Abstract
Counting is one of the most basic mathematical skills. Being procedural in nature, it gives birth to many concepts that form the foundation of mathematics. For example, knowing from counting experiments that different arrangements of objects in a set do not change their total count (alternatively, changing ordinalities of objects in a set does not change the set’s cardinality) leads to the following big idea of mathematics—integers can be represented as sums of other integers in many different ways.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
See also in Chap. 9, Sect. 9.2.4, a citation from Vygotsky (1930) about the number 9.
- 2.
Blaise Pascal (1623–1662)—a French mathematician, physicist, and philosopher.
- 3.
For more recent discussion of mathematics versus didactics see Thompson et al. (2014).
- 4.
For example, all monetary values of three coins selected from pennies, nickels, and dimes are different. One may want to think what makes the triple (1, 2, 3) different from the triple (1, 5, 10) in that sense.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Abramovich, S., Connell, M.L. (2021). Combinatorics. In: Developing Deep Knowledge in Middle School Mathematics. Springer Texts in Education. Springer, Cham. https://doi.org/10.1007/978-3-030-68564-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-68564-5_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-68563-8
Online ISBN: 978-3-030-68564-5
eBook Packages: EducationEducation (R0)