Ensino de Funções Polinomiais com o Polibot App
Um Estudo de Pesquisa Baseada em Design
DOI:
https://doi.org/10.46312/gh6g9h03Keywords:
Mathematics Education, Polynomial Functions, Educational Technology, Robotics, Design-Based ResearchAbstract
This article presents the results of a Design-Based Research (DBR) project aimed at developing, implementing, and refining an interactive application for teaching polynomial functions, within a real school setting. Grounded in constructivist learning theory, cognitive load theory, and the pedagogical affordances of educational technologies, the study was conducted through four iterative cycles, involving problem analysis, prototype development, classroom implementation, and redesign. The educational product, named Polibot, employs robotic simulations to foster conceptual understanding through contextualized and progressively challenging activities. Findings suggest that the tool enhanced student engagement, supported graphical interpretation, and promoted more meaningful learning of polynomial function concepts, particularly by bridging theoretical knowledge and practical application within a virtual problem-solving environment.
References
ALDALALAH, Osamah Mohammad Ameen et al. The Effectiveness of Interactive Digital Content Based on the TPACK Model in Developing the Skills of Educational Aids Production and Improving Cognitive Achievement among Early Childhood University Students. Contemporary Educational Technology, v. 17, n. 2, 2025.
ANDERSON, Terry; SHATTUCK, Julie. Design-based research: A decade of progress in education research?. Educational researcher, v. 41, n. 1, p. 16-25, 2012. Disponível em: https://doi.org/10.3102/0013189X11428813. Acesso em: 12 jan. 2024.
AYRES, Paul; SWELLER, John. The split-attention principle in multimedia learning. The Cambridge handbook of multimedia learning, v. 2, p. 135-146, 2005.
BAKKER, Arthur; VAN EERDE, Dolly. An introduction to design-based research with an example from statistics education. Approaches to qualitative research in mathematics education: Examples of methodology and methods, p. 429-466, 2015.
BOALER, Jo; SELLING, Sarah Kate. Psychological Imprisonment or Intellectual Freedom? A Longitudinal Study of Contrasting School Mathematics Approaches and Their Impacton Adults' Lives. Journal for Research in Mathematics Education, v. 48, n. 1, p. 78-105, 2017. Disponível em: https://pubs.nctm.org/view/journals/jrme/48/1/article-p78.xml.
CHANDLER, Paul; SWELLER, John. Cognitive load theory and the format of instruction. Cognition and instruction, v. 8, n. 4, p. 293-332, 1991. Disponível em: https://www.tandfonline.com/doi/abs/10.1207/s1532690xci0804_2.
COLLINS, Allan; JOSEPH, Diana; BIELACZYC, Katerine. Design research: Theoretical and methodological issues. In: Design-based research. Psychology Press, 2016. p. 15-42.
DA SILVA, Cleomacio Miguel et al. Ajuste de funções matemáticas de crescimento aos números de casos de pessoas contaminadas com o COVID-19 no Brasil: uma abordagem para o ensino médio. Research, Society and Development, v. 10, n. 16. Disponível em: https://rsdjournal.org/index.php/rsd/article/view/23881
DÍAZ, Frida; HERNÁNDEZ, Gerardo. Estrategias docentes para un aprendizaje significativo. México: McGraw-Hill, 2002. Disponível em: https://www.academia.edu/download/53051798/EstratDocParaUnAprendSignif.pdf.
EVIYANTI, Cut Yuniza et al. Improving the students’ mathematical problem solving ability by applying problem based learning model in VII grade at SMPN 1 Banda Aceh Indonesia. International Journal of Novel Research in Education and Learning, v. 4, n. 2, p. 138-144, 2017.
FITRIA, Tira Nur. Artificial intelligence (AI) in education: Using AI tools for teaching and learning process. In: Prosiding Seminar Nasional & Call for Paper STIE AAS. 2021. p. 134-147.
FOSSA, John A. Algumas considerações teóricas sobre o ensino de matemática por atividades. REMATEC, v. 15, n. 35, p. 10-26, 2020. Disponível em:
http://www.rematec.net.br/index.php/rematec/article/view/92
FUCHS, Lynn S. et al. Improving language comprehension to enhance word-problem solving. Reading & Writing Quarterly, v. 36, n. 2, p. 142-156, 2020. Disponível em: https://www.tandfonline.com/doi/abs/10.1080/10573569.2019.1666760.
GALUPAR, Ian John M. et al. Advancing Pedagogical Methodologies through the Development of a Robotics Training Manual (RTM) for Mathematics. International Journal of Information and Education Technology, v. 14, n. 12, 2024.
GUPTA, Udita; ZHENG, Robert Z. Cognitive Load in Solving Mathematics Problems: Validating the Role of Motivation and the Interaction among Prior Knowledge, Worked Examples, and Task Difficulty. European Journal of STEM Education, v. 5, n. 1, p. 5, 2020. Disponível em: https://eric.ed.gov/?id=EJ1276025.
HOFER, Mark; HARRIS, Judi. Topics & Sequences in Experienced Teachers’ Instructional Planning for Technology Integration. Research Highlights in Technology and Teacher Education, v. 35, 2019.
MACEDO, Cássio Lima; SOUZA, Cleidinaldo Aguiar. Função polinomial do segundo grau com o Lumibot-CoppeliaSim. Revista do Professor de Matemática Online, v. 11, n. 02, p. 295-314, 2023.
MACEDO, Cássio Lima; SOUZA, Cleidinaldo Aguiar. Proposição de atividades com o uso do Lumibot-Coppeliasim para a aprendizagem do conceito de função exponencial. Boletim Cearense de Educação e História da Matemática, v. 11, n. 31, p. 1-21, 2024. https://revistas.uece.br/index.php/BOCEHM/article/view/11257
MCKENNEY, Susan; REEVES, Thomas C. Educational design research. In: Handbook of research on educational communications and technology. New York, NY: Springer New York, 2013. p. 131-140.
MISHRA, Punya; KOEHLER, Matthew J. Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers college record, v. 108, n. 6, p. 1017-1054, 2006.
OLIVER, Kevin M. Methods for developing constructivist learning on the web. Educational technology, v. 40, n. 6, p. 5-18, 2000.
PAAS, Fred; RENKL, Alexander; SWELLER, John. Cognitive load theory and instructional design: Recent developments. Educational psychologist, v. 38, n. 1, p. 1-4, 2003. Disponível em: https://www.tandfonline.com/doi/abs/10.1207/s15326985ep3801_1.
PAPERT, Seymour. The children's machine. Technology Review-Manchester NH-, v. 96, p. 28-28, 1993.
PIAGET, Jean. Part I: Cognitive Development in Children--Piaget Development and Learning. Journal of research in science teaching, v. 40, 2003. Disponível em: https://doi.org/10.1002/tea.3660020306.
PUTRI, Amelia Defrianti et al. Mastering the TPACK framework: Innovative approaches by mathematics teachers. Jurnal Elemen, v. 10, n. 3, p. 582-594, 2024. Disponível em: https://e-journal.hamzanwadi.ac.id/index.php/jel/article/view/26311.
Rokaya, Bhim Bahadur. "Constructive Learning Approach in Mathematics Education: Challenges and Possibilities." Academic Journal of Mathematics Education 4.1 (2021): 1-6.Disponível em: https://nepjol.info/index.php/ajme/article/view/45583.
SAMPAIO, Patrícia Alexandra da Silva Ribeiro; COUTINHO, Clara Pereira. Integração do TPACK no processo de ensino/aprendizagem da matemática. Revista Paidéi@-Revista Científica de Educação a Distância, v. 6, n. 10, 2014. Disponível em: https://periodicosunimes.unimesvirtual.com.br/index.php/paideia/article/view/358.
SWELLER, John. Cognitive load during problem solving: Effects on learning. Cognitive science, v. 12, n. 2, p. 257-285, 1988. Disponível em: https://www.sciencedirect.com/science/article/pii/0364021388900237.
TAN, Paulo. Advancing Inclusive Mathematics Education: Strategies and Resources for Effective IEP Practices. International Journal of Whole Schooling, v. 13, n. 3, p. 28-38, 2017.
TRACTENBERG, Rochelle E. et al. Guidelines for curriculum and course development in higher education and training. 2020. Disponível em: https://doi.org/10.31235/osf.io/7qeht.
VALENTE, José Armando. Aspectos críticos das tecnologias nos ambientes educacionais e nas escolas. Revista Educação e Cultura Contemporânea, v. 2, n. 3, p. 11-28, 2005.
VINTERE, Anna et al. A constructivist approach to the teaching of mathematics to boost competences needed for sustainable development. Rural Sustainability Research, v. 39, n. 334, p. 1-7, 2018. Disponível em: https://sciendo.com/pdf/10.2478/plua-2018-0001.
VYGOTSKY, Lev S. Mind in society: The development of higher psychological processes. Harvard university press, 1978.
WILIAM, D. Embedded formative assessment. 2. ed. Bloomington, IN: Solution Tree Press, 2017.
YILMAZ, Kaya. Constructivism: Its theoretical underpinnings, variations, and implications for classroom instruction. Educational horizons, v. 86, n. 3, p. 161-172, 2008. Disponível em: https://www.jstor.org/stable/42923724.
ANDERSON, Terry; SHATTUCK, Julie. Design-based research: A decade of progress in education research?. Educational researcher, v. 41, n. 1, p. 16-25, 2012. Disponível em: https://doi.org/10.3102/0013189X11428813. Acesso em: 12 jan. 2024.
AYRES, Paul; SWELLER, John. The split-attention principle in multimedia learning. The Cambridge handbook of multimedia learning, v. 2, p. 135-146, 2005.
BAKKER, Arthur; VAN EERDE, Dolly. An introduction to design-based research with an example from statistics education. Approaches to qualitative research in mathematics education: Examples of methodology and methods, p. 429-466, 2015.
BOALER, Jo; SELLING, Sarah Kate. Psychological Imprisonment or Intellectual Freedom? A Longitudinal Study of Contrasting School Mathematics Approaches and Their Impacton Adults' Lives. Journal for Research in Mathematics Education, v. 48, n. 1, p. 78-105, 2017. Disponível em: https://pubs.nctm.org/view/journals/jrme/48/1/article-p78.xml.
CHANDLER, Paul; SWELLER, John. Cognitive load theory and the format of instruction. Cognition and instruction, v. 8, n. 4, p. 293-332, 1991. Disponível em: https://www.tandfonline.com/doi/abs/10.1207/s1532690xci0804_2.
COLLINS, Allan; JOSEPH, Diana; BIELACZYC, Katerine. Design research: Theoretical and methodological issues. In: Design-based research. Psychology Press, 2016. p. 15-42.
DA SILVA, Cleomacio Miguel et al. Ajuste de funções matemáticas de crescimento aos números de casos de pessoas contaminadas com o COVID-19 no Brasil: uma abordagem para o ensino médio. Research, Society and Development, v. 10, n. 16. Disponível em: https://rsdjournal.org/index.php/rsd/article/view/23881
DÍAZ, Frida; HERNÁNDEZ, Gerardo. Estrategias docentes para un aprendizaje significativo. México: McGraw-Hill, 2002. Disponível em: https://www.academia.edu/download/53051798/EstratDocParaUnAprendSignif.pdf.
EVIYANTI, Cut Yuniza et al. Improving the students’ mathematical problem solving ability by applying problem based learning model in VII grade at SMPN 1 Banda Aceh Indonesia. International Journal of Novel Research in Education and Learning, v. 4, n. 2, p. 138-144, 2017.
FITRIA, Tira Nur. Artificial intelligence (AI) in education: Using AI tools for teaching and learning process. In: Prosiding Seminar Nasional & Call for Paper STIE AAS. 2021. p. 134-147.
FOSSA, John A. Algumas considerações teóricas sobre o ensino de matemática por atividades. REMATEC, v. 15, n. 35, p. 10-26, 2020. Disponível em:
http://www.rematec.net.br/index.php/rematec/article/view/92
FUCHS, Lynn S. et al. Improving language comprehension to enhance word-problem solving. Reading & Writing Quarterly, v. 36, n. 2, p. 142-156, 2020. Disponível em: https://www.tandfonline.com/doi/abs/10.1080/10573569.2019.1666760.
GALUPAR, Ian John M. et al. Advancing Pedagogical Methodologies through the Development of a Robotics Training Manual (RTM) for Mathematics. International Journal of Information and Education Technology, v. 14, n. 12, 2024.
GUPTA, Udita; ZHENG, Robert Z. Cognitive Load in Solving Mathematics Problems: Validating the Role of Motivation and the Interaction among Prior Knowledge, Worked Examples, and Task Difficulty. European Journal of STEM Education, v. 5, n. 1, p. 5, 2020. Disponível em: https://eric.ed.gov/?id=EJ1276025.
HOFER, Mark; HARRIS, Judi. Topics & Sequences in Experienced Teachers’ Instructional Planning for Technology Integration. Research Highlights in Technology and Teacher Education, v. 35, 2019.
MACEDO, Cássio Lima; SOUZA, Cleidinaldo Aguiar. Função polinomial do segundo grau com o Lumibot-CoppeliaSim. Revista do Professor de Matemática Online, v. 11, n. 02, p. 295-314, 2023.
MACEDO, Cássio Lima; SOUZA, Cleidinaldo Aguiar. Proposição de atividades com o uso do Lumibot-Coppeliasim para a aprendizagem do conceito de função exponencial. Boletim Cearense de Educação e História da Matemática, v. 11, n. 31, p. 1-21, 2024. https://revistas.uece.br/index.php/BOCEHM/article/view/11257
MCKENNEY, Susan; REEVES, Thomas C. Educational design research. In: Handbook of research on educational communications and technology. New York, NY: Springer New York, 2013. p. 131-140.
MISHRA, Punya; KOEHLER, Matthew J. Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers college record, v. 108, n. 6, p. 1017-1054, 2006.
OLIVER, Kevin M. Methods for developing constructivist learning on the web. Educational technology, v. 40, n. 6, p. 5-18, 2000.
PAAS, Fred; RENKL, Alexander; SWELLER, John. Cognitive load theory and instructional design: Recent developments. Educational psychologist, v. 38, n. 1, p. 1-4, 2003. Disponível em: https://www.tandfonline.com/doi/abs/10.1207/s15326985ep3801_1.
PAPERT, Seymour. The children's machine. Technology Review-Manchester NH-, v. 96, p. 28-28, 1993.
PIAGET, Jean. Part I: Cognitive Development in Children--Piaget Development and Learning. Journal of research in science teaching, v. 40, 2003. Disponível em: https://doi.org/10.1002/tea.3660020306.
PUTRI, Amelia Defrianti et al. Mastering the TPACK framework: Innovative approaches by mathematics teachers. Jurnal Elemen, v. 10, n. 3, p. 582-594, 2024. Disponível em: https://e-journal.hamzanwadi.ac.id/index.php/jel/article/view/26311.
Rokaya, Bhim Bahadur. "Constructive Learning Approach in Mathematics Education: Challenges and Possibilities." Academic Journal of Mathematics Education 4.1 (2021): 1-6.Disponível em: https://nepjol.info/index.php/ajme/article/view/45583.
SAMPAIO, Patrícia Alexandra da Silva Ribeiro; COUTINHO, Clara Pereira. Integração do TPACK no processo de ensino/aprendizagem da matemática. Revista Paidéi@-Revista Científica de Educação a Distância, v. 6, n. 10, 2014. Disponível em: https://periodicosunimes.unimesvirtual.com.br/index.php/paideia/article/view/358.
SWELLER, John. Cognitive load during problem solving: Effects on learning. Cognitive science, v. 12, n. 2, p. 257-285, 1988. Disponível em: https://www.sciencedirect.com/science/article/pii/0364021388900237.
TAN, Paulo. Advancing Inclusive Mathematics Education: Strategies and Resources for Effective IEP Practices. International Journal of Whole Schooling, v. 13, n. 3, p. 28-38, 2017.
TRACTENBERG, Rochelle E. et al. Guidelines for curriculum and course development in higher education and training. 2020. Disponível em: https://doi.org/10.31235/osf.io/7qeht.
VALENTE, José Armando. Aspectos críticos das tecnologias nos ambientes educacionais e nas escolas. Revista Educação e Cultura Contemporânea, v. 2, n. 3, p. 11-28, 2005.
VINTERE, Anna et al. A constructivist approach to the teaching of mathematics to boost competences needed for sustainable development. Rural Sustainability Research, v. 39, n. 334, p. 1-7, 2018. Disponível em: https://sciendo.com/pdf/10.2478/plua-2018-0001.
VYGOTSKY, Lev S. Mind in society: The development of higher psychological processes. Harvard university press, 1978.
WILIAM, D. Embedded formative assessment. 2. ed. Bloomington, IN: Solution Tree Press, 2017.
YILMAZ, Kaya. Constructivism: Its theoretical underpinnings, variations, and implications for classroom instruction. Educational horizons, v. 86, n. 3, p. 161-172, 2008. Disponível em: https://www.jstor.org/stable/42923724.
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2026-09-11
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AGUIAR SOUZA, Cleidinaldo; GOMES DOS SANTOS, Mário; LAURINDO ALVES, Ediney. Ensino de Funções Polinomiais com o Polibot App: Um Estudo de Pesquisa Baseada em Design. Perspectivas da Educação Matemática, [S. l.], v. 19, n. 55, 2026. DOI: 10.46312/gh6g9h03. Disponível em: https://periodicos.ufms.br/index.php/pedmat/article/view/23512. Acesso em: 22 sep. 2026.
