Skip to main content Accessibility help
×
×
Home
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 13
  • Cited by
    This chapter has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Mejía-Ramos, Juan Pablo Lew, Kristen de la Torre, Jimmy and Weber, Keith 2017. Developing and validating proof comprehension tests in undergraduate mathematics. Research in Mathematics Education, Vol. 19, Issue. 2, p. 130.

    Chang, Briana L. Cromley, Jennifer G. and Tran, Nhi 2016. Coordinating Multiple Representations in a Reform Calculus Textbook. International Journal of Science and Mathematics Education, Vol. 14, Issue. 8, p. 1475.

    Overmann, Karenleigh A. 2016. Number Concepts Are Constructed through Material Engagement: A Reply to Sutliff, Read, and Everett. Current Anthropology, Vol. 57, Issue. 3, p. 352.

    Kotelawala, Usha 2016. The Status of Proving Among US Secondary Mathematics Teachers. International Journal of Science and Mathematics Education, Vol. 14, Issue. 6, p. 1113.

    Stylianou, Despina A. Blanton, Maria L. and Rotou, Ourania 2015. Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof. International Journal of Research in Undergraduate Mathematics Education, Vol. 1, Issue. 1, p. 91.

    Kashefi, Hamidreza Ismail, Zaleha and Yusof, Yudariah Mohammad 2012. Outcome-Based Science, Technology, Engineering, and Mathematics Education. p. 221.

    Selden, Annie and Selden, John 2005. Perspectives on Advanced Mathematical Thinking. Mathematical Thinking and Learning, Vol. 7, Issue. 1, p. 1.

    Choi-koh, Sang Sook 2003. Effect of a Graphing Calculator on a 10th-Grade Student's Study of Trigonometry. The Journal of Educational Research, Vol. 96, Issue. 6, p. 359.

    Albano, Giovannina D'Apice, Ciro and Tomasiello, Stefania 2002. Simulating harmonic oscillator and electrical circuits: a didactical proposal. International Journal of Mathematical Education in Science and Technology, Vol. 33, Issue. 2, p. 157.

    ALMEIDA, D. F. 1999. Visual aspects of understanding group theory. International Journal of Mathematical Education in Science and Technology, Vol. 30, Issue. 2, p. 159.

    Gagatsis, Athanassios and Thomaidis, Jannis 1995. Eine Studie zur historischen Entwicklung und didaktischen Transposition des Begriffs „absoluter Betrag“. Journal für Mathematik-Didaktik, Vol. 16, Issue. 1-2, p. 3.

    Moore, Robert C. 1994. Making the transition to formal proof. Educational Studies in Mathematics, Vol. 27, Issue. 3, p. 249.

    Armendáriz, M.a Victoria G. Azcárate, Carmen and Deulofeu, Jordi 1993. Didáctica de las Matemáticas y Psicología. Infancia y Aprendizaje, Vol. 16, Issue. 62-63, p. 77.

    ×
  • Print publication year: 1990
  • Online publication date: April 2011

6 - Advanced Mathematical Thinking

Summary

This chapter presents the principal currents and results in recent cognitive research on advanced mathematical thinking processes. The ambiguity in the phrase advanced mathematical thinking processes is intentional: The word advanced can and should refer to either mathematics or processes or both. Advanced mathematical thinking processes thus include on the one hand, thinking about topics in advanced mathematics, which in this context means mathematics beyond Euclidean geometry and intermediate algebra, and on the other hand, advanced processes of mathematical thinking such as abstracting, proving, and reasoning under hypothesis.

Although the domain of mathematics subsumed under the term advanced mathematics is vast, only a restricted number of topics are commonly taught in upper secondary and beginning college classes. Far more hours of teaching and learning are spent on analysis than on any other topic in mathematics, and it is therefore not surprising that the majority of research on the teaching and learning of advanced mathematics has been concerned with topics in analysis, among them functions, differentiation and integration, and differential equations. This tendency has been strengthened by the fact that the teaching of analysis poses a large number of nontrivial problems.

There do not seem to be clear-cut characteristics that set advanced mathematical concepts apart from those in elementary mathematics. Each advanced concept is, however, based on more elementary concepts and cannot be grasped without a solid and sometimes very specific understanding of these.

Recommend this book

Email your librarian or administrator to recommend adding this book to your organisation's collection.

Mathematics and Cognition
  • Online ISBN: 9781139013499
  • Book DOI: https://doi.org/10.1017/CBO9781139013499
Please enter your name
Please enter a valid email address
Who would you like to send this to *
×