Ensino de Funções Polinomiais com o Polibot App
Um Estudo de Pesquisa Baseada em Design
DOI:
https://doi.org/10.46312/gh6g9h03Palavras-chave:
Ensino de Matemática, Funções Polinomiais, Tecnologia Educacional, Robótica, Pesquisa Baseada em DesignResumo
Este artigo apresenta os resultados de uma Pesquisa Baseada em Design (DBR) que teve como objetivo desenvolver, implementar e refinar um aplicativo interativo para o ensino de funções polinomiais, em um contexto escolar real. Fundamentado na teoria da aprendizagem construtivista, na teoria da carga cognitiva e nas possibilidades pedagógicas oferecidas por tecnologias educacionais, o estudo foi realizado ao longo de quatro ciclos iterativos, envolvendo diagnóstico do problema, desenvolvimento do protótipo, aplicação em sala de aula e reconfiguração da ferramenta. O produto educacional, intitulado Polibot, utiliza simulações robóticas para promover a compreensão conceitual por meio de atividades contextualizadas e progressivas. Os resultados indicam que a ferramenta contribuiu para ampliar o engajamento dos alunos, facilitar a interpretação gráfica e promover uma aprendizagem mais significativa dos conceitos de função polinomial, especialmente ao aproximar teoria e prática em um ambiente virtual de resolução de problemas.
Referências
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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: 21 set. 2026.
