Browse > Article
http://dx.doi.org/10.7468/jksmee.2019.33.3.255

A pedagogical discussion based on the historical analysis of the the development of the prime concept  

Kang, Jeong Gi (Jinyeong Middle School)
Publication Information
Communications of Mathematical Education / v.33, no.3, 2019 , pp. 255-273 More about this Journal
Abstract
In order to help students to understand the essence of prime concepts, this study looked at the history of prime concept development and analyzed how to introduce the concept of textbooks. In ancient Greece, primes were multiplicative atoms. At that time, the unit was not a number, but the development of decimal representations led to the integration of the unit into the number, which raised the issue of primality of 1. Based on the uniqueness of factorization into prime factor, 1 was excluded from the prime, and after that, the concept of prime of the atomic context and the irreducible concept of the divisor context are established. The history of the development of prime concepts clearly reveals that the fact that prime is the multiplicative atom is the essence of the concept. As a result of analyzing the textbooks, the textbook has problems of not introducing the concept essence by introducing the concept of prime into a shaped perspectives or using game, and the problem that the transition to analytic concept definition is radical after the introduction of the concept. Based on the results of the analysis, we have provided several pedagogical implications for helping to focus on a conceptual aspect of prime number.
Keywords
Prime number; History of prime concept development; Factorization into prime factor; Fundamental theorem of arithmetic;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Hungerford, T. W. (2013). Abstract algebra: an introduction (3rd ed.). Cengage Learning.
2 Katz, K. U., & Katz, M. G. (2011) Stevin numbers and reality, available from http://arxiv.org/abs/1107.3688v2.
3 Oladejo, N. K., & Adetunde, I. A. (2009). A numerical test on the Riemann hypothesis with applications. Journal of Mathematics and Statistics, 5(1), 47-53.   DOI
4 Prestet, J. (1689). Nouveaux elemens des mathematiques, Paris: Andre Pralard.
5 Reddick, A., & Xiong, Y. (2012). The search for one as a prime number: from ancient greece to modern times. Electronic Journal of Undergraduate Mathematics. Volume 16, 1-13.
6 Sautoy, M. (2003). The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics. New York: HaperCollins.
7 Smith, D. E. (1958). History of Mathematics, Vol. II, New York: Dover.
8 Starbird, M. L. (2008). The mathematics behind prime numbers. J. Math. Comput. Sci. Scholarship, 1, 15-19.
9 Stein, W., & Mazur, B. (2007). What is Riemann's hypothesis? Lecture presented at Summer Institute for Mathematics at the University of Washington, DC.
10 Wikipedia (2017). https://en.wikipedia.org/wiki/Prime_number
11 Agargun, A. G., & Fletcher, C. R. (1997) The fundamental theorem of arithmetic dissected, Math. Gazette, 81, 53-57.   DOI
12 Agargun, A. G., & Ozkan, E. M. (2011) A historical survey of the fundamental theorem of arithmetic, Historia Math. 28, 207-214.   DOI
13 Andre, W. (2007) Number Theory: An Approach through History from Hammurapi to Legendre. Modern Birkhauser Classics. Boston, MA: Birkhauser.
14 Caldwell. C. K., Reddick, A., Xiong, Y., & Keller, Wilfrid (2012). The history of the primality of one: a selection of sources. Journal of Integer Sequences, 15, 1-40.
15 Caldwell, C. K., & Xiong, Y. (2012). What is the smallest prime? Journal of Integer Sequences, 15, Article 12.9.7
16 Curtis, M., & Tularam, G. A. (2011). The importance of numbers and the need to study primes: the prime questions. Journal of Mathematics and Statistics, 7(4), 262-269.   DOI
17 Euler, L. (1770). Vollstandige Anleitung zur Algebra (2 vols.), der Wiss., St.-Petersburg: Kays. Acad.
18 Fitzpatrick, R. (2007). Euclid's elements of geometry. The Greek text of J. L. Heiberg(1883-1885) from Euclids Elementa, edidit et Latine interpretatus est I. L. Heiberg, in aedibus. B. G. Teubneri, 1883-1885. (R. Fitzpatrick, Ed., & R. Fitzpatrick, Trans.).
19 Zazkis, R., & Liljedahl, P. (2004). Understanding Primes: the role of representation. Journal for Research in Mathematics Education, 35(3), 164-186.   DOI
20 Goles, E., Schulz, O., & Markus, M. (2000). A biological generator of prime numbers. Nonlinear Phenomena in Complex Systems, 3, 208-213.
21 Heath, T. L. (1908). The thirteen books of Euclid's elements translated from the text of Heiberg with introduction and commentary. Volume II books III-IX, Cambridge: Cambridge University Press.
22 Heaton, L. (2015). A brief history of mathematical thought: key concepts and where they come form. London: Robinson.
23 Park, J., & Kim, Y. (trans.) (2000). Plato's Timaeus. Seoul: Seokwangsa.
24 Stanford Encyclopedia of Philosophy (2019). https://plato.stanford.edu/entries/plato-timaeus.
25 Ko, H., Kim, E., Kim, I., Lee, B., Han, J., Choi, S., Kim, J., Kim, H., Jeong, S., Jo, J., Choi, H., & Choi, H. (2018). Secondary mathematics 1. Seoul: Kyohaksa.
26 Min, S. Y. (2002). A study on the historico-genetic principle of learning and teaching mathematics. An unpublished doctoral dissertation at the Graduate School of Seoul National University.
27 Lee, J., Choi, B., Kim, D., Lee, J., Kim, S., Won, Y., Kim, H., Kim, S., & Kang, S. (2018). Secondary mathematics 1. Seoul: Chunjae education.
28 Chang, K., Kang, H., Kim, D., Ahn, J., Lee, D., Park, J., Jeong, K., Hong, E., Kim, M., Park, J., Ji, Y., & Goo, N. (2018). Secondary mathematics 1. Seoul: Jihaksa.
29 Jo, K., & Kwon, O. (2010). Middle school students' understanding about prime number. School Mathematics, 12(3), 371-388.