Strategy Switch Costs in Arithmetic Problem Solving

Article excerpt

Three experiments tested whether switching between strategies involves a cost. In three experiments, participants had to give approximate products to two-digit multiplication problems (e.g., 47 × 76). They were told which strategy to use (Experiments 1 and 2) or could choose among strategies (Experiment 3). The participants showed poorer performance when they used different strategies on two consecutive trials than when they used the same strategy. They also used the same strategy over two consecutive problems more often than they used different strategies. These effects, termed strategy switch costs, were found when the participants executed the easiest strategy and when they solved easy problems. We discuss possible processes underlying these strategy switch costs and the implications of these strategy switch costs for models of strategy choices.

One of the hallmarks of human cognition is that participants use several strategies when they accomplish cognitive tasks (Siegler, 2007). This multiple-strategy use permits one to alternate flexibly between different strategies and to adapt to the demands of problems and situations. Two central issues with regard to cognitive strategies concern how we choose among strategies for solving each problem and how we execute a strategy once it has been selected. The present study contributes to these issues by showing that participants obtain poorer performance when they use different strategies on two consecutive trials than when they use the same strategy and tend to repeat the same strategy over successive problems.

Previous findings on cognitive strategies showed that both strategy choices and strategy execution are influenced by problem and strategy characteristics, as well as by participants' skills, working memory capacities, and age. For example, in arithmetic, participants tend to retrieve correct solutions to problems like 3 × 4 directly from memory when retrieval is accurate and fast and to use counting on problems like 7 × 8 when retrieval is not accurate (e.g., Campbell & Xue, 2001; LeFevre, Bisanz, Daley, Buffone, & Sadesky, 1996). As another example, in episodic memory, participants tend to use mental imagery more often to memorize concrete words and mental rehearsal to store more abstract words (e.g., Dunlosky & Hertzog, 2001).

Computational models of strategy choices (e.g., Lovett & Anderson's [1996] ACT-R model; Lovett & Schunn's [1999] RCCL model; Payne, Bettman, & Johnson's [1993] adaptive decision maker model; Rieskamp & Otto's [2006] SSL model; and Siegler & Arraya's [2005] SCADS* model) share several core assumptions regarding how we choose among strategies. All these models propose that choosing among multiple strategies crucially involves associative mechanisms such as activating the relative costs/ benefits of each strategy and selecting the strategy that works best for a given problem on the basis of problem and strategy characteristics. All models also assume that strategies including fewer and/or simpler procedures (e.g., retrieving the correct solution of arithmetic problems like 3 × 4 directly from memory) are easier to execute than strategies including more and/or more complex procedures (e.g., adding 3 four times). These assumptions have proven sufficient to account for most findings on strategy choices and strategy execution.

However, several strategy phenomena are not accounted for by models of strategy choices. For example, it is unknown why some groups of participants, such as older adults (see, e.g., Lemaire & Arnaud, 2008), sometimes use fewer strategies even when they know and can use all available strategies. Also, it is unknown why problem features and relative strategy efficacy together never fully account for strategy choices or why participants are sometimes biased in strategy choices (i.e., they continue to use a strategy when an alternative is faster and/or more accurate; e. …