Indeterminate Problems in Greek Primary Education
DOI:
https://doi.org/10.23756/sp.v5i1.343Keywords:
indeterminate, open-ended problems, Primary EducationAbstract
Indeterminate problems are problems that can be written with κ equations with more than κ unknowns and have been used since ancient times from many civilizations.Problem solving constitutes a critical part of Mathematics Educations, in which emphasis is given on the Curricula of Mathematics. Open-ended problems may have several correct answers or differed ways of finding the correct answer.In the present study the way students of the 5th grade manage an open-ended problem is examined and also elements of the way they solve it are presented.Downloads
References
Ore, O. (1988). Number Theory and Its History, Dover Publications, Inc., republication of the edition of 1948, p.120.
Polya, G. (1981). Mathematical Discovery. On Understanding, Learning, and Teaching Problem Solving, J.Wiley and Sons, New York, p.55.
Katz, V.J.(2013). History of Mathematics, in Greek, Publications of Crete’s University, Heraclion, p.199
Boyer, C.B. revised by U.C. Merzbach foreword by Isaac Asimov (1991). A History of Mathematics, second edition John Wiley & Sons, Inc. p. 180, p.256, p.605 and p.613.
Colebrooke, H.T. (1817). Algebra, with Arithmetic and Mensuration Translated from the Sanscrit of Brahmagupta and Bhaskara, J.Murray, London.
Mikami, Y. (1974). The Development of Mathematics in China and Japan, Chelsea Publishing Company, New York, p. 25.
Loria, G. (1971). History of Mathematics, in Greek, volume I, Greek Hellenic Society, Papazissis eds, Athens, p.212.
Martzloff, J.C. (2006). A History of Chinese Mathematics, Springer-Verlag Berlin Heidelberg, p.308, 309.
Singler, L. (2003). Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation, Springer Science and Business Media, p.257,258.
Euler, L. (1828). Elements of Algebra, translated form French, J.Hewlett, F.Horner, J.Bernoulli, J.L.Lagrange, Printed for Longman, Rees, Orme, and Co., London, p.299, 300 and p.312, 313.
Schoenfeld, A.H. (1985). Mathematical problem solving. Orlando Florida, Academic Press Inc., p.74.
Polya, G. (1973). How to solve it. A New Aspect of Mathematical Method, Princeton University Press, New Jersey, (1st ed.1945),, p.5-19.
Mayer, R. E. (2003). ‘Mathematical problem solving’, in Mathematical Cognition, M. Royer (ed.), Greenwich, CT: Info age Publishing, p.69-92, p.73
Willson, J. W., Fernandez, M. L. and Hadaway, N. (1993). ‘Mathematical problem solving’, in Research Ideas for the Classroom: High School Mathematics, P. S. Wilson ed, New York: MacMillan, available in http://jwilson.coe.uga.edu/emt725/PSsyn/PSsyn.html
Gallagher, A. M., DeLisi, R., Holst, P. C., McGillicuddy-DeLisi, A. V., Morely, M. and Cahalan, C. (2000). ‘Gender differences in advanced mathematical problem solving’, Journal of Experimental Child Psychology, 75, p.166-167.
Byrnes, J. P., & Takahira, S. (1993). ‘Explaining gender differences on SAT-math items’, Developmental Psychology, 29, p.805–810.
NCSM (1989). ‘Essential Mathematics for the Twenty–first Century’, Mathematics Teacher 82 (6), 470–474.
NCTM (2000), ‘Standards for Pre-K 12-Mathematics’, p.4, available in https://www.nctm.org/uploadedFiles/Standards_and_Positions/PSSM_ExecutiveSummary.pdf
Interdisciplinary Unified Context of Mathematics Curriculum (2003), in Greek Διαθεματικό Ενιαίο Πλαίσιο Προγραμμάτων Σπουδών Μαθηματικών, p.250.
New Curriculum for Mathematics in Compulsory Education (2011), in Greek Νέο Πρόγραμμα Σπουδών για τα Μαθηματικά στην Υποχρεωτική Εκπαίδευση, p.6,7.
Becker, J. and Shimada, L. (1997). The open-ended approach, Reston VA: NCTM.
Pehkonen, E. (1995). ‘Introduction: Use of Open-ended Problems’, International Reviews on Mathematical Education, 27 (2), 55-57.
Pehkonen, E. (1999). ‘Open-ended problems: A method for an educational change’, in Proceedings of International Symposium on Elementary Maths Teaching, Prague, M. Hejny and J. Novotna Eds., p. 56-62.
Pehkonen E. (1997). ‘The State-of-Art in Mathematical Creativity’, International Review on Mathematical Education, 29.3, 63–67.
Lee, S.Y. (2011). ‘The Effect of Alternative Solutions on Problem Solving Performance’. International Journal for Mathematics Teaching and Learning, available in http://www.cimt.org.uk/journal/lee.pdf
Kwon, O. N., Park, J. S., and Park, J. H. (2006). ‘Cultivating divergent thinking in mathematics through an open-ended approach’, Asia Pacific Education Review, 7(1), 51–61.
Pehkonen, E. (2007). ‘Problem solving in mathematics education in Finland’, available in http://www.unige.ch/math/EnsMath/Rome2008/WG2/Papers/PEHKON.pdf [28] Bonotto, C. (2013). ‘Artifacts as sources for problem-posing activities’, Educational studies in Mathematics, 83(1), 37 – 55, p. 53.
Klavir, R., and Hershkovitz, S. (2008). ‘Teaching and evaluating "open-ended" problems, in International Journal for Mathematics Teaching and Learning, 20.5 p.23 available in http://www.mathgifted.org/publications/KLAVIR.pdf
Lemonidis, C. et al, Mathematics for 1st grade. Nature’s and Life’s Mathematics. Organization of School Textbooks’ Publications, Students book, vol.I, p.34.
Emry, K., Lewis L., and Morfett, C. (2008). Open-Ended Maths Tasks, Space, Chance and Data, Hawker Brownlow Education HB8168, available in https://www.hbe.com.au
Maclellan, E. (2001). ‘Mental calculation: its place in the development of numeracy’, Westminster Studies in Education, 24, 145-154.
Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). Helping children learn mathematics, Kendalville: John Wiley & Sons.
Van de Walle, J., Karp, K., & Bay-Williams, J. (2010). Elementary and middle school mathematics: Teaching developmentally, Boston: Allyn & Bacon.
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