Abstract
The ability to solve problems is a major component of mathematical comprehension. In education, “mathematical thinking” is defined as a student’s ability to solve mathematical problems: first the most basic ones, and then progressing through more complex ones, culminating with non-standard problems that require higher thinking skills (Avital & Shettleworth, 1968; Barton, 1984).
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References
APEC [Asia-Pacific Economic Cooperation]. (2011). Thinking systematically (Grade 6, Japan). Retrieved from http://hrd.apecwiki.org/index.php/Thinking_Systematically_Grade_6_%28Japan%29
Avital, S. M., & Shettleworth, S. J. (1968). Objectives for mathematics learning, Some ideas for the teacher. OISE Bulletin No. 3.
Barton, L. (1984). Mathematical thinking: The struggle for meaning. Journal for Research in Mathematics Education, 15(1), 35–49.
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.
Billings, E. M. H. (2001). Problems that encourage proportion sense. Mathematics Teaching in the Middle School, 7(1), 10–14.
Bogomolny, A. (2016a). Peasant multiplication. Retrieved from http://www.cut-the-knot.org/Curriculum/Algebra/PeasantMultiplication.shtml
Bogomolny, A. (2016b). Aliquot game. Retrieved from http://www.cut-the-knot.org/SimpleGames/Aliquot.shtml
Falkner, K. P., Levi, L., & Carpenter, T. P. (1999). Children’s understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6(4), 232–236.
Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317–326.
Movshovitz-Hadar N., & Webb, J. (1998). One equals zero and other mathematical surprises: Paradoxes, fallacies, and mind bogglers. Berkeley, CA: Key Curriculum Press.
Nunes, T., & Bryant, P. (1996). Children doing mathematics (Understanding children’s worlds). Oxford, UK: Blackwell.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical recipes: The art of scientific computing (3rd ed.). New York, NY: Cambridge University Press.
Sinitsky, I. (2002). Clear as 2×2. Mispar Hazak 2000, 3, 42–45 (in Hebrew).
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Sinitsky, I., Ilany, BS. (2016). Introducing Change for the Sake of Invariance. In: Change and Invariance. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6300-699-6_4
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DOI: https://doi.org/10.1007/978-94-6300-699-6_4
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