“…Classifications of situations that can be modeled by multiplication have consistently included rectangular areas (e.g., Greer, 1992;Schmidt & Weiser, 1995;Schwartz, 1988;Vergnaud, 1983Vergnaud, , 1988, and research on multiplication has used rectangles to illustrate multiplication of fractions and the commutative property (Greer, 1992). Some researchers have suggested, however, that students connect multiplication to areas of rectangles by reciting, but not understanding, the length times width formula (De Corte, Verschaffel, & Van Coillie, 1988;Nesher, 1992;Peled & Nesher, 1988;Simon & Blume, 1994). Several multiplication studies have taken place in classrooms (e.g., Confrey & Scarano, 1995;Hino, 2002;Izsák, 2004b;Lampert, 1986aLampert, , 1986bMechmandarov, 1987, as discussed by Nesher, 1988;Scarano & Confrey, 1996;Treffers, 1987), but only those by Hino and by Izsák have had a primary focus on arrays and rectangular areas.…”