Transformations of Mathematical and Stimulus Functions

Abstract

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.

Teaching Brain—behavior Relations Economically With Stimulus Equivalence Technology

“…By contrast, many academic assignments in higher education require topographybased responding (e.g., this is a critical difference between multiple-choice and essay assignments), as do many professional tasks beyond higher education (e.g., writing a research report to submit for publication). Because topography-based responding was not assessed in the present study (or in the previously mentioned studies by Ninness et al, 2005Ninness et al, , 2006, it is not known whether the repertoires established in selection-based procedures would contribute to student success on topography-based tasks. This defines an important direction for future EBI research.…”

“…We are aware of only two relevant reports, in which college students learned algebra skills through a combination of spoken instruction and stimulus class formation (Ninness et al, 2005(Ninness et al, , 2006. The dearth of applications with sophisticated learners might not appear to be much of an oversight if it is assumed that such learners require little academic assistance.…”

Unique Outcome Expectations as a Training and Pedagogical Tool

“…More complex training of derived stimulus relations involving algebraic and trigonometric functions has recently received significant attention from researchers such as Ninness et al (2005) and Ninness et al (2006). Their main focus was to train the relations of standard formula-to-factored formula (A-B) and of formula-to-graph (B-C) using conditional discrimination procedures.…”

Efeito do treino de composição (cópia) na aprendizagem do conceito de proporção

“…Estudos mostram que alunos do sexto ano do Ensino Fundamental apresentam dificuldades para resolver problemas fracionários que exigem o conceito de proporção (e.g., Carraher & Shliemann, 1992;Santos, 1999). Em geral, alunos resolvem problemas fracionários quando os problemas apresentam frações absolutas, mas erram quando apresentam frações relativas.A literatura sobre equivalência de estímulos evidencia que o treino de relações condicionais, segundo o paradigma proposto por Sidman e Taiby (1982), pode ser uma forma alternativa e eficiente para o ensino de conceitos matemáticos mais básicos, como os de número (Carmo, 2000) e de quantidade (Green, 2010), e de conceitos mais complexos que envolvem relações trigonométricas (Ninness et al, 2006;Ninness et al, 2009). Existem também sugestões quanto à aplicação do paradigma de equivalência de estímulos na aprendizagem de relações entre expressões numéricas fracionárias e decimais (Lynch & Cuvo, 1995) e do conceito de proporção e de equivalência entre frações (Santos,…”

“…A literatura sobre equivalência de estímulos evidencia que o treino de relações condicionais, segundo o paradigma proposto por Sidman e Taiby (1982), pode ser uma forma alternativa e eficiente para o ensino de conceitos matemáticos mais básicos, como os de número (Carmo, 2000) e de quantidade (Green, 2010), e de conceitos mais complexos que envolvem relações trigonométricas (Ninness et al, 2006;Ninness et al, 2009). Existem também sugestões quanto à aplicação do paradigma de equivalência de estímulos na aprendizagem de relações entre expressões numéricas fracionárias e decimais (Lynch & Cuvo, 1995) e do conceito de proporção e de equivalência entre frações (Santos, Souza, & Bay, 1997;Santos, Cameschi, & Hanna, 2009).…”