Detotaliseerimine ja tagasiulatuv jõud: musta püramiidi semiootika

Väitekirja üldiseks probleemiks on semiootika integreeritavus. Detotalisatsioon kirjeldab semiootikatraditsiooni, mille kohaselt suletud terviklikkus pole võimalik, ning mis oma põhiliste teoreetiliste koordinaatidena näeb psühhoanalüüsi, ideoloogia kriitikat ja strukturaalset semioloogiat. Oluliseks analüüsivahendiks on autori poolt välja töötatud nn “musta püramiidi” skeem-mudel, mille abil otsitakse vastust küsimusele: kuidas saab puhtdiferentsiaalne, erinevustel põhinev (internaalne) süsteem suhestuda välisega (eksternaalsega)? Järgnevalt jõutakse semiootikas esineva subjektiivse relativismi kriitikani ja võetakse kasutusele retroaktiivsuse mõiste, mille kaudu kirjeldatakse väliseid mõjusid. Semiootika osavaldu vaadeldakse retroaktiivsuse toimimise aspektist. “Musta püramiidi” skeem-mudel ühendab hübriidselt Peirce’i ja Hjelmslev’ semiootikat, integreerides Peirce’i detotalisatsiooniga. Skeem eristab märgifunktsiooni ja märgiproduktsiooni ala ning selle jaotuse kaudu sulandab Peirce’i trihhotoomia kokku Saussure’i dihhotoomiaga. Taolisel sünteesil on kaks eelist. Esmalt on detotalisatsiooni subjektivistlik relativism ankurdatud kognitiivsemiootika ja biosemiootika empiiriliste ja loogiliste rakenduste poolt. Teisalt on kognitiivsemiootika ja biosemiootika rikastatud retroaktiivsuse tekstiliste protseduuridega, mis võimaldab ligipääsu välisele ilma märgi määratlust kahjustamata. Seeläbi on olemas artikulatoorse alusmaatriksi teaduslik seletus, kuid samuti vajadus teaduslikus semiootikas detotalisatsioonile iseloomuliku tekstuaalse eksperimenteerimise järele. Just retroaktiivsus on see ühendav mõiste, mis seob kaks semiootika lahusolevat valda. Integreerides ka kognitiivsemiootika ja biosemiootika detotaliseeritud semiootika pildile, pakub väitekiri kokkuvõttes mittereduktiivse ja empiirilise vastuse relativismi probleemile semiootikas, säilitades seejuures semiootika teoreetilise terviklikkuse ja pakkudes välja ühtse metakeele killustatud sotsiaalteaduste tarbeks.  Detotalization describes the tradition of semiotics which takes psychoanalysis, ideology critique, and structural semiology as its major theoretic coordinates. Interest in these coordinates has declined against the ascent of the semiotics of Charles Peirce, the two approaches are sometimes construed as irreconcilable, but the dissertation seeks to integrate Peirce to the coordinates of detotalization. This integration requires that Peirce be read in the way that Jacques Derrida and Umberto Eco propose to read him, by moderating his realism. This is achieved through theorization of the notion of retroactivity. Chapters one through four restate the coordinates of detotalization in terms of retroactivity, and chapter five searches the domains of cognitive and biosemiotics for the Peircean equivalent of retroactivity. The black pyramid schema is a picture of the Peirce-Hjelmslev hybrid, where Peirce is integrated to detotalization. In the schema, semiotics is organized by the domains of sign function and sign production, and the Peircean trichotomy is reconciled to the Saussurean dichotomy by means of this division. The synthesis has two advantages. In one direction, the subjectivist relativism of detotalization is anchored by the empirical and logical applications of cognitive and biosemiotics. In the other direction, cognitive and biosemiotics are enhanced by the textual procedures of retroactivity, which account for the external without compromising the definition of the sign by importing a naïve referent. There is a scientific explanation for the profound articulatory matrix, but there is also a need within scientific semiotics for the textual experimentation characteristic of detotalization. Retroactivity as the bridge concept between the two divided camps of semiotics also restores its original ambition, to provide a unifying vocabulary for the fractured social sciences.https://www.ester.ee/record=b540146

“TEACHING REAL NUMBERS IN THE HIGH SCHOOL: AN ONTO-SEMIOTIC APPROACH TO THE INVESTIGATION AND EVALUATION OF THE TEACHERS' DECLARED CHOICES”

The thesis addresses the topics of investigating teachers' declared choices of practices concerning real numbers and the continuum in the high school in Italy, evaluating their didactical suitability and the impact of a deep reflexion about some historical and didactical issues on the teachers' decision-making process. Our research hypothesis was that teachers' choices of teaching sequences concerning real numbers, with particular attention to the representations of real numbers, could be very relevant in order to interpret some of the well-known students' difficulties. After a pilot study in form of a teaching experiment and a literature review concerning students' and teachers' difficulties with real numbers and the continuum, we observed that some causes of potential difficulties could be situated indeed in the very beginning of the teaching-learning process, even before entering the classrooms: the phase in which a teacher choose the practices and objects by means of whom introducing and work with real numbers and the continuum. In particular the choice of the objects involved in the practice seemed to be relevant, since every object emerge from previous practices and its meaning is identified by the practices in which it emerged. Thus we got interested in investigating the personal factors that affect the process of selection of practices: personal meaning, goals and orientations, as it was stressed by Schoenfeold in his goal-oriented decision-making approach to the analysis of teachers choices. Furthermore we decided to explore the teachers' choices of sequences of practices and of representation of the mathematical objects and then to evaluate their suitability in relation to the literature review concerning students' difficulties with real numbers and to the complexity of the mathematical object as it emerge from an historical analysis. After having analysed the theoretical frameworks in mathematics education that could permit us to carry out our research, we decided to use the OSA, (onto-semiotioc approach) elaborated by Godino, Batanero & Font, described in their paper in 2007, and some evolutions like the CDM (conoscimiento didactico matematico) model proposed by Godino in 2009. We evaluated also other frameworks, in particular the ATD (Chevallard, 2014), but we found the OSA better for the analysis we would like to carry out. In particular the operationalization of the methodologies of analysis of the teachers' personal meaning of mathematical objects and the construct of didactical suitability were more effective for our porpouses. Our main results are the following: mny teachers' personal meanings of real numbers are far from the epistemic one; many of the teachers who studied real numbers at a formal level at school and at the University and perceived them as difficult and unuseful try to avoid to deepen the issues concerning real numbers with their stundent, thinking they would not understand; in general the experiences as students affect the teachers' choices; the teachers usually refer to real numbers also when the meaning is partial and doesn't coincide with one of the most general epistemic meanings of real numbers; very few teachers are aware of the complexity of the real numbers and are as aware of it to be able to control the relations between their many facets; also the teachers with a PhD in Mathematics operate choices that we can evaluate as unsuitable standing on the literature review and our framework; the teacher consider very hard to work with discrete and dense sets and prefer the intuitive approach to continuous sets rather then deepen the relation between dense and continuous sets, different degrees of infinity and so on; some teachers reasoning during the interviews changed their mind, getting aware of the complexity and admitting that simplifying too much can constitute a further cause of difficulty; the teachers refer to the students difficulties to justify their choice of simplifying, but when they face some crucial issues, often they admit to consider them unuseful or too difficult; nevertheless no teachers declare that would renounce to introduce the field of real numbers, at least intuitively; the most of the teachers declare that nothing more is introduced about real numbers in the last years and that the partial meanings introduced in the first years are used to face the Calculus problems (intuItive approach to the Calculus); all the teachers consider necessary to introduce R or adequate subsets of R as domains of the functions expressed analytically because of their continuous graphic.The thesis addresses the topics of investigating teachers' declared choices of practices concerning real numbers and the continuum in the high school in Italy, evaluating their didactical suitability and the impact of a deep reflexion about some historical and didactical issues on the teachers' decision-making process. Our research hypothesis was that teachers' choices of teaching sequences concerning real numbers, with particular attention to the representations of real numbers, could be very relevant in order to interpret some of the well-known students' difficulties. After a pilot study in form of a teaching experiment and a literature review concerning students' and teachers' difficulties with real numbers and the continuum, we observed that some causes of potential difficulties could be situated indeed in the very beginning of the teaching-learning process, even before entering the classrooms: the phase in which a teacher choose the practices and objects by means of whom introducing and work with real numbers and the continuum. In particular the choice of the objects involved in the practice seemed to be relevant, since every object emerge from previous practices and its meaning is identified by the practices in which it emerged. Thus we got interested in investigating the personal factors that affect the process of selection of practices: personal meaning, goals and orientations, as it was stressed by Schoenfeold in his goal-oriented decision-making approach to the analysis of teachers choices. Furthermore we decided to explore the teachers' choices of sequences of practices and of representation of the mathematical objects and then to evaluate their suitability in relation to the literature review concerning students' difficulties with real numbers and to the complexity of the mathematical object as it emerge from an historical analysis. After having analysed the theoretical frameworks in mathematics education that could permit us to carry out our research, we decided to use the OSA, (onto-semiotioc approach) elaborated by Godino, Batanero & Font, described in their paper in 2007, and some evolutions like the CDM (conoscimiento didactico matematico) model proposed by Godino in 2009. We evaluated also other frameworks, in particular the ATD (Chevallard, 2014), but we found the OSA better for the analysis we would like to carry out. In particular the operationalization of the methodologies of analysis of the teachers' personal meaning of mathematical objects and the construct of didactical suitability were more effective for our porpouses. Our main results are the following: mny teachers' personal meanings of real numbers are far from the epistemic one; many of the teachers who studied real numbers at a formal level at school and at the University and perceived them as difficult and unuseful try to avoid to deepen the issues concerning real numbers with their stundent, thinking they would not understand; in general the experiences as students affect the teachers' choices; the teachers usually refer to real numbers also when the meaning is partial and doesn't coincide with one of the most general epistemic meanings of real numbers; very few teachers are aware of the complexity of the real numbers and are as aware of it to be able to control the relations between their many facets; also the teachers with a PhD in Mathematics operate choices that we can evaluate as unsuitable standing on the literature review and our framework; the teacher consider very hard to work with discrete and dense sets and prefer the intuitive approach to continuous sets rather then deepen the relation between dense and continuous sets, different degrees of infinity and so on; some teachers reasoning during the interviews changed their mind, getting aware of the complexity and admitting that simplifying too much can constitute a further cause of difficulty; the teachers refer to the students difficulties to justify their choice of simplifying, but when they face some crucial issues, often they admit to consider them unuseful or too difficult; nevertheless no teachers declare that would renounce to introduce the field of real numbers, at least intuitively; the most of the teachers declare that nothing more is introduced about real numbers in the last years and that the partial meanings introduced in the first years are used to face the Calculus problems (intutive approach to the Calculus); all the teachers consider necessary to introduce R or adequate subsets of R as domains of the functions expressed analytically because of their continuous graphic