Theses Doctoral

# The Effects of Equivalence Based Instruction on Mathematical Problem-Solving

Shapiro, Lauren

In 2 experiments, I studied the effects of an Equivalence Based Instruction (EBI) math intervention on the emergence of untaught selection responses and abstraction to production responses. In Experiment I, using a multiple baseline design, I implemented the EBI intervention among a group of 17 first grade participants with varying levels of math prerequisites and verbal behavior development. The intervention sought to develop a comprehensive relational network for the part-whole relations involved in addition and subtraction operations.

This intervention, informed by Verbal Behavior Development Theory, Relational Frame Theory, and research on math proficiency, utilized visual and verbal stimulus presentations of fact families to establish the concepts underlying addition and subtraction. The key concept was that of a fact-family, in which two parts are equivalent to the whole and the whole is equivalent to the sum of its parts. The goal of the EBI intervention was to establish a relational network involving pictures, number bonds, sentences, and equations such that the part-whole relations involved in fact-families could be related to both addition and subtraction.

The EBI intervention consisted of 3 phases to build this relational network. In Phase I, participants learned to match sentences describing complete fact-families with pictures and number bonds. In Phase II, participants learned to match sentences describing incomplete fact-families with number bonds. In Phase III, participants learned to match incomplete number bonds with addition and subtraction equations presented in various topographies. Before and after each phase of the intervention, I assessed the degree to which participants acquired untaught responses as well as their performance on production, or problem-solving, probes. Results revealed that the combinatorially entailed response (i.e., matching pictures with number bonds) emerged for all participants, while the mutually entailed response (i.e., selecting sentences) emerged for only some participants. Participants generally improved their problem-solving following the intervention; however, further examination was needed to supplement initial visual analyses of the graphs.

Accordingly, I conducted a series of statistical analyses to evaluate individual and group-level differences in responding during the EBI intervention. These analyses also sought to reveal whether math prerequisites or level of verbal behavior development were associated with performance during Phases I, II, and III. Results showed that the EBI intervention was associated with standardized math performance and problem-solving accuracy, and results suggested that verbal behavior development has a meaningful relation with rate of learning. In Experiment II, I aimed to evaluate the educational significance of the repertoires involved in the EBI intervention by conducting a correlational study with 32 additional first grade participants. This experiment revealed that the response-types targeted in Phase III of the intervention were significantly associated with standardized math performance.