Abstract:

This article is to review the tie effect in simple arithmetic. Tie effect means that simple arithmetic problems with repeated operands(i.e., ties such as 3+3，4×4) are solved more quickly and accurately than similar nontie problems(e.g., 3+4,4×5). Furthermore, problem size and tie effects interact, such that latencies on both ties and nonties increase with problem size, but the increase is much greater on nonties than on ties. There are two possible explanations for the tie effect, such as encoding-based and access-based accounts. Encoding-based accounts propose that the tie advantage occurs because repetition of the same physical stimulus results in faster encoding of ties than of nonties. Alternatively, access-based accounts propose that ties may be easier to solve than nonties because of differences in accessibility in memory or differences in the solution processes. Access-based accounts fall into three categories: familiarity, interference, variability in solution approaches. According to familiarity explanations, accessibility varies with practice such that tie effect is related to the frequency with which problems are encountered. Ties receive more practice and the connections between operands and answers in memory are greater. So ties are solved more quickly. According to interference explanations, ties and nonties are defined as separate categories of problems and the interference is greater within category than between category. Thus, because the tie category includes relatively few problems, ties received less inhibitory input than nonties. According to solution approach explanations, even simple arithmetic is solved not only by direct retrieval from memory but by nonretrieval procedures. Ties are solved by direct retrieval procedures and nonties are solved by nonretrieval procedures which is slower than direct retrieval. The encoding-account can’t provide reasonable explanations for tie×size interaction. Access-based accounts propose that there is no obvious tie advantage in solution latencies because the small ties and nonties are both solved by direct retrieval. The large ties are solved more quickly because of using more efficient direct retrieval than large nonties. So there is obvious tie advantage for large problems and the less problem-size effect for ties than for nonties. In summary, the studies about tie effect mainly use two methods. First, the researchers explore the effect on tie effect by manipulating format of figures(digit/word). But various figure format lead to the change of procedure strategies and it is hard to decide if the encoding is influenced. Second, participants’ self-report of the procedure strategies is used to explore the effect on tie effect. This method would neglect the effect of other factors. So new experiment paradigm should be used to help us know more about the procedure mechanism of tie effect in future.

Key words: tie effect, encoding-based account, access-based account

摘要：

tie effect主要表现为tie比nontie更快更准确解决，以及tie/nontie与问题大小的交互作用，较大题目的tie比nontie具有更明显的反应时优势，tie的问题大小效应比nontie要小的多。有关tie effect加工机制的解释主要有基于编码的理论和基于结果通达的理论。目前的研究主要通过操作问题呈现方式以及报告加工策略的方法分别考察编码方式及加工策略的影响，今后研究应开拓新的研究范式以加深对其加工机制的认识。

关键词: tie effect, 编码理论, 通达理论