Reasoning and proof in classroom (9th grade)

This paper is research oriented and pretends to contribute toward giving empirical evidence about how students develop their reasoning and how they achieved to a proof construction in school context. Its main theme is epistemology. It describes the way in which four students in 9th Grade explored a task related with the discovery of symmetry axes in various geometric figures. The proof constructed by students had essentially an explaining function and it was related with the symmetry axes of regular polygons. The teacher’s role in meaning negotiation of the proof and its need is described through illustrative episodes. The paper presents part of a study which purpose is to analyse the nature of mathematical proof in classroom, its role and the nature of the relationship between the construction of a proof and the social interactions. Assuming a social perspective, attention is focussed on the social construction of knowledge and on the structuring resources that shape mathematical experience. The study’s methodology has an interpretative nature. One outcome of the study discussed here is that students develop first a practical understanding with no awareness of the reasons founding mathematical statements and after a theoretical one leading them to a proof elaboration.

Producing an explanatory proof in a 9th grade classroom

Este artigo apresenta parte de um estudo fundamentado na problemática da demonstração na matemática escolar. Descreve o modo como quatro alunos do 9.º ano exploraram uma tarefa relacionada com a descoberta de eixos de simetria em várias figuras geométricas. A demonstração, que os mesmos construíram, teve essencialmente uma função explicativa. O papel da professora na negociação do significado de demonstração e da sua necessidade é igualmente analisado. Os alunos desenvolvem primeiro uma compreensão prática sem consciência das razões que fundamentam as afirmações matemáticas e só depois uma compreensão teórica que os conduz à construção de uma demonstração.

Differential expression of the eukaryotic release factor 3 (eRF3/GSPT1) according to gastric cancer histological types

Background: There are now several lines of evidence to suggest that protein synthesis and translation factors are involved in the regulation of cell proliferation and cancer development. Aims: To investigate gene expression patterns of eukaryotic releasing factor 3 (eRF3) in gastric cancer. Methods: RNA was prepared from 25 gastric tumour biopsies and adjacent non-neoplastic mucosa. Real time TaqMan reverse transcription polymerase chain reaction (RT-PCR) was performed to measure the relative gene expression levels. DNA was isolated from tumour and normal tissues and gene dosage was determined by a quantitative real time PCR using SYBR Green dye. Results: Different histological types of gastric tumours were analysed and nine of the 25 tumours revealed eRF3/GSPT1 overexpression; moreover, eight of the 12 intestinal type carcinomas analysed overexpressed the gene, whereas eRF3/GSPT1 was overexpressed in only one of the 10 diffuse type carcinomas (Kruskal-Wallis Test; p , 0.05). No correlation was found between ploidy and transcript expression levels of eRF3/GSPT1. Overexpression of eRF3/GSPT1 was not associated with increased translation rates because the upregulation of eRF3/GSPT1 did not correlate with increased eRF1 levels. Conclusions: Overexpression of eRF3/GSPT1 in intestinal type gastric tumours may lead to an increase in the translation efficiency of specific oncogenic transcripts. Alternatively, eRF3/GSPT1 may be involved in tumorigenesis as a result of its non-translational roles, namely (dis)regulating the cell cycle, apoptosis, or transcription.

The histopathological approach to inflammatory bowel disease: a practice guide

Inflammatory bowel diseases (IBDs) are lifelong disorders predominantly present in developed countries. In their pathogenesis, an interaction between genetic and environmental factors is involved. This practice guide, prepared on behalf of the European Society of Pathology and the European Crohn's and Colitis Organisation, intends to provide a thorough basis for the histological evaluation of resection specimens and biopsy samples from patients with ulcerative colitis or Crohn's disease. Histopathologically, these diseases are characterised by the extent and the distribution of mucosal architectural abnormality, the cellularity of the lamina propria and the cell types present, but these features frequently overlap. If a definitive diagnosis is not possible, the term indeterminate colitis is used for resection specimens and the term inflammatory bowel disease unclassified for biopsies. Activity of disease is reflected by neutrophil granulocyte infiltration and epithelial damage. The evolution of the histological features that are useful for diagnosis is time- and disease-activity dependent: early disease and long-standing disease show different microscopic aspects. Likewise, the histopathology of childhood-onset IBD is distinctly different from adult-onset IBD. In the differential diagnosis of severe colitis refractory to immunosuppressive therapy, reactivation of latent cytomegalovirus (CMV) infection should be considered and CMV should be tested for in all patients. Finally, patients with longstanding IBD have an increased risk for the development of adenocarcinoma. Dysplasia is the universally used marker of an increased cancer risk, but inter-observer agreement is poor for the categories low-grade dysplasia and indefinite for dysplasia. A diagnosis of dysplasia should not be made by a single pathologist but needs to be confirmed by a pathologist with expertise in gastrointestinal pathology.