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.

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 computerinteractive matching-to-sample procedure in which they received training on particular formulato-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

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.

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The present study evaluates the effects of a social story procedure as developed by Gray (2010). The social story alone was presented in a video modeled format to four middle school students who were eligible for the special education autism criteria and who were instructed primarily in a public middle school general education setting. Using a multiple baseline design across participants in their natural school setting, this study found consistent improvements in all participants' social responses when greeted by peer helpers. During the follow-up phase, participants' prosocial greeting responses remained consistent with intervention phase responses. One of the primary purposes of this study was to find more reliable evidencebased treatments and outcomes for those individuals afflicted with autism, a growing population within our society. Importantly, this study placed particular emphasis on a social story protocol as employed in the absence of other concurrent treatments. Participants were exposed to a video modeling protocol within a natural school setting. Social stories videos were focused on peer-interactive greeting behaviors. Techniques for establishing generalization of prosocial peer-interactive behaviors are discussed, and strategies for observing students during follow-up conditions are described.