Skip to main content

Introducing Change for the Sake of Invariance

  • Chapter
Change and Invariance
  • 201 Accesses

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).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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.

    Google Scholar 

  • Barton, L. (1984). Mathematical thinking: The struggle for meaning. Journal for Research in Mathematics Education, 15(1), 35–49.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Billings, E. M. H. (2001). Problems that encourage proportion sense. Mathematics Teaching in the Middle School, 7(1), 10–14.

    Google Scholar 

  • 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.

    Google Scholar 

  • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317–326.

    Article  Google Scholar 

  • Movshovitz-Hadar N., & Webb, J. (1998). One equals zero and other mathematical surprises: Paradoxes, fallacies, and mind bogglers. Berkeley, CA: Key Curriculum Press.

    Google Scholar 

  • Nunes, T., & Bryant, P. (1996). Children doing mathematics (Understanding children’s worlds). Oxford, UK: Blackwell.

    Google Scholar 

  • 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.

    Google Scholar 

  • Sinitsky, I. (2002). Clear as 2×2. Mispar Hazak 2000, 3, 42–45 (in Hebrew).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Sense Publishers

About this chapter

Cite this chapter

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

Download citation

  • DOI: https://doi.org/10.1007/978-94-6300-699-6_4

  • Publisher Name: SensePublishers, Rotterdam

  • Online ISBN: 978-94-6300-699-6

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics