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Handbook of the Mathematics of the Arts and Sciences pp 1–16Cite as

Probabilistic Thinking from Elementary Grades to Graduate School

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Abstract

The study of probability began about 400 years ago with an attempt to address questions related to gambling. Although methods were quickly developed to work with certain types of problems, stating an actual definition of probability proved to be a long and difficult process, and even today there are differing opinions about how probabilities should be interpreted. This chapter introduces the subject through its historical roots and explores some of the ways in which people perceive probabilities. It then looks at how those perceptions have influenced the way probability is taught, all the way from kindergarten through graduate school. The chapter concludes with a brief look at the nature of interaction between mathematics and science.

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References

  • Borovcnik M, Kapadia R (2014) A historical and philosophical perspective on probability. In: Chernoff EJ, Sriraman B (eds) Probabilistic thinking. Springer, New York

    Google Scholar 

  • Cardano G (1961) The book on games of chance. English translation: Gould SH (translator). Holt, Rinehart and Winston, New York, 1961

    Google Scholar 

  • Coxford A (2003) Mathematics curriculum reform: a personal view. In: Stanic GMA, Kilpatrick J (eds) A history of school mathematics. National Council of Teachers of Mathematics, Reston

    Google Scholar 

  • David FN (1962) Games, gods and gambling: a history of probability and statistical ideas. Charles Griffin Co. Ltd., London. Reprint: Dover, Mineola, NY, 1998

    Google Scholar 

  • Educational Services, Inc. (1963) Goals for school mathematics: the report of the Cambridge conference on school mathematics. Houghton Mifflin, Boston

    Google Scholar 

  • Fey JT, Graeber AO (2003) From the new math to the agenda for action. In: Stanic GMA, Kilpatrick J (eds) A history of school mathematics. National Council of Teachers of Mathematics, Reston

    Google Scholar 

  • de Finetti B (1972) Probability, induction and statistics: the art of guessing. Wiley, New York

    MATH  Google Scholar 

  • de Finetti B (1974) Theory of Probability: a critical introductory treatment, vol 1. English translation: Machí A, Smith A (translators). Wiley, New York

    MATH  Google Scholar 

  • de Finetti B (1975) Theory of probability: a critical introductory treatment, vol 2. English translation: Machí A, Smith A (translators). Wiley, New York

    MATH  Google Scholar 

  • Glimne D (2017) Dice. In: Encyclopaedia Britannica https://www.britannica.com/topic/dice. Accessed 25 Dec 2018

  • Handa Y, Yakes C (2010) Delving deeper: a problem in probability. Math Teach 104(1):71–75

    Google Scholar 

  • Kolmogorov AN (1933) Foundations of the theory of probability. English translation: Morrison N (translator). Chelsea Publishing Company, New York, 1950

    Google Scholar 

  • Konold C, Madden S, Pollatsek A et al (2011) Conceptual challenges in coordinating theoretical and data-centered estimates of probability. Math Think Learn 13:68–86

    Article  Google Scholar 

  • Laplace PS (1951) A philosophical essay on probabilities. English translation: Truscott FW, Emory FL (translators). Dover Publications, New York

    Google Scholar 

  • Mathematical Association of America (MAA) (2015) 2015 CUPM Curriculum Guide to Majors in the Mathematical Sciences. MAA, Washington, DC

    Google Scholar 

  • Merriam-Webster Dictionary (2018) https://www.merriam-webster.com. Accessed 25 Dec 2018

  • von Mises R (1957) Probability, statistics and truth. George Allen Unwin Ltd., London. Reprint: Dover, New York, 1981

    Google Scholar 

  • National Governors Board Association Center for Best Practices, Council of Chief State School Officers (2010) Common Core State Standards. Washington, DC

    Google Scholar 

  • National Council of Teachers of Mathematics (NCTM) (1980) An agenda for action. NCTM, Reston, VA

    Google Scholar 

  • National Council of Teachers of Mathematics (NCTM) (1989) Curriculum and evaluation standards for school mathematics. NCTM, Reston

    Google Scholar 

  • National Council of Teachers of Mathematics (NCTM) (2000) Principles and standards for school mathematics. NCTM, Reston

    Google Scholar 

  • Rourke REK (1959) The commission on mathematics of the CEEB and teacher education. Bull Natl Assoc Second Sch Princ 43(247):173–179

    Google Scholar 

  • Stigler SM (1986) The history of statistics: the measurement of uncertainty before 1900. The Belknap Press of Harvard University Press, Cambridge

    MATH  Google Scholar 

  • Tucker A (2013) The history of the undergraduate program in mathematics in the United States. Am Math Mon 120(2013):689–705

    Article  MathSciNet  Google Scholar 

  • Wigner E (1960) The unreasonable effectiveness of mathematics in the natural sciences. Commun Pure Appl Math 13(1):1–14

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin Oshkosh, Oshkosh, WI, USA

    John Beam

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  1. John Beam
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Correspondence to John Beam .

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Editors and Affiliations

  1. Dept of Mathematical Sciences, The University of Montana Dept of Mathematical Sciences, Missoula, MT, USA

    Bharath Sriraman

Section Editor information

  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

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Beam, J. (2019). Probabilistic Thinking from Elementary Grades to Graduate School. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_49-1

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  • DOI: https://doi.org/10.1007/978-3-319-70658-0_49-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70658-0

  • Online ISBN: 978-3-319-70658-0

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

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