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.     

Expert knowledge as mnemonic cues

It is proposed that expert knowledge can operate as a cognitive cueing structure for the acquisition and retention of new information in memory. Two experiments are reported which demonstrate that expert knowledge about football and clothing can act as mnemonic cues for the recall of information newly associated with that knowledge. In Experiment 1 expert terms from the domains of football and clothing and those neutral nouns paired with them were both better recalled by experts than by non-experts. In Experiment 2 passages containing information contrary to factual knowledge about football and clothing were recalled better by experts than by non-experts, in spite of the fact that information in the passages contradicted what the experts already knew. The results of the two experiments were interpreted as showing that expert knowledge provides mental cues that have desirable mnemonic properties such as constructibility, associability, discriminability and invertibility. Also, the interpretation of expert knowledge as a cognitive cueing structure is compared to Ausubel's ideas regarding advance organizers.     

Encouraging children to think counterfactually enhances blocking in a causal learning task

According to a higher order reasoning account, inferential reasoning processes underpin the widely observed cue competition effect of blocking in causal learning. The inference required for blocking has been described as modus tollens (if p then q, not q therefore not p). Young children are known to have difficulties with this type of inference, but research with adults suggests that this inference is easier if participants think counterfactually. In this study, 100 children (51 five-year-olds and 49 six- to seven-year-olds) were assigned to two types of pretraining groups. The counterfactual group observed demonstrations of cues paired with outcomes and answered questions about what the outcome would have been if the causal status of cues had been different, whereas the factual group answered factual questions about the same demonstrations. Children then completed a causal learning task. Counterfactual pretraining enhanced levels of blocking as well as modus tollens reasoning but only for the younger children. These findings provide new evidence for an important role for inferential reasoning in causal learning.     

An Investigation of Teachers' Beliefs of Students' Algebra Development

Elementary, middle, and high school mathematics teachers (N = 105) ranked a set of mathematics problems based on expectations of their relative problem-solving difficulty. Teachers also rated their levels of agreement to a variety of reform-based statements on teaching and learning mathematics. Analyses suggest that teachers hold a symbol-precedence view of student mathematical development, wherein arithmetic reasoning strictly precedes algebraic reasoning, and symbolic problem-solving develops prior to verbal reasoning. High school teachers were most likely to hold the symbol-precedence view and made the poorest predictions of students' performances, whereas middle school teachers' predictions were most accurate. The discord between teachers' reform-based beliefs and their instructional decisions appears to be influenced by textbook organization, which institutionalizes the symbol-precedence view. Because of their extensive content training, high school teachers may be particularly susceptible to an expert blindspot, whereby they overestimate the accessibility of symbol-based representations and procedures for students' learning introductory algebra.     

质性比较专家与新手的物理问题解决过程

本实验致力于回答两个问题 :(1 )在何种任务限制下 ,专家表现出对新手的解题优势 ;(2 )可以采用何种实验手段 ,来细致刻画解题过程中运用的程序性知识 (“条件 -行动”)。本实验以物理学领域的“欧姆定律”为研究内容 ,采用专家 -新手比较范型 ,对被试的言语报告进行编码与分析 ,进而描绘了解题活动所依赖的“条件 -行动”关系 ,从中展现了专家解题相对于新手的整体优势。对这些优势的进一步个案分析表明 ,物理学解题专长的实质在于 :(1 )条件化操作 (从已知条件得出复杂关系 ) ;(2 )精致化知识 (比例公式与嵌套公式 )。     

The relation between problem categorization and problem solving among experts and novices

These investigations were conducted to examine the relationship between problem-solving ability and the criteria used to decide that two classical mechanics problems would be solved similarly. We began by comparing experts and novices on a similarity judgment task and found that the experts predominantly relied on the problems' deep structures in deciding on similarity of solution, although the presence of surface-feature similarity had a clear adverse effect on performance. The novices relied predominantly on surface features, but were capable of using the problems' deep structures under certain conditions. In a second experiment, we compared groups of novices, at the same level of experience, who tended to employ different types of reasoning in making similarity judgments. Compared to novices who relied predominantly on surface features, novices who made greater use of principles tended to categorize problems similarly to how experts categorized them, as well as score higher in problem solving. These results suggest that principles play a fundamental role in the organization of conceptual and procedural knowledge for good problem solvers at all levels.     

Social interaction in the peer group: Relationship to perceptions of parenting and to children's interpersonal awareness and problem-solving ability

The rates at which 56 preschoolers dispensed positive and negative behaviors toward peers were recorded during classroom free play. The Borke Empathy Scale and the Preschool Interpersonal Problem-Solving Test were administered to the children. The children's mothers and fathers were asked to complete the Iowa Parenting Inventory. Analyses focused on the association between parental modes of functioning and children's peer-group behaviors, and on the association between peer-group behavior and interpersonal awareness and interpersonal problem-solving ability. The analyses indicated that maternal involvement and reasoning guidance and paternal reasoning guidance were significant predictors of children's positive behaviors directed at peers. Maternal reasoning guidance showed an inverse relationship with negative behaviors directed at peers. Interpersonal awareness, but not problem-solving ability, was an effective predictor of behavior with peers. The data reflect the need to examine peer-group social competence from a multifaceted perspective. Implications of the findings for the development of intervention strategies and parent-teacher relations are suggested.     

Reasoning and Instruction in Medical Curricula

We describe two experiments that examine the knowledge and explanatory processes of students in two medical schools with different modes of instruction. One school had a conventional curriculum with basic science courses taught 1 '/2 years before the clinical training; the other had a problem-based learning curriculum with basic science taught in the context of clinical problems and general problem-solving strategies involving knowledge elaboration and hypothetico-deductive reasoning. Both before and after being exposed to relevant basic science information, students were asked to provide diagnostic explanations of a clinical case. In this study, students in the problem-based learning curriculum reasoned in a manner consistent with the way they were taught, using a backward directed pattern of reasoning and extensive elaborations based on detailed biomedical information. However; these students had a greater tendency to commit errors of scientific fact, to generate less coherent explanations, and to use flawed patterns of explanation, such as circular reasoning. These results are viewed as reflecting the operation of two factors: context and method of instruction. The interaction between these factors is expressed in terms of the hypothesis that basic science and clinical knowledge constitute two different worlds.     

Casuistic Reasoning in Expert Narratives on Healthy Eating

Individualisation of healthy eating is a broad tendency in Western culture and is becoming a popular ideal in nutrition science. Public perception of dietary knowledge is central to this individualisation and many experts now aim to present dietary knowledge in a way which relates to individual experience, as well as a casuistic style in which particular cases are discussed in relation to general, universal principles. Analysis of casuistic narrative styles in the public communication about healthy eating by experts makes explicit their flexible use of both particular cases and universal claims, in which clinical and personal cases are narratively employed by the experts to invite readers to personally consider dietary knowledge. Such casuistic narration by experts relates human agency and particular bodies to universal concepts in a way that has generative and critical functions with respect to dietary knowledge and understanding. The public articulation of clinical narratives by experts make salient the intersubjective emergence and accumulation of dietary knowledge between expert reasoning and lay understanding. Personal narratives have an essential role in presenting casuistic reasoning through experts’ personal lives and making their own bodies relevant to public communication about healthy eating. This emphasises the experts’ personal agency in relationship to common norms and general knowledge. Furthermore, both clinical and personal narratives are used by experts in their assessment of the shortcomings in public health messages. Experts’ casuistic narration thus does not merely construct credibility but has epistemic functions in constructing dietary knowledge tangible with respect to actual eating practices.     

Value Priorities and Organ Donation in Young Adults

This research identifies major personal values among American university students that predict organ-donation registration with the Department of Motor Vehicles. Participants responded to a factual test of their knowledge about organ donation, indicated whether or not they had registered as posthumous donors, and filled out a personality inventory measuring their personal values (Schwartz, 1992, 1994). The data indicated a high level of factual knowledge about organ donation; and the greater the level of knowledge, the more likely participants were registered to donate their organs. Also, participants higher in benevolence, universalism, achievement, and stimulation were more likely to have registered to donate their organs. The results are discussed in terms of the need to develop more effective health-communication campaigns by using specific health-education messages tailored to students majoring in different disciplines or to people in various occupations as a means of increasing their willingness to donate.     

The Generality/Specificity of Expertise in Scientific Reasoning

Previous research on scientific reasoning has shown that it involves a diverse set of skills. Yet, little is known about generality or domain specificity of those skills, an important issue in theories of expertise and in attempts to automate scientific reasoning skills. We present a study designed to test what kinds of skills psychologists actually use in designing and interpreting experiments and contrast expertise within a particular research area with general expertise at designing and interpreting experiments. The results suggest that psychologists use many domain-general skills in their experimentation and that bright and motivated Carnegie Mellon undergraduates are missing many of these skills. We believe that these results have important implications for psychological and artificial intelligence models of expertise, as well as educational implications in the domain of science instruction.     

Designing Computer Games to Help Physics Students Understand Newton's Laws of Motion

This research, explores, the design of a computer environment for helping science students to learn about Newtonian dynamics. The learning environment incorporates games set in the context of a Newtonian computer microworld, where students have to control the motion of a spaceship in order to achieve goals such as hitting a target or navigating a maze. The purpose of the games is to focus the students' attention on various aspects of the implications of Newton's laws. A set of general design principles guided the design of the games and microworld. These include: (I) represent the phenomena of the domain clearly; (2) eliminate irrelevant complexities from the computer microworld; (3) focus the students on as peers of their knowledge.that need revising; (4) facilitate the use of problem-solving heuristics; (5) encourage the application of relevant knowledge from other domains; and (6) encourage better ways of representing and thinking about the domain. A controlled study indicated that playing the games improved the students' ability to solve dynamics problems. The students utilized various components of their knowledge, including their intuitions concerning how forces affect motion and their partial understanding of the formal physics, to generate strategies for the games. The use of such knowledge is combined with the use of general problem-solving heuristics and feedback from the computer microworld to facilitate the evolution of the students' knowledge of Newtonian dynamics. An examination of the results in light of the original design principles suggested numerous improvements that could be made to the sequence of games and microworld. The design process could best be characterized as a series of successive refinements.     

Experts in Dialogue: An Introduction

Different approaches to expertise and argumentation are discussed. After introducing the problem of expertise and its present day significance in a historical context, various connections with the study of arguments are highlighted. The need for and potential of argumentation analysis to contribute to existing research in social epistemology, science studies, and cognitive science, is discussed, touching on the problems of reasoning and argumentation, embodiment, tacit knowledge, expert context versus public context, expert disagreement, persuasion versus justification, and argument analysis as meta-expertise. As the arguments used by experts constitute a boundary object, we presume that a dialogue format is suitable to address central problems of the special issue “Rethinking Arguments from Experts”.     

Applying artificial neural network models to clinical decision making

Because psychological assessment typically lacks biological gold standards, it traditionally has relied on clinicians' expert knowledge. A more empirically based approach frequently has applied linear models to data to derive meaningful constructs and appropriate measures. Statistical inferences are then used to assess the generality of the findings. This article introduces artificial neural networks (ANNs), flexible nonlinear modeling techniques that test a model's generality by applying its estimates against "future" data. ANNs have potential for overcoming some shortcomings of linear models. The basics of ANNs and their applications to psychological assessment are reviewed. Two examples of clinical decision making are described in which an ANN is compared with linear models, and the complexity of the network performance is examined. Issues salient to psychological assessment are addressed.     

CaMeRa: A Computational Model of Multiple Representations

This research aims to clarify, by constructing and testing a computer simulation, the use of multiple representations in problem solving, focusing on their role in visual reasoning. The model is motivated by extensive experimental evidence in the literature for the features it incorporates, but this article focuses on the system's structure. We illustrate the model's behavior by simulating the cognitive and perceptual processes of an economics expert as he teaches some well-learned economics principles while drawing a graph on a blackboard. Data in the experimental literature and concurrent verbal protocols were used to guide construction of a linked production system and parallel network, CaMeRa (Computation with Multiple Representations), that employs a "Mind's Eye" representation for pictorial information, consisting of a bitmap and associated node-link structures. Propositional list structures are used to represent verbal information and reasoning. Small individual pieces from the different representations are linked on a sequential and temporary basis to form a reasoning and inferencing chain, using visually encoded information recalled to the Mind's Eye from long-term memory and from cues recognized on an external display. CaMeRa, like the expert, uses the diagrammatic and verbal representations to complement one another, thus exploiting the unique advantages of each.     

Special issue on problem-solving,creativity and spatial reasoning

Problem-solving, creativity and spatial reasoning are high level abilities of cognitive systems with high potential for synergies. However, they have been treated separately by different fields. This special issue presents research work on these topics, aiming to observe their interrelations in order to create theoretical approaches, methodologies and computational tools to advance work on creativity and spatial problem-solving in cognitive systems.