Academic journal article Exceptional Children

Testing the Efficacy of a Tier 2 Mathematics Intervention: A Conceptual Replication Study

Academic journal article Exceptional Children

Testing the Efficacy of a Tier 2 Mathematics Intervention: A Conceptual Replication Study

Article excerpt

Replication is a fundamental principle of scientific research (Flay et al., 2005; Gottfredson et al., 2015; Schmidt, 2009; Valentine et al., 2011). Replication studies allow the research community to rule out chance as a plausible explanation of previous findings and build a convergence of empirical evidence in favor of an intervention or instructional practice (Coyne, Cook, & Therrien, 2016; Gottfredson et al., 2015). These studies also serve as a way to determine if findings obtained in a previous study hold up to variations in settings and contextual factors (Coyne et al., 2013). Establishing evidence of replication, therefore, adds credibility and generalizability to the hypotheses and claims of the original research (Schmidt, 2009).

Operationalizing Replication in Educational Research

Within most scientific fields, replication studies are categorized in two ways: direct replication and conceptual replication (Coyne et al., 2016; Makel, Plucker, & Hegarty, 2012; Schmidt, 2009). Direct replications are conducted using the same methods and under the same conditions as the original research. In the field of education research, direct replications are difficult, if not impossible, to conduct given the complex and dynamic environments of schools. A more feasible option for educational researchers is to conduct closely aligned conceptual replications (Coyne et al., 2016). Closely aligned conceptual replications are conducted to verify whether findings generalize across settings, conditions, and participants. Such replications typically vary from the original study on one or two elements (Schmidt, 2009). If such variations are minimal, conceptual replications can demonstrate similar capacity as direct replications. For example, a closely aligned replication can uncover whether treatment effects demonstrated in the original study replicate in a different geographical region (Coyne et al., 2013).

Replication Research and the Changing Landscape of the Counterfactual

Another aspect of replication studies concerns the control condition, or the counterfactual. The counterfactual represents what might have occurred had the treated sample not received the treatment (Lemons, Fuchs, Gilbert, & Fuchs, 2014; Shadish, Cooke, & Campbell, 2002). Replication studies of beginning reading interventions have discovered that dimensions of the counterfactual change across time (Lemons et al., 2014) and vary by school and across different geographical regions (Coyne et al., 2013). Results from these studies suggest that an intervention implemented in a similar fashion to the same population may produce vastly different results based on the nature and strength of the counterfactual. Variability of the counterfactual therefore may change interpretation of observed treatment effects across a program of research (Lemons et al., 2014). For example, a study that establishes a mathematics intervention as evidence based relative to a counterfactual could lose its treatment effect if the counterfactual shifts or strengthens in a subsequent replication study.

Instructional dimensions of the counterfactual are commonly billed as "business-as-usual" (BAU) instruction. In many mathematics intervention studies, BAU instruction represents the core mathematics instruction provided in general education settings. The aim of core mathematics instruction is to address the range of mathematics standards that students are expected to know at the end of each grade level (e.g.. Common Core State Standards; National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010). When core mathematics instruction represents the counterfactual in mathematics intervention studies, its nature and strength is also expected to vary within and across classrooms. In part this is due to the diverse range of commercially available core mathematics programs and instructional approaches used to teach mathematics in U. …

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