“…In fact, numerous empirical studies have provided evidence of better learning and problem solving in a variety of domains when such diagrams are used (e.g., Bartram, 1980;Guri-Rozenblit, 1988;Holliday, 1976;Novick & Hmelo, 1994;Scanlon, 1989;Schwartz, 1971;Vessey & Weber, 1986). The usefulness of these diagrams appears to derive from three sources: They simplify complex situations by providing a concise means of depicting their abstract structure (Greer & Harel, 1998;NCTM, 2000;Woleck, 2001), they make abstract concepts more concrete (Winn, 1989), and they substitute easier perceptual inferences for more computationally-intensive search processes and sentential deductive inferences (Barwise & Etchemendy, 1991;Larkin & Simon, 1987).…”