Didactic Sequence for Teaching Exponential Function

Marconni Augusto Pock de Oliveira OLIVEIRA, M. A. P.; Miguel Chaquiam CHAQUIAM, M.; Natanael Freitas Cabral CABRAL, N. F.; Gustavo Nogueira Dias DIAS, G. N.; Cássio Pinho dos Reis REIS, C. P.; Eldilene da Silva Barbosa BARBOSA, E. S.; Jamile Carla Oliveira Araújo ARAÚJO, J. C. O.; ANTONIO THIAGO MADEIRA BEIRÃO BEIRÃO, A. T. M.; Katiane Pereira da Silva SILVA, K. P.; Herson Oliveira da Rocha ROCHA, H. O.; Nazaré Doriene de Melo Reis REIS, N. D. M.; Wagner Davy Lucas Barreto  BARRETO, W. D. L.

doi:10.31686/ijier.vol9.iss8.3270

Authors

Marconni Augusto Pock de Oliveira OLIVEIRA, M. A. P. Secretaria Municipal de Educação e Desporto (SEMED) Cidade de Tomé Açu Pará.
Miguel Chaquiam CHAQUIAM, M. STATE UNIVERSITY OF PARÁ
Natanael Freitas Cabral CABRAL, N. F. STATE UNIVERSITY OF PARÁ
Gustavo Nogueira Dias DIAS, G. N. FEDERAL COLLEGE OF AERONAUTICS TENENTE REGO BARROS
Cássio Pinho dos Reis REIS, C. P. Federal University of Mato Grosso of South (UFMS)
Eldilene da Silva Barbosa BARBOSA, E. S. RURAL FEDERAL UNIVERSITY OF AMAZON
Jamile Carla Oliveira Araújo ARAÚJO, J. C. O. RURAL FEDERAL UNIVERSITY OF AMAZON
ANTONIO THIAGO MADEIRA BEIRÃO BEIRÃO, A. T. M. RURAL FEDERAL UNIVERSITY OF AMAZON
Katiane Pereira da Silva SILVA, K. P. RURAL FEDERAL UNIVERSITY OF AMAZON
Herson Oliveira da Rocha ROCHA, H. O. RURAL FEDERAL UNIVERSITY OF AMAZON
Nazaré Doriene de Melo Reis REIS, N. D. M. Estácio do Para Faculty
Wagner Davy Lucas Barreto BARRETO, W. D. L. FEDERAL COLLEGE OF AERONAUTICS TENENTE REGO BARROS

DOI:

https://doi.org/10.31686/ijier.vol9.iss8.3270

Keywords:

Math, Teaching, Didactic Sequence, Exponential Function

Abstract

This paper presents a methodological proposal for the teaching of exponential function, resulting from the application of a didactic sequence involving exponential function, where evidence of learning and the consolidation and application of mathematical concepts in problem solving were identified and analyzed. The Didactic Engineering of Michèle Artigue (1988) was used as a research methodology. As theoretical contributions that guided and enabled the development of the research, we chose the use of Mathematical Investigation in the classroom; Didactic Sequence in the conception of Zabala (1999); the Articulated Units of Conceptual Reconstruction proposed by Cabral (2017) and assumptions of Vygotsky's theory. A didactic sequence composed of five UARC's was elaborated to work the exponential function, with a view to minimizing the difficulties naturally imposed by the content to be explained. Microgenetic analysis of verbal interactions between teacher and students was used to analyze the results of the application. The results show that the students participating in the experiment showed evidence of learning, recorded during the process, and began to have a good understanding of the concepts and properties related to the topic, in addition to a good performance in carrying out the activities, facts that corroborate the potential of the didactic sequence proposed herein.

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Author Biographies

Marconni Augusto Pock de Oliveira OLIVEIRA, M. A. P. , Secretaria Municipal de Educação e Desporto (SEMED) Cidade de Tomé Açu Pará.

Degree in Mathematics from the State University of Pará (UEPA - 2015) and Master in Mathematics Teaching by the Post-Graduate Program in Mathematics Teaching at the State University of Para (PPGEM UEPA - 2018). He is currently Professor of Mathematics (conducted) linked to the Municipal Department of Education and Sports (SEMED), of the Municipality of Tomé-Açu (PMTA), State of Pará and is currently taking a second degree in Chemical Engineering - Bachelor's Degree from the Federal University of Pará - UFPA. Member of the Research Group on the History of Mathematics and Mathematics Education in the Amazon (GHEMAZ - UEPA). He was Scholarship Monitor of the discipline Fundamentals of Elementary Mathematics 1 - FME 1 (2014 - 2015) and Volunteer Monitor of the discipline Fundamentals of Elementary Mathematics 2 - FME 2 (2015) by the State University of Pará. He was Professor of Mathematics of the Cursinho Extension Project Alternative of UEPA, on a Voluntary basis (2013 - 2015). He was Mathematics Professor at the Futuro-Reforço Escolar Course (2013), Mathematics Monitor at the Ideal Alcindo Cacela Course (2013) and Mathematics and Chess Monitor at the More Education Program of the Federal Government (2013-2015). He has experience in Mathematics, with an emphasis on Mathematics, Mathematical Problem Solving and Mathematics Teaching for Elementary School - Final Years (6th to 9th year), High School and Higher Education (Analytical Geometry, Differential and Integral Calculus and Differential Equations).
Miguel Chaquiam CHAQUIAM, M., STATE UNIVERSITY OF PARÁ

Degree in Science from the Center for Higher Studies of the State of Pará (1983), Degree in Mathematics from the Center for Higher Studies of the State of Pará (1984), Specialist in Mathematics from UNESPA (1989), Master in Mathematics from the Federal University of Pará ( 2001) and PhD in Education from the Federal University of Rio Grande do Norte - UFRN (2012). He is currently a professor at the University of the State University of Pará-UEPA. He works in higher education as a teacher in the Licentiate Degree in Mathematics, Licentiate Science and Pedagogy courses, and in the Specialization Courses in Mathematics Education and Fundamentals of Mathematics. He has experience in Mathematics, with an emphasis on Computational Mathematics, Linear Algebra; Algebraic Structures, Real Analysis, History of Mathematics, History of Science and Teacher Education. He was a Mathematics teacher in Elementary and High School for 18 years, Director of SBEM-PA during the 2004/2007 triennium, member of the SBEM DNE in the 2007/2010 triennium. He is an evaluator of the Revista Iberoamericana de Educação Matemática-UNIÓN, member of the Scientific Committee of the Revista REMATEC, Member of the Editorial Board of the Contextos da Ciência collection, a publication of the Editora Livraria da Physics. Professor in Higher Education for over 30 years. Linked to the Professional Master's Program in Mathematics Teaching (PMPEM) of the State University of Pará (UEPA) and Leader of the Research Group on History, Education and Mathematics in the Amazon (GHEMAZ). Member of the Board of SBHMat and Scientific Coordinator of the XIII National Seminar on the History of Mathematics (XIII SNHM), which will be held in Fortaleza (CE), from April 14 to 17, 2019, at the State University of Ceará (UECE).
Natanael Freitas Cabral CABRAL, N. F., STATE UNIVERSITY OF PARÁ

Degree in Science from the Federal University of Pará (1985), Degree in Mathematics from the Federal University of Pará (1988), Bachelor of Theology - Equatorial Baptist Theological Seminary (1994), and Master in Education in Science and Mathematics from the Federal University of Pará ( 2004). PhD in Education from PUC-Rio. He has experience in the field of Education, with an emphasis on Mathematics. He currently teaches the subjects: Instrumentation I and II in the Mathematics Degree course at the State University of Pará (UEPA) and Mathematics Teaching I and II in the Professional Master's Program in Mathematics Teaching (PMPEM/UEPA). He was a teacher of Basic Education for 36 years at the public school and Escola Tenente Rêgo Barros. He has been working in higher education for over 15 years. He currently coordinates the Laboratory of Mathematics Education (LABEM/UEPA) and is the Leader of the Research Group on History, Education and Mathematics in the Amazon (GHEMAZ), linked to the University of the State of Pará.
Gustavo Nogueira Dias DIAS, G. N., FEDERAL COLLEGE OF AERONAUTICS TENENTE REGO BARROS

Doctor in Education from the National University of Rosario, Argentina (2017); Master in Geophysics from the Federal University of Pará, Belém (2011); Specialist in School Management by the University Center of Pará (2008); Full Degree in Mathematics from the Federal University of Pará (2001). Worked in private schools from 1991 to 2005. Joined SEDUC(PA) as a full professor from 2006 to 2016. Participated as a professor with a scholarship at PARFOR, at IFPA (Federal Institute of Education , Science and Technology of Pará), in 2012. He also served as a professor at UFRA (Federal Rural University of the Amazon) in 2013. He joined UNAMA (University of the Amazon) as a full professor from 2015 to 2016. of the Federal Elementary School of Colégio Ten. Rêgo Barros, which he joined in 2005 and from 2017 onwards he carries out his activities under the exclusive dedication regime. Participates in the study group GHEMAZ at UEPA, State University of Pará. He also works as a researcher in the areas: Environmental Science, Teaching and Learning, Mathematics Education, History of Mathematics, Mathematical Modeling, Administration, Accounting and Statistics.
Cássio Pinho dos Reis REIS, C. P. , Federal University of Mato Grosso of South (UFMS)

Bachelor in Statistics from the Federal University of Pará (2007), Master in Applied Statistics and Biometrics from the Federal University of Viçosa (2013) and Ph.D. in Biometrics from the Universidade Estadual Paulista - Botucatu (2019). He is currently Adjunct Professor A, level 1, at the Federal University of Mato Grosso do Sul. He teaches Statistics, Probability and Statistics, Biostatistics, Zootechnical Experimentation and Experimental Statistics. He has experience in Experimental Statistics, Regression and Correlation Analysis and Spatial Statistics.
Eldilene da Silva Barbosa BARBOSA, E. S., RURAL FEDERAL UNIVERSITY OF AMAZON

PhD student in Agronomy at the Federal Rural University of the Amazon; Master in Administration from UNAMA; MBA in Accounting Management, Auditing, Expertise and Controllership; Graduated in Accounting from the University Center of the State of Pará. Professor of Higher Education at the Federal Rural University of the Amazon.
Jamile Carla Oliveira Araújo ARAÚJO, J. C. O., RURAL FEDERAL UNIVERSITY OF AMAZON

Assistant Professor with exclusive dedication at the Federal Rural University of the Amazon (UFRA), who is currently working provisionally at the Federal University of Pernambuco (UFPE), public servant, of the Bachelor of Accounting course, working in the areas of entrepreneurship, cooperativism, controllership , accounting information system and actuarial accounting. Master in Administration - With a line of Research in Organizational Management, from the University of Amazônia (UNAMA), where she worked with studies focused on cooperation and cooperative networks. In 2009 to 2016 he held the position of commercial registration technician performing analysis of opening processes, changes, filing of balance sheets, Minutes of meetings of the various legal types (Individual entrepreneur, EIRELI, Limited Company, Cooperative Society, Joint-stock Company, Consortia, Special Purpose Company) and also held the position of commercial registry manager in a deconcentrated Capanema unit, and interim director of commercial registry. MBA- Accounting Management, Audit, Expertise and Controllership, as an object of study in accounting information systems and hospital controllership, being responsible for the systematization of hospital accounting accounts at Hospital D. Luiz Benemerita Beneficente Portuguesa de Belém- Pará. Amazon Higher Education Institute - Iesam (2007). Member of the DELIBERATIVE BOARD OF RESEX MARINHA DE TRACUATEUA., representing UFRA ordinance No. 2466 of October 4, 2018
ANTONIO THIAGO MADEIRA BEIRÃO BEIRÃO, A. T. M., RURAL FEDERAL UNIVERSITY OF AMAZON

He holds a PhD (2018) and a Master's (2014) from the Graduate Program in Electrical Engineering at the Federal University of Pará (UFPA). Specialization in Contemporary Physics (2012), Bachelor's Degree in Physics (2018) and Degree in Mathematics (2010) all from the Federal University of Pará (UFPA). In addition, he has a degree in Physics (2009) from the Federal Institute of Education, Science and Technology of Pará (IFPA). He has experience in Condensed Matter Physics, acting mainly on the following topics: (i) Electronic Transport using Green out of balance (NEGF) formalism in the presence of Majorana Fermions; (ii) Electronic Transport in 2D allotropes of carbon under the effects of hydrogenation and doping; (iii) Teaching Physics using active methodologies and digital technologies. He is currently an Adjunct Professor at the Federal Rural University of Amazonia-UFRA.
Katiane Pereira da Silva SILVA, K. P., RURAL FEDERAL UNIVERSITY OF AMAZON

Graduated in Licenciatura in Natural Sciences - Physics from the University of the State of Pará (2006). Master in Physics from the Federal University of Maranhão (2010). PhD in Physics from the Federal University of Ceará (2014) with a PhD internship (sandwich) from the Institut de Cièncias de Materials de Barcelona (with research in semiconductor materials). She is currently an Adjunct Professor at the Federal Rural University of the Amazon - Campus Belém. She has experience in the area of Condensed Matter Physics in the experimental area, working mainly on the following topics: optical and structural properties of materials, using mainly the techniques of Raman Spectroscopy and Spectroscopy Infrared. Application of high hydrostatic pressures to organic and inorganic materials, X-ray diffraction and Rietveld refinement method
Herson Oliveira da Rocha ROCHA, H. O., RURAL FEDERAL UNIVERSITY OF AMAZON

Herson Rocha has a degree in Mathematics from the State University of Pará (UEPA, 2005), a master's degree in Geophysics from the Geosciences Institute of the Federal University of Pará (IG/UFPA, 2012), and a Ph.D. in Reservoir and Exploration Engineering from the Laboratory of Petroleum Engineering and Exploration at the State University of Norte Fluminense Darcy Ribeiro (LENEP/CCT/UENF, 2020). He is also a member of the Brazilian Society of Geophysics (SBGf) and the European Association of Geoscientists & Engineers (EAGE). He currently holds the position of adjunct professor at the Federal Rural University of Amazônia (UFRA).
Nazaré Doriene de Melo Reis REIS, N. D. M., Estácio do Para Faculty

Degree in ACCOUNTING SCIENCES from the University of Amazônia (2005). He is currently studying Law at Faculdade Estácio do Pará. He has a postgraduate degree in TAX MANAGEMENT at Faculdade Ideal (FACI), and in STRATEGIC ADMINISTRA-TION at Faculdade Uniamericas (2014). She is currently Coordinator of the Accounting Sciences Course and professor at FACULTY ESTÁCIO DO PARA, MA in Administration from Universidad San Lorenzo (2015), and MA in Education from Universidade Metodista (2015). She is currently a Full University Professor at Faculdade Estácio do Pará (FAP) and an accountant and partner at MS CONTABILIDADE LTDA. He has experience in the field of Accounting Sciences, with an emphasis on Tax Management, Personnel and Accounting, working mainly on the following topics: Commercial and Financial Accounting, Management Accounting, Cost Accounting, Structures of Financial Statements, Computerized Practices, Management of Labor Practices , Tax Accounting and General Accounting.
Wagner Davy Lucas Barreto BARRETO, W. D. L., FEDERAL COLLEGE OF AERONAUTICS TENENTE REGO BARROS

Graduated in Mathematics from the Federal University of Pará (2009) , and in science from the State University of Maranhão (2008). Specialist in Didactics of Mathematics by UFPA, Master's Degree in Mathematics in National Network by the Federal University of Pará (2020). Master's Degree in Environmental Sciences from the University of Taubaté (2012) . He is currently an instructor professor at the Air Force Command at Colégio Tenente Regô Barros CTRB and adjunct professor at Faculdade Pan Amazônica FAPAN. He has experience In preparation for the Mathematics Olympiads, he has experience in elementary, middle and higher education in face-to-face and distance education.

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