Characteristics
Number lines figure prominently in mathematics education. They may take various shapes and forms, from a clothesline with number cards in the early grades, to straight lines on paper representing rational numbers or integers. Number lines may feature all numbers under consideration or just a selection, depending on the function the number line has to fulfill. The 1st-grade number cards, for instance, are to support the learning of the number sequence. Whereas a more schematized number line may be used to illuminate the structure and magnitude of rational numbers and decimals. In this contribution we will focus on the empty number line, which is kept even more sparse than the latter in order to fulfill its role as a specifically designed instructional tool.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Beishuizen M (1993) Mental strategies and materials or models for addition and subtraction up to 100 in Dutch second grades. J Res Math Educ 24(4):294–323
Gravemeijer K (1999) How emergent models may foster the constitution of formal mathematics. Math Think Learn 1(2):155–177
Gravemeijer K (2004) Learning trajectories and local instruction theories as means of support for teachers in reform mathematics education. Math Think Learn 6(2):105–128
Klein AS, Beishuizen M, Treffers A (1998) The empty number line in Dutch second grades: realistic versus gradual program design. J Res Math Educ 29(4):443–464
Kraemer J-M (2011) Oplossingsmethoden voor aftrekken tot 100. Dissertatie, Cito, Arnhem
Selter C (1998) Building on children’s mathematics – a teaching experiment in grade three. Educ Stud Math 36(1):1–27
Stephan M, Bowers J, Cobb P, Gravemeijer K (eds) (2003) Supporting students’ development of measuring conceptions: analyzing students’ learning in social context, Journal for research in mathematics education monograph no. 12. National Council of Teachers of Mathematics, Reston
Treffers A (1991) Didactical background of a mathematics program for primary education. In: Streefland L (ed) Realistic mathematics education in primary school. Cd-β Press, Utrecht, pp 21–57
van den Heuvel-Panhuizen M (ed) (2001) Children learn mathematics. Freudenthal Institute, Utrecht University/SLO, Utrecht/Enschede
van Galen F, Feijs E, Gravemeijer K, Figueiredo N, van Herpen E, Keijzer R (2008) Fractions, percentages, decimals and proportions: a learning-teaching trajectory for grade 4, 5 and 6. Sense Publishers, Rotterdam
Whitney H (1985) Taking responsibility in school mathematics education. In: Streefland L (ed) Proceedings of the ninth international conference for the psychology of mathematics education, vol 2. OW&OC, Utrecht
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this entry
Cite this entry
Gravemeijer, K. (2020). Number Lines in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_121
Download citation
DOI: https://doi.org/10.1007/978-3-030-15789-0_121
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-15788-3
Online ISBN: 978-3-030-15789-0
eBook Packages: EducationReference Module Humanities and Social SciencesReference Module Education