SCADS: A Model of Children's Strategy Choices and Strategy Discoveries

Preschoolers show surprising competence in choosing adaptively among alternative strategies and in discovering new approaches. The SCADS computer simulation illustrates how simple processes can generate this impressive competence. The model's behavior parallels data on children's addition in at least eight ways: It uses diverse strategies over prolonged periods of time, makes adaptive choices among strategies, discovers the same strategies as children, discovers strategies in the same sequence as children, makes discoveries without trial and error, makes discoveries without having experienced failure, narrowly generalizes new approaches, and generalizes more broadly following challenging problems. SCADS thus indicates plausible sources of young children's surprising competence at strategy choice and strategy discovery.     

Stability and change in children's division strategies

Age-related changes in children's performance on simple division problems (e.g., 6/2, 72/9) were investigated by asking children in Grades 4 through 7 to solve 32 simple division problems. Differences in performance were found across grade, with younger children performing more slowly and less accurately than older children. Problem size effects were also found in that children were faster and more accurate on small problems than on large problems. Two strategies changed across age, with children in Grade 4 relying heavily on the strategy of "addition" (adding the divisor until the dividend was reached) to solve the problems and children in Grades 5 through 7 relying primarily on the strategy of "multiplication" (recasting the division problem as a multiplication problem) to solve the problems. Surprisingly, the frequency of direct retrieval (retrieving the answer directly from memory) did not increase across grade and never became the dominant strategy of choice. Reasons for why retrieval use remains infrequent and age invariant are discussed. Overall, the results suggest that division is a unique operation and that the continued study of division may have implications for further understanding of how procedural and conceptual knowledge of arithmetic develops.     

SOME GENERAL CONCLUSIONS ABOUT CHILDREN'S STRATEGY CHOICE PROCEDURES

This article presents conclusions that have emerged from my recent work on how children choose strategies on familiar tasks such as arithmetic, time-telling, and spelling. Among these conclusions are that children use diverse strategies on many tasks; that ignoring this diversity of strategies can lead to seriously flawed cognitive models; that children's pattern of strategy choices have considerable adaptive value; that children's strategy choices do not always reflect the operation of metacognitive processes; that associative knowledge directs at least some strategy choices; that among the factors that influence the development of strategy choices are the difficulty of executing backup strategies, the impact of related problems and operations, and the frequency of problem presentation; and that individual differences in both knowledge and cognitive style influence strategy choices.     

Adults' age-related differences in adaptivity of strategy choices: evidence from computational estimation

Four experiments document adults' age-related changes in computational estimation performance and in adaptivity of strategy choices (i.e., the ability to choose the most precise strategy on each trial). Young and older adults were asked to provide estimates of 2-by-2-digit multiplication problems (e.g., 43 x 78) under varying conditions of speed and accuracy emphasis. The main findings showed that (a) older adults provided less accurate estimates and took more time to estimate, especially on the most difficult problems or when using harder strategies; (b) young and older adults had similar strategy preferences; and (c) older adults chose estimation strategies less adaptively than young adults. Implications of these findings for understanding strategic changes during adulthood in a wide variety of cognitive domains are discussed.     

Simple mental addition in children with and without mild mental retardation.

The speeded performance on simple mental addition problems of 6- and 7-year-old children with and without mild mental retardation is modeled from a person perspective and an item perspective. On the person side, it was found that a single cognitive dimension spanned the performance differences between the two ability groups. However, a discontinuity, or "jump," was observed in the performance of the normal ability group on the easier items. On the item side, the addition problems were almost perfectly ordered in difficulty according to their problem size. Differences in difficulty were explained by factors related to the difficulty of executing nonretrieval strategies. All findings were interpreted within the framework of Siegler's (e.g., R. S. Siegler & C. Shipley, 1995) model of children's strategy choices in arithmetic. Models from item response theory were used to test the hypotheses.     

Executive control of thought and action

In addition to processing information about stimuli in the environment, the cognitive system performs executive functions to control and coordinate the processes that deal with environmental stimuli. Several executive functions may be distinguished: (1) Making choices about alternative strategies for processing environmental stimuli; (2) constructing or instantiating a version of the chosen strategy to enable performance on the task; (3) controlling and coordinating execution of the strategy during real-time performance on the task; and (4) disabling or disengaging the strategy in response to changes in goals or changes in the task environment that make the current strategy inappropriate. This paper presents a selective review of research addressing each of these executive functions, focusing on the time and resources used to accomplish each one.     

Strategy switch costs in arithmetic problem solving

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.     

Emotion regulation and its effects on mood improvement in response to an in vivo peer rejection challenge

This study examined children's spontaneous use of behavioral emotion regulation (ER) strategies and their effects on subsequent mood change in response to an in vivo peer rejection manipulation. Participants (N = 186), ranging between 10 and 13 years of age, played a computer game based on the television show Survivor and were randomized to either peer rejection (being voted out of the game) or nonrejection control. In response to rejection, more than one third of the participants (38%) displayed a marked worsening (i.e., reliable change) in state mood. After receiving feedback, time spent on several behavioral ER strategies during a 5-minute postfeedback period was assessed. At the end of the postfeedback period, children's cognitive activity was also assessed. More time spent on behavioral distraction was positively linked to subsequent increases in positive affect, whereas the reverse pattern was found for disengagement/passive behavior. Moreover, higher endorsement ratings for the strategy of "cognitive analysis" were associated with stronger increases in negative affect.     

Cognitive, motivational, social, and environmental influences on children's food choices

This study tested the applicability of a cognitive-motivational model of health behavior to children's food choices. A sample of 107 elementary schoolchildren provided ratings of 15 foods in terms of possible choice criteria (e.g., how tasty or healthful specific foods were) and social or environmental influences (e.g., whether foods were eaten by friends or were easy to get). Several measures of food consumption were taken, and cognitive-developmental level was assessed. Within-person correlations were calculated between food choices and each choice criterion and social/environmental factor. These "correlational indices" of influences on food choice subsequently were used to identify five distinct subgroups in the sample. Children at the operational level of cognitive development tended to be in one of three groups characterized by health orientation in food choice, taste orientation, or multiple-motive orientation. Dietary quality was poorest in the taste-oriented group. Children at the preoperational level tended to have one of two undifferentiated patterns of values across the correlational indices. Results provide evidence of: the viability of cognitive-motivational models to explain children's food choices, the promise of within-person research methodology, and the potential for enhanced health behavior-change programs by use of population segmentation and tailored interventions.     

Self-instruction training following neurological injury

The teaching of cognitive strategies is a potentially effective intervention technique for some students with acquired neurological injuries; however, educators have only infrequently reported on the systematic application of cognitive strategies to the academic challenges of this population. This study represents such an attempt by investigating the effects of a self-instruction strategy on the academic performance of a student with acquired neurological damage. The intervention programme pertained to performing 2-digit by 1-digit multiplication problems and consisted of: (1) a six-step multiplication procedure; (2) self-instruction cues; and (3) procedural prompts. The intervention package resulted in improved performance on the multiplication task with levels being maintained despite fading of procedural prompts and self-instruction cues. Results are discussed in terms of implications for training and future research.     

4～6岁儿童未来时间认知教学的实验研究

本研究在Friedman实验范式的基础上,增加了“系统教学”变量,探究教学与4~6岁儿童未来时间认知能力发展的关系。结果表明:(1)“教学”是影响儿童未来时序认知的主要因素;(2)“点估计策略”与“习俗时间单元概念策略”是两种主要时间认知策略;(3)儿童未来时间认知策略的发展遵循从感性直观到抽象概括的发展规律;(4)“教学”是影响其未来时间认知策略的主要因素;(5)4岁儿童已能区分未来事件的时距信息,且其未来时距认知具有分段性。     

Effects of problem size,operation, and working-memory span on simple-arithmetic strategies: differences between children and adults?

Adult's simple-arithmetic strategy use depends on problem-related characteristics, such as problem size and operation, and on individual-difference variables, such as working-memory span. The current study investigates (a) whether the effects of problem size, operation, and working-memory span on children's simple-arithmetic strategy use are equal to those observed in adults, and (b) how these effects emerge and change across age. To this end, simple-arithmetic performance measures and a working-memory span measure were obtained from 8-year-old, 10-year-old, and 12-year-old children. Results showed that the problem-size effect in children results from the same strategic performance differences as in adults (i.e., size-related differences in strategy selection, retrieval efficiency, and procedural efficiency). Operation-related effects in children were equal to those observed in adults as well, with more frequent retrieval use on multiplication, more efficient strategy execution in addition, and more pronounced changes in multiplication. Finally, the advantage of having a large working-memory span was also present in children. The differences and similarities across children's and adult's strategic performance and the relevance of arithmetic models are discussed.     

Instruction and load effects on high-skill and low-skill individuals: A study in the domain of mental arithmetic

What happens when people are asked to respond as quickly or as accurately as possible? This study tested the effects of speed/accuracy instructions and working-memory load on people's strategy efficiency and strategy selection. Adult participants solved simple addition problems (Experiment 1) and simple multiplication problems (Experiment 2) under load and no-load conditions and provided trial-by-trial strategy reports. High-skill participants were more efficient than low-skill participants, but the underlying causes of these skill-related effects differed across experiments. In the addition experiment, high-skill participants responded adaptively to the changing situations by changing their strategy choices, which resulted in smaller effects on their actual performance. Low-skill participants in contrast, did not change their strategy choices as adaptively, which resulted in less efficient performance—and especially so under load conditions. In the multiplication experiment, high-skill and low-skill participants differed in strategy efficiencies rather than in strategy choices. In the discussion, the results are further interpreted and future adaptations for the adaptive strategy choice model (ASCM; Siegler & Jenkins, 1989) are suggested.     

4～6岁儿童三种时间副词理解能力及策略的实验研究

采用定量与定性相结合的研究方法,对4～6岁儿童理解时间副词的能力进行了初步的探查,结果表明:(1)学前儿童对不同时间副词的理解能力是不同的。对现在时间副词的理解优于对过去时间副词的理解,对将来时间副词的理解能力最低,基本处于萌芽阶段。但这种理解能力的年龄发展效应不明显。(2)在表示将来的时间副词中,儿童对不同的具体时间副词表现出认知差异。(3)学前儿童在理解时间副词时多种策略并存。随着年龄的增长,有效策略的生成能力有了明显的提高。     

The strategic nature of changing your mind

In two experiments, we studied how people’s strategy choices emerge through an initial and then a more considered evaluation of available strategies. The experiments employed a computer-based paradigm where participants solved multiplication problems using mental and calculator solutions. In addition to recording responses and solution times, we gathered data on mouse cursor movements. Participants’ motor behavior was revealing; although people rapidly initiated movement to the calculator box or the answer input box, they frequently changed their minds and went to the other box. Movement initiation direction depended on problem difficulty and calculator responsiveness. Ultimate strategy selection also depended on these factors, but was further influenced by movement initiation direction. We conclude that strategy selection is iterative, as revealed by these differences between early cursor movement and eventual strategy implementation. After rapidly initiating movement favoring one strategy, people carefully evaluate the applicability of that strategy in the current context.     

Adults' strategies for simple addition and multiplication: verbal self-reports and the operand recognition paradigm

Accurate measurement of cognitive strategies is important in diverse areas of psychological research. Strategy self-reports are a common measure, but C. Thevenot, M. Fanget, and M. Fayol (2007) proposed a more objective method to distinguish different strategies in the context of mental arithmetic. In their operand recognition paradigm, speed of recognition memory for problem operands after solving a problem indexes strategy (e.g., direct memory retrieval vs. a procedural strategy). Here, in 2 experiments, operand recognition time was the same following simple addition or multiplication, but, consistent with a wide variety of previous research, strategy reports indicated much greater use of procedures (e.g., counting) for addition than multiplication. Operation, problem size (e.g., 2 + 3 vs. 8 + 9), and operand format (digits vs. words) had interactive effects on reported procedure use that were not reflected in recognition performance. Regression analyses suggested that recognition time was influenced at least as much by the relative difficulty of the preceding problem as by the strategy used. The findings indicate that the operand recognition paradigm is not a reliable substitute for strategy reports and highlight the potential impact of difficulty-related carryover effects in sequential cognitive tasks.     

信息提供者的先前准确性对幼儿选择性信任的影响

作为社会学习的个体,幼儿从3岁起就能根据信息提供者先前准确性的差异对其可信程度进行评估。通过对以往研究效应量的整理分析发现,随年龄增长,幼儿对高先前准确性信息提供者的信任程度表现出增长趋势（3岁幼儿选择的效应量中值为d_询问=0.60,d_赞同=0.61;4岁幼儿的效应量中值为d_询问=0.80,d_赞同=0.96）。在运用先前准确性进行评估时,幼儿主要关注信息提供者是否犯错,灵活使用"整体印象"和"特质推测"两种认知策略对其未来行为进行推测。幼儿能够根据自身对材料的感知对信息提供者的可信程度进行动态调整,其心理理论发展水平和执行功能限制了他们的选择信任,而信息提供者同时具有的社会性因素对幼儿的选择也具有干扰作用（幼儿信任准确的信息提供者的效应量中值为d_询问=-0.03,d_赞同=-0.17）。未来研究可以改进实验范式,进一步探查先前准确性对幼儿选择性信任的影响,拓展信息提供者的呈现方式和其它多重特征,关注不同类别的信息提供者。     

Flexible Strategy Use in Young Children's Tic-Tac-Toe

In domains with multiple competing goals, people face a basic challenge: How to make their strategy use flexible enough to deal with shifting circumstances without losing track of their overall objectives. This article examines how young children meet this challenge in one such domain, tic-tac-toe. Experiment 1 provides an overviews of development in the area; it indicates that children's tic-tac-toe strategies are rule based and that new rules are added one at a time. Experiment 2 demonstrates that even young children flexibly tailor their strategy use to meet shifting circumstances. Experiment 3 indicates that these adaptations are accomplished through a process of goal-based resource allocation, whereby children focus their cognitive resources on applying rules most consistent with their current primary goal. A computer simulation specifies how this process works and demonstrates its sufficiency for producing behavior much like that of the children. The findings are discussed as part of a broader framework of mechanisms for generating problem-solving approaches.     

The relation between young children's cognitive role-taking and mothers' preference for a conflict-inducing childrearing method

In this study, we examined children's cognitive role-taking in relation to their mothers' choices of techniques to solve domestic dilemmas involving children's misbehavior, social skills, and logical reasoning. Results showed that a mother's preference for the childrearing strategy known as distancing, which uses a Socratic or dialectical inquiry to create cognitive conflict in the child, bore a significant association to her child's advancement in cognitive role-taking skill. This finding is discussed in relation to theories of cognitive development that postulate that mental conflict or tension stimulates cognitive growth. Practical factors that might inhibit mothers from making effective use of the distancing technique are also considered.     

Cognitive processes of numerical estimation in children

We tested children in Grades 1 to 5, as well as college students, on a number line estimation task and examined latencies and errors to explore the cognitive processes involved in estimation. The developmental trends in estimation were more consistent with the hypothesized shift from logarithmic to linear representation than with an account based on a proportional judgment application of a power function model; increased linear responding across ages, as predicted by the log-to-lin shift position, yielded reasonable developmental patterns, whereas values derived from the cyclical power model were difficult to reconcile with expected developmental patterns. Neither theoretical position predicted the marked "M-shaped" pattern that was observed, beginning in third graders' errors and fourth graders' latencies. This pattern suggests that estimation comes to rely on a midpoint strategy based on children's growing number knowledge (i.e., knowledge that 50 is half of 100). As found elsewhere, strength of linear responding correlated significantly with children's performance on standardized math tests.