Developmental Differences in Understanding of Balance Scales in the United States and Zimbabwe

This cross-cultural, developmental study of understanding of the physics of a balance scale involved 2 age groups (5- and 22-year-olds) in 2 countries (the United States and Zimbabwe). A factorial design was used. Each participant solved 6 types of balance scale problems, and the patterns of errors for these problem types were analyzed to determine which rules and concepts the participant used (e.g., whether number of weights was considered). As expected, on average, older participants were more accurate than younger participants, although significant age differences in the Zimbabwean sample were not found for problems solved by weight or distance cues. One finding differing from earlier research was that problems in which the beam balanced were more difficult for all participants. Generally, understanding of the physics of a balance scale appeared fairly similar in the 2 countries. Some cultural practices may account for the findings—in particular, the availability of preschool and age at time of academic specialization in higher education.     

How Mathematics Propels the Development of Physical Knowledge

Three studies examined whether mathematics can propel the development of physical understanding. In Experiment 1, 10-year-olds solved balance scale problems that used easy-to-count discrete quantities or hard-to-count continuous quantities. Discrete quantities led to age typical performances. Continuous quantities caused performances like those of 5-year-olds. In Experiment 2, 11-year-olds solved problems with feedback. They were encouraged to use math or words to justify their answers. Children who used math developed an understanding superior to most adults, whereas children who used words did not. In Experiment 3, 9-year-olds solved problems with or without prompts to use math. Children encouraged to use math exhibited greater qualitative understanding, even though they were unable to discover metric proportions. The results indicate it is possible to design symbolic experiences to propel the development of physical understanding, thereby relating developmental psychology to instructional theory.     

Adults' representations of division facts: a consequence of learning history?

There has been a recent increase in the study of adults' performance on simple division problems. Researchers up to now have focused on the relationship between multiplication and division and have found that multiplication often has a mediating role in the solution of division problems (Campbell, 1997, 1999; LeFevre & Morris, 1999; Mauro, LeFevre, & Morris, 2002). In this study, division was exclusively examined to determine the strategies that are used to solve these problems and to identify factors relating to particular strategy use. Thirty-two participants were asked to solve two sets of 64 simple division problems (from 4 divided by 2 to 81 divided by 9) and error, latency, and strategy report data were collected. Fewer errors were made on easy problems, which were also solved more quickly than difficult problems. Participants used retrieval, multiplication, and other strategies to solve the problems and tended to use retrieval more on easy than difficult problems and used multiplication more on difficult problems than easy problems. Unexpected age differences in strategy use were also found. Older participants tended to rely more heavily on retrieval than younger participants. These results suggest that older participants may have stronger representations for simple division problems than younger participants.     

Spontaneous gestures influence strategy choices in problem solving

Do gestures merely reflect problem-solving processes, or do they play a functional role in problem solving? We hypothesized that gestures highlight and structure perceptual-motor information, and thereby make such information more likely to be used in problem solving. Participants in two experiments solved problems requiring the prediction of gear movement, either with gesture allowed or with gesture prohibited. Such problems can be correctly solved using either a perceptual-motor strategy (simulation of gear movements) or an abstract strategy (the parity strategy). Participants in the gesture-allowed condition were more likely to use perceptual-motor strategies than were participants in the gesture-prohibited condition. Gesture promoted use of perceptual-motor strategies both for participants who talked aloud while solving the problems (Experiment 1) and for participants who solved the problems silently (Experiment 2). Thus, spontaneous gestures influence strategy choices in problem solving.     

Adults' understanding of inversion concepts: how does performance on addition and subtraction inversion problems compare to performance on multiplication and division inversion problems?

Problems of the form a + b - b have been used to assess conceptual understanding of the relationship between addition and subtraction. No study has investigated the same relationship between multiplication and division on problems of the form d x e / e. In both types of inversion problems, no calculation is required if the inverse relationship between the operations is understood. Adult participants solved addition/subtraction and multiplication/division inversion (e.g., 9 x 22 / 22) and standard (e.g., 2 + 27 - 28) problems. Participants started to use the inversion strategy earlier and more frequently on addition/subtraction problems. Participants took longer to solve both types of multiplication/division problems. Overall, conceptual understanding of the relationship between multiplication and division was not as strong as that between addition and subtraction. One explanation for this difference in performance is that the operation of division is more weakly represented and understood than the other operations and that this weakness affects performance on problems of the form d x e / e.     

Knowledge in transition: Adults' developing understanding of a principle of physical causality

What are the conditions that make it likely that cognitive change will occur? We investigate this issue with respect to 25 college students' developing understanding of gear movement (a particular problem in the domain of physical causation). The participants solved problems, then received minimal instruction, and solved additional problems. Significantly, only some of the participants changed their approach to solving the problems after receiving instruction; the remainder of the participants were stable in their understanding and either continued to solve all problems correctly or continued to solve key problems incorrectly. Most analyses focused on the participants who began by solving problems incorrectly. In particular, we attempted to differentiate those participants who exhibited cognitive change from those who did not. To do this, we examined precursors of knowledge change that were motivated by different theoretical positions on mechanisms of cognitive change and development (i.e., consideration of multiple approaches, cognitive conflict, and instruction as an example of a sociocultural process). Results suggest that having multiple approaches available and using instructional information to build on not-well-developed conceptions are likely candidates for understanding knowledge change for adult participants with respect to their developing understanding of physical causality.     

Young children's performance on the balance scale: the influence of relational complexity

Three experiments investigated the effect of complexity on children's understanding of a beam balance. In nonconflict problems, weights or distances varied, while the other was held constant. In conflict items, both weight and distance varied, and items were of three kinds: weight dominant, distance dominant, or balance (in which neither was dominant). In Experiment 1, 2-year-old children succeeded on nonconflict-weight and nonconflict-distance problems. This result was replicated in Experiment 2, but performance on conflict items did not exceed chance. In Experiment 3, 3- and 4-year-olds succeeded on all except conflict balance problems, while 5- and 6-year-olds succeeded on all problem types. The results were interpreted in terms of relational complexity theory. Children aged 2 to 4 years succeeded on problems that entailed binary relations, but 5- and 6-year-olds also succeeded on problems that entailed ternary relations. Ternary relations tasks from other domains--transitivity and class inclusion--accounted for 93% of the age-related variance in balance scale scores.     

Errors in subtractions: judged and observed frequencies

In a first study 10 adults, aged 24-44 years, solved all 105 subtraction problems in the form M - N = , where 0 < or = M < or = 13, 0 < or = N < or = 13 and N < or = M. Each participant solved every problem 10 times and in total there were 10 500 answers. Answers, response latencies and errors were registered. Retrospective verbal reports were also given, indicating how a solution was reached: (1) via a (conscious) reconstructive cognitive process or (2) via an (unconscious) reproductive (retrieval) process. The participants made 291 errors (2.8%) when solving the subtractions in study 1. The rate of self-correction was very high, 92%. In a second study 27 undergraduate students estimated overall error rates, including self-corrected errors for the 105 subtraction problems used in the first study. Judged and actual error rates were compared. The participants systematically underestimated error rates for error prone problems and overestimated error rates for error free problems. The participants were fairly accurate when they predicted problems that were most error prone, with a hit rate of 0.67 for the (18) problems predicted as the most error prone ones. In contrast, predictions of which problems were error free were very poor with a hit rate of only 0.20 of the problems predicted as error free really having no errors in study 1. The correlation between judged error rates and frequencies for actually made errors was 0.69 for answers belonging to reconstructive solutions. In contrast, there was no significant correlation between judged and actual error rates at all for retrieved solutions, possibly reflecting the inaccessibility to consciousness of quick retrieval processes.     

Dual processes,evolution and rationality

In three experiments we tested hypotheses derived from the goal specificity literature using a real-world physics task. In the balance-scale paradigm participants predict the state of the apparatus based on a configuration of weights at various distances from the fulcrum. Non-specific goals (NSG) have been shown to encourage hypothesis testing, which facilitates rule discovery, whereas specific goals (SG) do not. We showed that this goal specificity effect depends on task difficulty. The NSG strategy led to rule induction among some participants. Among non-discoverers, SG participants were faster and more accurate on difficult problems than NSG participants. The use of misleading exemplars (scale configurations that obscured the rule governing outcomes) led to fixation on inappropriate hypotheses for NSG but not SG participants. When more diagnostic learning exemplars were used, NSG non-discoverers still performed worse than SG participants on difficult problems. SG participants also outperformed NSG participants on a post-test of difficult problems. These findings qualify the generality of goal specificity effects.     

The development of children's rule use on the balance scale task

Cognitive development can be characterized by a sequence of increasingly complex rules or strategies for solving problems. Our work focuses on the development of children's proportional reasoning, assessed by the balance scale task using Siegler's (1976, 1981) rule assessment methodology. We studied whether children use rules, whether children of different ages use qualitatively different rules, and whether rules are used consistently. Nonverbal balance scale problems were administered to 805 participants between 5 and 19 years of age. Latent class analyses indicate that children use rules, that children of different ages use different rules, and that both consistent and inconsistent use of rules occurs. A model for the development of reasoning about the balance scale task is proposed. The model is a restricted form of the overlapping waves model (Siegler, 1996) and predicts both discontinuous and gradual transitions between rules.     

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.     

An evaluation of the properties of attention as reinforcement for destructive and appropriate behavior

The analogue functional analysis described by Iwata, Dorsey, Slifer, Bauman, and Richman (1982/1994) identifies broad classes of variables (e.g., positive reinforcement) that maintain destructive behavior (Fisher, Ninness, Piazza, & Owen-DeSchryver, 1996). However, it is likely that some types of stimuli may be more effective reinforcers than others. In the current investigation, we identified 2 participants whose destructive behavior was maintained by attention. We used concurrent schedules of reinforcement to evaluate how different types of attention affected both destructive and appropriate behavior. We showed that for 1 participant praise was not an effective reinforcer when verbal reprimands were available; however, praise was an effective reinforcer when verbal reprimands were unavailable. For the 2nd participant, we identified a type of attention that effectively competed with verbal reprimands as reinforcement. We then used the information obtained from the assessments to develop effective treatments to reduce destructive behavior and increase an alternative communicative response.     

Reliability of 16 balance tests in individuals with Down syndrome

To assess test-retest reliability scores on 16 balance tests of 21 individuals with Down syndrome whose ages ranged from 5 to 31 yr., participants performed a standing test on firm and soft surfaces with the eyes open and closed, the balance subset of the Bruininks-Oseretsky test, full turn, timed-up-and-go test, forward reach, and sit-to-stand. Each participant completed all 16 tests twice in one day and then again on a subsequent day for a total of 4 sessions. The interclass reliability correlation coefficients (ICC) value for each measure of balance varied considerably by age and sex. Based on having an ICC > .50, only 3 tests were reliable in young males and young females, whereas 5 tests could reliably be used in adult females and 9 tests could reliably be used in adult males. The results of this study raise suspicions as to the reliability of tests commonly used to assess balance and differences in reliability due to age and sex. Results of balance tests should be interpreted with caution in males and females with Down syndrome across the age span.     

Three aspects of cognitive development

An attempt was made to characterize and explain developmental differences in children's thinking, specifically in their understanding of balance scale problems. Such differences were sought in three domains: existing knowledge about the problems, ability to acquire new information about them, and process-level differences underlying developmental changes in the first two areas. In Experiment 1, four models of rules that might govern children's performance on balance scale problems were proposed. The rules proved to accurately describe individual performance and also to accurately predict developmental trends on different types of balance scale problems. Experiment 2 examined responsiveness to experience; it was found that older and younger children, equated for initial performance on balance scale problems, derived different benefits from identical experience. Experiment 3 examined a potential cause of this discrepancy, that younger children might be less able than older ones to benefit from experience because their encoding of stimuli was less adequate. Independent assessment procedures revealed that the predicted differences in older and younger children's encoding were present; it was also found that these differences were not artifactual and that reducing them also reduced the previously observed differences in responsiveness to experience. It was concluded, therefore, that the encoding hypothesis explained a large part of the developmental difference in ability to acquire new information.     

Strategy use,the development of automaticity,and working memory involvement in complex multiplication

Participants practiced a set of complex multiplication problems (e.g., 3 x 18) in a pre-/postpractice design. Before, during, and after practice, the participants gave self-reports of problem-solving strategies. At prepractice, the most common strategy was a mental version of the standard multidigit algorithm, and dual tasks revealed that working memory load was high and heavier for problems solved via nonretrieval strategies. After practice, retrieval was used almost exclusively, and participant variability, automaticity level of problems (proportion of trials on which retrieval was used over the entire experiment), and error rates were significant predictors of problem-solving latencies. Practice reduced working memory involvement to minimal levels, and there was no relationship between automaticity level and working memory load. The commonalities between the present findings and findings related to automaticity development in simple arithmetic are discussed.     

An Analysis of Speech Disfluencies of Turkish Speakers Based on Age Variable

The focus of this research is to verify the influence of the age variable on fluent Turkish native speakers’ production of the various types of speech disfluencies. To accomplish this, four groups of native speakers of Turkish between ages 4–8, 18–23, 33–50 years respectively and those over 50-year-olds were constructed. A total of 84 participants took part in this study. Prepared and unprepared speech samples of at least 300 words were collected from each participant via face-to-face interviews that were tape recorded and transcribed; for practical reasons, only the unprepared speech samples were collected from children. As a result, for the prepared speech situation, there was no statistically significant difference in terms of age in the production rates of filled gaps, false starts, slips of the tongue and repetitions; however, participants in the over 50-year-old group produced more hesitations and prolongations than participants in the 18–23 and 33–50-year-old groups. For the unprepared speech situation, age variable was not effective on the production rates of filled gaps. However, 4–8 and over 50-year-old participants produced more hesitations and prolongations than the 18–23 and 33–50-year-old groups. 4–8-year-old children produced more slips of the tongue than the 18–23 and 33–50-year-old groups, and more false starts and repetitions than the participants in the other three age groups (18–23, 33–50, over 50). Further analyses revealed more extensive insights related to the types of disfluencies, the position of disfluencies, and the linguistic units involved in disfluency production in Turkish speech.     

Behavioral problems in adolescents raised by their grandparents

This research analyzes, for the first time using a Spanish sample, the behavioral problems of adolescents in the custody of their grandparents. The sample consisted of 68 adolescents (31 boys and 37 girls, with a mean age of 13.7 years) in the custody of 54 grandparents with an average age of 65.9 years for the grandfathers, and 63.6 years for the grandmothers. The instrument employed was the Child Behavior Checklist (CBCL; Achenbach, 2001). The results indicate that the majority of both boys and girls can be classified within the normal range on scales of internal behavior, external behavior and total behavioral problems. When gender and age differences were analyzed, it was found that boys had more behavioral problems than girls on scales of incompliance with rules and external behavior. Meanwhile, it was shown that older adolescents had more somatic problems, as well as more behavioral problems, as measured by both the internal scale and total scale of the CBCL, than the younger participants.     

Impact of rewarding and parenting styles on young children’s cheating behavior

The purpose of this study was to examine the impact of rewarding and parenting styles on kindergarteners’ cheating behavior. The participants were 77 young children enrolled in one of three public kindergartens in the ?anl?urfa province of Turkey. Ages ranged from 54 to 76 months, with a mean age of 67.36 months (SD = 4.69). Participants were randomly assigned to reward and control groups. Each participant was tested individually. Participants were asked to solve a labyrinth puzzle without looking at the solution in the absence of an applicator (research assistants). Reward group participants were informed that if they successfully solved the puzzle they would get a lollipop. Findings revealed that the reward group exhibited significantly more cheating behavior than the control group. Cheating behavior was not related to parenting styles. The investigator concluded that using rewards as an educational tool may increase children’s tendency to cheat.     

Evaluation of a “mental effort” hypothesis for correlations between cortical metabolism and intelligence

Previous research indicates that low scores on the Raven's Advanced Progressive Matrices (RAPM) test are associated with increased cortical glucose utilization during problem solving. We hypothesized that previous results may reflect the neurophysiological consequences of patterns of effort requirements; that is, high-effort expenditure from lower aptitude participants (for whom the problems are hard) and low-effort expenditure from higher aptitude participants (for whom the problems are easy). In this experiment, positron emission tomography (PET) data were gathered on participants (N = 28) who solved easy and hard problems that were tailored to the participants' own ability levels, thereby eliminating aptitude group differences in effort requirements. Contrary to previous results, high aptitude was associated with high cortical glucose use. Average aptitude participants showed diminished glucose use in the hard condition. A significant Group X Condition X Hemisphere Effect was also noted, with greater right hemisphere activation in the hard condition for the high-aptitude group. These results demonstrate that the relation of cerebral glucose use and cognitive ability is sensitive to participant and task selection.     

Observer age and the social transmission of attractiveness in humans: Younger women are more influenced by the choices of popular others than older women

Being paired with an attractive partner increases perceptual judgements of attractiveness in humans. We tested experimentally for prestige bias, whereby individuals follow the choices of prestigious others. Women rated the attractiveness of photographs of target males which were paired with either popular or less popular model female partners. We found that pairing a photo of a man with a woman presented as his partner positively influenced the attractiveness of the man when the woman was presented as more popular (Experiment 1). Further, this effect was stronger in younger participants compared to older participants (Experiment 1). Reversing the target and model such that women were asked to rate women paired with popular and less popular men revealed no effect of model popularity and this effect was unrelated to participant age (Experiment 2). An additional experiment confirmed that participant age and not stimulus age primarily influenced the tendency to follow others' preferences in Experiment 1 (Experiment 3). We also confirmed that our manipulations of popularity lead to variation in rated prestige (Experiment 4). These results suggest a sophisticated model‐based bias in social learning whereby individuals are most influenced by the choices of those who have high popularity/prestige. Furthermore, older individuals moderate their use of such social information and so this form of social learning appears strongest in younger women.