Skip to main content
SpringerLink
Log in

A Notation for Sets, Sequences and Series

Possible Benefits for Understanding and Use

  • Conference paper
  • First Online:
Informatics in Schools: Focus on Learning Programming (ISSEP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10696))

Abstract

The use of a well-designed and uniform notational system is imperative to improve communication and understanding. Currently, a fairly consistent notational system is used to notate the elements of sets, but the notations for sequences, series and other quantifications often vary from one author to another. The most widely used notation for sets has limitations and cannot easily be generalised to sequences and series. Furthermore, the well-known sigma notation for series is ambiguous and difficult to grasp. This article proposes a clear notation that can be used for all of the above. We aim to test the hypothesis that this notation could aid an understanding of concepts which build on the use of this notation. As a first step, we conducted a pilot study to inform the design of an experiment to evaluate the effect of the proposed notation on understanding. Secondary-school learners who had never been exposed to the sigma notation participated in the pilot study.

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

Access this chapter

Log in via an institution
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 EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    https://www.siyavula.com/maths/grade-12.

References

  1. Dijkstra, E.W., van Gasteren, A.J.M.: On notation, January 1986. http://www.cs.utexas.edu/users/EWD/ewd09xx/EWD950a.PDF. Accessed 27 Nov 2013

  2. Lipton, R.: Notation and thinking, November 2010. http://rjlipton.wordpress.com/2010/11/30/notation-and-thinking/. Accessed 12 May 2016

  3. Hoch, M., Dreyfus, T.: Structure sense in high school algebra: the effect of brackets. In: Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Bergen University College (2004)

    Google Scholar 

  4. Kisiel, V.M.: I saw the sign and it opened up my eyes I saw the sign! A study of the impacts of the use of different multiplication symbols in the mathematics classroom. Master’s thesis, Department of Mathematical Sciences at the State University of New York at Fredonia, Fredonia, New York, July 2010

    Google Scholar 

  5. Torigoe, E., Gladding, G.: Symbols: weapons of math destruction. AIP Conf. Proc. 951(1), 200–203 (2007)

    Article  Google Scholar 

  6. Chirume, S.: How does the use of mathematical symbols influence understanding of mathematical concepts by secondary school students. Int. J. Soc. Sci. Educ. 3(1) (2012). ISSN: 2223–4934 E and 2227-393X

    Google Scholar 

  7. Bardini, C., Pierce, R.: Assumed mathematics knowledge: the challenge of symbols. Int. J. Innov. Sci. Math. Educ. 23(1), 1–9 (2015). Formerly CAL-laborate International

    Google Scholar 

  8. Simistira, F., Katsourosa, V., Carayannis, G.: Recognition of online handwritten mathematical formulas using probabilistic SVMs and stochastic context free grammars. Pattern Recogn. Lett. 53, 85–92 (2014)

    Article  Google Scholar 

  9. Cuartero-Olivera, J., Hunter, G., Prez-Navarro, A.: Reading and writing mathematical notation in e-learning environments. ELC Research Paper Series Issue 4 (2012)

    Google Scholar 

  10. Wees, D.: Mathematical notation is broken, May 2012. http://davidwees.com/content/mathematical-notation-broken. Accessed 24 Nov 2013

  11. ISO/TC 12: ISO 80000–2:2009 Quantities and units – Part 2: Mathematical signs and symbols to be used in the natural sciences and technology, November 2009. http://www.iso.org/iso/catalogue_detail.htm?csnumber=31887. Accessed 22 Dec 2013

  12. Dijkstra, E.W.: EWD1300: The notational conventions I adopted, and why. Formal Aspects Comput. 14, 99–107 (2002)

    Article  MATH  Google Scholar 

  13. Pieterse, V.: Topic maps for specifying algorithm taxonomies: a case study using transitive closure algorithms. Ph.D. thesis, University of Pretoria (2017)

    Google Scholar 

  14. Euler, L.: Foundations of differential calculus. Transl. by Blanton, J.D. Springer, New York (1755/2000)

    Google Scholar 

  15. du Plessis, S.H., Pieterse, V.: Die effek vann alternatiewe notasie op die begrip van wiskundige konsepte vir graad 12 leerders. Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 36(1), 1–2 (2017)

    Google Scholar 

  16. Abadir, K., Magnus, J.: Notation in econometrics: a proposal for a standard. Econometrics J. 5(1), 76–90 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  17. Bernoulli, J.: Ars conjectandi. Impensis Thurnisiorum, fratrum (1713)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Pretoria, Pretoria, South Africa

    Susanna H. du Plessis & Vreda Pieterse

Authors
  1. Susanna H. du Plessis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vreda Pieterse
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vreda Pieterse .

Editor information

Editors and Affiliations

  1. Mathematics and Informatics, Vilnius University, Vilnius, Lithuania

    Valentina Dagienė

  2. University of Helsinki, Helsinki, Finland

    Arto Hellas

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

du Plessis, S.H., Pieterse, V. (2017). A Notation for Sets, Sequences and Series. In: Dagienė, V., Hellas, A. (eds) Informatics in Schools: Focus on Learning Programming. ISSEP 2017. Lecture Notes in Computer Science(), vol 10696. Springer, Cham. https://doi.org/10.1007/978-3-319-71483-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-71483-7_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71482-0

  • Online ISBN: 978-3-319-71483-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation