O processo de invenção de si: um estudo sobre a construção identitária de pedagogas em formação

This work was developed in the course of Pedagogy, Universidade Federal do Rio Grande do Norte. Aims to understand the process of identity construction of teachers and educators in initial training. We started from the idea that such process was made by a complex and interdependent movement, once it was an inventive phenomenon wrought by individuals who are authors and actors of the story of their "real life" (KAUFMANN). This identity is rooted in the trajectories and social biographical experiences (FERREIRA), relationships with the constructed and accumulated knowledge in this route (CHARLOT) and in the developing of a sense of cultural belonging institutionally constructed (Luckmann, Berger). Then, the training involves relationships with knowledge in several instances, considering the effects, in one hand, the historic-social production and, in another hand, from the positions of subject and their biographical itinerary, existential and formative. We used the methodology of the Comprehensive Interview (KAUFMANN; SILVA), associated with a network of theoretical references, empirical and very analytical and interpretive activity. She researcher also relied on the "sensitive listening" (BARBIER), empathic attitude of "listening / seeing" the subject, and the notion of "intellectual artisan" (MILLS). The individual interviews were supplemented by the Focus Group. The approach was multi-referential (ARDOINO; MACEDO), with the intertwining of different perspectives, allowing a more complex configuration and less reductionist. In the analysis and interpretation we located the starting point, genesis of identity whose dynamics is not rigidly determined, but localized in space-time that precedes entry into the initial training. It is the time of concerns, questions and reflections about what you want to be in the future professional life. In sequence, we saw the route, multifaceted process whose the direction is the increasing involvement of individuals with their training. This training is engendered by the relations with the curricular, extracurricular and discursive knowledge, as simultaneous dynamics of self training and socio training. The self training of the individuals, understanding the critical, ethic and authority reading of their own experiences, is also seen as an exercise of shared responsibility, it assumes that the relationship with others meanings and professor mediation. The socio training refers to the collective subject and turns to the historical production and diversified knowledge, and comprehension of the various training instances. Self training and socio training are both objects of negotiation, because they are provocative of new designs, and cultural and identity maps, mobilizing the senses towards new meanings of themselves and the professional reality. It is in this interdependence between what is historically produced and the experiences of the subjects, who we located the arrival, considering it as a radically incomplete process of the professional identity and the building itself.

Globos e mapas ao alcance das mãos : ensino de matemática numa perspectiva de alfabetização funcional na EJA

The following dissertation has as its main advantage the privilege of visualizing the literacy processes through the angle of the functional perspective, which does not see the literary process as a practice solely based on the decoding of alphabetical codes, and then allows for the opening of ample spaces for the allocation of mathematical skills in the realms of the functional literacy. The main object of this study was to investigate which are the contributions that a sequence of activities and of methodologies developed for the teaching of Geometry could provide for a part of the functional literacy process in mathematics of youngsters and adults of EJA, corresponding to the acquisition or to the improvement of skills related to the orientation capacity. The focus of the analyses consisted in the practice of these activities with the young and adult students of an EJA class belonging to a municipal public school of Natal/RN. The legacies of Paulo Freire about the redimensioning of the role of the teacher, of the students, of the knowledge and of their connections within the teaching-learning process, prevailed in the actions of the methodology implemented in the classroom and, especially, in the establishing of dialogic connections with the students, which directed all the observations and analyses regarding the collected information. The results indicated that the composition of articulations between the teaching of mathematics and the exploration of maps and the earth globe enabled the creation of multidisciplinary learning environments and situations, where we could observe, gradually, the development of procedures and attitudes indicating the evolution of space-visual type skills

Histórias de leituras e de leitores: práticas e representações de leitura em narrativas de professores de diferentes disciplinas escolares

Nous avons pris comme point de départ le préssuposé que en exerçant ses practiques de lecture en salle de classe, les professeurs récuperent des signes de ses expériences socioculturelles par rapport à la lecture, construites au long de ses trajectoires. Indépendemment de sa discipline scolaire, la mémoire de ces expériences interviennent certainement, de manière positive ou négative, dans la médiation de la formation de l élève lecteur. C est donc, par l articulation entre les perspectives de ses études qui parlent sur l histoire de la lecture, narratives (auto)biographiques et formation du professeur que je prétends récupérer et reconstruire, par les narratives de lectures racontées par les professeurs de différentes disciplines scolaires, les processus d appropriation de la lecture en considérant ses tactiques d accès et d utilisation des matériels écrits en circulation dans les groupes sociaux auxquels ils appartennaient. Pour ça ce travail s inquérit : Quels models de lectures émergent dans les narratives de professeurs de différentes disciplines scolaires ? Comment se manifestent-elles les représentations sur sa performance pour la formation de l élève lecteur ? L objectif central est d inférer les rapports existants entre des expériences de lecture et la médiation dans la formation de lecteurs. Douze professeurs de l éducation de base des écoles de la ville de Belém y ont participé. Le corpus est constitué par les transcriptions de deux genres d instruments: douze interviews narratives et deux groupes de débats. Les analyses montrent deux grandes fases de la rencontre avec la lecture : une antérieure à l école et l autre à partir de l école. Ces fases montrent des pratiques et des représentations de lecture hétérogènes différenciés par rapport à ses aspects fonctionnaux. Elles revellent encore que la formation du lecteur professeur et élève se lie, d abord, à la constitution culturelle de l homme, marquée, fondamentalement, par son interlocution avec l autre. La famille, l école et le lieu de travail se présentent comme des espaces qui impriment des marques profondes dans le rapport avec la lecture. Malgré ça, le même matériel écrit, un fois mis en scène le lu dans ces espaces n ont pas de significat coincidents pour les différentes personnes qui s en approprient. Cette raison montre la possibilité de la construction d une histoire de la lecture, basée pas exclusivement à la description des matériels lus pendant le cours de leurs vies, mais surtout, sur les indicateurs de ses différentes manières de lire. Cette trajectoire exerce de cette façon une forte influence sur la prise de décision et les manifestations du travail du professeur en situation de salle de classe. Comme ça on peut conclure, premièrement, que les représentations et pratiques de lecture se sont constitués et se sont (re)configurés dans des différentes formes, concepts, temps et espaces, dans un entrecroisement de différents discours. Deuxièmement que la reflexion sur les mémoires de lecture a resulté un nouveau regard des participants sur son travail de professeur et a confirmé l hipothèse selon laquelle la production des narratives autoréférencées offre, à qui les narre, la possibilité de transformation des représentations du sujet avec lui-même, avec l autre et avec le monde, ce qui démontre l importance de la recherche (auto)biographique comme méthode d investigation en éducation et sa contribuition pour la formation des formateurs de lecteurs dans des différents domaines de la connaissance , comme territoires constitutifs du sujet et de ses pratiques sociales, à l école et ailleurs

Aprendendo a pertencer: uma leitura da trezena de Santo Antônio em Pradoso enquanto territorialidade humana

The Novena of St. Anthony in Pradoso, is an annual celebration that takes place between June 1 and June 13. Since its preparation to the conclusion of the celebration are employed traditional knowledges and techniques, which are shared by the community. Such knowledges, built over generations, associated with popular religion, form it into the educational processes that build, through orality, practices and experiences of everyday life, the sense of belonging. An analysis of scenes, knowledges and subjects involved in the celebration, shows the form and content of practices capable of building symbolic territories of belonging. Thus, the Novena of St. Anthony in Pradoso, while an human territoriality, is designed as a locus of learning of belonging, reaffirming community values such as solidarity, service, brotherhood, integration, among others. While empirical reference for an analysis of the importance of belonging, the Novena of St. Anthony in Pradoso, offers subsidies for the production of knowledge, focused on understanding the need for a reconnection of technical and humanistic knowledges

Alimento como metáfora, metáfora como alimento : a arte de nutrir uma educação complexa

Cette narrative fait le parcours d une recherche et de ses reflexions ici annoncé comme une odissée gastronomique et une géografie gourmante , dont les elements interpretatifs rendent possible concevoir qu une lecture de la métaphore et de la stéthique alimentaire puissent contribuer pour penser une éducation sensible, complexe, une education guidée par une experimentation esthétique de la condition humaine, qui provoque les sens, qui permettent évoquer et récuperer les connaissances et les savoirs pertinents, et qui confirme l indissociabilité du sujet dans ses plusieurs poles : nature et culture, émotion et raison. Comme contribution epistémologique, la dissertation, cherche étendre la compréhension d études qui abordent le Corp, l Aliment, la Métaphore, l Esthétique et l Éducation, en déclanchant des relations entre les espaces académicien et cotidien, en expérimentant d autres formes de sentir, penser et d être dans le monde. Poussée par une raison gourmande, et comme dans un rituel de préparation d aliment, j opte par les rélations transversales des savoirs ; je construis un dialogue entre les auteurs de domaine de connaissances multiples, comme la Filosophie, l Antropologie, l Étologie et l Éducation, en travaillant une reconstruction de concepts. Pour la tâche de cette odissée gastronomique, je découvre l approche entre un programme, comme méthode, et un livre de recettes culinaires hermétiques. J ai choisi de construir des estratégies métodologiques qui indiquent les chemins sur les quelles l imagination, la créativité et la réinvention, non seulement puissent mais doivent servir comme des épiceries qui emprègne d odeurs, de saveurs et de couleurs la connaissance, sans laisser de côté la rigueur, principe inégociable dans une science ouverte. J ai choisi, pour m accompagner dans cet étude, des sages, des scientistes et des poètes, entre eux je fais remarquer Michel Onfray, Boris Cyrulnik, Merleau-Ponty, Edgar Morin e Conceição Almeida. Avec eux, j ai déssiné des cartes, goûté des géographies, des terres, des ciels. J ai fréquenter des histoires et des personnages concrets et imaginaires; j ai convoqué des souvenirs acumulés pendant l enfance, avec ses trames, ses textures, ses saveurs, ses parfuns, ses couleurs, ses images, ses gestes, ses mots et ses silences, où le corp devient un médiateur d accès à la connaissance. Comme artifice complémentaire pour suivre la route, je parie sur le rapport fondamental entre le corp, l aliment, la métaphore, l esthétique et l Éducation, je m utilise du Cinéma, en cherchant d apprendre dans cet art, une éxistentialité humaine par le rapport entre la vie, l aliment et les personnages. Finalement, je reaffirme l importance de nourir des affections par une formation et une manière de penser capables de conecté des connaissances d univers dinstingués, et qui contribuent pour une conscience de la condition humaine et l apprentissage d une éducation de la vie et pour la vie

Política de formação de professores: uma leitura a partir da análise do programa especial de formação de professores para a educação básica PROEB/UFMA

Study of Teacher Education Policy: a reading from the analysis of Programa Especial de Formação de Professores para a Educação Básica Proeb - aims to analyze the initial teacher training developed by the Universidade Federal do Maranhão - UFMA. Proeb is a policy of in-service training of teachers, formulated and implemented in the context of current educational policies for basic education. This work assumes that the guidelines developed in the last decades of the twentieth century are linked to international organizations that spread in Latin America continent a homogeneous model of training which has as main features to be held in service through the mode the distance and the school as a leading locus. In Brazil, these guidelines are supported on the Law of Directives and Bases of National Education No. 9.394/96 and Report 09/2001, which deals with the Syllabus Guidelines for the formation of Basic Education Teachers. To carry out the study was taken as reference, the syllabus developed for the deployment of Proeb from 1998 to 2002, specifically the proposal operationalized in the Degree Course of Mathematics in the city of Vitória do Mearim in Maranhão. To conduct the study, it was used literature as a way to deepen understanding, clarify and aim the conceptual aspect of the object researched. The documental research was consisted in the analysis of legal documents concerning the reform of education policies, teacher training and pedagogical project Proeb/UFMA and, finally, the semi-structured interviews were used to allow a better understanding of the subjects involved with research. The data analysis has shown that the curriculum designed to operationalize the course of undergraduate mathematics Proeb/UFMA, despite having guidelines that point to the separation of theory/practice dichotomy and establish as a principle work as an educational principle, has an disciplinary curriculum organization that reinforces the instrumental view of the syllabus, not enabling in practice, the execution of their initial proposal. Concerning to the view of graduates on the course, they highlight the weaknesses of the course, but also evidence that it has allowed an improvement of initial training, through the disciplines of the common core syllabus of courses and special training. It is possible seeing in graduates words, that the course have had repercussions in their teaching and improving their integration into the labor market and in the community of Vitória do Mearim. Overall, these developments have indicated evidence of teacher professionalization, although they are incipient. The work has shown that for the professionalization of teachers is introduced, the syllabus of undergraduate teacher education must overcome the traditional view of syllabus and implement contextualized curricula in a multidisciplinary approach involving, in equal proportions, the general education and training specific course. Accordingly, it is believed in need to review the role of the University in the formative process, as well as recovering as part of educational policies, the omnilateral size of teacher education

A educação destina a algumas crianças no Piauí (1730 1859)

L'histoire culturelle de l'éducation de l'enfant dans le Piauí, de l'année de 1730 à l'année de 1859, je mange écriture dans ce travail de thèse, est motivé dans l'analyse sócio-histórica de la forme scolaire à la lumière des théorisations des historiens Gui Vincent, Bernard Lahire et Daniel Thin, avec l'objectif de refléter concernant le passage d'instauration de la socialisation des enfants dans les écoles publiques, religieuses, particulières et domestiques. La recherche concernente à la thématique éducation de l'enfant dans leurs conceptions politiques et culturelles levou-em à définir, je mange objet d'étude, les manières d'instruire les enfants dans l'(s) école (s) et dans la (s) famille (s). La thèse du travail ici défendu est de que l'éducation destinée aux enfants dans le Piauí, dans la période de 1730 à 1859, était soumise aux acquisitions des habilités de lecture et d'écriture, principalement, analogue à leurs conceptions politiques et culturelles. La judicieuse recherche de corpus documentaire (licences, avertissements, troupeaux, lettres, correspondances, consultations, métiers, règlements, régiments, rapports, lois, dispositions, cartes scolaires, cartes d'inscriptions) pour l'écriture de la thèse il se procède nous quantités formulaires et digitales du Portugal, Brésil, Pará, Maranhão et Piauí. L'analyse de l'ensemble des sources nous a permis de comprendre que la socialisation scolaire de l'enfant dans le Piauí n'a pas maintenu le mêmes façons pendant cette longue période qui a été de 129 ans, malgré des récurrences, celui-là a acquis des formes et des sens divers qui variaient comme les circonstances politiques et culturelles, les exigences du commerce, les espaces et les sujets qui l'ont vécue intensément

O livro de leitura da campanha de pé no chão também se aprende a ler/RN: um estudo dos pressupostos histórico-culturais

This work is about the historical and cultural assumptions inserted in the contents of literacy of the Campanha de Pé no Chão Também se Aprende a Ler, a movement of culture and popular education, developed in the State of Rio Grande do Norte in the period between 1961 and 1964. The hypothesis is the one of the existence of a romantic-political ideology which permeated a national developmentalist conception sited in its didactic-pedagogic instrument of literacy, the Book of Lecture of De Pé no Chão Também se Aprende a Ler/RN (1963). It has the aim to understand how the popular critical consciousness marked by conceptions of culture and popular education in its social, cultural and ideological relations, happened. Analyses the object of study by the symbolical cartography, methodological procedures which have as principles to retire from an antecedent source implicit meanings that can discover new realities, articulating the keywords of that document to the ideology that surrounded the Campanha de Pé no Chão Também se Aprende a Ler /RN. As results, the research showed that, considering the historical-cultural assumptions of the national developmentalist thought sited in the studied Book of Lecture, the conditions of the political-cultural context and of the advance of the Brazilian national industry on the beginning of the 1960th , admitted a process of social integration lavished by the popular literacy on the Campanha de Pé no Chão/RN, linked with the possibility of transition of the popular conscience, in a romantic-political perspective of the culture and the popular education

A função mediadora do planejamento na aula de leitura de textos literários

This dissertation sutdies the mediative function in the planning of literary text reading classes of Portuguese. Its main central focus proposes that planning favors the pedagogical reading work of literary texts in the teaching of Portuguese, for they are regarded as one of the mediative elements the teaching-learning process. It also allows for its subjects to rethink the practice, theorizing it. As a theoretical basis the studies on participative planning are used, especially the studies concerning dialogic planning. The language/literature teaching perspective adopted in this work is guided by the socio-interactive conception of language, in a way that reading is seen as a comprehensive and interactive activity. Given the research process, the analysis of the reading process involved the Reader s Response, once that this theory considers the role of the reader and her/his interaction with the text. The study is grounded upon the following research question: which role(s) does the pedagogical planning play as a mediator of the reading teaching-learning process? The main objective of this dissertation is to investigate the pedagogical planning activity as a mediative instrument in the practice of reading in the Portuguese classes. The study is constituted of three stages, the third being emphasized (2002/2005) in which the direction of the participative action-research was used, as a way of acknowledging the pedagogical role in the teaching plan, as an instrument capable of rendering reorganization in the teaching-learning process of reading classes. We have as participants teachers of Portuguese in the elementary school (Ensino Fundamental, 3º ciclo), besides other segments of public schools, in the city of Pau dos Ferros RN, in which the previous studies were developed. The results point to the relevance in the role of the teacher, as a more experienced reader, in developing of pedagogical strategies that may come to favor the teaching of reading, having in the pedagogical sphere an instrument of theoretical reflection and sistematization of activities to be implemented in the classroom. The conclusions highlight the class plan as the mediative instrument to be incorporated and internalized into the teaching practice, amplifying and modifying the teacher s intervention forms, favoring, thus, her/his pedagogical mediation

A leitura de literatura na escola: por uma educação emocional de crianças na educação infantil

This dissertation examines the contributions of juvenile literature reading for the problematization of the emotional experiences and conflicts of children at infant education. Its importance consists in providing useful information for the pedagogic work orientated to literature reading at the initial series of basic education, in order to increase the teacher s ability to explore the literary text from its instigating and enriching nature in view of the child s emotional experiences and conflicts. It is methodologically based on the principles of the qualitative research, what characterizes it as a case study. The research focused a level V-infant education class with 28 students in 5-6 age group, at a public school of Natal, State of Rio Grande do Norte (Brazil). The used resources were: audio recording, field diary, and interviews. Seventeen classes were carried out and they consisted in reading sessions of classic and contemporaneous tales, fables, and legends which used different didactic strategies. These sessions were developed in accordance with the reading experience through scaffolding instructions as it was described by Graves & Graves. The theoretical references were the studies of Amarilha (1997/ 2006), Bettelheim (2004), Coelho (1987/2000), Damásio (2005), Del Nero (2003), Eco (1994/2006), Held (1980), Iser (1996), Jauss (2002), Stierle (2002), Wallon (2007), Telles (2006), Yunes (2003), and Zilberman (1987). The analyses showed that literary reading in class is a special environment for inclusion of the reader s subjectivity; as well as the inclusion of their emotional experiences and their conflicts within the story by way of helping children think and become suitable for dealing with their inner feelings. The literary reading is presented as an experiential and formative activity which helps children understand their emotions through a process of identification, exteriorization, and catharsis; what implies that the esthetic experience from the text makes possible the reader s self-knowledge and increases the perception of his inner feelings and objective reality so that this reader has emotional capital to deal with life difficulties. It is important to highlight that the discussions carried out in the class represented a field of sharing experiences through which each reader had the chance to present their experience of life to the others, including their sorrows and sufferings, in order to help them to develop best strategies to deal with the social environment

Já li muita coisa, então, eu posso inventar mais! A leitura literária e o desenvolvimento do pensamento criativo na infância

This study investigates the contributions of reading literature for the development of creative thinking in childhood. Its relevance consists in exploring practices that contemplate the creative thinking development in apprentices at school space and understanding the literature like a significant way to promote the creative thinking. The study is connected to the qualitaty strand. The exploratory observation and the intervention were adopted as research techniques. The field diary and the audio and video recording of the reading sections were adopted as methodological instruments. The research was conducted in the application s college from the Federal University of Rio Grande do Norte, in a 1th grade class, with 18 students between 6 and 7 years old. During the intervention, 8 readind class happened, with varied strategies and literary genres. The reading sessions were conducted through the principles of scaffolding, defended by Graves and Graves (1995). The corpus is made of speaks episodes, whose encoding semantics allowed the grouping into two central categories: divergent thinking and coauthoring of literary reader. It was taken as a theoretical framework the studies of Amarilha (2011; 2006; 2001; 1991; 1993; 1994), Alencar (2001), Coelho (2000; 1997), Culler (1999), De Masi (2005), Gallo (2000), Guilford (1977), Iser (1996), Jouve (2002), Kneller (1978), Martínez (1997), Smith (2003), Stierle (1979), Vigotski (2009; 1998), Wechsler; Nakano (2003; 2002). The analysis points to the formation of creative individuals in the classroom, through the reading of literature. Reposition the literary education front of the new social demands. Resizes the function of school in children s development, considering the children s skill in exploring, testing hypotheses and making use of their creative thinking, in climate of freedom mental. It signals, in this way, the teacher like a mediator, promoting a favorable to the development of creative thinking environment, a stimulating atmosphere, which enhances the expression of creative thinking in community

Gestão estratégica no terceiro setor: uma análise comparativa da construção de mapas estratégicos de organizações sem fins lucrativos

The strategy has an important role in organizations by identifying factors that need to be emphasized to organizational success and strategic map currently contemplates as a preview of organizational strategy, prepared from your planning. Third sector organizations need to take a competitive posture, establishing a sustainable position and maximizing the use of resources towards their social or humanitarian goals. This research aims to investigate the process of building strategic maps of two non-profit organizations by identifying and characterizing the steps common to these organizations. The research is characterized as qualitative descriptive and applied knowledge. Developed from bibliographical reviews and participant observation gathered in a case study, the data was collected in two third sector organizations and the results show that how to conduct the process may influence directly on your result lists. Among the steps identified, emphasis can be given to the formation of a team, the definition of strategy, the definition of strategic objectives, the gathering of those goals into perspective and the identification of the cause-effect relationship that relate. Marked as optional, but effective, conducting an event outside the premises of the company to complete the process, or any portion thereof. However, stands out as essential the active participation of senior management in the process, as a way to give credit to the initiative. These steps, its characteristics and its factors are described from comparisons between the processes adopted by the organizations surveyed

Uma proposição para o cálculo de mapas de disparidade de imagens estéreo usando um interpolador neural baseado em funções de base radial

This study aims to seek a more viable alternative for the calculation of differences in images of stereo vision, using a factor that reduces heel the amount of points that are considered on the captured image, and a network neural-based radial basis functions to interpolate the results. The objective to be achieved is to produce an approximate picture of disparities using algorithms with low computational cost, unlike the classical algorithms

Contribuições a técnicas de agrupamento e visualização de dados multivariados utilizando mapas auto-organizáveis

Self-organizing maps (SOM) are artificial neural networks widely used in the data mining field, mainly because they constitute a dimensionality reduction technique given the fixed grid of neurons associated with the network. In order to properly the partition and visualize the SOM network, the various methods available in the literature must be applied in a post-processing stage, that consists of inferring, through its neurons, relevant characteristics of the data set. In general, such processing applied to the network neurons, instead of the entire database, reduces the computational costs due to vector quantization. This work proposes a post-processing of the SOM neurons in the input and output spaces, combining visualization techniques with algorithms based on gravitational forces and the search for the shortest path with the greatest reward. Such methods take into account the connection strength between neighbouring neurons and characteristics of pattern density and distances among neurons, both associated with the position that the neurons occupy in the data space after training the network. Thus, the goal consists of defining more clearly the arrangement of the clusters present in the data. Experiments were carried out so as to evaluate the proposed methods using various artificially generated data sets, as well as real world data sets. The results obtained were compared with those from a number of well-known methods existent in the literature

A leitura como instrumento facilitador da compreensão matemática

This research builds on a qualitative approach and proposes action research to develop, implement and evaluate a strategy grounded in the teaching of geometry reading from different text types, in order to enhance the understanding of mathematical concepts by students in the 6th grade of elementary school. The teaching of mathematics, strengthened by a reading practice that fosters a greater understanding of science, because it would contribute to the expansion of vocabulary, acquire a higher level of reasoning, interpretation and understanding, providing opportunities thus a greater contextualization of the student, making out the role of mere spectator to the builder of mathematical knowledge. As a methodological course comply with the following steps: selecting a field of intervention school, the class-subject (6 years of elementary school) and teacher-collaborator. Then there was a diagnostic activity involving the content of geometry - geometric solids, flat regions and contours - with the class chosen, and it was found, in addition to the unknown geometry, a great difficulty to contextualize it. From the analysis of the answers given by students, was drawn up and applied three interventional activities developed from various text (legends, poems, articles, artwork) for the purpose of leading the student to realize, through reading these texts, the discussions generated from these questions and activities proposed by the present mathematics in context, thus getting a better understanding and interaction with this discipline as hostility by most students. It was found from the intervention, the student had a greater ability to understand concepts, internalize information and use of geometry is more consistent and conscientious, and above all, learning math more enjoyable