Inductive Reasoning of Prospective Mathematics Teachers in Proofs
Keywords:
inductive reasoning, deductive reasoning, students.
Abstract
This study investigated how prospective mathematics teachers use inductive reasoning in constructing mathematical proofs. Using a qualitative research design, data were collected through assignments and semi-structured interviews, from 13 fourth-year subjects of the mathematics education study program. The findings showed that although the subjects generally could recognize rules and formulate conjectures, they sometimes lacked rigor in arguing. In addition, Subjects used inductive insights to form conjectures and deductive methods to prove them. This research contributes to understanding how inductive reasoning can be developed and integrated into mathematics teaching practices to improve the quality of mathematics education.
References
Barkl, S., Porter, A., & Ginns, P. (2012). Cognitive training for children: Effects on inductive reasoning, deductive reasoning, and mathematics achievement in an Australian school setting. Psychology in the Schools, 49(9), 828-842.
Byrne, R. M., Evans, J. S. B., & Newstead, S. E. (2019). Human reasoning: The psychology of deduction. Psychology Press.
Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Identifying kinds of reasoning in collective argumentation. Mathematical Thinking and Learning, 16(3), 181-200.
Ferreirós, J. (2015). Mathematical knowledge and the interplay of practices. Princeton University Press.
Imenda, S. (2014). Is there a conceptual difference between theoretical and conceptual frameworks?. Journal of social sciences, 38(2), 185-195.
Komatsu, K., & Jones, K. (2022). Generating mathematical knowledge in the classroom through proof, refutation, and abductive reasoning. Educational Studies in Mathematics, 109(3), 567-591.
Lynch, A. G., & Lockwood, E. (2019). A comparison between mathematicians’ and students’ use of examples for conjecturing and proving. The Journal of Mathematical Behavior, 53, 323-338.
Niiniluoto, I., & Tuomela, R. (2012). Theoretical concepts and hypothetico-inductive inference (Vol. 53). Springer Science & Business Media.
Pellegrino, J. W., & Glaser, R. (2021). Components of inductive reasoning. In Aptitude, learning, and instruction (pp. 177-218). Routledge.
Polya, G. (2020). Mathematics and plausible reasoning, Volume 1: Induction and analogy in mathematics. Princeton University Press.
Prawitz, D. (2015). Explaining deductive inference. Dag Prawitz on proofs and meaning, 65-100.
Stewart, S., & Thomas, M. O. (2019). Student perspectives on proof in linear algebra. ZDM, 51(7), 1069-1082.
Suchyadi, Y., & Suharyati, H. (2021). The Use Of Multimedia As An Effort To Improve The Understanding Ability Of Basic School Teachers ‘Creative Thinking In The Era ‘Freedom Of Learning,’. Yogyakarta: Zahir Publishing, 42-53.
Sznajder, M. (2021). Inductive reasoning with multi-dimensional concepts. The British Journal for the Philosophy of Science.
Zalaghi, H., & Khazaei, M. (2016). The role of deductive and inductive reasoning in accounting research and standard setting. Asian Journal of Finance & Accounting, 8(1), 23-37.
Byrne, R. M., Evans, J. S. B., & Newstead, S. E. (2019). Human reasoning: The psychology of deduction. Psychology Press.
Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Identifying kinds of reasoning in collective argumentation. Mathematical Thinking and Learning, 16(3), 181-200.
Ferreirós, J. (2015). Mathematical knowledge and the interplay of practices. Princeton University Press.
Imenda, S. (2014). Is there a conceptual difference between theoretical and conceptual frameworks?. Journal of social sciences, 38(2), 185-195.
Komatsu, K., & Jones, K. (2022). Generating mathematical knowledge in the classroom through proof, refutation, and abductive reasoning. Educational Studies in Mathematics, 109(3), 567-591.
Lynch, A. G., & Lockwood, E. (2019). A comparison between mathematicians’ and students’ use of examples for conjecturing and proving. The Journal of Mathematical Behavior, 53, 323-338.
Niiniluoto, I., & Tuomela, R. (2012). Theoretical concepts and hypothetico-inductive inference (Vol. 53). Springer Science & Business Media.
Pellegrino, J. W., & Glaser, R. (2021). Components of inductive reasoning. In Aptitude, learning, and instruction (pp. 177-218). Routledge.
Polya, G. (2020). Mathematics and plausible reasoning, Volume 1: Induction and analogy in mathematics. Princeton University Press.
Prawitz, D. (2015). Explaining deductive inference. Dag Prawitz on proofs and meaning, 65-100.
Stewart, S., & Thomas, M. O. (2019). Student perspectives on proof in linear algebra. ZDM, 51(7), 1069-1082.
Suchyadi, Y., & Suharyati, H. (2021). The Use Of Multimedia As An Effort To Improve The Understanding Ability Of Basic School Teachers ‘Creative Thinking In The Era ‘Freedom Of Learning,’. Yogyakarta: Zahir Publishing, 42-53.
Sznajder, M. (2021). Inductive reasoning with multi-dimensional concepts. The British Journal for the Philosophy of Science.
Zalaghi, H., & Khazaei, M. (2016). The role of deductive and inductive reasoning in accounting research and standard setting. Asian Journal of Finance & Accounting, 8(1), 23-37.
Published
2024-08-07
Section
Articles
