Η λεκάνη του ποταμού Γλαύκου εκτείνεται επί των δυτικών κλιτύων του Παναχαϊκού, στο ΒΔ/κό τμήμα του νομού Αχαΐας, NA/κά της πόλης των Πατρών καταλαμβάνοντας συνολική έκταση 101,67 Km2 και αποτελεί την κύρια πηγή κάλυψης των υδατικών αναγκών της. Χαρακτηρίζεται από μέτρια ανάπτυξη υδρογραφικού δικτύου δενδριτικού τύπου αποστράγγισης και κατά συνέπεια υψηλή διαπερατότητα των πετρωμάτων και σημαντική κατείσδυση, σε βάρος της επιφανειακής απορροής. Οι σπουδαιότεροι από τους χείμαρρους που διαρρέουν την περιοχή έρευνας είναι ο Ξηροπόταμος, ο Φίλιουρας, η Σούτα, του Βερβενίου και το Ελεκιστριάνικο, οι οποίοι συμβάλουν εντός του Γλαύκου. Το αλπικά πτυχωμένο υπόβαθρο της λεκάνης περιλαμβάνει μια ακολουθία προορογενετικών ιζημάτων (πελαγικοί ασβεστόλιθοι, ραδιολαρίτες, κ.α.) της ζώνης Πίνδου, και μια συνορογενετική κλαστική ακολουθία (φλύσχης), που αποτελείται από εναλλαγές ιλυολίθων, ψαμμιτών και σπανιότερα κροκαλοπαγών. Τα στρώματα της ζώνης Πίνδου αναδύθηκαν με την τελική φάση των πτυχώσεων στο Κάτω Ολιγόκαινο, όπου έλαβε χώρα η επώθηση της Πίνδου, υπό μορφή καλύμματος, πάνω στη ζώνη Γαβρόβου – Τριπόλεως. Τα μέτωπα των επωθήσεων μεταξύ των λεπιών και οι άξονες των πτυχώσεων έχουν διεύθυνση ΒΔ – ΝΑ με κατεύθυνση της κίνησης από τα ανατολικά προς τα δυτικά και άμεση σχέση με την πλειονότητα των καρστικών πηγών. Στην περιοχή του Πατραϊκού κόλπου επικρατεί ένα ρομβοειδές σύστημα ρηγμάτωσης με μεγάλης κλίσης και ΑΒΑ/κής και ΔΒΔ/κής διεύθυνσης κανονικά ρήγματα που δημιουργεί ένα μωσαϊκό κατατεμαχισμένων τεκτονικών μπλοκ και μια γενική ανύψωση της περιοχής που συνεχίζεται μέχρι σήμερα. Τη διάνοιξη των κοιλάδων της ευρύτερης περιοχής έρευνας, η οποία συχνά συνοδεύεται από κατολισθήσεις, την καθορίζουν 4 δέσμες νεοτεκτονικών ρηγμάτων, ΒΔ/κής, ΒΑ/κής, ΔΒΔ/κής, και ΒΒΑ/κής διεύθυνσης. Το Πλειοτεταρτογενές επικάλυμμα που εμφανίζεται στην παράκτια και λοφώδη περιοχή αποτελείται από δύο λιθοστρωματογραφικές ενότητες. Η κατώτερη συνίσταται από αργίλους και άμμους, που αποτέθηκαν σε ένα λιμναίο έως υφάλμυρο περιβάλλον ιζηματογένεσης κατά τη διάρκεια του Πλειόκαινου έως το Κατώτερο Πλειστόκαινο και η ανώτερη από Καλάβριας ηλικίας δελταϊκά και χερσαία κροκαλοπαγή. Γενικά οι προσχώσεις χαρακτηρίζονται από λιθολογική ανομοιομορφία τόσο κατά την κατακόρυφη όσο και κατά την οριζόντια διεύθυνση και το πάχος τους παρουσιάζει βαθμιαία αύξηση από τα βορειότερα και νοτιότερα όρια προς το κεντρικό τμήμα της λεκάνης, όπου και υπερβαίνει τα 200 μ. Το ετήσιο ύψος βροχόπτωσης (1071 mm) στην περιοχή έρευνας είναι αρκετά υψηλό για τα δεδομένα της χώρας μας και κυμαίνεται από 640 – 900 mm στις πεδινές περιοχές, ενώ στις ορεινές περιοχές φθάνει τα 1560 mm. Τα τελευταία χρόνια παρουσιάζεται μια εποχιακή μετακίνηση των βροχοπτώσεων από τον χειμώνα προς την άνοιξη και το φθινόπωρο, η οποία συνεπάγεται απώλεια του διαθέσιμου νερού της ενεργής κατείσδυσης, λόγω αυξημένης εξατμισοδιαπνοής. Από υδρολογικής άποψης η λεκάνη του Γλαύκου δέχεται ετησίως κατά μέσο όρο 108,89 106 m3 νερού από βροχόπτωση, εκ’ των οποίων ποσοστό 48,9 % επανέρχεται στην ατμόσφαιρα με τις διαδικασίες της εξάτμισης και διαπνοής, 28,6 % απορρέει επιφανειακά και 22,5 % κατεισδύει, κυρίως σε σημαντικούς από υδρογεωλογική άποψη σχηματισμούς (ασβεστόλιθους και τεταρτογενείς αποθέσεις). Χαρακτηριστικό υδρογεωλογικό γνώρισμα της περιοχής έρευνας αποτελούν οι ημιαυτόνομες υδρογεωλογικά καρστικές ενότητες, που αναπτύσσονται λόγω της λεπιοειδούς και ρηξιγενούς τεκτονικής στην περιοχή και διαφοροποιούν την κίνηση του υπόγειου νερού. Σχετικά με τις προσχωματικές αποθέσεις του Τεταρτογενούς ο ελεύθερος υδροφόρος ορίζοντας της ανώτερης ζώνης κάμπτεται προοδευτικά και μεταπίπτει σε επάλληλους υπό πίεση υδροφόρους ορίζοντες στην παράκτια ζώνη. Στις αρχές της δεκαετίας του ’90 στην παράκτια περιοχή, λόγω της υπεράντλησης, διαπιστώθηκαν αρνητικές τιμές της πιεζομετρικής επιφάνειας σε απόσταση έως 3 Κm από την ακτή, με συνέπεια την αλμύρινση του προσχωματικού υδροφόρου από τη διείσδυση της θάλασσας. Η μείωση των αντλήσεων στα μέσα της δεκαετίας του ’90 οδήγησαν στην άνοδο των πιεζομετρικών στάθμεων και στην επανεμφάνιση φαινομένων αρτεσιανισμού των γεωτρήσεων της παράκτιας ζώνης. Από την επεξεργασία των αντλητικών δεδομένων διαπιστώθηκε η εμφάνιση υψηλών τιμών του συντελεστή της υδραυλικής αγωγιμότητας τόσο στους προσχωματικούς υδροφόρους της παράκτιας ζώνης, όσο και στους καρστικούς σχηματισμούς. Μικρότερες ταχύτητες κίνησης του υπόγειου νερού εμφανίζουν οι υδροφόροι των αποθέσεων του Νεογενούς, αλλά και των προσχώσεων της νότιας όχθης του ποταμού Γλαύκου σε σχέση με αυτούς της βόρειας όχθης, λόγω της επικράτησης των λεπτομερών έναντι των αδρομερών υλικών. Ο σημαντικότερος παράγοντας τροφοδοσίας του προσχωσιγενή υδροφόρου της λεκάνης του Γλαύκου είναι η πλευρική τροφοδοσία κατά μήκος της κοίτης του ποταμού και εν’ συνεχεία αυτός της πλευρικής τροφοδοσίας από τους ασβεστόλιθους, ενώ λιγότερο σημαντικοί εμφανίζονται οι παράγοντες του απευθείας κατεισδύοντος νερού από τις βροχοπτώσεις και από το περίσσευμα του προς αρδευτική χρήση νερού. Με βάση το ισοζύγιο εισροών – εκροών των προσχωματικών υδροφόρων της λεκάνης του Γλαύκου, για τα υδρολογικά έτη 1999 – 2002 προέκυψε μέσο ετήσιο πλεόνασμα 6,5*106 m3 νερού. Γενικά, αν εξαιρεθεί η παράκτια ζώνη της λεκάνης του Γλαύκου, η ποιότητα του νερού των προσχωσιγενών υδροφόρων, καθώς και των νεογενών αποθέσεων, αλλά και των καρστικών σχηματισμών της λεκάνης, κρίνεται καλή. Στην πλειονότητά τους τα υπόγεια νερά, όπως και τα επιφανειακά και τα πηγαία, εμφάνιζαν τον τύπο Ca-HCO3, που περιλαμβάνει γενικά νερά με καλή τροφοδοσία και ανανέωση κυρίως κατά μήκος των αξόνων αποστράγγισης. Η χωροχρονική μετακίνηση της ζώνης υφαλμύρινσης στην παράκτια ζώνη, την περίοδο 1999 – 2002, διαπιστώθηκε εκτός από την αυξημένη κατανομή διάφορων ιόντων και με την χρησιμοποίηση των συντελεστών S.A.R., Revelle και Schoeller, αλλά και των λόγων rBr-/rCl- και rBr-/rI-. Στη διάρκεια της περιόδου 1999 – 2002, προέκυψε μια αισθητή μείωση της ρύπανσης από τη διείσδυση θαλασσινού νερού στην παράκτια περιοχή. Σημαντικό ρόλο στην επιτάχυνση του ρυθμού της αποκατάστασης των παράκτιων υδροφόρων της λεκάνης του Γλαύκου διαδραμάτισε η πληθώρα γεωτρήσεων αυτόματης ροής στην παράκτια ζώνη, οι οποίες παροχετεύουν περί τα 3,5*106 m3 ρυπασμένου νερού, σε ετήσια βάση, προς τη θάλασσα. Η θέση και η χωροχρονική μετακίνηση της ζώνης υφαλμύρινσης στην παράκτια ζώνη διαπιστώθηκε επίσης από γεωηλεκτρικές έρευνες που πραγματοποιήθηκαν με τις διατάξεις Schlumberger, Wenner – Schlumberger και Pole – Pole. Από τη γεωηλεκτρική έρευνα διαπιστώθηκε ότι η διείσδυση του υφάλμυρου νερού σπανίως εμφανίζεται με τη μορφή μετώπου, αλλά ακολουθεί επιλεκτικές οδούς μέσω των αδρομερέστερων σχηματισμών, ενώ οι λεπτομερείς αργιλικοί σχηματισμοί παίζουν τον ρόλο υδραυλικού φραγμού. Τέλος, με τη μέθοδο της σεισμικής ανάκλασης προσδιορίστηκαν η γεωμετρία και το βάθος συνάντησης του υποβάθρου στην παράκτια ζώνη. Επισημαίνεται η ανάγκη τεχνητού εμπλουτισμού του προσχωσιγενή υδροφόρου ορίζοντα με τις χειμερινές απορροές του Γλαύκου για την ταχύτερη αποκατάσταση της ποιότητας του νερού και την αύξηση του υδατικού δυναμικού της λεκάνης. Εφαρμόστηκε η μέθοδος DRASTIC για την εκτίμηση της τρωτότητας των υπόγειων νερών απέναντι σε εξωτερική ρύπανση, όπου με βάση τις τιμές του δείκτη DRASTIC κατασκευάστηκε χάρτης τρωτότητας της περιοχής. Περιοχές υψηλής τρωτότητας εντοπίζονται στο παράκτιο τμήμα του υδροφορέα, ενώ αντίθετα περιοχές μέσης τρωτότητας στο Α/κό τμήμα του υδροφορέα. Τέλος, κατασκευάστηκε μαθηματικό ομοίωμα των υδροφορέων της προσχωματικής λεκάνης του Γλαύκου με την εφαρμογή του κώδικα MODFLOW παρέχοντας έτσι ένα όσο το δυνατόν πιο αξιόπιστο πρότυπο διαχείρισης του υπόγειου υδατικού δυναμικού της περιοχή έρευνας. / The Glafkos’ river basin is extended on the west side of the Panaxaikon mountain in the northwest area of the prefecture of Achaia, southeast of the city of Patras, occupying a total extent of 101,67 Km2 and constituting the main source of Patras’ water needs. It is characterized by the mediocre growth of the hydrographical network (a dendrite type of draining) and consequently the high permeability of rocks and the important infiltration at the expense of the runoff. The most important torrents that flow through the region of research are Xiropotamos, Filiouras, Souta, Verveniou and Elekistrianiko, which contribute inside the Glafkos River. The Alpine folded basin’s basement includes a sequence of pre-orogenetic sediments (marine limestone, radiolarites, etc) of the Pindos zone, and a clastic orogenetic sequence (flysch), which is constituted by alternations of silt rocks, sandstones and rarely conglomerates. The layers of the Pindos zone emerged at the final phase of the folding tectonics in the Lower Oligocene, where the Pindos’ thrust occurred in the form of a nappe, above the Gavrovo – Tripolitsa zone. The foreheads of the thrusts between the slices as well as the axes of folds have a NW – SE direction, with the direction of movement from east to west, and have a direct relation to the majority of the karstic springs. In the region of Patraikos Gulf, what prevails is a rhomboid faulting system with high slope and ENE, WNW directed normal faults that create a mosaic of fragmentized tectonic blocks and a general rising of region that continues until today. The opening up of the valleys in the wider region of research, which is often accompanied by landslides, is determined from 4 bunches of neotectonic faults directed NW, NE, WNW and NNE. The Plio-quaternary cover that appears in the coastal and hilly region is constituted by two stratigraphical units. The lower one consists of clays and sands, which were deposited in a lacustrine to brackish environment of sedimentation during the Pliocene to the Lower Pleistocene and the upper one consists of Calabria dating from the deltaic and land conglomerates. Generally the alluvium deposits are characterized by lithological heterogeneity both at the vertical and the horizontal direction and their thickness presents a gradual increase from the northerner and southerner limits to the central department of the basin, which exceeds 200 m. The annual height of rainfall (1071 mms) in the region of research is quite high for our country’s data and fluctuates from 640 to 900 mms in flat regions, whereas in the mountainous regions it reaches 1560 mms. During the last years, what takes place is a seasonal displacement of rainfall from winter to spring and autumn, which leads to the loss of the available water of the active infiltration because of increased evaporotranspiration. From a hydrologic aspect, the Glafkos basin receives annually, on average, 108,89 106 m3 of the water from rainfall, from which 48,9 % comes back to atmosphere with the processes of evaporation and transpiration, 28,6 % rises on the surface and 22,5 % infiltrates, mainly in important, from a hydrogeological aspect, formations (limestones and quaternary depositions). The semi-independent hydrogeologically karstic units, which are developed because of the laminated and faulty tectonics in the region and differentiate the movement of groundwater, constitute a characteristic hydrogeological feature of the region of research. In relation to the alluvium deposits, the unconfined aquifer of the superior area is progressively bent and falls into successive under pressure (confined) aquifers in the coastal area. At the beginning of the ‘90s in the coastal region, because of the overpumping, negative values of the piezometric surface in a distance up to 3 Km from the coastline were realised, having as a consequence the salinity of coastal alluvium aquifer from the seawater intrusion. The reduction of pumping in the middle of the ‘90s led to the rise of piezometric levels and to the reappearance of the phenomena of artesian wells in the coastal area. Due to the elaboration of the pumping data, what was realised is the appearance of high values of the hydraulic conductivity’s factor in the alluvium aquifers of the coastal zone as well as in the karstic aquifers. The aquifers of the Neogene formations as well as the alluvium aquifers of the southern bank of the river Glafkos present a smaller speed of movement of groundwater as compared to those of the northern bank, because of the predominance of the fine-grained clastics. The most important factor of the recharge of the Glafkos’ basin alluvium aquifer is basically the costal recharge from the river bank and then follows the inductive recharge from the limestones, whereas the direct infiltrated water from the rainfall and from the surplus of the irrigation water seem to be the least important factors. Based on the balance of the inflows – outflows of the Glafkos’ basin alluvium aquifer, an average annual surplus of 6,5*106 m3 of water has resulted, during the hydrologic years 1999 –2002. Generally, the quality of water in the alluvium aquifers as well as in the aquifers of Neogene formations, but also that in the karstic aquifers is considered to be good, if the coastal area of the Glafkos’ basin is excluded. Most of the groundwater, as well as the surface and spring water, presented the geochemical type Ca-HCO3, which generally includes water of good recharge and renewal, mainly along the drainage axes. The time-space movement of the brackish zone in the coastal area, in the period 1999 –2002, was realised not only by the increased distribution of various ions but also by the utilisation of factors S. A. R., Revelle and Schoeller, as well as the ratios rBr-/rCl- and rBr-/rI-. During the period 1999 – 2002, a perceptible reduction of the pollution from the saline intrusion in the coastal region took place. The abundance of wells of automatic flow into coastal area, which drain 3,5*106 m3 of brackish water, annually, to the sea played an important role in the acceleration of the restoration of the coastal basin aquifers of the river Glafkos. The position and the time-space movement of the brackish zone in the coastal area was realised also by geoelectrical researches that took place with the dispositions Schlumberger, Wenner – Schlumberger and Pole – Pole. Geoelectrical research revealed that seawater intrusion rarely appears in the form of a forehead, but follows selective paths via the coarse-grained clastics, while the fine-grained clastic formations play the role of a hydraulic barrier. Finally, the geometry and the depth of the basement in the coastal area were determined with the application of the seismic reflection method. The need of artificial enrichment of the alluvium aquifer from the wintry flows of the Glafkos River is pointed out, for a more rapid restoration of the water quality and the increase of the Glafkos’ basin water potential. The DRASTIC method was applied for the estimation of the vulnerability of the groundwater towards exterior pollution, where based on the DRASTIC indicator’s values, a map of the vulnerability of the region of research was constructed. Areas of high vulnerability are located in the coastal part of the aquifer, while areas of medium vulnerability are located in the eastern part of the basin. Finally, a mathematic model of the Glafkos’ basin alluvium aquifers was constructed with the application of code MODFLOW, thus providing an as much as possible reliable model of the management of the Glafkos’ basin groundwater potential.

I denna studie undersöks vad som sker i intensivundervisning där en SUM-elev, elev med särskilda utbildningsbehov i matematik, erbjuds multisensorisk undervisning. Vilken utveckling som sker vad gäller elevens taluppfattning, samt olika uttryck för lärande i undervisningsprocessen är också något som studeras. Studien har en kvalitativ ansats och har genomförts som en fallstudie med en SUM-elev i årskurs ett. Fallstudien innehåller en intervention med matematiktester vilka genomförts före och efter en intensivundervisning i grundläggande taluppfattning. Deltagande observationer av undervisningssekvensen har genomförts, vilka också har filmats. Till analysen används Bruners teori om representationer tillsammans med Vygotskijs teori om lärande ur ett sociokulturellt perspektiv. Representationerna i Bruners teori beskrivs som den enaktiva som är handlingsbaserad, den ikoniska som är bildbaserad och den symboliska som är språkbaserad. Resultatet visar i detta fall att en intensivundervisning med multisensorisk approach påverkar elevens taluppfattning positivt och elevens lösningsfrekvens mellan för- och eftertest tredubblats. En utveckling av bland annat matematiska förmågor var synlig. Eleven utvecklade lärande i de olika representationerna där inledningsvis den enaktiva representationen användes och succesivt även den ikoniska- och symboliska representationen. Resultatet visar en positiv påverkan på elevens självförtroende i matematiska situationer, främst gällande symbolhantering. / This study examines what happens in the situation of intense, multi-sensory instruction for a SEN-student in the subject of mathematics, a student with special education needs in mathematics. What kind of development is happening in terms of the student's number sense, as well as various forms of learning in the teaching process is also something that is studied. The study has a qualitative approach and was implemented as a case study with a SEN-student in the subject of mathematics in year one. The case study includes an intervention with math tests which were taken before and after an intensive teaching of basic number sense. Participant observation of the teaching sequence has been implemented, which also have been filmed. For the analysis Bruner's theory of representations along with Vygotsky's theory of learning from a sociocultural perspective is used. The representations in Bruner's theory is described as the enactive that is action-based, the iconic that is image based and the symbolic which is language-based.  The result in this case shows that an intensive instruction with a multi-sensory approach affects the student's number sense in a positive way. The pupils solution frequency between pre- and posttest tripled. The Pupil developed learning in the different representations where initially the enactive representation was used and gradually even the iconic- and symbolic representation. A development including mathematical competences were visible. The results show a positive impact on the pupil self-confidence in mathematical situations, primarily in situations for symbol processing.

Orientador: Arlete de Jesus Brito / Banca: Virginia Cardia Cardoso / Banca: César Donizete Pereira Leite / Anexos da dissertação estão no CD-ROM / Resumo: Nosso objetivo, nesta pesquisa, foi contribuir para a reflexão sobre a formação continuada dos professores polivalentes por meio do processo de análise de erros em Matemática produzidos pelos alunos dos quarto e quinto anos1 do ensino fundamental. Realizamos uma revisão da literatura que trata dos temas relacionados à avaliação, a erros e ao exercício do poder envolvido no processo avaliativo. As categorias geradas por nós em nossa análise dos erros, revelaram justificativas conceituais para os erros dos alunos. Com a realização de sessões interativas com professoras de primeiro a quinto ano do ensino fundamental, vislumbramos a possibilidade de utilizar aquela análise como recurso orientador da atividade pedagógica. Nossas conclusões apontam para a percepção das professoras que a análise dos erros de seus alunos é importante para a reflexão sobre suas práticas docentes e que tais erros podem desempenhar um papel construtivo no processo de ensino/aprendizagem da Matemática. / Abstract: Our aim in this research was to contribute for the reflection about the continued elementary teacher formation by the analysis process in Mathematical mistakes committed by the K-3 and K-4 elementary school pupil's. We realized a revision of the literature about the theme connected to valuation, to mistakes and de power's exercise involving in the valuation process. The categories generating for us in our mistake's analysis exposed conception's justifications for the pupil's mistakes. With the realization of the interchanges sessions with the K-1 to K-4 elementary teachers, we descried the possibility to make useful that analysis like orientation recourse of the pedagogical activities. Our conclusions pointing to the teachers perceptions that the mistakes analysis of their pupils is important to reflection about their pedagogical practices and these mistakes could fulfill a constructive paper in the Mathematical learning/teaching process. / Mestre

This dissertation dicusses the main concepts involved in the non-photorealistic rendering techniques and proposes a general scheme to implement such techniques. The work discusses also a non-photorealistic rendering style from line drawing to 3D models presented by Stéphane Grabli et al, in such a way that the line styles are programmable. We also present an implementation from portion of the work of Grabli. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta dissertação são discutidos os principais conceitos envolvidos nas técnicas de renderização não-fotorrelística e propõe um esquema geral para implementação de tais técnicas. É discutido também um estilo de renderização não-fotorrealística de desenhos de linha para modelos 3D apresentado por Stéphane Grabli e colaboradores, cujos estilos de linha sejam programáveis. Também apresentamos uma implementação de parte do trabalho de Grabli.

This work brings the importance of the Mathematical Olympiads for teaching and learning in Brazilian public schools, emphasizing the OBMEP that during its 12 years of accomplishment has transformed the way of teaching and learning the mentioned area, at the same time, it portrays the Project Developing and Applying Mathematics aimed at producing winners in OBMEP, applied in the municipal schools of the city of Branquinha, Alagoas between the years of 2015 and 2016. This project was born from the extreme difficulty presented by the students and teachers of the municipality in working the issues And the contents of OBMEP in the school context. For many years the competition was seen only as an obligation to be on the national calendar, but clearly there was no commitment to do the tests and much less expectations in obtaining good results. The teachers always claimed that due to the difficulties presented in the learning of their classes, it would be practically impossible to focus OBMEP and to work the contents of the curricular matrix determined for each grade year. The students, considering that there was no previous preparation in the classroom, did the tests simply because they were put in their pews, they hardly read the questions, they did not understand the statements, they marked the alternatives of random form and when by pure luck they were selected For the second phase, were surprised and therefore the vast majority did not appear in the second stage of the competition. The objective of this study is to improve the quality of mathematics teaching in the municipality, emphasizing the use of OBMEP questions in school life, in order to achieve significant results of the students in said competition, as well as in the national, state and local evaluations. municipal. The methodology applied in the elaboration of this work occurred through a bibliographical review and the works carried out in the elementary schools of the municipality. The bibliographical revision happened from the readings of the works of Polya, Asimov and Machado, magazines, articles and theses. The work was developed in the three elementary schools of the municipal school network; Escola Demócrito José, Escola Santo Antônio da Boa Vista and Escola Zumbi dos Palmares, where questionnaires and interviews were applied to faculty, parents and students. In these educational institutions a work was done to improve the quality of teaching mathematics learning, involving the school community with OBMEP and consequently producing champions students in the competition. The results obtained during and after the application of the work show that there was a notorious awakening of students regarding mathematical learning, a significant improvement in their academic performance and consequently a significant evolution in the national level evaluations, in the IDEB and especially in the OBMEP. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho traz a importância das olimpíadas de matemática para o ensino e aprendizagem nas escolas públicas brasileiras, dando ênfase a OBMEP que ao longo dos seus 12 anos de realização tem transformado a maneira de ensinar e aprender a referida área, ao mesmo tempo, retrata o projeto Desenvolvendo e Aplicando a Matemática, voltado para produzir vencedores na OBMEP, aplicado nas escolas da rede municipal da cidade de Branquinha, Alagoas, entre os anos de 2015 e 2016. Esse projeto nasceu da extrema dificuldade apresentada pelos alunos e professores do município em trabalhar as questões e os conteúdos da OBMEP no contexto escolar. Por muitos anos, a competição foi vista apenas como uma obrigação por estar no calendário nacional, mas nitidamente não havia empenho algum em fazer as provas e muito menos expectativas em obter bons resultados. Os professores sempre alegavam que devido às tamanhas dificuldades apresentadas no aprendizado de suas turmas, seria praticamente impossível focar a OBMEP e ao mesmo tempo trabalhar os conteúdos da matriz curricular determinada para cada ano/série. Já os alunos, tendo em vista que não havia uma preparação prévia em sala, faziam as provas simplesmente porque eram postas em suas bancas, mal liam as questões, não entendiam os enunciados, marcavam as alternativas de forma aleatória e quando por pura sorte eram selecionados para a segunda fase, se mostravam surpresos e, por conseqüência, a maioria não comparecia na segunda etapa da competição. O estudo em questão tem como objetivo geral melhorar a qualidade no ensino-aprendizagem de matemática no município em questão, dando ênfase ao uso das questões da OBMEP no cotidiano escolar, visando alcançar resultados significativos dos alunos na referida competição, assim como nas avaliações a nível nacional, estadual e municipal. A metodologia aplicada na elaboração desse trabalho ocorreu através de revisão bibliográfica e dos trabalhos realizados nas escolas de ensino fundamental do município. A revisão bibliográfica aconteceu a partir das leituras das obras de Polya, Asimov e Machado, revistas, artigos e teses. O trabalho foi desenvolvido em três escolas de ensino fundamental da rede municipal de ensino; Escola Demócrito José, Escola Santo Antônio da Boa Vista e Escola Zumbi dos Palmares, nas quais foram aplicados questionários e entrevistas ao corpo docente, pais e alunos. Nessas instituições de ensino foi realizado um trabalho voltado para melhorar a qualidade do ensino aprendizagem de matemática, envolvendo a comunidade escolar com a OBMEP e consequentemente produzindo alunos campeões na competição. O resultado obtido durante e após a aplicação do trabalho mostram que ocorreu um notório despertar dos alunos referente a aprendizagem de matemática, uma melhora significativa no desempenho escolar dos mesmos e, por fim, uma expressiva evolução nas avaliações a nível nacional, no IDEB e principalmente na OBMEP.

The purpose of this study has been to investigate how math teachers in the last three years in compulsory school and in the upper secondary school perceive how they work with feedback. Another aspect of the study was to describe the context of the feedback given by the teachers and what the teachers focus on in their feedback. In this text, feedback is defined as different ways of giving the student a way to take the learning process to the next level. The theoretical framework has been Hatties and Timperleys (2007) "model of feedback". Qualitative interview was the method chosen for this study. The interviews were semi-structured which is a method that's right in between a questionnaire and an open interview. In total, eight interviews with math teachers were conducted. The result of the study showed that the teachers like to work with feedback, but that the time they are given isn't enough to formulate it in a, for them, satisfactory way. The teachers generally gave feedback directly to the student during the lessons which was centered around the task at hand or directed towards the student. Many of the teachers would like to see a more individualized feedback. They would also like to work more with teaching the students different strategies for feedback, in order to increase their learning. / Syftet med denna studie har varit att undersöka hur lärare som undervisar i årskurs 7–9 och gymnasiet i ämnet matematik, uppfattar att de arbetar med feedback. Syftet har även varit att beskriva vilken nivå lärarna uppfattar att de ger feedback på, samt vad lärarna fokuserar på i sin feedback. Feedback definieras i arbetet som olika sätt att ge eleven återkoppling som för lärandet framåt. Den teoretiska utgångspunkten har varit Hattie och Timperleys (2007) ”model of feedback”. Metoden som har använts i denna studie är kvalitativ intervju. Intervjuerna utgick från en halvstrukturerad intervjuform, som ligger mellan den öppna intervjun och ett strikt frågeformulär. Totalt genomfördes åtta enskilda intervjuer med lärare som undervisar i matematik.  Resultatet från studien visade att lärarna gärna arbetar med feedback, men att de upplever att de skulle behöva mer tid för att kunna utforma den på det sätt de skulle vilja. Lärarna gav i huvudsak feedback i stunden som var centrerad till uppgiften som eleverna arbetade med eller till eleven som person. Många av lärarna skulle gärna se en mer individualiserad feedback. De skulle även vilja arbeta mer med att lära eleverna olika strategier för feedback, för att på så vis öka deras inlärning.

Este trabalho apresenta uma proposta didática desenvolvida em uma escola da Rede Adventista de Educação no município de Cachoeirinha, que utilizou a linguagem LOGO em aulas de Matemática. O experimento prático, realizado com estudantes do sétimo ano do Ensino Fundamental e respaldado pelas teorias de Seymour Papert e Gèrard Vergnaud, buscou responder à seguinte questão: Como a utilização do ambiente LOGO auxilia na aprendizagem dos conceitos de Ângulos e Coordenadas Cartesianas, estudados durante o Ensino Fundamental? Outras investigações envolvendo a utilização da linguagem LOGO são mencionadas, bem como suas influências para o trabalho. A partir dos dados analisados qualitativamente, observou-se um crescente interesse pelo estudo dos tópicos de Geometria e um avanço nas elaborações de estratégias de soluções de problemas. Ao final deste trabalho, encontra-se a sequência didática elaborada e aplicada, produto desta dissertação. / This dissertation presents a didactic proposal developed in a school of Adventist Education in the city of Cachoeirinha, which used the LOGO language in Mathematic classes. The practical experiment was conducted with students in the seventh grade of elementary school and supported by the theories of Seymour Papert and Gerard Vergnaud, and tried to answer the following question: How the use of the LOGO environment can help the learning of the concepts of angles and Cartesian Coordinates, which were studied during elementary school? Further investigations involving the use of LOGO language are mentioned, as well as their influences for this paper. From the qualitatively analyzed data, it was noticed a growing interest in the study of topics of Geometry and an improvement in the elaboration of strategies for problem solving. At the final of this work, we can find the didactic sequence, made and applied, product of this dissertation.

Made available in DSpace on 2014-06-11T19:24:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-03-25Bitstream added on 2014-06-13T19:26:00Z : No. of bitstreams: 1 fonseca_a_me_rcla.pdf: 1869089 bytes, checksum: d89edd2922ec12c36bba64ad1a216a47 (MD5) / O trabalho intitulado “A construção do conhecimento matemático de uma turma de alunos do Ensino Médio num espaço sociocultural: uma postura etnomatemática” é uma pesquisa, de caráter etnográfico, que tem como objetivo observar, descrever e analisar como acontece a construção de conhecimento matemático de um grupo social específico, que neste caso, é uma turma de alunos do Ensino Médio Estadual. Realizada na Escola Estadual Prof. Marcelo de Mesquita, da cidade de Ipeúna-SP, esta pesquisa também procura mostrar que a sala de aula pode se constituir como um espaço sociocultural, onde o diálogo simétrico e as relações de alteridade estão presentes, de modo a se considerar os princípios da Etnomatemática, quais são, respeito, solidariedade e cooperação. Todas as discussões presentes neste trabalho emergiram do projeto desenvolvido com este grupo social, intitulado “Projeto de Leitura de Mundo Com Um Olhar Etnomatemático” e da teoria adotada. Para que tudo isto seja possível, é preciso que o educador perceba que é necessário uma mudança de postura tanto conceitual, quanto prática, que envolve principalmente a reflexão na relação com o “outro”. / The task entitled “The Construction of the mathematic knowledge of a high school student´s class in a sociocultural space: an ethnomathematic posture” is a search, of ethnographic character, that has like objective to observe, to describe and to analyze like happens the construction of mathematic knowledge in a specific social group, that in this case, is a state high school student´s class. It realized in the state school “Professor Marcelo de Mesquita”, in Ipeúna city – SP, this search also looking for to show that a classroom can constitute like a sociocultural place, where the symmetric dialogue and the alterity relations are present, in a way to consider the ethnomathematic principles, like respect, solidarity and cooperation. All the discussions present in this work emerge of the project developed with this social group, entitled “World reading project with an ethnomathematic view” and the theory adapted. For everything be possible, is precise that the educator percepts that is necessary a posture change as much conceptual as practice, that involves meanly the reflexion in the relation with “the other”.

Made available in DSpace on 2014-06-11T19:24:20Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-09-02Bitstream added on 2014-06-13T19:06:12Z : No. of bitstreams: 1 correia_cef_me_rcla.pdf: 871281 bytes, checksum: 979ce98f101466438d259a934422c7c2 (MD5) / Nosso objetivo, nesta pesquisa, foi contribuir para a reflexão sobre a formação continuada dos professores polivalentes por meio do processo de análise de erros em Matemática produzidos pelos alunos dos quarto e quinto anos1 do ensino fundamental. Realizamos uma revisão da literatura que trata dos temas relacionados à avaliação, a erros e ao exercício do poder envolvido no processo avaliativo. As categorias geradas por nós em nossa análise dos erros, revelaram justificativas conceituais para os erros dos alunos. Com a realização de sessões interativas com professoras de primeiro a quinto ano do ensino fundamental, vislumbramos a possibilidade de utilizar aquela análise como recurso orientador da atividade pedagógica. Nossas conclusões apontam para a percepção das professoras que a análise dos erros de seus alunos é importante para a reflexão sobre suas práticas docentes e que tais erros podem desempenhar um papel construtivo no processo de ensino/aprendizagem da Matemática. / Our aim in this research was to contribute for the reflection about the continued elementary teacher formation by the analysis process in Mathematical mistakes committed by the K-3 and K-4 elementary school pupil’s. We realized a revision of the literature about the theme connected to valuation, to mistakes and de power’s exercise involving in the valuation process. The categories generating for us in our mistake’s analysis exposed conception’s justifications for the pupil’s mistakes. With the realization of the interchanges sessions with the K-1 to K-4 elementary teachers, we descried the possibility to make useful that analysis like orientation recourse of the pedagogical activities. Our conclusions pointing to the teachers perceptions that the mistakes analysis of their pupils is important to reflection about their pedagogical practices and these mistakes could fulfill a constructive paper in the Mathematical learning/teaching process.

Made available in DSpace on 2014-06-11T19:24:50Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-03-13Bitstream added on 2014-06-13T20:32:19Z : No. of bitstreams: 1 caetano_rs_me_bauru.pdf: 3426394 bytes, checksum: 1e282fa710b2a0fc3cb679b2dc7d142d (MD5) / Secretaria da Educação de SP / A presente pesquisa investigou a utilização da Espistemologia Genética piagetiana através da análise das ações didáticas adotadas por quatro professores (sendo cada um pertencente às quatro séries iniciais do Ensino Fundamental) durante a abordagem dos conteúdos matemáticos. Além disso, observou-se como ocorreu a apropriação do construtivismo piagetiano à constituição da prática docente dos referidos professores. Configurando uma pesquisa qualitativa, do tipo estudo de caso, a coleta dos dados foi realizada por meio dos seguintes instrumentos/métodos: I - Entrevistas estruturadas, II - Questionários abertos, fechados e mistos, III - Observação de campo. Após dois meses de pesquisa de campo, em duas escolas pertencentes à Diretoria de Ensino da Região de Bauru, identificaram-se os seguints aspectos com relação às ações didáticas: as professoras da 1ª e 2ª séries utilizaram exclusivamente o método expositivo-transmissivo (caracteristicamente do Ensino Tradicional); a docente da 3ª série usou conjuntamente com a exposição-transmissão alguns elementos construtivistas (a operação sobre o material concreto, o questionamento visando à ocorrência do pensar sobre a ação, a interação entre alunos e professora); o professor da 4ª série foi o que mais apresentou estratégias didáticas construtivistas, tais como a dinâmica de grupo, a avaliação diagnóstica, a proposição de situações problema e questionamentos, permitindo aos estudantes tomarem consciência (em maior probabilidade) de suas ações. A respeito da apropriação da teoria de Piaget, observaram-se algumas compreensões distorcidas, sendo possível afirmar que esta apropriação ocorreu de modo difuso/fragmentado e (em alguns casos) contraditório. Por fim, as 'idéias construtivistas' mais discursadas pelos quatro professores participantes foram: a construção contínua... / The present study investigated the utilization of the Piaget's Genetic Epistemology through the analysis of the didactic actions adopted by four professors (being each one from the first four grades of the Elementary Education) during the teaching of elementary mathematics. In addition, it was observed the manner in which the Piaget's constructivist approach was developed within the teaching practice of these professors. Throughout a qualitative research, such as case study, the data gathering was realized through the following methods: I - Structured interviews, II - Opened, closed and mixed questionnaires, III - Field observation. After two months of field research in two different schools that belong to the Department of Education of the County of Bauru, the following aspects were observed regarding the teaching actions: the teachers of the '1 POT. st' and '2 POT. nd' grades utilized only the exposing method (characteristically to the traditional teaching method); the teacher of the '3 POT. rd' grade in addition to the exposing method utilized also a few constructivist elements (the operation of the concrete material, the questioning utilizing the thought processing over the action, as well as the interrelationship between the teacher and students); the '4 POT. th' grade teacher was the professional who most presented constructivist didactic strategies, such as the group dynamic, diagnostic evaluation, the presentation of problem-situations with questions that promotes students' conscientization (in higher probability) of their actions. Regarding the Piaget's theory approach, some distorted comprehensions were observed, which leaded us to conclude that it occurred in a diffused/fragmented manner and in some cases contradictory. Finally, the constructivist ideas most adopted by the four teachers were: the continue construction of the logical-mathematical knowledge and the necessity of concrete manipulation.