The study of functions, as we define it here, overlaps substantially with the topic of “algebra” traditionally taught in the United States in ninth grade, though national and many state standards now recommend that aspects of algebra be addressed in earlier grades (as is done in most other countries). Although functions are a critical piece of algebra, other aspects of algebra, such as equation solving, are not addressed in this chapter.


Thomas, 1972, p. 17.


Goldenberg, 1995; Leinhardt et al., 1990; Romberg et al., 1993.


Nathan and Koedinger, 2000.


Koedinger and Nathan, 2004.


Koedinger and Nathan, 2004.


Koedinger et al., 1997.


Kalchman, 2001.


Schoenfeld et al., 1993.


Schoenfeld et al., 1987.


Schoenfeld et al., 1998, p. 81.


Chi et al., 1981.


Chi et al., 1981; Schoenfeld et al., 1993.


Kalchman, 2001.


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