Children's strategies in computational estimation

We investigated strategies used to estimate answers to addition problems. Two hundred and sixteen participants (72 adults, 72 sixth graders, and 72 fourth graders) had to provide estimates of three-by-three digit addition problems (e.g., 249 + 743). The choice/no-choice method was used to obtain unbiased estimates of the performance characteristics of strategies. Results showed that (a) at all ages, the most common strategy was to round both operands down to the closest smaller decades, (b) strategy use and execution were influenced by participants' age, problem features, and relative strategy performance, and (c) age-related changes in computational estimation include changes in relative strategy use and execution, as well as in the relative influences of problem and strategy characteristics on strategy choices. Implications of these findings for understanding age-related differences in strategic aspects of computational estimation performance are discussed.     

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.     

Age-related changes in children's executive functions and strategy selection: A study in computational estimation

Third, fifth, and seventh graders selected the best strategy (rounding up or rounding down) for estimating answers to two-digit addition problems. Executive function measures were collected for each individual. Data showed that (a) children's skill at both strategy selection and execution improved with age and (b) increased efficiency in executive functions contributed significantly to age-related improvement in children's strategy selection skill. These findings have implications for understanding of age-related differences in computational estimation, strategy selection processes, and mechanisms of strategic development in children.     

双任务协调、任务呈现方式影响成人算术策略执行:估算证据

前人研究显示中央执行影响算术策略的执行。双任务协调作为中央执行的执行功能之一,是否会影响个体的策略执行?采用选择无选法与改进的心理不应期范式,探讨随机/固定呈现方式下,双任务协调对算术策略执行的影响。结果表明:双任务协调影响策略执行,双反应策略执行效能显著差于单反应;任务呈现方式影响策略执行,固定方式优于随机方式;任务呈现序列影响策略执行反应时,数字先呈现的估算策略执行效能显著差于图形先呈现。总之,双任务协调、任务呈现方式影响算术策略执行,固定方式引起更明显的双任务协调代价。     

Children's use ofGet passives

Children's use ofget in passivelike constructions was examined in this study. Fifty-eight children at three age levels were tested twice on imitation, comprehension, and production tasks. For the imitation and comprehension tasks, passive sentences withget were modeled in one instance and withbe in the other instance. On both tasks, children performed significantly better on theget items than on thebe items. For the production tasks, active sentences were used as the experimental stimuli. Among 928 production responses possible, children produced 423get passives and 6be passives. The frequency ofget passives increased with increasing age. Qualitative analyses were performed to determine agerelated changes in the pattern of linguistic strategies chosen. These data were consistent with predictions derived from a model of lexical directionality: Children used moreget thanbe passives and more truncated than full passives.     

A computational model of retrospective time estimation

Retrospective time estimation is an important aspect of dynamic systems and needs to be integrated in cognitive architectures. This article gives an overview of theoretical accounts of retrospective and prospective time estimation. Assumptions based on an experiment investigating retrospective time estimation conducted in our research group are presented. Integrating both we introduce a retrospective timer-module for ACT-R 6.0 and the corresponding estimation algorithm. The successful validation of the module is shown and further implications are discussed.     

Children's use of inanimate transitional objects in coping with hassles.

This study examined children's use of inanimate transitional objects when coping with daily hassles. Mothers of 50 preschoolers rated their children on frequency of hassles, intensity of reaction to daily hassles, coping effectiveness, and frequency of object use. No significant differences were found between those children with an inanimate transitional object and those without such an object. Among those children with an object, a significant object effect on frequency of hassles (p less than .05) and a significant object effect on coping effectiveness were found. A significant age effect was also found, indicating that older children used their inanimate transitional objects more often than younger children. Among those children with an inanimate transitional object, significant positive relationships were found between frequency of hassles, intensity of reaction to hassles, coping effectiveness, and frequency of object use. The results indicated that children who used their thumb as an inanimate transitional object experienced fewer hassles than children who used a soft object. The results also suggested that an increase in the number of hassles experienced was related to more intense reactions to hassles, less effective coping, and an increase in object use. The nature of the object and the developmental issue of separation-individuation are considered as well.     

Cultural differences in strategic behavior: a study in computational estimation

Imbo and LeFevre (2009) observed that Asians (responding in their 2nd language) selected strategies less adaptively than did non-Asians (responding in their 1st language). In the present research, we tested whether adaptive strategy selection is (a) really more resource demanding for Asians than for non-Asians or (b) more resource demanding for participants answering in a nonpreferred language. Three groups of participants were tested on a computational estimation task (e.g., 42 × 57 ≈ ?) in no-load and load conditions: 40 Belgian-educated adults who answered in their first language (Dutch), 40 Chinese-educated adults who answered in their first language (Chinese), and 40 Chinese-educated adults who answered in their second language (English). Although the Chinese were faster and more accurate than the Belgians, they selected strategies less adaptively. That is, the Chinese were less likely to choose the strategy that produced the best estimate; this was especially so when their working memory was loaded. Further, we also observed that the Chinese who answered in English were slower than the Chinese who answered in Chinese; this difference was larger for difficult strategies and under working memory load. These results are interpreted in terms of the encoding complex model, whereas the explanation for the adaptivity results is based on cultural differences in educational history.     

Developmental and intellectual differences in self-report and strategy use.

The veridicality and reactivity of children's self-report of covert and overt memory strategies were investigated in a task allowing a direct comparison of self-report and the strategy observed. External memory strategies (e.g., moving objects) were investigated with 7-, 9-, 11-, and 17-year-old typical children and 11- and 17-year-old children with mild mental retardation. Participants placed objects in specified spatial locations after hearing sequences of tape-recorded sentences. After each trial, half of the children immediately reported the strategy used. There were strong positive correlations between the frequency of reported strategy use and observed strategy use. Self-reports were accurate but not always complete. There was no effect of the self-reporting procedure on measures of verbal strategies, external memory strategies, and accuracy of recall. Children were less likely to report strategies not related to recall; these results are compatible with a "goal-sketch" mechanism.     

Children's use of geometric information in mapping tasks

Accumulating evidence, particularly from research using the disorientation technique, demonstrates early sensitivity to geometric properties of space. However, it is not known whether children can use geometric cues to interpret a map. The current study examined how 3- to 6-year-olds use geometric features of layouts in solving mapping tasks. Children were asked to identify a target location in a layout shaped as an isosceles triangle by using information provided in a picture of that layout. Performance depended on whether the shape was presented explicitly or needed to be inferred. Younger participants performed better when the triangle was formed by continuous connected lines than when it was formed by separate objects. Performance also depended on the type of geometric cues available. Children found it easier to establish mapping for targets located in the unique corner of the triangle than for targets located in equal-sized corners. Overall, the findings reveal both a remarkable early ability to use geometric information in mapping and limits in this ability.     

Children's use of verbal collaterals in DRL performance

This study examines the effects of a verbal collateral (counting) on a series of three differential reinforcement of low rates of response (DRL) tasks with progressively longer interresponse time requirements (DRL-2, DRL-6 and DRL-12). Forty-eight 10-year-old children, divided according to sex and conceptual tempo (fast-inaccurate vs. slow-accurate) participated in DRL training, half of them being instructed to count aloud between responses. Counting was found to be related to faster learning of all the tasks and to greater efficiency in obtaining reinforcement in most cases. It also eliminated differences due to sex and conceptual tempo except in DRL-12. However, it had the disadvantage of causing inexact temporal discrimination. The results were replicated in a group of 8-year-old subjects performing the same tasks.     

Children's use of geometry for reorientation

Research on navigation has shown that humans and laboratory animals recover their sense of orientation primarily by detecting geometric properties of large-scale surface layouts (e.g. room shape), but the reasons for the primacy of layout geometry have not been clarified. In four experiments, we tested whether 4-year-old children reorient by the geometry of extended wall-like surfaces because such surfaces are large and perceived as stable, because they serve as barriers to vision or to locomotion, or because they form a single, connected geometric figure. Disoriented children successfully reoriented by the shape of an arena formed by surfaces that were short enough to see and step over. In contrast, children failed to reorient by the shape of an arena defined by large and stable columns or by connected lines on the floor. We conclude that preschool children's reorientation is not guided by the functional relevance of the immediate environmental properties, but rather by a specific sensitivity to the geometric properties of the extended three-dimensional surface layout.     

Children's use of language context in lexical ambiguity resolution

Lexical ambiguity resolution was examined in children aged 7 to 10 years and adults. In Experiment 1, participants heard sentences supporting one (or neither) meaning of a balanced ambiguous word in a cross-modal naming paradigm. Naming latencies for context-congruent versus context-incongruent targets and judgements of the relatedness of targets to the sentence served as indices of appropriate context use. While younger children were faster to respond to related targets regardless of the sentence context, older children and adults showed priming only for context-appropriate targets. In Experiment 2, only a single-word context preceded the homophone, and in contrast to Experiment 1, all groups showed contextual sensitivity. Individual working-memory span and inhibition ability were also measured in Experiment 2, and more mature executive function abilities were associated with greater contextual sensitivity. These findings support a developmental model whereby sentential context use for lexical ambiguity resolution increases with age, cognitive processing capacity, and reading skill.     

Children's use of the bearing angle in interceptive actions

The authors investigated the effect of ball velocity and walking direction on children's adherence to the constant bearing angle (CBA) strategy. Children (N = 20) approached a moving ball to manually intercept it at a predefined target area. Results revealed that 10- to 12-year-olds adhered more than 5- to 7-year-olds to the CBA strategy. Younger children deviated more than older children from smaller angles of approach and lower ball velocities. The present findings suggest that younger children have difficulty adjusting to task requirements because they fail to couple walking velocity with ball velocity. The improvement seen with increasing age suggests that compliance with the CBA strategy may be attributed to older children's enhanced coincidence anticipation.     

Adolescent parental affinity-seeking: age- and gender-mediated strategy use.

The focus of the present study was the use of parental affinity-seeking strategies by adolescents. Both the type of strategies used and the degree to which age and gender factors mediated their use were examined. The results were consistent with Bell and Daly's (1984) constraints dimension of the affinity-seeking process, with adolescents employing a narrower range of strategies with the parent as a familiar target. Additionally, significant differences in the use of strategies were apparent on the basis of adolescent's age and gender and parent's gender.     

Metacognition and mathematics strategy use

The role of children's metacognitive knowledge in their mathematics strategy use was studied by a longitudinal examination of second graders' effort attributions, metacognition for mathematics, and strategy use while solving mathematics problems. Children's correct use of retrieval, internal and external strategies, and the prevalence of strategy use were assessed in September and the following January. Effort attributions for success and failure were also assessed at both points in time. In January, metacognitive knowledge about mathematics strategies was measured. Second graders possess metacognitive knowledge about mathematics strategies, and this knowledge is correlated most strongly with the tendency to use internal strategies in September and correct internal strategy use in September. Effort attributions measured at both timepoints were significantly related to metacognition. Effort attributions in January also correlated with the tendency to use internal strategies in January. In general, the results are consistent with self-system theories, which posit that metacognition, motivation, and strategy use work together to promote learning.     

Children's use of conversational rules in a referential communication task

Three experiments investigating first-grade children's comprehension, of referentially ambiguous messages are reported. In the first one children were shown to interpret a literally ambiguous message by means of the strategy based on the conversational Maxim of Antecedent rather than that based on the more appropriate Maxim of Quantity. The results of the second experiment suggest that the Maxim of Quantity can be used by children, provided the situation is quite simple; they also suggest that after having used such a maxim in a simple situation, children can apply it in a more complex situation. This generalization to new situations, however, is not a mere perseveration since, as shown in the third experiment, children can adjust their comprehension strategy to the situation requirements. The results are discussed with reference to the recent proposals on referential ambiguity and children communication failures.