Chris Ninness, Robin Rumph, Glen McCuller, Carol Harrison, Angela M. Ford, & Sharon K. Ninness (2005).
A functional analytic approach to computer-interactive mathematics.
Journal of Applied Behavior Analysis,
38, 1-22.
Following a pretest, 11 participants who were naive with
regard to various algebraic and trigonometric transformations
received an introductory lecture regarding the fundamentals of the
rectangular coordinate system. Following the lecture, they
took part in a computer-interactive matching-to-sample
procedure in which they received training on particular formula-to-formula
and formula-to-graph relations as these formulas pertain
to reflections and vertical and horizontal shifts. In
training A-B, standard formulas served as samples
and factored formulas served as
comparisons. In training B-C, factored formulas served
as samples and graphs served as comparisons. Subsequently,
the program assessed for mutually entailed B-A and C-B relations as well
as combinatorially entailed C-A and A-C relations. After all
participants demonstrated mutual entailment and combinatorial
entailment, we employed a test of novel relations to assess 40 different
and complex variations of the original training formulas and their
respective graphs. Six of 10 participants who completed training
demonstrated perfect or near-perfect performance in identifying
novel formula-to-graph relations. Three of the 4 participants who
made more than three incorrect responses during the assessment
of novel relations showed some commonality among their
error patterns. Derived transfer of stimulus control using
mathematical relations is discussed.
DESCRIPTORS: mutual entailment, combinatorial entailment,
mathematical relations, stimulus equivalence, novel relations,
matching to sample, relational frame theory