Abstract
Given a function f and an initial value a 1, we consider properties and representations of the iteration sequence a 1 , f(a 1 ), f(f(a 1 )),.... Because iteration sequences often cannot be expressed in explicit algebraic terms, there is an emphasis on using various graphical and numerical representations. An empirical investigation examined the influence of representations on the discovery of properties and on problem solving abilities for iteration sequences. A total of 79 students (11th graders) and 22 secondary mathematics teachers participated. The empirical study was implemented with a computer program, developed by the author.
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Weigand, HG. Iteration sequences and their representations. Educ Stud Math 22, 411–437 (1991). https://doi.org/10.1007/BF00367906
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DOI: https://doi.org/10.1007/BF00367906