Mathematics reasoning and proving of students in generalizing the pattern

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


    The purpose of this study was to identify students' reasoning in generalizing the patterns that proved by generalizing the structural generalizations with involve the mathematical structures and empirical generalizations that emphasize perceptions or evidence derived from the found regularities. The subjects in this research were the 7th semester students of Mathematics Education of University of Madura, Indonesia. The research steps in this research were (1) giving the reasoning tests to the research subjects, (2) analyzing the results of reasoning tests to identify reasoning and mathematical proofs, (3) conducting in-depth interviews as the triangulation method, and (4) summarizing the tendencies of reasoning and proof of student in generalize pattern. Based on the results and discussion can be obtained that in the process of reasoning and verification, students in identifying the same pattern with trial and error, so by using trial and error students find many ways to generalize the existing pattern. However, sometimes through the use of ways of trial and error students find the right pattern. Therefore, the student only identifies a reasonable pattern and does not identify mathematical patterns, then makes reasonable assumptions about finding a relationship but only hypothetical and needs to prove the allegations and only do a few stages of reasoning and not doing the stages of proof, giving no argument and not doing a validation of the evidence.

     

     


  • Keywords


    Mathematics Reasoning, Mathematical Proof, Generalize the Pattern

  • References


      [1] Windsor W (2009), Algebraic Thinking-More to Do with Why, Than X and Y. Queensland: Griffith University.

      [2] Lakotos I (1976), Proofs and refutations: the logic of mathematical discovery. Cambridge, UK: Cambridge University Press.

      [3] Polya G (1954), Induction and analogy in mathematics. Princeton, New Jersey: Princeton University Press.

      [4] Healy L & Hoyles C (2000), “A Study of Proof Conceptions in Algebra,” J. Res. Math. Educ., 31(4), 396–428,.

      [5] Harel G & L (1998), Sowder, Students’ proof schemes: results from exploratory studies’. Research in Collegiate Mathematics Education, Providence, RI, American Mathematical Society.

      [6] Stylianides GJ (2008), AN ANALYTIC FRAMEWORK OF. Canada: FLM Publishing Association, Edmonton.

      [7] Birken M & Coon AC (2008), Discovering Patterns in Mathematics and Poetry. New York.

      [8] Mulligan J & Mitchelmore M (2009), “Awareness of Pattern and Structure in Early Mathematical Development,” Math. Educ. Res. J., 21(2), 33–49.

      [9] Kaput JJ (1999), Teaching and Learning a New Algebra With Understanding 1. University of Massachusetts–Dartmouth.

      [10] Beatty R & Bruce C (2012), Linear Relationships: From Patterns to Algebra. Toronto: Nelson Publications, Canada..

      [11] Bills L & Rowland T (1999), “EXAMPLES, GENERALISATION AND PROOF,” Adv. Math. Educ.

      [12] Dubinsky E & Tall D (1991), ADVANCED MATHEMATICAL THINKING. The Netherlands: Kluwer Academic.


 

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Article ID: 10945
 
DOI: 10.14419/ijet.v7i2.10.10945




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