Probabilistic Ideas and Methods in Undergraduate Mathematics: Axiological Aspects

Elena Kuznetsova

doi:10.29333/iejme/5720

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Elena Kuznetsova ¹ ^*

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¹ Lipetsk State Technical University, Moskovskaya, Lipetsk, RUSSIA^* Corresponding Author

Abstract

The goal the article is to answer the questions: “Why the probability theory and its applications should be studied?” and “What is the attitude of students to the study of probabilistic branches of mathematics?”. The values of probabilistic branches of mathematics (stochastics) are revealed on the analysis of scientific publications on the philosophy and history of probability theory, as well as pedagogical works of mathematicians known for their achievements in this area. Further, to examine the attitude of students to study probability theory and its applications, a survey of 76 mathematics sophomores was conducted. The results of the survey were investigated using cluster analysis. It has been found that students, who have a positive attitude and motivation to study probabilistic branches of mathematics, realize the value of probabilistic ideas and methods at the philosophical level and recognize the practical utility of this. Therefore, the scientific publications on the philosophy and history of probability theory, as well as the pedagogical works of well-known mathematicians, can be the valuable resource that could be of use in the educational process to improve the motivation of students in learning probability theory.

Keywords

probability
purposes
values
training of Bachelors of Mathematics

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 14, Issue 2, May 2019, 363-373

https://doi.org/10.29333/iejme/5720

Publication date: 17 Feb 2019

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References

Aiken, L.R. (1974). Two Scales of Attitude toward Mathematics. Journal for Research in Mathematics Education, 5(2), 67-71. https://doi.org/10.2307/748616 Retrieved from https://www.jstor.org/stable/748616
Bailey, B., Spence, D. J., & Sinn, R. (2013). Implementation of Discovery Projects in Statistics. Journal of Statistics Education, 21(3). https://doi.org/10.1080/10691898.2013.11889682
Biehler, R. (1991). Computers in Probability Education. In Chance encounters: Probability in education, eds. Kapadia and Borovcnik, Netherlands: Springer. https://doi.org/10.1007/978-94-011-3532-0_6
Bisgaard, S. (1991). Teaching Statistics for Engineers. The American Statistician, 45(4), 274-283. https://doi.org/10.1080/00031305.1991.10475820
Blalock, H.M. (1987). Some General Goals in Teaching Statistics. Teaching Sociology, 15(2), 164-172. https://doi.org/10.2307/1318031 Retrieved from https://www.jstor.org/stable/1318031
Borovcnik, M., & Bentz, H.J. (1991), Empirical Research in Understanding Probability. In Chance encounters: Probability in education, eds. Kapadia and Borovcnik, Netherlands: Springer. https://doi.org/10.1007/978-94-011-3532-0_3
Brown, M. (2017). Making Students Part of the Dataset: a Model for Statistical Enquiry in Social Issues. Teaching Statistics, 39(3), 79-83. https://doi.org/10.1111/test.12131
Byun, K.J., & Croucher, J.S. (2018). Teaching Statistics through the Law. Teaching Statistics, 40, 46-50. https://doi.org/10.1111/test.12153
Cobb, G.W., & Moore, D.S. (1997). Mathematics, Statistics, and Teaching. The American Mathematical Monthly, 104(9), 801-823. https://doi.org/10.1080/00029890.1997.11990723
Cramer, H. (1979), Polveka s teoriej verojatnostej: nabroski vospominanij [Half a century with probability theory: the outline of memories]. Moscow: Znanie. Russian. (Trans. from Swedish).
David, F. N. (1962). Games, Gods, and Gambling: A history of probability and statistical ideas, London: Griffin.
David, I., & Brown, J.A. (2012). Beyond Statistical Methods: Teaching Critical Thinking to First-year University Students. International Journal of Mathematical Education in Science and Technology, 43(8), 1057-1065. https://doi.org/10.1080/0020739X.2012.678901
Debnath, L., & Basu, K. (2015). A Short History of Probability Theory and Its Applications. International Journal of Mathematical Education in Science and Technology, 46(1), 13-39. https://doi.org/10.1080/0020739X.2014.936975
Ernest, P. (1998). The History of Mathematics in the Classroom. Mathematics in school, 27(4), 25-31. Retrieved from https://www.jstor.org/stable/30211871
Fauvel, J. (1991). Using History in Mathematics Education. For the Learning of Mathematics, 11(2), 3-6. Retrieved from https://www.jstor.org/stable/40248010
Field A. (2009). Discovering Statistics Using SPSS, London: Sage Publishing.
Fine, T.L. (1973), Theories of Probability: An Examination of Foundations, London: Academic Press.
Gal I., & Ginsburg L. (1994). The Role of Beliefs and Attitudes in Learning Statistics: Towards an Assessment Framework. Journal of Statistics Education, 2, https://doi.org/10.1080/10691898.1994.11910471
Garfield, J., & Ahlgren, A. (1988). Difficulties in Learning Basic Concepts in Probability and Statistics: Implications for Research. Journal for Research in Mathematics Education, 19(1), 44-63. https://doi.org/10.2307/749110 Retrieved from https://www.jstor.org/stable/749110
Gigerenzer, G., & Porter, T. (1990). The Empire of Chance: How Probability Changed Science and Everyday Life (Vol. 12), Cambridge University Press.
Gnedenko, B. V. (1954). Kratkij ocherk po istorii teorii verojatnostej [A short essay on the history of probability theory]. In Kurs teorii verojatnostej (pp. 360-382). Moscow, Russia: GITTL. Russian.
Gnedenko, B. V., & Khinchin, A. Ja. (1970). Jelementarnoe vvedenie v teoriju verojatnostej [An elementary introduction to the theory of probability], Moscow: Nauka. Russian.
Gnedenko, B. V. (1978). Matematika i kontrol’ kachestva produkcii [Mathematics and quality control], Moscow: Znanie. Russian.
Gnedenko, B. V. (1982). Formirovanie mirovozzrenija uchashhihsja v processe obuchenija matematike [Formation of world outlook of the pupils in learning mathematics], Moscow: Prosveshhenie. Russian.
Gnedenko, B. V. (1985). Matematika i matematicheskoe obrazovanie v sovremennom mire [Mathematics and mathematical education in the modern world], Moscow: Prosveshhenie. Russian.
Gnedenko, B. V. (2010a). Besedy o matematicheskoj statistike [Conversations about mathematical statistics], Moscow: URSS. Russian.
Gnedenko, B. V. (2010b). Besedy o teorii massovogo obsluzhivanija [Conversations about queuing theory], Moscow: URSS. Russian.
Gnedenko, B. V. (2013). Ocherk po istorii teorii verojatnostej [Essay on the history of probability theory], Moscow: Librokom. Russian.
Grigorian, A. A. (2004). Zakonomernosti i paradoksy razvitija teorii verojatnostej [Patterns and paradoxes of probability theory]. Moscow: URSS. Russian.
Hacking, I. (1977). The emergence of probability: A philosophical study of early ideas about probability, induction and statistical inference, Cambridge: Cambridge University Press.
Hacking, I. (1990). The taming of chance (Vol. 17), Cambridge: Cambridge University Press.
Heitele, D. (1975). An Epistemological View on Fundamental Stochastic Ideas. Educational Studies in Mathematics, 6(2), 187-205. https://doi.org/10.1007/BF00302543
Jiang, Z., & Potter, W.D. (1994). A Computer Microworld to Introduce Students to Probability. Journal of Computers in Mathematics and Science Teaching, 13(2), 197-222.
Joosten, H. (2013). Learning and Teaching in Uncertain Times: A Nietzschean Approach in Professional Higher Education. Journal of Philosophy of Education, 47, 548-563. https://doi.org/10.1111/1467-9752.12038
Khinchin, A.Ja. (1980). Matematika kak professija [Mathematics as a profession], Moscow: Znanie. Russian.
Klymchuk, S., & Kachapova, F. (2012). Paradoxes and Counterexamples in Teaching and Learning of Probability at a University. International Journal of Mathematical Education in Science and Technology, 43(6), 803-811. https://doi.org/10.1080/0020739X.2011.633631
Knypstra, S. (2009). Teaching Statistics in an Activity Encouraging Format. Journal of Statistics Education, 17, https://doi.org/10.1080/10691898.2009.11889518
Kolmogorov, A. N. (1947), Rol’ russkoj nauki v razvitii teorii verojatnostej [The role of Russian science in the development of probability theory], Uchenye zapiski MGU, (91), 53-64. Russian.
Kolmogorov, A. N., Zhurbenko, I. G., & Prohorov, A. V. (1982), Vvedenie v teoriju verojatnostej [Introduction to Probability Theory], Moscow: Nauka. Russian.
Kolmogorov, A. N. (1988), Matematika – nauka i professija [Mathematics – the science and profession], Moscow: Nauka. Russian.
Kriiger, L., Daston, L. J., & Heidelberger, M. (1987a). The Probabilistic Revolution, vol. 1, Ideas in History, Cambridge: MIT Press.
Kriiger, L., Gigerenzer, G., & Morgan, M. S. (1987b). The Probabilistic Revolution, vol. 2, Ideas in the Sciences. Cambridge: MIT Press.
Kuznetsova, E. & Matytcina, M. (2018a). A multidimensional approach to training mathematics students at a university: improving the efficiency through the unity of social, psychological and pedagogical aspects. International Journal of Mathematical Education in Science and Technology, 49(3), 401-416. https://doi.org/10.1080/0020739X.2017.1363421
Kuznetsova, E. (2018b). Evaluation and interpretation of student satisfaction with the quality of the university educational program in applied mathematics. Teaching Mathematics and its Applications: An International Journal of the IMA, hry005. https://doi.org/10.1093/teamat/hry005
Kuznetsova, E. (2018c). Issledovanie otnosheniya studentov matematicheskih napravlenij k izucheniyu veroyatnostnyh razdelov matematiki [A research into mathematics undergraduates’ attitude towards the study of probabilistic sections of mathematics]. Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2(50), 142-150. https://elibrary.ru/item.asp?id=35449826
Lakoma E. (2000). How May History Help the Teaching of Probabilistic Concepts? In History in Mathematics Education: the ICMI Study, eds. Fauvel and van Maanen, Kluwer, Dordrecht, 248-252.
Leech, N. L. (2008) Statistics Poker: Reinforcing Basic Statistical Concepts. Teaching Statistics, 30(1), 26-28. https://doi.org/10.1111/j.1467-9639.2007.00309.x
Lesser, L. (1998). Countering Indifference Using Counterintuitive Examples. Teaching statistics, 20(1), 10-12. https://doi.org/10.1111/j.1467-9639.1998.tb00750.x
Libman, Z. (2010). Integrating Real-Life Data Analysis in Teaching Descriptive Statistics: A Constructivist Approach. Journal of Statistics Education, 18(1), https://doi.org/10.1080/10691898.2010.11889477
Lipnevich, A. A., Preckel, F., & Krumm, S. (2016). Mathematics Attitudes and Their Unique Contribution to Achievement: Going Over and Above Cognitive Ability and Personality. Learning and Individual Differences, 47, 70-79. https://doi.org/10.1016/j.lindif.2015.12.027
Ma, X., & Kishor, N. (1997). Assessing the Relationship between Attitude toward Mathematics and Achievement in Mathematics: A Meta-analysis. Journal for Research in Mathematics Education, 28(1), 26-47. https://doi.org/10.2307 / 749662
Majstrov, L. E. (1967). Teorija verojatnostej. Istoricheskij ocherk [The theory of probability. Historical review], Moscow: Nauka. Russian.
Majstrov, L. E. (1980), Razvitie ponjatija verojatnosti [The development of the concept of probability], Moscow: Nauka. Russian.
Maltby, J. (2001). Learning Statistics by Computer Software is Cheating. Journal of Computer Assisted Learning, 17(3), 329-330. https://doi.org/10.1046/j.0266-4909.2001.00188.x
Mega C., Ronconi, L., & De Beni R. (2016). What Makes a Good Student? How Emotions, Self-regulated Learning, and Motivation Contribute to Academic Achievement. Journal of Educational Psychology, 106(1), 121-131. https://doi.org/10.1037/a0033546
Mills, J. D. (2002). Using Computer Simulation Methods to Teach Statistics: A Review of the Literature. Journal of Statistics Education, 10(1), https://doi.org/10.1080/10691898.2002.11910548
Neumann, D. L., Hood, M., & Neumann, M. M. (2013). Using Real-life Data when Teaching Statistics: Student Perceptions of this Strategy in an Introductory Statistics Course. Statistics Education Research Journal, 12(2), 59-70. Retrieved from http://iase-web.org/documents/SERJ/SERJ12(2)_Neumann.pdf
Nolan, M. M., Beran, T., & Hecker, K. G. (2012). Surveys Assessing Students’ Attitudes toward Statistics: a Systematic Review of Validity and Reliability. Statistics Education Research Journal, 11(2), 103-123. Retrieved from https://iase-web.org/documents/SERJ/SERJ11(2)_Nolan.pdf
Panarin, A. S. (1999), Filosofija istorii [Philosophy of history], Moscow: Gardariki. Russian.
Pekrun R., Lichtenfeld S., Marsh, H.W., Murayama K., & Goetz T.(2017). Achievement Emotions and Academic Performance: Longitudinal Models of Reciprocal Effects. Child development, 88(5), 1653-1670. https://doi.org/10.1111/cdev.12704
Platonov, K. K. (1986). Struktura i razvitie lichnosti [Structure and development of a personality], Moscow: Nauka.
Prins, S. C. B. (2009). Student-Centered Instruction in a Theoretical Statistics Course. Journal of Statistics Education, 17(3), https://doi.org/10.1080/10691898.2009.11889530
Prodromou, T. (2014). Developing a modeling approach to probability using computer-based simulations. In Probabilistic Thinking, eds. Chernoff and Sriraman, Netherlands: Springer. https://doi.org/10.1007/978-94-007-7155-0_22
Pjatnicyn, B. N. (1976). Filosofskie problemy verojatnostnyh i statisticheskih metodov [Philosophical Problems of probabilistic and statistical methods], Moscow: Nauka. Russian.
Radke-Sharpe, N. (1991). Writing as a Component of Statistics Education. The American Statistician, 45(4), 292-293. https://doi.org/10.1080/00031305.1991.10475825
Renyi, A. (1980). Trilogija o matematike [Trilogy about math], Moscow: Mir. Russian (Trans. from Hungarian).
Roseth, C. J., Garfield, J. B., & Ben-Zvi, D. (2008). Collaboration in Learning and Teaching Statistics. Journal of Statistics Education 16(1), https://doi.org/10.1080/10691898.2008.11889557
Sachkov, Ju. V. (1971). Vvedenie v verojatnostnyj mir [Introduction to the probabilistic world]. Moscow: Nauka. Russian.
Sachkov, Ju. V. (1996). Verojatnost’. Sluchajnost’. Nezavisimost’ [Probability. Randomness. Independence]. Retrieved from http://rusnauka.narod.ru/lib/philos/3467/sachkov.htm
Sachkov, Ju. V. (1998). Verojatnost’ – na putjah poznanija slozhnosti [The probability – in the ways of the complexity of knowledge]. Filosofija nauki, 4, 134-149. Russian. Retrieved from https://iphras.ru/uplfile/root/biblio/ps/ps4/13.pdf
Sachkov, Ju. V. (1999). Verojatnostnaja revoljucija v nauke. (Verojatnost’, sluchajnost’, nezavisimost’, ierarhija) [Probabilistic revolution in science. (Probability, randomness, independence, hierarchy)]. Moscow: Nauchnyj mir. Russian.
Sandman, R. S. (1980). The Mathematics Attitude Inventory: Instrument and User’s Manual. Journal for Research in Mathematics Education, 11(2), 148-149.
Shanks, J. A. (2007). Probability in Action: The Red Traffic Light. Journal of Statistics Education, 15, https://doi.org/10.1080/10691898.2007.11889457.
Shaw C. T., & Shaw V. F. (1997). Attitudes of First‐year Engineering Students to Mathematics - A Case Study. International Journal of Mathematical Education in Science and Technology, 28(2), 289-301. https://doi.org/10.1080/0020739970280210
Sherman, B. F., & Wither, D. P. (2003). Mathematics Anxiety and Mathematics Achievement. Mathematics Education Research Journal, 15(2), 138-150. https://doi.org/10.1007/BF03217375
Shirjaev, A. N. (1998). Matematicheskaja teorija verojatnostej. Ocherk istorii stanovlenija [The mathematical theory of probability. Essay on the history of formation]. In A.N. Kolmogorov Osnovnye ponjatija teorii verojatnostej (pp. 103-129). Moscow: Fazis. Russian.
Stigler, S. M. (1986). The history of statistics: The measurement of uncertainty before 1900, Cambridge: Harvard University Press.
Tapia, M., & Marsh, G. E. (2004). An Instrument to Measure Mathematics Attitudes. Academic Exchange Quarterly, 8(2), 16-22. Retrieved from http://rapidintellect.com/AEQweb/
Tryfos, P. (2004). The ‘Probabilistic Revolution. In The Measurement of Economic Relationships, US: Springer. https://doi.org/10.1007/978-1-4020-2839-7_7
Woltman, M. (2017). Promoting Statistical Thinking in Schools with Road Injury Data. Teaching Statistics, 39(1), 26-29. https://doi.org/10.1111/test.12117

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APA

Kuznetsova, E. (2019). Probabilistic Ideas and Methods in Undergraduate Mathematics: Axiological Aspects. International Electronic Journal of Mathematics Education, 14(2), 363-373. https://doi.org/10.29333/iejme/5720

Vancouver

Kuznetsova E. Probabilistic Ideas and Methods in Undergraduate Mathematics: Axiological Aspects. INT ELECT J MATH ED. 2019;14(2):363-73. https://doi.org/10.29333/iejme/5720

AMA

Kuznetsova E. Probabilistic Ideas and Methods in Undergraduate Mathematics: Axiological Aspects. INT ELECT J MATH ED. 2019;14(2), 363-373. https://doi.org/10.29333/iejme/5720

Chicago

Kuznetsova, Elena. "Probabilistic Ideas and Methods in Undergraduate Mathematics: Axiological Aspects". International Electronic Journal of Mathematics Education 2019 14 no. 2 (2019): 363-373. https://doi.org/10.29333/iejme/5720

Harvard

Kuznetsova, E. (2019). Probabilistic Ideas and Methods in Undergraduate Mathematics: Axiological Aspects. International Electronic Journal of Mathematics Education, 14(2), pp. 363-373. https://doi.org/10.29333/iejme/5720

MLA

Kuznetsova, Elena "Probabilistic Ideas and Methods in Undergraduate Mathematics: Axiological Aspects". International Electronic Journal of Mathematics Education, vol. 14, no. 2, 2019, pp. 363-373. https://doi.org/10.29333/iejme/5720