What Leads Children to Adopt New Strategies ?

Learning of class inclusion by 5-year-olds in response to empirical and logical explanations of an adult’s answers was examined. Contrary to the view that young children possess an empirical bias, 5-year-olds learned more, and continued learning for longer, when given logical explanations of correct answers than when given empirical explanations. Once children discovered how to solve the problems, they showed few regressions. Many children in the microgenetic experiment followed the path of change anticipated from previous cross-sectional studies, but children in the cross-sectional part of the study seemed to follow a different path. Reasons for the superior effectiveness of the logical explanations were discussed. What Leads Children to Adopt New Strategies 3 What Leads Children to Adopt New Strategies? A Microgenetic / Cross Sectional Study of Class Inclusion The primary goal of the present study was to compare young children’s learning from logical and empirical explanations of reasoning. A second main goal was to examine the relation between short-term microgenetic changes and longterm age-related changes. These goals were pursued in the context of the classic Piagetian class inclusion task, a task that can be solved either logically or empirically and that therefore allows direct comparison of the effects of encountering the two types of explanations. This introductory section includes four parts. In the first part, we describe current understanding and unresolved issues regarding children’s adoption of new strategies in general. In the second, we examine current knowledge and unresolved issues regarding acquisition of class inclusion. In the third, we introduce the microgenetic / cross-sectional design as a way of addressing the main issues in the present study. In the fourth, we describe what we did in the study and our hypotheses regarding the results. Acquiring New Strategies A number of recent studies have examined how children discover new strategies (e.g., Alibali, 1999; Chen & Klahr, 1999; Goldin-Meadow & Alibali, 2002; Granott, 2002; Kuhn et al., 1995). These studies have shown that discovering a strategy is often only the first step in strategic change; prior strategies often persist, even when the newly discovered strategy has clear advantages and even when children can describe those advantages (Siegler & Jenkins, 1989). Thus, the adoption of new strategies is often quite slow. It is also the case, however, that the rate of adoption of new strategies varies considerably across studies. Two factors that seem to be related to this rate have What Leads Children to Adopt New Strategies 4 been identified: accuracy and efficiency. A recent literature review (Siegler, in press) concluded that the largest factor in determining the rate of adoption of newly discovered strategies is the difference between their accuracy and that of previously available strategies. In the relatively few cases in which newly discovered strategies quickly replace previous approaches, the new strategies have entailed large improvements in accuracy, generally from consistently incorrect to consistently correct. Differences between the efficiency of new and previous strategies also appear to influence the rate of adoption of new strategies, though to a lesser degree than differences in accuracy do. When both new and old strategies generate correct performance, new strategies that confer large advantages in speed or substantial reductions in processing steps are adopted more rapidly than new strategies that confer less dramatic advantages (Siegler, in press). In the present study, we examined a third factor that may influence the rate and completeness of adoption of new strategies: whether there are logical as well as empirical reasons for adopting them. Some strategies are based on the fundamental logic of the problem. For example, on conservation of weight problems, one correct logical strategy is to note that nothing was added or subtracted when the clay was remodeled, so the weight must be the same. Other strategies are empirical; for example, rather than solving the conservation of weight problem logically, a child could take the empirical approach of weighing the clay before and after its shape was transformed, and noting that the weight remained the same. Many other problems also can be solved either empirically or logically. For example, number conservation tasks can be solved either by counting the objects in each row or by noting that nothing was added or subtracted; transitivity of length problems can be solved either by measuring the length of the sticks being compared or by drawing the logical inference “If A > B and B > C, then A > C”; arithmetic problems of the form A + B – B = ___ can be solved either by adding the first two numbers and What Leads Children to Adopt New Strategies 5 subtracting the third or by deducing that the answer must be “A,” because adding and subtracting the same number cannot have an effect; and so on. The specific issue addressed in the present study was whether young children learn more rapidly and completely when they are encouraged to use logical or empirical strategies for solving a problem. In particular, we compared 5-year-olds’ learning in response to logical and empirical explanations of correct answers to class inclusion problems. Contrasting acquisition of two strategies for solving the same problem was a more direct way of establishing factors that influence acquisition of new strategies than previous techniques, which involved reviewing findings from different tasks and populations, and then attempting to isolate the factors associated with more and less rapid and complete acquisition (Siegler, in press). There were reasonable arguments for expecting either logical or empirical strategies to be acquired more effectively. First consider arguments that suggest that young children should acquire empirical strategies more easily. Age peers of the children whose learning was examined in the present study, 5-year-olds, have been found to rely on empirical strategies in a number of situations in which older children and adults use logical reasoning strategies. When presented tautologies (e.g., “I either am holding a green chip in my hand or I’m not”) or contradictions (“I am holding and not holding a green chip in my hand”), and asked whether they needed the experimenter to open her hands to tell if the statement was true or false, 5-year-olds usually chose the empirical strategy; in both cases, most children said they needed the experimenter to open her hands to tell (Osherson & Markman, 1975). Most 5-year-olds also confuse logically determinate and logically indeterminate problems and are subject to “positive capture,” in which they think that a case consistent with a conclusion implies that the conclusion must be true (Fay & Klahr, 1996; Klahr & Chen, 2003). On class inclusion tasks in which What Leads Children to Adopt New Strategies 6 children are asked whether a set or the larger of two subsets has more objects (e.g., “I have five dogs and three cats; do I have more dogs or more animals”), most 5year-olds compare the number of objects in the two subsets (e.g., five dogs versus three cats) rather than reasoning that there must be more in a set than in any of its subsets (Piaget, 1952). Young children also have been found to use empirical strategies on other tasks somewhat similar to class inclusion. When asked if they could place more spoons than silverware on the table (Markman, 1978) or whether they could draw a picture that has more cats than animals (S. Miller, 1986), most 5year-olds said “yes,” rather than reasoning that this was logically impossible. Also favoring the prediction that children should learn more from empirical explanations, 5-year-olds seem to have a particular fondness for the type of empirical strategy relevant to class inclusion, counting. They use counting even on tasks where such a strategy is inappropriate. For example, K. Miller (1984) found that 5-year-olds created “fair” divisions of food between two birds by counting out equal numbers of pieces of food, regardless of the sizes of the pieces. Similarly, Levin (1989) found that 5-year-olds often counted the passage of two temporal durations and judged the higher number to indicate the longer time, regardless of whether the counting had proceeded at the same speed. This reliance on counting strategies, and on empirical rather than logical strategies in general, suggested that 5-year-olds would learn empirical strategies more readily than logical ones. On the other hand, Siegler and Svetina (2002) suggested that logical strategies might be learned more quickly than empirical ones. The above-cited findings of young children using empirical strategies in situations where older children and adults use logical ones may reflect the young children not understanding the logical strategies. If the logic was made clear to them, they might prefer the logical strategies (or have no preference between the two). In addition, several of the microgenetic studies in which newly discovered strategies have been What Leads Children to Adopt New Strategies 7 adopted most rapidly have involved acquisition of logical reasoning strategies. These include strategies for solving matrix completion, A + B B, and 20 Questions problems (Siegler & Stern, 1998; Siegler & Svetina, 2002; Thornton, 1999). Thus, the fact that young children use empirical strategies to solve problems that adults and older children solve via logical strategies does not imply that children would choose empirical strategies if they understood that the logical strategies could be used to solve the problems. Moreover, there were reasons to think that young children might prefer logical reasoning strategies if they understood how to execute and apply them to particular problems. Logical strategies often have large advantages in speed and accuracy. In the co