Chris Ninness, Mark Dixon, Dermot Barnes-Holmes, Ruth Anne Rehfeldt, Robin Rumph,
Glen McCuller, James Holland, Ronald Smith, Sharon K. Ninness, & Jennifer McGinty. (2009).
Constructing and deriving reciprocal trigonometric relations: A functional analytic approach.
Journal of Applied Behavior Analysis,
42, 191-208.
Participants were pretrained and tested on mutually entailed
trigonometric relations and combinatorially entailed relations
as they pertained to positive and negative forms of sine, cosine,
secant, and cosecant. Experiment 1 focused on training and testing
transformations of these mathematical functions in terms of
amplitude and frequency followed by tests of novel relations.
Experiment 2 addressed training in accordance with frames of
coordination (same as) and frames of opposition (reciprocal of)
followed by more tests of novel relations. All assessments of
derived and novel formula-to-graph relations, including reciprocal
functions with diversified amplitude and frequency transformations,
indicated that all 4 participants demonstrated substantial improvement
in their ability to identify increasingly complex trigonometric formula-to-graph
relations pertaining to same as and reciprocal of to establish mathematically
complex repertoires.
DESCRIPTORS: combinatorial entailment, construction-based training, mathematical relations,
mutual entailment, matching to sample, trigonometry, relational frame theory