Calculating ellipse area by the Monte Carlo method and analysing dice poker with Excel at high school

References

• Baker J, Sugden S. Spreadsheets in education-the first 25 years. Spreadsheets in Education [Internet]. 2003 [cited 2015 Jul 26]. Available from: http://epublications.bond.edu. au/ejsie/vol1/iss1/2
   Google Scholar
• Healy L, Sutherland R. The use of spreadsheets within the mathematics classroom. Int J Math Educ Sci Technol. 1990;21:847–862.
   Google Scholar
• Sutherland R, Balacheff N. Didactical complexity of computational environments for the learning of mathematics. Int J Comput Math Learn. 1999;4:1–26.
   Google Scholar
• Bills L, Ainley J, Wilson K. Modes of algebraic communication: moving from spreadsheets to standard notation. Learn Math. 2006;26:36–41.
   Google Scholar
• Tabach M, Friedlander A. Understanding equivalence of symbolic expressions in a spreadsheet-based environment. Int J Comput Math Learn. 2008;13:27–46.
   Google Scholar
• González-Calero JA, Arnau D, Puig L. Solving word problems algebraically in a spreadsheet environment in a primary school. Res Math Educ. 2013;15:305–306.
   Google Scholar
• Molyneux-Hodgson S, Rojano T, Sutherland R, et al. Mathematical modelling: the interaction of culture and practice. Educ Stud Math. 1999;39:167–183.
   Google Scholar
• Sivasubramaniam P. Distributed cognition, computers and the interpretation of graphs. Res Math Educ. 2000;2:169–190.
   Google Scholar
• Neurath RA, Stephens LJ. The effect of using Microsoft Excel in a high school algebra class. Int J Math Educ Sci Technol. 2006;37:721–756.
   Google Scholar
• Forster PA. Technologies for teaching and learning trend in bivariate data. Int J Math Educ Sci Technol. 2007;38:143–161.
   Google Scholar
• Topcu A. Effects of using spreadsheets on secondary school students’ self-efficacy for algebra. Int J Math Educ Sci Technol. 2011;42:605–613.
   Google Scholar
• Benacka J, Ceretkova S. Excel modelling in upper secondary mathematics – a few tips for learning functions and calculus. In: Ubuz B, Haser C, Mariotti MA, editors. Proceedings of CERME 8. Ankara: Middle East Technical University; 2013. p. 970–979.
   Google Scholar
• Benacka J. Introduction to integral calculus at high school through calculating area and volume with spreadsheets. Int J Math Educ Sci Technol. 2015. Available from: http://dx.doi.org/10.1080/0020739X.2015.1050708
   Web of Science ®Google Scholar
• European Commission. Europe 2020 [Internet]. Available from: http://ec.europa.eu/europe 2020/index_en.htm
   Google Scholar
• US Department of Education. National education technology plan 2010 [Internet]. Available from: http://www.ed.gov/sites/default/files/netp2010.pdf
   Google Scholar
• Lingefjärd T, Meier S. The Sun hour project. In: Kaiser G, Blum W, Borromeo Ferri R, Stillman G, editors. Trends in teaching and learning of mathematical modelling. Heidelberg: Springer; 2011. p. 97–106.
   Google Scholar
• Nisawa Y, Moriya S. Evaluation of teaching activities with multi-variable functions in context. In: Kaiser G, Blum W, Borromeo Ferri R, Stillman G, editors. Trends in teaching and learning of mathematical modelling. Heidelberg: Springer; 2011. p. 117–126.
   Google Scholar
• Benacka J. Spreadsheet application showing the proper elevation angle, points of shot and impact of a projectile. Phys Educ. 2015;50:342–347.
   Google Scholar
• Wood D, Brunet J, Ross G. The role of tutoring in problem solving. J Child Psychol Psychiatry. 1976;17:89–100.
   PubMed Web of Science ®Google Scholar
• Hogan K, Pressley M. Scaffolding student learning: instructional approaches and issues. Northampton (MA): Brookline Books; 1997.
   Google Scholar
• Petty G. Teaching today: a practical guide. Cheltenham: Nelson Thornes; 2004.
   Google Scholar
• Metropolis N. The beginning of the Monte Carlo method. Los Alamos Science, special issue dedicated to Stanislaw Ulam. 1987;15:125–130. Available from: http://library.lanl.gov/cgibin/getfile?00326866.pdf
   Google Scholar
• Fishman GS. Monte Carlo: concepts, algorithms, and applications. New York (NY): Springer; 1995.
   Google Scholar
• Dijksterhuis FJ. Moving around the ellipse. Conic sections in Leiden, 1620–1660. In: Dupré S, Lüthy CH, editors. Silent messengers: the circulation of material objects of knowledge in the early modern low countries. Münster: LIT Verlag; 2011. p. 89–124.
   Google Scholar
• Hald A. A history of probability and statistics and their applications before 1750. Hoboken (NJ): John Wiley & Sons; 2003.
   Google Scholar
• Encyclopaedia Britannica. Poker dice [Internet]. Available from: http://www.britannica. com/EBchecked/topic/466642/poker-dice
   Google Scholar