Prior research shows that multiple representations can enhance learning, provided that students make connections among them. We hypothesized that support for connection making is most effective in enhancing learning of domain knowledge if it helps students both in making sense of these connections and in becoming perceptually fluent in making connections. We tested this hypothesis in an experiment with 428 4th- and 5th-grade students who worked with different versions of an intelligent tutoring system for fractions learning. Results did not show main effects for sense-making or fluency-building support but an interaction effect, such that a combination of sense-making and fluency-building support is most effective in enhancing fractions knowledge. Causal path analysis of log data from the system shows that sense-making support enhances students' benefit from fluency-building support, but fluency-building support does not enhance their benefit from sense-making support. Our results suggest that both understanding of connections and perceptual fluency in connection making are critical aspects of learning of domain knowledge with multiple graphical representations. Findings from the causal path analysis lead to the testable prediction that instruction should provide sense-making support and fluency-building support for connection making. [This paper was published in "Journal of Educational Psychology" v109 n3 p355-373 2017 (EJ1136559).]