

Although palatal shelf adhesion is a crucial event during palate development, little work has been carried out to determine which molecules are responsible for this process. Furthermore, whether altered palatal shelf adhesion causes the cleft palate presented by Tgf-β3 null mutant mice has not yet been clarified. Here, we study the presence/distribution of some extracellular matrix and cell adhesion molecules at the time of the contact of palatal shelves in both wild-type and Tgf-β3 null mutant palates of two strains of mice (C57/BL/6J (C57), and MF1) that develop cleft palates of different severity. We have performed immunohistochemistry with antibodies against collagens IV and IX, laminin, fibronectin, the α5- and β1-integrins, and ICAM-1; in situ hybridization with a Nectin-1 riboprobe; and palatal shelf cultures treated or untreated with TGF-β3 or neutralizing antibodies against fibronectin or the α5-integrin. Our results show the location of these molecules in the wild-type mouse medial edge epithelium (MEE) of both strains at the time of the contact of palatal shelves; the heavier (C57) and milder (MF1) alteration of their presence in the Tgf-β3 null mutants; the importance of TGF-β3 to restore their normal pattern of expression; and the crucial role of fibronectin and the α5-integrin in palatal shelf adhesion. We thus provide insight into the molecular bases of this important process and the cleft palate presented by Tgf-β3 null mutant mice. [ABSTRACT FROM AUTHOR]

In this article we introduce and study the first cohomology categorical group ℋ1(𝔾,𝔸) of a categorical group 𝔾 with coefficients in a braided categorical group 𝔸 provided of a coherent 𝔾-action. The fundamental exact sequence connecting ℋ0 and ℋ1 in this context is then established. [ABSTRACT FROM AUTHOR]

The cleft palate presented by transforming growth factor-β3 (Tgf-β3) null mutant mice is caused by altered palatal shelf adhesion, cell proliferation, epithelial-to-mesenchymal transformation and cell death. The expression of epidermal growth factor (EGF), transforming growth factor-β1 (Tgf-β1) and muscle segment homeobox-1 (Msx-1) is modified in the palates of these knockout mice, and the cell proliferation defect is caused by the change in EGF expression. In this study, we aimed to determine whether this change in EGF expression has any effect on the other mechanisms altered in Tgf-β3 knockout mouse palates. We tested the effect of inhibiting EGF activity in vitro in the knockout palates via the addition of Tyrphostin AG 1478. We also investigated possible interactions between EGF, Tgf-β1 and Msx-1 in Tgf-β3 null mouse palate cultures. The results show that the inhibition of EGF activity in Tgf-β3 null mouse palate cultures improves palatal shelf adhesion and fusion, with a particular effect on cell death, and restores the normal distribution pattern of Msx-1 in the palatal mesenchyme. Inhibition of TGF-β1 does not affect either EGF or Msx-1 expression., (© 2014 S. Karger AG, Basel.)

Transforming growth factor-beta3 (TGF-beta3) plays a critical role during palate development, since mutations of the TGF-beta3 gene give rise to cleft palate in both humans and mice. Striking alterations have been reported in the behaviour and differentiation of medial edge epithelial (MEE) cells in TGF-beta3 knockout mouse palates. In the present paper, we provide evidence of alterations in MEE intercellular adhesion in TGF-beta3 -/- mouse palates using immunohistochemistry with monoclonal antibodies to a panel of cell adhesion and cytoskeletal molecules including E-cadherin, alpha and beta catenin, beta actin, vinculin and beta2 integrin. In vitro labeling of opposing MEE with two different lipophilic markers and subsequent analysis by confocal microscopy revealed that wild type MEE cells intercalate as soon as the midline epithelial seam forms. This finding indicates that the palate may elongate in a dorso-ventral direction by means of convergent extension, as occurs in other embryonic developmental processes. In contrast, this intercalation does not occur in the TGF-beta3 -/- MEE but it can be rescued by the exogenous addition of TGF-beta3. Thus, the substantial alteration of MEE intercellular adhesion observed in TGF-beta3 -/- palates may account for the defect in palatal shelf adhesion and the formation of cleft palate.