Development of Product Relatedness and Distance Effects in Typical Achievers and in Children With Mathematics...

The current study examined the development of two effects that have been found in single-digit multiplication errors: relatedness and distance. Typically achieving (TA) second, fourth, and sixth graders and adults, and sixth and eighth graders with a mathematics learning disability (MLD) performed a verification task. Relatedness was defined by a slow and inaccurate response to false results that were related to one of the operands via a shared multiplication row (e.g., 3 × 4 = 16). Distance was defined by a slow and inaccurate response to false results that were close in magnitude to the true result (e.g., 6 × 8 = 49). The presence of these effects indicates that participants are sensitive to numerical features of products. TA children demonstrated sensitivity to relatedness and distance from second grade onward. With age their sensitivity expanded from easy problems (e.g., 2 × 3) to difficult ones (e.g., 8 × 9). Children with MLD were sensitive to relatedness on easy problems. Their sensitivity to distance differed from the pattern seen in sixth grade and was partial in eighth grade. The presence of numerical sensitivity in children with MLD calls for instructional methods that would further develop their number sense.