The concept of "implementation fidelity" is broadly used to capture the extent to which an intervention is executed as intended by the designers of the intervention (Century, Rudnick, & Freeman, 2010; Huntley, 2005, McNaught, Tarr, & Sears, 2010, Munter, 2010). Though implementation fidelity instruments are often used to assess…

This paper illustrates how information collected through interviews can develop a richer understanding of the assignment mechanism, which can result in more plausible causal effect estimates from observational studies and provides a roadmap for sensitivity analysis. Focusing on the issue of assignment to algebra in 8th grade, the author shows how…

A pentagonal model, based on the star model of function understanding of C. Janvier (1987), is presented as a framework for the design and interpretation of research in the area of learning the concept of mathematical function. The five vertices of the pentagon correspond to five common representations of mathematical function: (1) graph; (2)…