Teaching and Learning of Calculus

This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions

Quaderni di Ricerca in Didattica

Abstract In the present paper we refer to the status of the mathematics teacher in the contemporary society. In particular we consider the role that the teacher plays for the learning of mathematics and the desirable characteristics of a competent mathematics teacher. The proper professional training, that helps the acquisition and development of these characteristics is also a parameter of our investigation. Examples from Greece are used to illustrate our remarks and conclusion

Array comparative genomic hybridization-based characterization of genetic alterations in pulmonary neuroendocrine tumors

The goal of this study was to characterize and classify pulmonary neuroendocrine tumors based on array comparative genomic hybridization (aCGH). Using aCGH, we performed karyotype analysis of 33 small cell lung cancer (SCLC) tumors, 13 SCLC cell lines, 19 bronchial carcinoids, and 9 gastrointestinal carcinoids. In contrast to the relatively conserved karyotypes of carcinoid tumors, the karyotypes of SCLC tumors and cell lines were highly aberrant. High copy number (CN) gains were detected in SCLC tumors and cell lines in cytogenetic bands encoding JAK2, FGFR1, and MYC family members. In some of those samples, the CN of these genes exceeded 100, suggesting that they could represent driver alterations and potential drug targets in subgroups of SCLC patients. In SCLC tumors, as well as bronchial carcinoids and carcinoids of gastrointestinal origin, recurrent CN alterations were observed in 203 genes, including the RB1 gene and 59 microRNAs of which 51 locate in the DLK1-DIO3 domain. These findings suggest the existence of partially shared CN alterations in these tumor types. In contrast, CN alterations of the TP53 gene and the MYC family members were predominantly observed in SCLC. Furthermore, we demonstrated that the aCGH profile of SCLC cell lines highly resembles that of clinical SCLC specimens. Finally, by analyzing potential drug targets, we provide a genomics-based rationale for targeting the AKT-mTOR and apoptosis pathways in SCLC