Understanding of derivative concepts by undergraduate mathematics students from three inland institutions in the state of Paraná

Authors

DOI:

https://doi.org/10.23925/1983-3156.2025v27i1p336-384

Keywords:

Instrumental understanding, Relational understanding, Logical understanding, Initial formation of the teacher, Derivatives

Abstract

Learning mathematics is intrinsically related to understanding, i. e. the apprehension and elaboration of meanings concerning mathematical objects, without neglecting their applications. Several official Brazilian documents emphasize that the focus on understanding should permeate the “initial and continuing training” of teachers or educators, indicating that training should have studies and practices on the subject on its agenda. This led us to ask: “What is the understanding of the concepts of derivative of a variable among mathematics undergraduate students at universities in western Paraná?” The subjects investigated come from three university campuses in the interior of Paraná. Richard Skemp's theoretical framework was used to produce the evaluations and study the research data. Analytical tables were drawn up based on the answers to the questionnaires and individual interviews. The analysis showed, according to established criteria, failures and shortcomings in the understanding of these concepts, indicating strong signs of non-lasting learning.

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Author Biographies

Jorge Fernandes de Lima Neto, UFAM

He holds a degree in Mathematics from the Federal University of Amazonas (1998), a master's degree in Mathematics from the Federal University of Ceará (2000) and a PhD in Mathematics from the University of Brasília (2005). He is currently a professor at the Federal University of Amazonas. He has experience in the area of ​​Mathematics, with an emphasis on Number Theory.

Tiago Emanuel Klüber, Unioeste

Graduated in Mathematics and specialist in Teaching in Higher Education from the State University of the Center-West - UNICENTRO. Master in Education from the State University of Ponta Grossa - UEPG and PhD in Scientific and Technological Education (2012) from the Federal University of Santa Catarina - UFSC. Research in the areas of Education and Teaching, with an emphasis on Mathematics Education, working mainly on the following themes: Mathematical Modeling, Teacher Training, Epistemology and philosophy of Mathematics Education. Professor at the Center for Exact and Technological Sciences, CCET, at Unioeste, Campus Cascavel. He was coordinator of the Postgraduate Program in Science Education and Mathematics Education at Unioeste (PPGECEM), master's and doctorate level, CAPES, concept 4, (2017-2021), Cascavel campus, where he is currently a permanent professor, guiding research at master's and doctoral level. He was deputy coordinator of GT-10 Mathematical Modeling (2012-2015 and 2015-2018), of the Brazilian Society of Mathematics Education, SBEM. President of the Society for Qualitative Studies and Research, SEPQ (2023-2027).

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Published

2025-04-30

How to Cite

LIMA NETO, J. F. de; KLÜBER, T. E. Understanding of derivative concepts by undergraduate mathematics students from three inland institutions in the state of Paraná. Educação Matemática Pesquisa, São Paulo, v. 27, n. 1, p. 336–384, 2025. DOI: 10.23925/1983-3156.2025v27i1p336-384. Disponível em: https://revistas-anterior.pucsp.br/index.php/emp/article/view/67010. Acesso em: 24 dec. 2025.

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Vol. 27 No. 1 (2025): Volume 27.1 of 2025

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