Developing Conceptual Understanding and Procedural Skill in Mathematics: An Iterative Process.

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Learning new problem-solving strategies leads to changes in problem representation (2009, background): “Indeed, when children begin to represent new problem features, they sometimes generate new strategies and abandon existing ones (Alibali, McNeil, & Perrott, 1998; Rittle-Johnson et al., 2001; Siegler, 1976).”
Promoting transfer: effects of self-explanation and direct instruction. (2006, background): “Procedural learning is the ability to execute action sequences to solve familiar problems, procedural transfer is the ability to extend known procedures to novel contexts, and conceptual knowledge is understanding principles governing a domain and the interrelations between units of knowledge in a d”
Improving At-Risk Learners' Understanding of Fractions (2013, background): “…during the period in which intervention occurred, this suggests that understanding of the measurement interpretation transfers to procedural skill, at least for adding and subtracting fractions (e.g., Hecht et al., 2003; Mazzocco & Devlin, 2008; Rittle-Johnson et al., 2001; Siegler et al., 2011).”