Retrieval-induced forgetting of multiplication facts and identity rule

This research investigated retrieval-induced interference between counterpart multiplication (2 × 3 = 6) and addition facts (2 + 3 = 5). Adults (N =72) repeatedly solved either a set of simple addition (0 + 2, 1 + 5, 2 + 3) or multiplication problems (0 × 2, 1 × 5, 2 × 3) during a practice phase and then switched operations during a test phase that included counterparts to the practiced problems and control problems. The paradigm afforded measurement in response time both of inter-operation retrieval-induced forgetting (RIF) and generalization of practice across different problems within operations. The experiment demonstrated generalization of practice for the rule-based 0 + N = N problems (e.g., practicing 0 + 2 facilitated performance on 0 + 7) as well as for problems governed by the multiplicative identity principle (1 × N = N) and zero-product principle (0 × N = 0), but not the fact-based 1 + N problems. The experiment also demonstrated for the first time inter-operation RIF of fact-based multiplication, which was as large as the effect observed for fact-based addition. The 0 × N, 0 + N, and 1 + N problems did not present item-specific RIF from practice of cross-operation counterparts, but 1 × N problems did, despite the generalization-of-practice evidence that 1 × N problems were solved using an item-general procedure. The item-specific RIF for 1 × N = N must reflect item-specific interference rather than item-level competitor inhibition given that there is no item-level representation of 1 × N = N facts in long-term memory.