Children's understanding of the inverse relation between multiplication and division

Children's understanding of the inversion concept in multiplication and division problems (i.e., that on problems of the form d * e/e no calculations are required) was investigated. Children in Grades 6, 7, and 8 completed an inversion problem-solving task, an assessment of procedures task, and a factual knowledge task of simple multiplication and division. Application of the inversion concept in the problem-solving task was low and constant across grades. Most participants approved of the inversion-based shortcut but only a slight majority preferred it. Three clusters of children were identified based on their performance on the three tasks. The inversion cluster used and approved of the inversion shortcut the most and had high factual knowledge. The negation cluster used the negation strategy, had lower approval of the inversion shortcut, and had medium factual knowledge. The computation cluster used computation and had the lowest approval and the weakest factual knowledge. The findings highlight the importance of addressing the multiplication and division inversion concept in theories of children's mathematical competence.     

Children's understanding of the arithmetic concepts of inversion and associativity

Previous studies have shown that even preschoolers can solve inversion problems of the form a+b-b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e/e was also examined. Grade 6 and 8 students solved inversion problems of both types as well as standard problems of the form a+b-c and d x e/f. Students in both grades used the inversion concept on both types of inversion problems, although older students used inversion more frequently and inversion was used most frequently on the addition/subtraction problems. No transfer effects were found from one type of inversion problem to the other. Students who used the concept of associativity on the addition/subtraction standard problems (e.g., a+b-c=[b-c]+a) were more likely to use the concept of inversion on the inversion problems, although overall implementation of the associativity concept was infrequent. The findings suggest that further study of inversion and associativity is important for understanding conceptual development in arithmetic.     

To feel is to know relations: James' concept of stream of thought and contemporary studies on procedural knowledge

The theory of William James concerning the temporal and dynamic nature of mind is analyzed as implying that thought is a flow of subjective experience that belongs to the material flow of living beings, and therefore, that knowledge is primarily affective and practical rather than declarative and contemplative. In this context, we will discuss contemporary theory and research relevant to the discussion about declarative and procedural knowledge, with the focus on a literature review in the neurosciences of knowledge. Then we reconstruct James' theory of mind as flow, in terms of relatedness, feeling, and temporality of experience. The Principles suggest that declarative knowledge is not independent, but derived and supported by a more basic knowledge that is both procedural and affective in nature. Finally, we discuss possible lesson for nowadays efforts to develop a dynamic account of the procedural nature of knowledge.     

Core knowledge and its limits: The domain of food

Adults, preschool children, and nonhuman primates detect and categorize food objects according to substance information, conveyed primarily by color and texture. In contrast, they perceive and categorize artifacts primarily by shape and rigidity. The present experiments investigated the origins of this distinction. Using a looking time procedure, Experiment 1 extended previous findings that rhesus macaques (Macaca mulatta) generalize learning about novel food objects by color over changes in shape. Six additional experiments then investigated whether human infants show the same signature patterns of perception and generalization. Nine-month-old infants failed to detect food objects in accord with their intrinsic properties, in contrast to rhesus monkeys tested in previous research with identical displays. Eight-month-old infants did not privilege substance information over other features when categorizing foods, even though they detected and remembered this information. Moreover, infants showed the same property generalization patterns when presented with foods and tools. The category-specific patterns of perception and categorization shown by human adults, children, and adult monkeys therefore were not found in human infants, providing evidence for limits to infants’ domains of knowledge.     

Children’s understanding of addition and subtraction concepts

After the onset of formal schooling, little is known about the development of children’s understanding of the arithmetic concepts of inversion and associativity. On problems of the form a + b − b (e.g., 3 + 26 − 26), if children understand the inversion concept (i.e., that addition and subtraction are inverse operations), then no calculations are needed to solve the problem. On problems of the form a + b − c (e.g., 3 + 27 − 23), if children understand the associativity concept (i.e., that the addition and subtraction can be solved in any order), then the second part of the problem can be solved first. Children in Grades 2, 3, and 4 solved both types of problems and then were given a demonstration of how to apply both concepts. Approval of each concept and preference of a conceptual approach versus an algorithmic approach were measured. Few grade differences were found on either task. Conceptual understanding was greater for inversion than for associativity on both tasks. Clusters of participants in all grades showed that some had strong understanding of both concepts, some had strong understanding of the inversion concept only, and others had weak understanding of both concepts. The findings highlight the lack of developmental increases and the large individual differences in conceptual understanding on two arithmetic concepts during the early school years.     

The different representational frameworks underpinning abstract and concrete knowledge: Evidence from odd-one-out judgements

Recent evidence from neuropsychological investigations of individuals with global aphasia and deep or deep-phonological dyslexia suggests that abstract and concrete concepts are underpinned by qualitatively different representational frameworks. Abstract words are represented primarily by their association to other words, whilst concrete words are represented primarily by their taxonomic similarity to one another. In the current study, we present the first evidence for this association/similarity distinction to be gathered from healthy research participants. Using a semantic odd-one-out task, it is shown that normal participants identify associative connections more quickly than similarity-based connections when processing abstract words, but that the pattern is reversed for concrete words. It is also demonstrated that the typical concrete-word advantage observed in many cognitive tasks is abolished and even reversed when participants have to comprehend the semantic associations between words. The data provide converging evidence for the different representational frameworks hypothesis and suggest that claims based on information from previous neuropsychological investigations can be generalized to normal cognition.     

The plausibility of spiritual intelligence: spiritual experience,problem solving and neural sites

Australian teachers in Church related schools have begun to use the term ‘spiritual intelligence’ in their educational discourse. Is it accurate to describe spirituality as a form of intelligence? This paper explores whether the notion of spiritual intelligence is plausible. It addresses this firstly by discussing the notion of spiritual experience as a mechanism for problem solving—one of the central themes that underlies the concept of intelligence. Secondly, it examines some of the neural sites of the human brain that have been found to be active in those who apperceive spiritual experience. In light of this discussion, this paper argues that although some concerns prevail in considering spirituality as a form of intelligence, the concept of spiritual intelligence may nonetheless be rendered as plausible.     

Perfectionism: The good,the bad,and the creative

The influence of adaptive and maladaptive perfectionism on creativity was examined. Initially, six measures of creativity were administered, including creative self-perceptions, behavior, and performance measures. Adaptive perfectionism was weakly positively related to creativity, whereas maladaptive perfectionism was unrelated to creativity across five of the six measures. A follow-up study assessed whether initial findings could be generalized to an everyday problem-solving task. Results indicated that adaptive perfectionism was related to higher quality but not originality of solutions. Further, a curvilinear relationship in the shape of an inverted “U” occurred between adaptive perfectionism and four of eight creativity measures. Overall, adaptive perfectionism was consistently, albeit weakly, related to creativity across various types of measures, whereas maladaptive perfectionism was not related to creativity.     

Self-construal level and voice procedures: The individual self as psychological basis for procedural fairness effects

In the current article, we investigate the influence of self-construal level on procedural fairness effects, that is, the finding that fair versus unfair procedures influence people’s evaluations of their relation with decision-making authorities. In two experiments, we manipulated self-construal level by activating the individual self (“I”) or the social self (“We”), and we induced a control condition. Furthermore, we manipulated procedural fairness by granting versus denying participants an opportunity to voice their opinion in a decision-making process. Results consistently revealed stronger procedural fairness effects if the individual self is activated than if the social self is activated. It is concluded that sometimes the individual self, rather than the social self, constitutes the psychological basis for procedural fairness effects.     

The egocentric nature of procedural justice: Social value orientation as moderator of reactions to decision-making procedures

In four studies, the authors investigated the individual-oriented versus social-oriented nature of procedural justice effects by comparing fairness-based responses to decision-making procedures among proself versus prosocial oriented individuals. In Studies 1 through 3, we measured participants’ social value orientation and manipulated whether or not they were granted or denied voice in a decision-making process. Results consistently revealed that the effects of voice versus no-voice on fairness-based perceptions, emotions, and behavioral intentions were significantly more pronounced for individuals with proself orientations than for individuals with prosocial orientations. These findings were extended in Study 4, a field study in which perceived procedural justice was a stronger predictor of satisfaction and organizational citizenship behaviors among proselfs than among prosocials. These findings suggest that procedural justice effects can be accounted for by self-oriented motives or needs, rather than prosocial motives that are often conceptualized as being associated with justice.     

Deconstructing the tower: Parameters and predictors of problem difficulty on the Tower of London task

The Tower of London (TOL) task has been widely used in both clinical and research realms. In the current study, 104 healthy participants attempted all possible moderate- to high-difficulty TOL problems in order to determine: (1) optimal measures of problem solving performance, (2) problem characteristics, other than the minimum moves necessary to solve the problem, that determine participants’ difficulty in solving problems successfully, quickly, and efficiently, and (3) effects of increased task experience on which problem characteristics determine problem difficulty. A factor analysis of six performance measures found that, regardless of task experience, problem difficulty could be captured well either by a single factor corresponding to general quality of solution or possibly by three subordinate factors corresponding to solution efficiency, solution speed, and initial planning speed. Regression analyses predicting these performance factors revealed that in addition to a problem’s minimum moves three problem parameters were critical in determining the problem difficulty: goal position hierarchy, start position hierarchy, and number of solution paths available. The relative contributions of each of the characteristics strongly depended on which performance factor defined performance. We conclude that TOL problem performance is multifaceted, and that classifying problem difficulty using only the minimum moves necessary to solve the problem is inadequate.     

Young children’s acquisition of knowledge about the Earth: A longitudinal study

This longitudinal study examined the acquisition of early knowledge of astronomy to determine whether children’s knowledge at any point in time is consistent with a naive “mental model.” Children were first assessed by means of open questions and drawing tasks at 2 and 3 years of age (N = 143). The knowledge was reassessed over the course of the following 3 years. The results showed that although a few indications of naive mental models were found, in most cases young children’s knowledge was fragmented and accurate knowledge was often expressed alongside inaccurate/synthetic ideas. Furthermore, it was shown that children need to know scientific facts before they start taking the global perspective when describing the world and, when faced with ambiguous open questions, children often experience difficulties that can induce them to change the types of answers they provide.     

Choosing between hearts and minds: Children's understanding of moral advisors

Moral development research has often focused on the development of moral reasoning without considering children's understanding of moral advisors. We investigated how children construe sources of moral advice by examining the characteristics that children deem necessary for reasoning about moral or scientific problems. In two experiments, children in grades K, 2, and 4 were presented with dilemmas of a moral nature or scientific nature and chose between two advisors. Second and fourth graders chose advisors differentially based on their expertise, while kindergartners did not discriminate between advisors. In a third experiment, older children indicated that only certain characteristics are needed to solve moral or scientific problems, and they endorsed these characteristics differentially based on the problem to be solved. Thus, by middle childhood, children construe moral knowledge as distinct from scientific knowledge and select advisors in each area accordingly.     

Working memory and literacy as predictors of performance on algebraic word problems

Previous studies on individual differences in mathematical abilities have shown that working memory contributes to early arithmetic performance. In this study, we extended the investigation to algebraic word problem solving. A total of 151 10-year-olds were administered algebraic word problems and measures of working memory, intelligence quotient (IQ), and reading ability. Regression results were consistent with findings from the arithmetic literature showing that a literacy composite measure provided greater contribution than did executive function capacity. However, a series of path analyses showed that the overall contribution of executive function was comparable to that of literacy; the effect of executive function was mediated by that of literacy. Both the phonological loop and the visual spatial sketchpad failed to contribute directly; they contributed only indirectly by way of literacy and performance IQ, respectively.     

Beyond objectivity: The performance impact of the perceived ability to learn and solve problems

The purpose of this research was to develop and provide initial validation evidence for the performance impact of a measure of an individual's perceived ability to learn and solve problems (PALS). Building on the self-efficacy literature and the importance of learning and problem solving, the fundamental premise of this research was that PALS would significantly explain employee performance. In addition to demonstrating that PALS represented a distinct construct, PALS was a significant predictor of performance for managerial and entry-level employees in two different organizational contexts. Moreover, PALS explained additional variance in performance beyond general mental ability, personality, and similar constructs related to learning and problem solving.     

Does playing blindfold chess reduce the quality of game: comments on chabris and hearst (2003)

Blindfold chess is a special type of chess game where both the board and pieces are not visible to its players. This paper aims to determine whether the quality of the game played blindfolded is lower than when played under normal conditions. The best chess program was used to analyze games played by the world's top Grandmasters under both conditions. We have analyzed the Monaco 1993–1998 data set introduced by Chabris and Hearst (2003) . The results showed that although a larger number of mistakes occurred while playing blindfolded, no significant statistical difference between the rapid and blindfold games has been found. Nevertheless, by applying the same methodology to the Monaco 2002–2007 data set a substantial difference between the blindfold and the rapid chess game was noticed. In this paper, we have addressed the possible improvement of the chess game quality and the advances in chess programs that may be responsible for detecting more blunders.     

Determining who to question, what to ask, and how much information to ask for: the development of inquiry in young children

To obtain reliable information, it is important to identify and effectively question knowledgeable informants. Two experiments examined how age and the ease of distinguishing between reliable and unreliable sources influence children’s ability to effectively question those sources to solve problems. A sample of 3- to 5-year-olds was introduced to a knowledgeable informant contrasted with an informant who always gave inaccurate answers or one who always indicated ignorance. Children were generally better at determining which informant to question when a knowledgeable informant was contrasted with an ignorant informant than when a knowledgeable informant was contrasted with an inaccurate informant. In some cases, age also influenced the ability to determine who to question and what to ask. Importantly, in both experiments, the strongest predictor of accuracy was whether children had acquired sufficient information; successful problem solving required integrating knowledge of who to question, what to ask, and how much information to ask for.     

Physiology and functioning: Parents' vagal tone, emotion socialization, and children's emotion knowledge

This study examined relationships among parents’ physiological regulation, their emotion socialization behaviors, and their children’s emotion knowledge. Parents’ resting cardiac vagal tone was measured, and parents provided information regarding their socialization behaviors and family emotional expressiveness. Their 4- or 5-year-old children (N = 42) participated in a laboratory session in which their knowledge of emotional facial expressions and situations was tested and their own resting vagal tone was monitored. Results showed that parents’ vagal tone was related to their socialization behaviors, and several parent socialization variables were related to their children’s emotion knowledge. These findings suggest that parents’ physiological regulation may affect the emotional development of their children by influencing their parenting behaviors.     

Playing on the typewriter, typing on the piano: manipulation knowledge of objects

Two experiments investigated sensory/motor-based functional knowledge of man-made objects: manipulation features associated with the actual usage of objects. In Experiment 1, a series of prime-target pairs was presented auditorily, and participants were asked to make a lexical decision on the target word. Participants made a significantly faster decision about the target word (e.g. ‘typewriter’) following a related prime that shared manipulation features with the target (e.g. ‘piano’) than an unrelated prime (e.g. ‘blanket’). In Experiment 2, participants' eye movements were monitored when they viewed a visual display on a computer screen while listening to a concurrent auditory input. Participants were instructed to simply identify the auditory input and touch the corresponding object on the computer display. Participants fixated an object picture (e.g. “typewriter”) related to a target word (e.g. ‘piano’) significantly more often than an unrelated object picture (e.g. “bucket”) as well as a visually matched control (e.g. “couch”). Results of the two experiments suggest that manipulation knowledge of words is retrieved without conscious effort and that manipulation knowledge constitutes a part of the lexical-semantic representation of objects.