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1
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ANDREA REGINA HENRIQUES DE MEDEIROS
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THE HISTORY OF INTEREST AND ITS TEACHING
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Leader : MIGUEL CHAQUIAM
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Data: 10 janv. 2023
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Afficher le Résumé
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Based on the History of Mathematics, it is possible to develop activities that can be used as a didactic resource in the teaching of mathematical content, as it includes, among its potentialities, the possibility of adding meaning, provoking student motivation and curiosity. Considering that few works portray the history of interest, much less the use of its history in teaching, the following question was raised to guide the research linked to the professional master's course in Mathematics Teaching: To what extent historical clippings involving interest, based on the model of Chaquiam (2020), can it contribute to the teaching of interest in Basic Education? It was established as an objective for this work to analyze the possible contributions to the teaching of interest resulting from historical clippings raised by Chaquiam (2020) for Basic Education, having interest as a mathematical object. Therefore, after a bibliographic review to survey historical facts related to interest, it can be said that this is a bibliographic research with a qualitative approach, based on the work of CHAQUIAM (2020, 2017) from the proposition of elaborating a diagram to guide the constitution of a text and from this a historical cut for the construction of activities for teaching in basic education. The presentation of this material in the classroom can add historical value to the constitution of this object during the teaching process, whose millenary existence precedes the very existence of money, banks and even more of Financial Mathematics, and to the student who recurrently watches this content as a package finished usually by means of an algorithm and lists of exercises without emphasizing the historically constructed meaning and consequently its use in your life. It should be noted that the research is in progress, therefore, the validation of the activities will occur after the analysis of the data obtained in the empirical studies
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2
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EUVALDO SOARES DA SILVA
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The Teaching of Function Bijection by Experimental Activities
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Leader : PEDRO FRANCO DE SA
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Data: 28 févr. 2023
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Afficher le Résumé
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The present work presents the results of a research that aimed to analyze the effects of applying a didactic sequence for teaching Function Bijection through experimental activities on class participation, concept construction and performance in problem solving and questions that address the subject and its application. The experimental part of the research was developed in a state public school in Imperatriz in the state of Maranhão, with 10 high school students as subjects, in order to investigate the following scientific problem: how teaching through experimental activities influences teaching and learning of Function Bijection and its application in comparing the cardinality of numerical sets? Didactic Engineering was adopted as a research methodology. The analysis of the results took place through the notes of the students in the activities, confrontation of a priori and a posteriori analyzes, comparing the results of the pre-test with the post-test, applying Pearson's Linear Correlation Coefficient and the Test of Hypothesis. The results of the comparison showed a considerable increase in the post-test scores; the hypothesis test proved that the post-test scores had a significant improvement in relation to the pre-test and the correlation analysis showed that none of the socioeconomic factors raised had direct interference in the results obtained, showing that there were improvements in learning and that good The result of the experiment is due, above all, to the methodology used.
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3
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WILLIAM BARROSO MELO
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The teaching of polyhedra from elements of the student's daily life
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Leader : FABIO JOSE DA COSTA ALVES
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Data: 8 mars 2023
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Afficher le Résumé
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This qualitative action-research sought to develop, test and verify the potential of a didactic sequence in learning polyhedrons. The guiding question is: Does a didactic sequence involving everyday objects enhance the learning of polyhedra? Therefore, the general objective is to verify the learning potential of a didactic sequence in the teaching of polyhedra. students' daily lives. The didactic sequence was applied to a group of 5 students from a second-year high school class at a public school on the outskirts of the city of Belém. Data analysis took place through written records on activity sheets distributed to students and transcription of voice data captured from students during the application of activities. The organization of the information obtained is structured in Introduction, Bibliographic Survey, which consists of the search for works that are similar to our research, Theoretical Base that are the theoretical contributions used, namely Rabardel's Instrumental Theory, Theory of Representation Registers Duval's Semiotics and Microgenetic Analysis, the Methodology in which we talk about Polyhedrons and the GeoGebra software, the Analysis of Results in which we analyze the written and voice records of the consulted subjects and teachers, contribute to the formulation of the didactic sequence. The research has positive results regarding the application of this didactic sequence along with the use of the GeoGebra application, it allows discussions about its application form, opens up possibilities for changes for the next teachers who use it and distances teaching mathematics from the traditional method.
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4
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BETANIA DE ALMEIDA PRESTES
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Potentialities of a Didactic Sequence using Tangram for teaching Algebraic Expressions.
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Leader : NATANAEL FREITAS CABRAL
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Data: 10 mars 2023
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Afficher le Résumé
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The final results of a Professional Master's Dissertation in Mathematics teaching are presented, whose objective was to identify the didactic potential of a Didactic Sequence built specifically for the teaching of Algebraic Expressions. Curriculum guidelines for teaching mathematics in elementary school and a preliminary bibliographic study on the teaching of Algebraic Expressions through dissertations, articles and textbooks on the subject were considered. Among the issues raised were the difficulty in giving meaning to algebraic symbolism, as well as the development of algebraic thinking and symbolic algebraic language. We also sought to investigate the perceptions of mathematics teachers about learning Algebraic Expressions and a historical and epistemological deepening of this mathematical object. In these preliminary researches, the relevance of an interactive and collaborative teaching with gradual construction of knowledge was verified. For that, the research was guided by the question “What contributions can a Didactic Sequence structured according to the Articulated Units of Conceptual Reconstruction (UARC) bring to reduce learning difficulties in teaching algebraic expressions directed to the 8th grade classes of elementary school?” To answer this question and achieve the objective of the research, the methodological path was guided by the Theory of Didactic Situations, and a structured didactic sequence was elaborated according to Cabral (2017). Considering the reality of the return to face-to-face classes after the COVID-19 pandemic, we opted for concrete, manipulative didactic material with educational and playful intentions to create an attractive and collaborative learning environment. Through the geometric properties of the pieces of the Tangram puzzle, six sequenced, planned and articulated activities on Algebraic Expressions were developed.
28 students from public schools in the city of Cametá-PA participated in the Experimentation. The data collected from the experimentation in audio and written protocol were analyzed according to Microgenetic Analysis and Discourse Analysis. The results showed that the constructed didactic sequence presented didactic potential in the pedagogical, epistemological and learning dimensions and that the dialogical quality of the didactic episodes helped to minimize difficulties diagnosed in preliminary research. In this way, the research and its construct presented developments related to affectivity in relation to mathematics and form the source and basis for future research.
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5
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MARCOS ROBERTO BERREDO DA SILVA
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A Didactic Sequence for The Teaching of Geometric Progression.
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Leader : MIGUEL CHAQUIAM
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Data: 10 mars 2023
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Afficher le Résumé
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This research presents a proposal for teaching geometric progression, developed during the Professional Master's Course in Mathematics Teaching, in order to answer the following research question: What potentialities presents a didactic sequence for the teaching of geometric progression structured under the articulated units of conceptual reconstruction for students of the first year of high school? From the questioning, I took as general objective to analyze the indications of the application of a didactic sequence elaborated for the teaching and learning of geometric progression according to the articulated units of conceptual reconstruction. I have made as theoretical foundation the Theory of Didactic Situations described by Brousseau (1986), which allowed me to develop a didactic sequence idealized by Zabala (1998) and structured according to as articulated units of conceptual reconstruction, by Cabral (2017). With the intention identified as difficulties in the process of teaching and learning geometric progression, a bibliographic survey of research related to the teaching of this theme, analysis of textbooks, in addition to the perception of teachers of Basic Education and students who graduated from the first year of high school was carried out. The validation of the didactic sequence will occur through the evaluation of mathematics teachers municipality of Belém-PA, for application in classes of the 1st year of high school. As a result, I hope to verify the potential of a didactic sequence elaborated from the articulated units of conceptual reconstruction for the teaching of geometric progression in order to minimize learning difficulties.
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6
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LUIZ AUGUSTO OLIVEIRA DA SILVA
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Problem solving for teaching logarithmic function in a didactic sequence.
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Leader : ROBERTO PAULO BIBAS FIALHO
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Data: 23 mars 2023
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Afficher le Résumé
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This research suggests verifying the use of a didactic sequence, in Guy Brousseau's Theory of Didactic Situations (TSD), elaborated according to the stages of Didactic Engineering, with problems that focus on real situations, encouraging research and activities related to the emergence of logarithms, contributing to the construction and understanding of the logarithmic function by the students. The study is based on the didactics of mathematics that is concerned with the results of experiences in the classroom. The methodology used follows the principles of Didactic Engineering, which is justified by the fact that it is a concept that gives importance to both the theoretical and experimental dimensions of the research and whose purpose is to analyze didactic situations, the object of study in mathematics education. The sequence activities were elaborated with the 1st year graduation students, from the State University of the State of Pará, in the resolution of problems through the logarithmic function. In this work, the productions of 19 (nineteen) students were analyzed, organized in pairs and trio. It can be inferred from the a posteriori analyses, that the activities of the sequence contributed to the understanding of the logarithmic function being the inverse of the exponential function. From the analysis carried out, it was possible to verify that the students participating in the research obtained a greater understanding about the teaching of the logarithmic function by the teacher-researcher, than in traditional classes. Therefore, the use of trends in Mathematics Education, applied to a certain content, facilitated even more the teaching and learning process of the same, and made the learning of the concept of logarithm and logarithmic function more significant, allowing the students to use this concept to understanding of real-world phenomena.
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7
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VALQUÍRIA MAGALHÃES DE OLIVEIRA
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Teaching multiplicative problems involving isomorphism of measures through experimental activities
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Leader : ANA KELY MARTINS DA SILVA
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Data: 20 avr. 2023
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Afficher le Résumé
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This dissertation presents the results of a research that aimed to analyze what effects a didactic sequence, different from the traditional one, has on learning in solving multiplicative problems involving isomorphism of measures in a 6th grade elementary school class, seeking an answer to the following scientific question: What are the benefits that a didactic sequence through experimental activities, can cause to the teaching of problems with multiplicative principle with isomorphism of measures in a 6th / 9th class? The experiment was carried out in a municipal public school in the municipality of Tucuruí in the State of Pará, with 35 students from a 6th grade class of Elementary School - Final Years. The theoretical contribution was the Theory of Conceptual Fields, teaching through Experimental Activities and Problem Solving. Didactic Engineering (assumptions) was the methodology adopted in our research, covering all its stages: previous analyses, a priori analyses, experimentation and validation. The analysis of the collected data took place by verifying the records of the students' conclusions in each activity performed, by comparing the results of the post- test in relation to the pre-test, analyzing the errors that occurred in the post-test, by applying the Coefficient of Pearson's Linear Correlation and Hypothesis Test.
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8
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JOSE HENRIQUE PEREIRA
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Teaching sine and cosine in dynamic environments.
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Leader : FABIO JOSE DA COSTA ALVES
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Data: 17 mai 2023
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Afficher le Résumé
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This research aims to present the results of a research, whose objective is to investigate the potentiality of a didactic sequence in the learning of trigonometric relations in the right triangle, sine, cosine and tangent functions, using a free software called GeoGebra, whose focus is to apply a didactic experiment, as an alternative for teaching trigonometry. The focus of the research will be the students of a public high school, of the Federal Institute of Education of Maranhão, in São Luís, on Campus Monte Castelo. The subjects were 35 students (who were divided into two groups) of the second year of high school. As a research instrument, a didactic sequence with 12 activities was used. The research methodology adopted was Rabardel's Instrumentation theory, Duval's theory of Semiotic Representations and Microgenetic Analysis. of Mathematics, served as a subsidy for the construction of the 12 activities of the didactic sequence, for learning the basic concepts, properties, and definitions of trigonometric ratios in the right triangle, of the sine, cosine, and tangent functions. The research results from the written records and recorded voices, show us that the learning of the students/participants was gradual and that the subjects had satisfactory results, since they point out that the activities in the GeoGebra application is a didactic resource that makes the activities more dynamic, favoring the construction of learning, in relation to the proposed trigonometric contents. Thus, we conclude that the learning of the subjects involved with our object of study, demonstrated at least two registers of representation, that is, in two different languages, feeling motivated to create possibilities for problem solutions.
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9
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BRENO SALGADO FERREIRA
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DIDACTIC SEQUENCE FOR TEACHING COSINE FUNCTION
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Leader : NATANAEL FREITAS CABRAL
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Data: 16 juin 2023
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Afficher le Résumé
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The present work is a research developed in the Professional Master's Program in Mathematics Teaching (PMPEM) of the State University of Pará. The objective of the research is to analyze the evidence of learning resulting from the application of a didactic sequence involving the cosine function from the following research question: What are the contributions that a didactic sequence elaborated according to the model of the Articulated Units of Conceptual Reconstruction (UARC) bring to the process of teaching and learning the cosine function to 2nd grade high school students in a public school in the metropolitan region of Belém (PA)? To this end, a historical and bibliographical survey was carried out to support and originate the suggested question with Gama (2020), Corrêa (2016) and Domingos Neto (2014) as interlocutors. We did a historical survey to understand how the Cosine Function theme evolved, looking for the main characters ranging from Hipparchus of Nicaea (190 - 120 BC) to Leonhard Euler (1707 - 1783). With regard to the analysis of the evidence of students' learning in the application of the Didactic Sequence, we intended that Microgenetic Analysis with Goés (2000) and Discourse Analysis with Mortimen and Scott (2002) be used. We did a survey on the use of the GeoGebra application in the classroom and the benefits that the movements generated by the constructed images can bring to the student in the learning process based on research by Bortolossi (2020). We built a didactic sequence structuring it according to the UARC's models proposed by Cabral (2017), resulting in 5 UARCs that address the content of the cosine function, starting with the association of real numbers to a point of the circle S^1, thus formulating Euler's function and ending with the construction of the graph of the function of the type E(t)=a+b.cos〖(c.t+d)〗. The sequence would be applied in a Public School in the city of Belém-PA. However, due to the circumstances caused by the COVID-19 pandemic, there was a need to redirect the process to a group of teachers, so that they could carry out the assessment of the construct through a questionnaire. In this way, we obtained as a result, that the Didactic Sequence developed presents potentialities for the teaching of Cosine Function, for several reasons pointed out by the teachers. Among which we highlight: the attractiveness linked to the use of technology, as well as the appropriate language that allows a gradual evolution of the mathematical object, in addition to the protagonist role that the student assumes during the sequence. In this way, we managed to overcome the difficulties presented by students in the literature, thus providing an effective educational product to fellow teachers.
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10
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VERACIV BRABO DE VASCONCELOS
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A Journey through the History of Probability in Mathematics Teaching.
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Leader : MIGUEL CHAQUIAM
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Data: 16 juin 2023
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Afficher le Résumé
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The Interest in the subject emerged during the development of the subject Topics in the History of Mathematics. Research indicates that teachers should rely on diverse teaching methods, and the History of Mathematics emerges with the Methodological Tendencies of Mathematics Education. In light of this, the question arose: what historical clippings can be elaborated from a history of probability, according to Chaquiam (2022), for use in the classroom? The general objective of this study was to develop historical excerpts based on a history of probability, for use in the classroom. The research had a qualitative nature, drawing on bibliographic and documentary sources, anchored by the Methodological Diagram of Chaquiam (2022), considered a guide in the bibliographic review for the survey of historical and literary facts; in construct a diagram about a history of probability; produce the historical clippings and in the elaboration of activities. The research was based on official curriculum documents, surveys teachers' perceptions, analysis of textbooks and other documents and authors that guide the History of Mathematics in Education and the History of Probability. Data collection had to be conducted through a virtual questionnaire due to the pandemic caused by COVID-19, limiting the validation of the material to mathematics teachers only. The results indicated a 90% or higher acceptance of the Historical Text and the set of activities, stipulating an accessible language and activities that expand the students' vocabulary and promote their autonomy in the teaching process. The result of the complementary evaluation revealed that 97.2% of teachers agreed with the use of the Educational Product, corroborating its validation to be used in the classroom. Teacher’s suggestions were incorporated to enhance the product. Finally, it is recommended to validate the material with students to analyze its effectiveness, production and new historical clippings, elaboration of additional activities and adaptation of texts and activities for different levels of education, according to the specific needs of students in each locality or region.
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11
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NATALI DE JESUS FERREIRA DE MIRANDA
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TEACHING ADDITION AND SUBTRACTION OF FRACTIONS THROUGH EXPERIMENTAL ACTIVITIES
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Leader : MARIA DE LOURDES SILVA SANTOS
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Data: 30 juin 2023
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Afficher le Résumé
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The search for more dynamic and effective alternatives for teaching mathematics has been a constant concern
of many teachers and for this reason this research has as its central question to investigate the effects of applying
a didactic sequence on conceptual and procedural learning of addition and subtraction of fractions, when worked with
students in the 6th year of elementary school? The general objective will be to analyze the effects of applying a
didactic sequence, based on experimental activities and problem solving, on the teaching of addition and subtraction
of fractions regarding the learning of conceptual and procedural aspects of students in the 6th year of elementary
school. The locus of the research will be a 6th grade class of a public school in the city of Thailand/Pa, and the
experiment will take place with the students of that class. We will adopt as Trends in Mathematics Education, the
Teaching of Mathematics through Experimental Activities and Problem Solving. As a research methodology, we will
follow the stages of Didactic Engineering by Artigue (1996), according to which, it will be developed in four stages.
The first stage (Previous analyses) consists of a historical survey, a theoretical study on our object of study,
consultation with Mathematics teachers and 6th grade students, on the teaching and learning process of adding
and subtracting Fractions. The second stage (Conception and a priori analysis) consists of the construction of a
didactic sequence composed of four activities that address the concept of addition and subtraction with fractions,
2 tests (Pre-test and Post-test), as well as the analyzes to priori carried out for each of the activities. The third
stage of the study, (Experimentation). In the fourth stage (A posteriori analysis and validation), we will analyze
the activities and evaluation tests through a qualitative and quantitative approach. The final intention of the
study is to generate an educational product, specifically a didactic sequence tested with the students and
validated by the class teacher, in order to collaborate with other teachers when they are going to teach addition
and subtraction of fractions.
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12
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VAGNEY DOS SANTOS E SANTOS
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Teaching related functions through experimental activities: in the 9th grade of elementary school in Altamira-PA
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Leader : PEDRO FRANCO DE SA
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Data: 29 août 2023
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Afficher le Résumé
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This work presents the results of a research that aimed to evaluate the effects of applying a didactic sequence based on the teaching of mathematics through experimental activities on the performance of problem solving and the understanding of affine function concepts by 9th grade students. fundamental year. The research sought to answer what effects does the application of a didactic sequence based on experimental activities have on the performance of question resolution and the understanding of affine function concepts of students in the 9th grade of elementary school?? The research methodology used was Didactic Engineering. And as research resources: bibliographical analysis of other works that directly or indirectly addressed the theme addressed here, application of questionnaires and tests. The didactic sequence elaborated in this work took place in six meetings, and was applied to 44 students of the 9th grade of the final years of elementary school in two public schools in the municipality of Altamira-PA. The analysis of the collected data occurred by verifying the record of the students' conclusions in each activity carried out, by comparing the results of the post-test in relation to the pre-test, by applying Pearson's Linear Correlation Coefficient and the Hypothesis Test and some observations in loco, these strategies of statistical inferences confirmed that the didactic sequences by applied activities produced better results for the understanding of the concept of affine function, as well as, in the interpretations and solutions of problems involving this theme. We also verified that the students obtained progressive advances within the process of institutionalization of the approached mathematical concepts and definitions; in addition, we noticed a more expressive participation of the students in the solutions of the questions, as perceived in the Post-test. In view of this and the results in the comparison of performance in the Pre and Post-test, we can say that the objective of this work was achieved and the problem raised initially was answered. The result is similar to others from researchers and authors who applied Didactic Engineering as a line of research in the application of didactic sequence by activities involving the affine function.
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13
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ERNANI SOEIRO DA COSTA
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TEACHING ARITHMETIC PROGRESSION THROUGH DIDACTIC SEQUENCE
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Leader : MIGUEL CHAQUIAM
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Data: 27 oct. 2023
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Afficher le Résumé
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This work presents a set of approaches for teaching arithmetic progression carried out during the Master's course in Mathematics Teaching, seeking to answer the following question: To what extent does a Didactic Sequence elaborated according to the structuring model of the Articulated Units of Conceptual Reconstruction (UARC) proposal by Cabral (2017) enhances the teaching and learning process of arithmetic progression? Therefore, it was defined as a general objective to verify the didactic potential of a Didactic Sequence elaborated for the teaching and learning of arithmetic progression. The research approach is quantitative and qualitative. As theoretical contributions that guided and enabled the development of the research, Mathematics Education was elected, which promotes teaching practice at theoretical and experimental levels, the Didactic Situation Theory described by Brousseau (1996), the didactic sequence marked by Zabala (1999 ) and structured according to the Articulated Units of Conceptual Reconstruction proposed by Cabral (2017). Thus, in order to identify the difficulties in the teaching and learning process of arithmetic progression, a bibliographical survey of research related to the teaching of arithmetic progression, analysis of textbooks, in addition to the opinion of teachers of Basic Education and of students who graduated from the 1st year of high school. In summary, the results of the bibliographic survey of research, the opinions of professors and students helped me in the planning, elaboration and execution of research activities. And yet, they contributed in a general way to the experience with the students, in particular, with those pointed out as learning deficits. In addition, the analysis of textbooks revealed that the theme approach is not allied to student learning, as well as, it does not correspond to a component that actually helps the teacher in the classroom.
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14
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JESSIE HEVENY SARAIVA LIMA
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The History of Trigonometry and its Teaching: Classroom Cutouts
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Leader : MIGUEL CHAQUIAM
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Data: 27 oct. 2023
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Afficher le Résumé
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The History of Mathematics is highlighted by literature and official documents as an efficient teaching resource for improving the student's teaching and learning process, however, despite the efficiency it can provide, there is a scarcity of theoretical references that make use of the History of Mathematics. Mathematics, which led me to become interested in this study, more specifically for the teaching of trigonometry, a fact that led me to the following research question: “What historical insights can be made from a history of trigonometry in order to integrate history and mathematics in a didactic-pedagogical context for use in the teaching process in Basic Education?”. To answer this question, the aim was to prepare texts with excerpts from the history of trigonometry, using the methodological diagram proposed by Chaquiam (2017, 2020, 2022), so that they can be used as a teaching resource during the teaching process of the contents involved. . To this end, this work reports a bibliographical research that falls within the area of Mathematics Education, in the line of History of Mathematics, in which we review the studies carried out by Costa (2003), Chaquiam (2017, 2020, 2022) Gomes (2009 ), Mendes (1997), Miguel (1993), Oliveira (2009), Prado (1990), Viana e Silva (2007) and among other studies that point to the History of Mathematics and warn the importance of using this didactic resource in teaching of trigonometry. Furthermore, a questionnaire was administered via Google Forms to teachers from different education networks with the aim of carrying out a diagnostic survey of the teaching process of trigonometry content. And another questionnaire, also via Google Forms, was applied with the aim of analyzing the historical text, its excerpts and their respective proposed activities. Given this context, from the literature, it was observed that the History of Mathematics has been seen as relevant to the teaching and learning process and that it can be considered as a teaching resource, capable of encouraging students during math classes. mathematics. Furthermore, based on the results of the questionnaires, we can see some difficulties experienced by teachers during the process of teaching trigonometric content and the need for innovative teaching resources that can improve this teaching, which allows us to conclude that the History of Mathematics in teaching mathematics, particularly trigonometry, can be efficient in improving the mathematics teaching and learning process. The results of this research generated the educational product entitled: “Teaching trigonometry through historical clippings2
”, available at the link indicated in the footer.
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15
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LUCAS BENJAMIN BARBOSA SOUZA
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Rational roots of polynomial equations: a teaching approach based on didactic sequence in the light of UARC's.
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Leader : NATANAEL FREITAS CABRAL
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Data: 27 oct. 2023
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Afficher le Résumé
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The educational question about teaching and learning mathematics is one of the inexhaustible aspects of Mathematics Education, since there is no perfect method or one that allows full learning. In this sense, the search for improvement of this process is of interest to education professionals in their research. This work presents a methodological proposal for teaching the theorem of polynomial rational roots of walking whose research aims to study the potentialities of a didactic sequence elaborated from the concepts of Articulable Units of Conceptual Reconstruction (UARC's) for teaching and learning of the polynomial rational roots of anxiety theorem. This research is configured as experimental, with descriptive objective, quantitative and qualitative character and phenomenological approach. Thus, we list as theoretical contributions the sociocultural theory of learning by Vygotsky (1984); Brousseau's theory of didactic situations (1978) and requests for the didactic sequence centered on Zabala (1999) with an approach in the articulable units of conceptual reconstruction by Cabral (2017). In order to investigate this mathematical object in the teaching and learning process, carrying out preliminary studies composed of mathematical foundations; consultation of official documents; review of studies; textbook analysis; considerations from students and teachers. Preliminary studies allowed the elaboration of a didactic sequence for teaching the theorem of rational roots to be applied with 3rd year high school students after initial diagnosis and necessary leveling. The experimentation will be recorded in audio and the results will be analyzed from the sequence applied together with the information initiated from the treated according to the concepts of discourse analysis in Góes (2000) and the microgenetic analysis of Mortimer and Scott (2000 ).
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16
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NILSON OSVALDO GAMA SANTA MARIA
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A Didactic Sequence for Teaching Congruence of Triangles.
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Leader : MIGUEL CHAQUIAM
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Data: 27 oct. 2023
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Afficher le Résumé
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The partial results of a professional master's research in Mathematics teaching are presented, whose objective was to investigate the didactic potential of a didactic sequence built specifically for teaching Congruence of Triangles. The problem raised in preliminary research indicated that the mathematical object Congruence of Triangles has been treated as a tool for the development of other mathematical objects, such as the study of quadrilaterals, so that some characteristics and properties of this object are not treated in research and teaching textbooks of Teaching Fundamental and, consequently, is not studied in all its complexity. This complexity was revealed throughout the research through a historical-epistemological study on the mathematical object, according to Chaquiam (2020; 2022). In the review of studies, methodological indications and didactic materials that have potential for teaching geometry were raised, the isometric mesh was chosen as a resource for the construction of knowledge that involves cases of congruence of triangles. The didactic sequence structured as Articulated Units of Conceptual Reconstruction (UARC) was adopted as a teaching proposal, according to Cabral (2017). As a guide for the methodological path of the research, the Theory of Didactic Situations (TSD) developed by Brousseau and the methodology developed by Silva, Chaquiam, Cabral (2022) were adopted. The construct developed presents three activities planned and articulated with each other for the development of knowledge and skills involving Congruence of Triangles. After carrying out the instructions in the qualification exam, the intention is to apply the sequence in a regular class of the 8th year of Elementary School, in the public school system. The data collected in the experiment will be audio transcriptions and written records of the research subjects, analyzed according to Microgenetic Analysis and Discourse Analysis. In the elaboration of this didactic material, the dialogical quality of the teaching and learning process was considered, as well as collaborative learning. The initial research presented indicates new perspectives on the teaching of geometry, both as a field of knowledge and as an essential element for the development of mathematical arguments.
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17
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CLAUDIO LIMA DA SILVA
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Teaching Trigonometry in the Triangle through Experimental Activities
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Leader : ANA KELY MARTINS DA SILVA
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Data: 31 oct. 2023
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Afficher le Résumé
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This work presents the results of a research conducted in the Professional Master's Program in Mathematics Education (PPGEM) at the State University of Pará, aiming to address the following research question: What are the effects of a set of experimental activities on the performance in solving trigonometric problems in triangles, using the methods of conceptualization and rediscovery, when applied to 2nd-year high school students? To achieve this, the guiding objective of the investigative process is to analyze the effects of a didactic sequence through experimental activities on the performance in solving trigonometric problems in triangles, using the methods of conceptualization and rediscovery, applied to a 2ndyear high school class. The research methodology adopted is based on the assumptions of the 1st Generation Didactic Engineering, which consists of four stages: (I) Prior Analyses; (II) Conceptions and A Priori Analyses; (III) Experimentation; and (IV) A Posteriori Analysis and Validation. The educational product resulting from this dissertation consists of a structured didactic sequence (DS) based on experimental activities, problem-solving, and mathematical games, with the purpose of enhancing the learning of trigonometry in the context of triangles for 2nd-year high school students. When comparing the a priori analyses with the a posteriori analysis, the results show positive progress among the students, indicating that the DS was effective in promoting student learning. Additionally, statistical tests, such as the Exact Fisher Test and the Hypothesis Test, confirmed that the Didactic Sequence had a positive impact on student performance and minimized the influence of socioeconomic factors on student performance. Therefore, the success in the application can be attributed to the teaching methodology adopted, which presented itself as an alternative to the conventional classroom routine observed in most schools.
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18
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JORGE SOARES MENOR FILHO
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SINE FUNCTION: A DIDACTIC SEQUENCE FOR HIGH SCHOOL INSPIRED BY NATURAL PHENOMENA
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Leader : ROBERTO PAULO BIBAS FIALHO
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Data: 1 déc. 2023
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Afficher le Résumé
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This investigation was developed from the restlessness as a high school teacher in teaching the content of Sine Function and the difficulty on the part of students in learning this subject. In this context, this investigation seeks to answer the following research question: How is it possible to teach sine function, through activities that are associated with periodic phenomena of nature, with the help of pedagogical and technological resources? Thus, this research aimed to: The elaboration and analysis of a didactic sequence, mediated by geogebra, for the teaching and learning of sine function content. In order to achieve the proposed objective, we chose to carry out a quantitative-qualitative research, in which we initially made a bibliographic study based on articles, dissertations, theses and books. Then, we conducted field research through questionnaires to 35 teachers of Mathematics in the teaching profession who teach the content of the sine function in their classroom practice. The theoretical framework of the research was based on the conception of Brousseau's Theory of Didactic Situations (1996) and the teaching by activities in the view of Sá and Jucá (2017). These conceptions served to guide the analysis of the research and the production process of the educational product. From this biographical review and the methodology described, a sequence of activities was built, in which the elaboration of the educational product was preceded by a field research, in which we consulted a group of fifty high school students, to know their perspectives on the teaching of the Sino function, through activities mediated by the Geogebra software as a practical guide defined by "Sino Function: A didactic sequence for high school, inspired by natural phenomena". Thus, it was concluded that from the proposed activities, it was demonstrated by the students an excellent mastery and understanding of the proposed theme, consolidating the educational product as a great possibility of activity for the teaching of the sine function.
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19
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DENIS HEITOR DAMASCENO DA SILVA
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Educational Robotics Possibilities for Teaching the Regular Prism.
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Leader : CINTHIA CUNHA MARADEI PEREIRA CAMPOS
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Data: 12 déc. 2023
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The present research was developed with the objective of studying the potential of a sequence of activities, using educational robotics, for the teaching and learning process of Straight Prisms, based on the construction of robotic prototypes. It was applied in 3rd year high school classes, from three rural schools in the municipality of Concórdia do Pará – PA, with a total of 59 students involved, through the Modular Education Organization System – SOME. As a theoretical contribution, Seymour Papert's Constructionism was adopted and as a methodology, Design Experiments by Allan Collins and Ann Brown was used. For the application of the research, a sequence of activities was prepared, guided under the TLS (Teaching-Learning Sequences), based on the elements of Straight Prism, developed collaboratively, in 04 groups, for the construction of parts (head, torso, legs and arms) of the robot prototype. The activities developed sought to involve questions relating to surface areas and recognition of Straight Prisms. In each construction, components from the Arduino-Uno board were coupled and specific programming was developed for each prototype created, using the educational software Scratch for Arduino – S4A, which were presented to the groups through a pedagogical robotics workshop divided into two stages: Components Arduino Electronics and Use of the Educational Software Scratch for Arduino – S4A, with the use of laptops, which, in addition to learning, provided stimuli for Computational Thinking. The act of building was supported by the ideas of toys in Lev Vygotsky's education. Regarding the connection and activation of components, the concepts of Physics, electricity – Electric circuit were explored in an interdisciplinary way with mathematical content. In the construction of the robot prototype, recyclable materials were used (remains of boxes, paper and paint residues) and for the directional motors, scrap residues (motors from damaged DVDs) and/or an Arduino kit were used. The project evaluation was carried out using Viana's (2007) observational techniques through the dependent variables of Design Experiments: Climate (cooperation between learners, commitment, level of effort, etc.), Learning (knowledge, content, skills and dispositions) and Systemic (change, expansion, sustainability, ease of adoption and costs), with two redesign cycles, through which photos, videos, pre-tests and post-tests were recorded. The results obtained were favorable in two variables, Climate and Learning, and in the intended objectives. During the process, the teacher acted as a mediator with few interventions and small modifications, leaving suggestions for a new redesign. As a result of this research, the emergence of an educational product entitled “Robotics & the Metric of Forms” stands out, which presents a sequence of activities aimed at learning the content of Straight Prisms (elements, surface areas and recognition), in line with the construction of a directional robot prototype, using low-cost Arduino components and the educational software Scratch for Arduino – S4A.
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20
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ALINE REIS DE ANDRADE
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TEACHING PROBLEM SOLVING WITH AN UNKNOWN THROUGH EXPERIMENTAL ACTIVITIES
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Leader : PEDRO FRANCO DE SA
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Data: 20 déc. 2023
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This work presents the results of a study on first grade problems with one unknown. The guiding question is: What are the effects of a didactic sequence based on experimental activities on student performance in solving problems with an unknown? The research methodology adopted was Didactic Engineering. And with the aim of investigating the effects caused by this sequence in the teaching and learning process of grade one problems with one unknown. And as methodological teaching resources: teaching through activities, with the use of some teaching resources to enhance and speed up problem solving; and for analysis and proof of learning we will use Duval's Theory of Semiotic Representations. The application of the didactic sequence developed in this work took place in a 7th year class of elementary school II at a public school located in the city of Óbidos-PA. And to achieve our objective, we will rely on David Paul Ausubel's theory of meaningful learning, characterized by the interaction between prior knowledge and new knowledge that contribute to giving meaning to the subject about the subject being worked on.
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21
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LEONARDO BENEDITO SARRAF CAETANO
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TEACHING PROBABILITY THROUGH EXPERIMENTAL ACTIVITIES
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Leader : DUCIVAL CARVALHO PEREIRA
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Data: 20 déc. 2023
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This work presents a research proposal on teaching probability through experimental activities that aims to analyze the effects of applying a didactic sequence based on teaching mathematics through experimental activities for teaching the subject. The experimental part of the work will be carried out in a 9th grade class at a public school in the Pará education network. The research methodology adopted will be didactic engineering. As a product of the research, it is expected to obtain a didactic sequence for teaching capitalization with guidance for teachers.
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22
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ANDERSON DINIZ PINHEIRO
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TEACHING FIRST GRADE EQUATIONS AND PROBLEMS THROUGH EXPERIMENTAL ACTIVITIES
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Leader : PEDRO FRANCO DE SA
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Data: 21 déc. 2023
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This work shows the progress of the stages of an investigation that aims to analyze the impacts of developing experimental activities on learning 1st grade problems and equations with an unknown with students from a 7th year elementary school class at a public school in city of Parauapebas/PA. The methodological approach used to conduct this study was Didactic Engineering. The information began to be produced from the month of May 2022, with theoretical studies on Didactic Engineering, then the preliminary analysis stage was experienced, which included historical data on the subject, with mathematical aspects, with review of current literature that deals with the mathematical object addressed and with information from 52 public school teachers who gave their opinion on teaching 1st grade problems with an unknown. The data were obtained through the application of questionnaires and their treatment was carried out through tables and graphs with their appropriate quantitative analyses. The text exposes the set of activities that make up a sequence of experimental activities proposed for the experimentation phase. The a priori analysis stage was also experienced, revealing expectations about each activity in the experimental sequence. We are currently in the experimentation phase, to later carry out post-mortem analyzes and validation of the activities developed during the application of the didactic sequence. The systematization of the information produced occurred through the construction of statistical tables and graphs. The results and validation of the didactic sequence will be considered based on the comparison between a priori analysis and a posteriori analysis. Based on the results of the study, an educational product will be created in the format of a didactic sequence.
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23
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CARMEN SIMONE DOS SANTOS LOPES
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TEACHING PROBLEM SOLVING IN THE MULTIPLICATION CONCEPTUAL FIELD WITH NATURAL NUMBERS BY EXPERIMENTAL ACTIVITIES
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Leader : PEDRO FRANCO DE SA
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Data: 21 déc. 2023
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Afficher le Résumé
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This work presents the results of a research, the objective of which was to analyze the possible effects of applying a
didactic sequence based on the teaching of mathematics through experimental activities on the performance of
students in the 6th year of elementary school in solving questions involving the multiplicative conceptual field. with
natural numbers. The research question of the study was what type of effect can the application of a didactic
sequence through experimental activities have on the performance of students in a 6th year elementary school
class in solving multiplicative problems with natural numbers? Its theoretical contribution was the theory of
conceptual fields, the multiplicative conceptual field and teaching through experimental activities. The path chosen
for this work considers the assumptions of didactic engineering as a research methodology, addressing all its
stages: prior analyses, a priori analyses, experimentation, a posteriori analyzes and validation. The
experimentation and information collection were obtained with students from a 6th year class at a municipal school
in Parauapebas (PA).
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24
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DEJACI SOARES DA SILVA
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ADDITIVE PROBLEM SOLVING: TEACHING THROUGH EXPERIMENTAL ACTIVITIES
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Leader : PEDRO FRANCO DE SA
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Data: 21 déc. 2023
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This work presents the partial results of research developed in the Professional Master's Program in Mathematics
Teaching (PPGEM) at the State University of Pará, with the purpose of answering the following problem: How to
apply a didactic sequence, based on the teaching of does mathematics through experimental activities influence
the performance of solving additive problems with natural numbers? With this purpose, the objective behind this
investigation is: to analyze the effects of applying a didactic sequence, based on teaching mathematics through
experimental activities, on the performance of solving additive questions with natural numbers of students in the
6th year of elementary school . The research methodology that will be adopted is Didactic Engineering of the 1st
Generation (ED1G), consisting of four stages: initially we present the previous analyses, consisting of a review of
studies on additive problems and a consultation with students in the 6th year of Education Fundamental about the
teaching-learning process of this content. In the second stage, called a priori conception and analysis, descriptions
of Teaching by Activities, Problem Solving, the use of Games as a methodology for teaching mathematics and
a didactic sequence for teaching additive problems are presented, consisting of 15 activities and organized
according to the methodologies mentioned. The third stage of the study is called experimentation, according
to ED1G. In the fourth stage, a posteriori analysis and validation, analyzes of activities and evaluative tests
will be carried out using a qualitative and quantitative approach. At the end of the research, an educational
product will be obtained based on the studies and results achieved, organized according to a didactic sequence
for teaching additive problem solving, enabling the teacher to use didactic sequences through experimental
activities and problem solving. , with the intention of contributing significantly to the teaching and learning
of this object of study.
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