Previously, we proposed a model of student reasoning which combines the roles of representation, analogy, and layering of meaning--analogical scaffolding [Podolefsky and Finkelstein, Phys. Rev. ST Phys. Educ. Res. 3, 010109 (2007)]. The present empirical studies build on this model to examine its utility and demonstrate the vital intertwining of representation, analogy, and conceptual learning in physics. In two studies of student reasoning using analogy, we show that representations couple to students' existing prior knowledge and also lead to the dynamic formation of new knowledge. Students presented with abstract, concrete, or blended (both abstract and concrete) representations produced markedly different response patterns. In the first study, using analogies to scaffold understanding of electromagnetic (EM) waves, students in the blend group were more likely to reason productively about EM waves than students in the abstract group by as much as a factor of 3 (73% vs 24% correct, p=0.002 ). In the second study, examining representation use within one domain (sound waves), the blend group was more likely to reason productively about sound waves than the abstract group by as much as a factor of 2 (48% vs 23% correct, p=0.002 ). Using the analogical scaffolding model we examine when and why students succeed and fail to use analogies and interpret representations appropriately. (Contains 13 figures, 4 tables, and 56 notes.)