| Abstract: | Students in Grades 1, 4, 7, and 10 were timed as they solved simple and complex addition problems, then were presented similar problems in an untimed interview. A manipulation of confusion between addition and multiplication, in which multiplication answers were given to addition problems (3 + 4 = 12), revealed evidence for the hypothesized interrelatedness of these operations in memory only in 10th graders. The overall pattern of results suggests a strong reliance on memory retrieval, even in the first-grade group, with discernible time differences when “procedural” knowledge of carrying is required for problem solution. The results were judged consistent with a fact retrieval model which invokes explicit procedural information when problem difficulty is high or when processes like carrying and estimating magnitudes are required. In agreement with several other reports, the overall slowing of performance to larger problems is best explained in terms of normatively defined problem difficulty or associative strength in memory. |
