“…In doing single-digit multiplication, for example, children may initially perform a repeated addition algorithm, but with sufficient practice will transition to direct retrieval (e.g., Siegler, 1988). Multiple laboratory studies have confirmed this shift over a variety of arithmetic and nonarithmetic tasks (Delaney, Reder, Staszewski & Ritter, 1998;Hertzog, Touron & Hines, 2007;Jenkins & Hoyer, 2000;Logan, 1988Logan, , 1992Onyper, Hoyer & Cerella, 2006;Palmeri, 1997;Rawson, 2004;Reder & Ritter, 1992;Rickard, 1997Rickard, , 1999Rickard, , 2004Rickard & Bajic, 2003Rogers, Hertzog & Fisk, 2000;Schunn, Reder, Nhouyvanisvong, Richards & Stroffolino, 1997;Touron, Hoyer & Cerella, 2001). An understanding of the temporal dynamics of strategy execution in these tasks is integral to the broader goal of modeling the underlying learning processes and performance mechanisms, as well as the factors that may modulate the rate of the strategy shift (e.g., Bourne, Raymond & Healy, 2010;Onyper et al, 2006;Salvucci & Taatgen, 2008;Touron & Hertzog, 2009).…”