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All Journal Al-Jabar : Jurnal Pendidikan Matematika Indonesian Journal of Science and Mathematics Education Journal of Instructional Mathematics Journal of Advanced Sciences and Mathematics Education JRAMathEdu (Journal of Research and Advances in Mathematics Education)
Alves, Francisco Regis Vieira
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Chemistry Education Mathematics Physics Social Sciences

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Journal : Journal of Instructional Mathematics

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Some Elementary Combinatory Properties and Fibonacci Numbers Alves, Francisco Régis Vieira; Sousa, Renata Teófilo de
Journal of Instructional Mathematics Vol. 4 No. 1 (2023): Mathematical Learning: Strategies, Factors, and Challenges
Publisher : Pendidikan Matematika STKIP Kusuma Negara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37640/jim.v4i1.1756

Abstract

In general, in the midst of History of Mathematics textbooks, we are faced with a discussion due to curiosity about the emblematic Fibonacci Sequence, whose popularization occurred with the proposition of the reproduction model of immortal rabbits. On the other hand, in the comparison of the multiple approaches and discussions of certain subjects in Elementary Mathematics, in the present work, we highlight combinatorial interpretations that, with the support of a characteristic and fundamental reasoning for the mathematics teacher, can be generalized and formalize some eminently intuitive components. In particular, this work deals with properties derived from the notion of tiling and decomposition of an integer that, depending on the board, will correspond to the numbers of the Fibonacci Sequence. We bring a theoretical discussion supported by great names that research in this area.
A Note on Leonardo’s Combinatorial Approach Vieira, Renata Passos Machado; Alves, Francisco Regis Vieira; Catarino, Paula Maria Machado Cruz
Journal of Instructional Mathematics Vol. 4 No. 2 (2023): Enhancing Mathematics Learning through Innovative Pedagogies
Publisher : Pendidikan Matematika STKIP Kusuma Negara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37640/jim.v4i2.1862

Abstract

The purpose of this research is to carry out a study of Leonardo's combinatorial approach so that it is possible to visualize these numbers through combinatorial interpretation. Thus, research is being developed regarding methods and approaches to linear and recurring sequences, based on the combinatorial study of the Fibonacci sequence. In fact, the Fibonacci sPquence is related to other sequences, one of which is the Leonardo sequence, which has similarities with the Fibonacci numbers according to some researchers in the field. Given this scenario, the present research addresses the combinatorial interpretation of Leonardo's sequence, allowing the definition of Leonardo's combinatorial model, considering the notion of board and bracelets in Lucas' sequence. As research results, the study deals with the integration of sequence content with the area of Combinatorial Analysis, allowing a mathematical advancement of Leonardo's sequence. Furthermore, you can visualize the sequence numbers in front of the tiles. The aspects studied in this research are linked to the teaching of sequences in the History of Mathematics, allowing the teaching of Mathematics.
Co-Authors Aires, Ana Paula Catarino, Paula Maria Machado Cruz de Sousa, Renata Teófilo Santiago, Paulo Vitor da Silva Santos, Maria José Costa dos Sousa, Renata Teófilo de Vieira, Renata Passos Machado