Definition and Brief History
The notion of function has three different, yet interrelated, aspects. Firstly, a function is a purely mathematical entity in its own right. Depending on the level of abstraction, that entity can be introduced, for example, as either a correspondence that links every element in a given domain to one and only one element in another domain, called the co-domain, or as a certain kind of relation, i.e., a class of ordered pairs (in a Cartesian product of two classes), which may be represented as a graph, or as a process – sometimes expressed by way of an explicit formula – that specifies how the dependent (output) variable is determined, given an independent (input) variable, or as defined implicitly as a parametrized solution to some equation (algebraic, transcendental, differential). Secondly, functions have crucial roles as lenses through which other mathematical objects or theoriescan be viewed or connected, for instance, when perceiving arithmetic...
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Boyer CB (1985/1698) A history of mathematics. Princeton University Press, Princeton
Carlson M, Oehrtman M (2005) Research sampler: 9. Key aspects of knowing and learning the concept of function. Mathematical Association of America. http://www.maa.org/t_and_l/sampler/rs_9.html
Dubinsky E, Harel G (eds) (1992a) The concept of function: aspects of epistemology and pedagogy, vol 25, MAA notes. Mathematical Association of America, Washington, DC
Dubinsky E, Harel G (1992b) The nature of the process conception of function. In: Dubinsky E, Harel G (eds) The concept of function: aspects of epistemology and pedagogy, vol 25, MAA notes. Mathematical Association of America, Washington, DC, pp 85–106
Even R (1993) Subject-matter knowledge and pedagogical content-knowledge: prospective secondary teachers and the function concept. J Res Math Educ 24(2):94–116
Goldenberg P, Lewis P, O’Keefe J (1992) Dynamic representation and the development of a process understanding of function. In: Dubinsky E, Harel G (eds) The concept of function: aspects of epistemology and pedagogy, vol 25, MAA notes. Mathematical Association of America, Washington, DC, pp 235–260
NCTM (1970) A history of mathematics education in the United States and Canada. National Council of Teachers of Mathematics, Reston
Nicholas CP (1966) A dilemma in definition. Am Math Mon 73(7):762–768
Schubring G (1989) Pure and applied mathematics in divergent institutional settings in Germany: the role and impact of Felix Klein. In: Rowe DE, McCleary J (eds) The history of modern mathematics, vol 2, Institutions and applications. AP, San Diego, pp 171–220
Sfard A (1992) Operational origins of mathematical objects and the quandary of reification – the case of function. In: Dubinsky E, Harel G (eds) The concept of function: aspects of epistemology and pedagogy, vol 25, MAA notes. Mathematical Association of America, Washington, DC, pp 59–84
Vinner S (1983) Concept definition, concept image and the notion of function. Int J Math Educ Sci Technol 14(3):293–305
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Niss, M.A. (2014). Functions Learning and Teaching. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_96
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