Fan effects reveal position-specific numerical concepts

We examined associative interference (i.e., fan) effects to determine if the numerical concepts mediating numerical fact retrieval can be position specific. Participants memorized 15 "diamond arithmetic" facts (e.g., 3 [symbol: see text] 5 = 97; Whalen, 1997) involving five different operands. Ignoring operand position (i.e., left vs. right), each operand appeared equally often across items (i.e., position-independent fan was constant). In contrast, position-specific fan values varied across items (e.g., 2 appeared five times as the left operand, but once in the right position; 3 appeared four times as the left operand, and twice as the right operand, etc). Thus, we expect a fan effect only if the concepts activated by arithmetic operands are position specific. Results indicated that position-specific fan was an excellent predictor of trials to criterion, error rate, and latency. The concepts mediating number fact retrieval can be position specific.