Chris Ninness, Dermot Barnes-Holmes, Robin Rumph, Glen McCuller,
Angela M. Ford, Robert Payne, Sharon K. Ninness, Ronald J. Smith,
Todd A. Ward, & Marc P. Elliott. (2006)
Transformations of mathematical and stimulus functions.
Journal of Applied Behavior Analysis,
39, 299-321.
Following a pretest, 8 participants who were unfamiliar with algebraic
and trigonometric functions received a brief presentation on the rectangular
coordinate system. Next, they participated in a computer-interactive
matching-to-sample procedure that trained formula-to-formula and
formula-to-graph relations. Then, they were exposed to 40 novel
formula-to-graph tests and 10 novel graph-to-formula tests. Seven
of the 8 participants showed substantial improvement in identifying
formula-to-graph relations; however, in the test of novel
graph-to-formula relations, participants tended to select equations
in their factored form. Next, we manipulated contextual cues in the
form of rules regarding mathematical preferences. First, we informed
participants that standard forms of equations were preferred over factored
forms. In a subsequent test of 10 additional novel graph-to-formula
relations, participants shifted their selections to favor equations in
their standard form. This preference reversed during 10 more tests when
financial reward was made contingent on correct identification of formulas
in factored form. Formula preferences and transformation of novel mathematical
and stimulus functions are discussed.
DESCRIPTORS: value, preference, mutual entailment, combinatorial entailment, transformation of function