Filippo Spagnolo

Confocal microscopy study of the distribution, content and activity of mitochondria during Paracentrotus lividus development

In the present paper we applied confocal microscopy and fluorescence technologies for studying the distribution and the oxidative activity of sea urchin (Paracentrotus lividus) mitochondria during development, by in vivo incubating eggs and embryos with cell‐permeant MitoTracker probes. We calculated, by a mathematical model, the intensity values, the variations of intensity, and the variation index of incorporated fluorochromes. Data demonstrate that mitochondrial mass does not change during development, whereas mitochondrial respiration increases. In addition, starting from 16 blastomeres stage, some regions of the embryo contain organelles more active in oxygen consumption.

A new approach in Zadeh's classification: Fuzzy implication through statistic implication

In relationship to the classification of the various approaches to the fuzzy logic of Zadeh (possibilistic, probabilistic, veristic) [14] the implication according to Gras is introduced as a new approach with its own characteristics. The notion of statistical implication is based on the statistical comparison between the inclusion of sets observed in a population and one that would have comparable sets, but chosen casually in the same population. Such an approach has to do with, in particular, variables-intervals. Therefore, it is suitable for representing fuzzy implication. The experimental comparison with classic fuzzy implications (Reichenbach and Lukasievicz) confirms a better semantic adequacy. The implicative methods are implemented in the statistic software (CHIC 3.1). The new epistemological perspective opens interesting application perspectives. The implication of variables of interval of Gras is neither completely descriptive nor completely inferential. We are in the presence of a new epistemological approach to fuzzy implication. The implication of Gras keeps in mind richer semantics when it is experimentally compared with other classical implications such as that of Reichenbach and Lukasiewicz. This type of implication can perhaps have some more interesting results in the applications of the Artificial Intelligence.

Modelling by Statistic in Research of Mathematics Education

Summary. The aim of this paper is to study the quantitative tools of the research in didactics. We want to investigate the theoretical-experimental relationships between factorial and implicative analysis. This chapter consists of three parts. The first one deals with the didactic research and some fundamental tools: the a priori analysis of a didactic situation, the collection of experimental data and the statistic analysis of data. The purpose of the second and the third section is to introduce the experimental comparison between the factorial and the implicative analysis in two researches in mathematics education.

The Chinese Written Language as Tool for a Possible Historical and Epistemological Reflections on the Mathematics and the Impact of Teaching/Learning of Mathematics

Strong and undisputed vector of the Chinese cultural tradition has been (till now), as told in the preceding chapters, its peculiar system of fixation grafemica.

The Experimental Epistemology as a Tool to Observe and Preview Teaching/Learning Phenomena

In previous chapters, we discussed some general considerations of epistemological nature, and in this chapter, we introduce two groups of investigations of experimental behaviors in the years and in the spirit of the experimental epistemology of mathematics. The first group refer to an experiment conducted with Palermo and Nanchino students of Superior Secondary School on the comparison of the schemes of reasoning regarding the logical–linguistic paradoxes in this two cultures. The analysis of two cases is introduced, then one of which had already been analyzed for about a year in 1984/85.

Strategy and Tactics in the Chinese and European Culture: Chess and Weich’i

In previous chapters we observed that hypothetic-deductive reasoning may represent in western culture a fundamental reference for “strategic” choices. It is concerned with maths and also with other cultural contexts including economy. What for Chinese Culture?

The Meta-rules between Natural Language and History of Mathematics

Before going on to outline teaching, we need a short historical–epistemological process that can draw criticism, quite basic, the key stages of the long journey and suffered from the trend on Algebra as the Arithmetic. We believe the combination of arithmetic-algebra as significant for the relationship between mathematical thinking. Considerations should be made parallel to the geometric area in which we mention in the discussion of the chapter but that remains an issue open to possible future theoretical and experimental investigations.

Common Sense and Fuzzy Logic

As mentioned in Chapter 1, it is our opinion we that believe different types of logic can lead to different patterns of reasoning. Examples are the use of the logic of a bivalent and fuzzy set of argumentation in stages used in mathematical contexts and beyond. This observation may be significant, in our opinion, problem addressed and on the integration of different cultural references. With this conviction, we believe useful in discussing, albeit briefly, some significant aspects of common sense and fuzzy logic. This chapter presents considerations within epistemological nature validated by experimental investigations conducted in the classroom in Palermo. It remains open to the interpretation of the results obtained from a comparison of cognitive styles between Chinese and Italian.

Rhythm and Natural Language in the Chinese and European Culture

Appendix 2 of Chapter 6 has been taken into account the classification of the arts in the two main cultures. In Chinese culture, the music was made in the first place: “Music, discipline related to hearing and also to sophisticated processes that regulate vibrations. It is the practice of the inner qi. It concerns also with embodiment referred to the musical rhythms. Today we know that it is related to natural language and numbers learning”. In European culture, the music is part of the quadrivium of the arts and is considered one of the sciences together with arithmetic, geometry and astronomy.