Abstract
Chapters 4 and 5 both present different aspects of relationships between invariance and change. Whereas in Chapter 4 we initiated some change for the express purpose of ensuring the preservation of some value or property, in Chapter 5 we present some problems in which the change takes place by itself – “without our intervention” – meaning that the invariance (either a preserved value or some preserved property) is concealed during some transformation. Through the discovery of this existing, yet hidden, invariance, we are provided with a way of dealing with the change that paves the way to solving the problem.
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References
Ben-Chaim, D., Keret, Y., & Ilany, B. (2012). Ratio and proportion. Research and teaching in mathematics teachers’ education (Pre- and in-Service mathematics teachers of elementary and middle school). The Netherlands: Sense Publishers.
Browne, A. W. (1915). The goals of scientific research: President’s address read before the Cornell Chapter of the Sigma Xi, May 17, 1915. Sigma Xi Quarterly, 3(4), 108–116. Retrieved from http://www.jstor.org/stable/27823984
Fomin, D., Genkin, S., & Itenberg, I. (1996). Mathematical circles (Russian experience). New York, NY: American Mathematical Society.
Gik, E. Y. (1983). Shakhmaty i matematika. Moscow: Nauka Publishers. (In Russian)
Green, B. F., McCloskey, M., & Caramazza, A. (1985). The relation of knowledge to problem solving, with examples from kinematics. In S. F. Chipman, J. W. Segal, & R. Glaser (Eds.), Thinking and learning skills: Research and open questions (pp. 141–159). Hillsdale, NJ: Lawrence Erlbaum.
Hershkovitz, S., Peled, I., & Littler, G. (2009). Mathematical creativity and giftedness in elementary school: Task and teacher promoting creativity for all. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 255–269). Rotterdam, The Netherlands: Sense Publishers.
Kordemsky, B. A. (1992 [1957]). The Moscow puzzles: 359 mathematical recreations (A. Parry, Trans.). New York, NY: Dover Publications.
Nesher, P., Greeno, J., & Riley, M. (1982). The development of semantic categories for addition and subtraction. Educational Studies in Mathematics, 13, 373–394.
Ore, O. (1988). Number theory and its history. New York, NY: Dover Publications.
Polya G. (2014 [1945]). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.
Rehmann, U. (Ed.). (2002). Encyclopedia of mathematics (online version). Retrieved from http://eom.springer.de/
Shapiro, H. (2005). Mathematical problem solving. Retrieved from http://www.math.kth.se/math/TOPS/index.html
Singh, S. (1999). The code book: The science of secrecy from Ancient Egypt to quantum cryptography. New York, NY: Anchor Books.
Sinitsky, I. (2011). Evident and hidden in hundred table and in multiplication table. Guest lecture at seminar for moderators of courses for in-service teachers of mathematics. Haifa: Israeli Center for Teachers of Mathematics in Elementary School. (in Hebrew)
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Sinitsky, I., Ilany, BS. (2016). Discovering Hidden Invariance. In: Change and Invariance. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6300-699-6_5
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DOI: https://doi.org/10.1007/978-94-6300-699-6_5
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