The representations of the arithmetic operations include functional relationships

Current theories of mathematical problem solving propose that people select a mathematical operation as the solution to a problem on the basis of a structure mapping between their problem representation and the representation of the mathematical operations. The structure-mapping hypothesis requires that the problem and the mathematical representations contain analogous relations. Past research has demonstrated that the problem representation consists of functional relationships, or principles. The present study tested whether people represent analogous principles for each arithmetic operation (i.e., addition, subtraction, multiplication, and division). For each operation, college (Experiments 1 and 2) and 8th grade (Experiment 2) participants were asked to rate the degree to which a set of completed problems was a good attempt at the operation. The pattern of presented answers either violated one of four principles or did not violate any principles. The distance of the presented answers from the correct answers was independently manipulated. Consistent with the hypothesis that people represent the principles, (1) violations of the principles were rated as poorer attempts at the operation, (2) operations that are learned first (e.g., addition) had more extensive principle representations than did operations learned later (multiplication), and (3) principles that are more frequently in evidence developed more quickly. In Experiment 3, college participants rated the degree to which statements were indicative of each operation. The statements were either consistent or inconsistent with one of two principles. The participants' ratings showed that operations with longer developmental histories had strong principle representations. The implications for a structure-mapping approach to mathematical problem solving are discussed.     

Intuition versus analysis: Strategy and experience in complex everyday problem solving

Research on dual processes in cognition has shown that explicit, analytical thought is more powerful and less vulnerable to heuristics and biases than is implicit, intuitive thought. However, several studies have shown that holistic, intuitive processes can outperform analysis, documenting the disruptive effects of hypothesis testing, think-aloud protocols, and analytical judgments. To examine the effects of intuitive versus analytical strategy and level of experience on problem solving, 1st- through 4th-year undergraduates solved problems dealing with college life. The results of two studies showed that the appropriateness of strategy depends on the problem solver's level of experience. Analysis was found to be an appropriate strategy for more experienced individuals, whereas novices scored best when they took a holistic, intuitive perspective. Similar effects of strategy were found when strategy instruction was manipulated and when participants were compared on the basis of strategy preference. The implications for research on problem solving, expertise, and dual-process models are discussed.     

Task Specificity in the Use of Words in Mathematics: Evidence from Bilingual Problem Solvers

Mathematics is often said to be a different language in itself. Three experiments were conducted to show some evidence for this common notion. It was hypothesized that in math word problem solving, people interpret words like “more” and “less” in specialized ways that are specific to the task of math word problem solving. Subjects were given texts with quantitative information, but the texts were framed either as math problems or as stories, and were written either in English or Filipino. Subjects were then asked to verify statements that describe quantitative relations given in the text; these relations either stated an exact or an inexact quantitative difference. The verification responses and verification times in three experiments show that subjects more often accepted the inexact difference as true when the text was framed as a story compared to when framed as a problem. These results support the hypothesis that the use of the specialized meaning is specific to the task of solving word problems in math. The data were equivocal about the role of the language used in the operation of this knowledge. The results were discussed in terms of the implications of specificity of knowledge, context sensitivity, and the possible role of language use in the process of learning and developing mathematical knowledge.     

Skill-set,success outcome,and mania as determinants of the illusion of control

The illusion of control, the tendency for individuals to approach chance tasks with skill-appropriate strategies, was studied. Subjects premeasured on a mania scale were classified as either high (HM) or low (LM) in mania. In the first phase of the study, HM and LM subjects performed 30 trials on either a skill (verbal associates) or chance (coin-toss) task and were given either 20, 50, or 80% success feedback. After Task 1 was completed, subjects filled out an attribution questionnaire. In the final phase of the study, subjects anticipated 30 more trials either on a skill or chance task. Subjects' predicted successes were measured. It was hypothesized that predicted successes on anticipated skill and chance tasks would be affected more by outcomes on a previous skill task than by outcomes on a previous chance task. The results for the anticipated skill task directly supported the hypothesis. On the anticipated chance task, the hypothesis was confirmed for HM subjects only. The results are discussed in terms of how previous skill experiences may induce a set to control ungovernable situations for individuals with manic reactions.     

Dual Space Search During Scientific Reasoning

The purpose of the two studies reported here was to develop an integrated model of the scientific reasoning process. Subjects were placed in a simulated scientific discovery context by first teaching them how to use an electronic device and then asking them to discover how a hitherto unencountered function worked. To do this task, subjects had to formulate hypotheses based on their prior knowledge, conduct experiments, and evaluate the results of their experiments. In the first study, using 20 adult subjects, we identified two main strategies that subjects used to generate new hypotheses. One strategy was to search memory and the other was to generalize from the results of previous experiments. We described the former group as searching an hypothesis space, and the latter as searching an experiment space. In a second study, with 10 adults, we investigated how subjects search the hypothesis space by instructing them to state all the hypotheses that they could think of prior to conducting any experiments. Following this phase, subjects were then allowed to conduct experiments. Subjects who could not think of the correct rule in the hypothesis generation phase discovered the correct rule only by generalizing from the results of experiments in the experimental phase.
Both studies provide support for the view that scientific reasoning can be characterized as search in two problem spaces. By extending Simon and Lea's (1974) Generalized Rule Inducer, we present a general model of Scientific Discovery as Dual Search (SDDS) that shows how search in two problem spaces (an hypothesis space and an experiment space) shapes hypothesis generation, experimental design, and the evaluation of hypotheses. The model also shows how these processes interact with each other. Finally, we interpret earlier findings about the psychology of scientific reasoning in terms of the SDDS model.     

The value of action and inference in dynamic decision making

The use of action- versus judgment-oriented decision strategies in a dynamic decision task is investigated. Subjects engaged in a simulated medical decision-making task, where the goal is to select treatments in order to cure patients suffering from an unknown disease. The experiment manipulated two task factors that were predicted to influence the effectiveness and efficiency of action- and judgment-oriented strategies: (1) the availability of a decision aid that promotes the interpretability of outcome feedback in the task and (2) the level of risk associated with treatment choices, which influences the opportunity for corrective actions to compensate for earlier decision errors. Results indicated that these manipulations did in fact influence performance. However, most subjects did not use action-oriented strategies even when they would have led to superior performance. Possible explanations for this finding are discussed and the implications for theoretical accounts of strategy acquisition and selection are considered.     

Do dichotic listening procedures measure lateralization of information processing or retrieval strategy?

The data from two dichotic studies, both of which evaluated spontaneously generated response strategies under free recall and one of which also manipulated retrieval strategy by instruction, supported a conception that what dichotic procedures mostly measure are response strategies—mobile and readily deployed without loss of mnemonic capability. Consequently, competitional methods which are heavily influenced by output factors appear to be unreliable as a means of evaluating input processing dominance.     

When experiences of failure promote expectations of success: The impact of attribution failure to ineffective strategies1

This experiment examined the effects of attributing initial failure to ineffective strategies on performance expectancies. Subjects were induced to attribute performance at a persuasion task to either their strategies (a controllable factor) or abilities (an uncontrollable factor). Subjects then failed at their initial persuasion attempt. Following failure, strategy subjects expected more successes in future attempts than did ability subjects. Strategy subjects also expected to improve with practice, while ability subjects did not. Comparisons to control subjects, who received no attribution manipulation prior to success or failure, clarify these results. Findings suggest that subjects attributing task outcomes to strategies monitored the effectiveness of their strategies and concluded that by modifying their strategies they would become more successful. In contrast, subjects attributing task outcome to abilities failed to attend to strategic features and concluded that they could not improve. Implications of this overlooked factor for attribution theory and learned helplessness are discussed.     

Concept Discovery in a Scientific Domain

The scientific reasoning strategies used to discover a new concept in a scientific domain were investigated in two studies. An innovative task in which subjects discover new concepts in molecular biology was used. This task was based upon one set of experiments that Jacob and Monod used to discover how genes are controlled, and for which they were awarded the Nobel prize. In the two studies reported in this article, subjects were taught some basic facts and experimental techniques in molecular biology, using a simulated molecular genetics laboratory on a computer. Following their initial training, they were then asked to discover how genes are controlled by other genes. In Study 1, subjects found no evidence that was consistent with their initial hypothesis. Subjects then set one of two goals for conducting experiments and evaluating data. One goal was to search for evidence consistent with the current hypothesis (and they did not attend to the features of discrepant findings); none of the subjects who only had this goal succeeded at discovering how the genes were controlled. Other subjects in Study 1 used a different goal: Upon noticing evidence inconsistent with their current hypothesis, these subjects set a new goal of attempting to explain the cause of the discrepant findings. Using this goal, a subset of these subjects discovered the correct solution to the problem. Study 2 was conducted to test the hypothesis that subjects' goals of finding evidence consistent with their current hypothesis blocks consideration of alternate hypotheses and generation of new goals, it was predicted that if subjects could achieve their initial goal of discovering evidence consistent with their current hypothesis, they would then attend to particular features of discrepant evidence and solve the problem. To test this prediction, an additional mechanism of genetic control that was consistent with subjects' initial goal was added to the genes. Here, subjects had to discover two mechanisms of control: one mechanism consistent with their current hypothesis, and one inconsistent with their hypothesis. Twice as many subjects reached the correct solution in Study 2 than in Study 1. The findings of the two studies indicate that goals provide a powerful constraint on the cognitive processes underlying scientific reasoning and that the types of goals that are represented determine many of the reasoning errors that subjects make.     

Mental search processes in problem solving

A new approach to problem solving was applied to multisolution problems in a memory search task. Subjects memorized a list of eight four-letter foods, and then searched mentally through the list for answers to questions. The times between successive answers (IRTs) were recorded along with the answers themselves. This allowed a comparison of two possible memory search strategies: (1) sampling with replacement, and (2) sampling without replacement. The results were largely in agreement with the sampling-without-replacement strategy. However, a more detailed breakdown of the data revealed that most subjects searched through the list in a rigid serial order. Further, an analysis of questions with identical answers showed that the IRTs were very nearly additive. This led to an additive time component model based on the independent summation of (a) read-in time, (b) memory-search time, (c) decision-making time, and (d)response-output time. This approach appeared generally more satisfactory than previous attempts to account for problem-solving behavior.     

Priming,analogy, and awareness in complex reasoning

The mechanisms by which a concept used in solving one complex task can influence performance on another complex task were investigated. We tested the hypothesis that even when subjects do not spontaneously make an analogy between two domains, knowledge of one domain can still spontaneously influence reasoning about the other domain via the mechanism of priming. Four groups of subjects (two experimental and two control) were given a simulated biochemistry problem on Day 1 and a simulated molecular genetics problem on Day 2. For the two experimental groups, the solution to the biochemistry problem involved inhibition. For the two control groups, the solution did not involve inhibition. On Day 2, all subjects received the same version of the molecular genetics problem in which the solution involved the concept of inhibition. Subjects in the experimental conditions were more likely to attain the correct answer, to propose inhibition, and to propose inhibition early in the problemsolving session than were subjects in the control conditions. However, subjects in the experimental conditions made no reference to the biochemistry problem either in their verbal protocols or in a posttask questionnaire. The results are interpreted as demonstrating that an implicit process—priming— can make old knowledge available for current problem solving.     

Socio-cognitive conflict and structure of individual and collective performances

A previous experiment (Doise, Mugny and Perret-Clermont, 1975) has shown that pairs of subjects perform better on a spatial representation task than subjects alone. As a conclusion the hypothesis was put forward that conflicts of cognitive centrations, embedded in a social situation, lead children to coordinate their centrations. The present research was planned to verify several predictions following from this general hypothesis. Results show that indeed more progress takes place when children with different cognitive strategies work together than when children with the same strategies do so, and that not only the less advanced but also the more advanced child progresses when they interact with each other.     

非熟练中——英双语者的第二语言的语义通达机制

使用跨语言启动条件下的真假字判断任务,通过变化启动刺激(英文单词)与目标刺激(汉字)采用4个实验研究了中-英非熟练双语者的第二语言的语义通达机制。被试为北京师范大学的学生63名。结果发现,当启动刺激(英文单词)的中文对译词与目标刺激之间的关系是翻译关系时,得到了显著的启动效应(实验一);当两者之间是语义联想关系时,前者对后者没有显著的影响(实验二);当两者之间是形似关系时,前者对后者产生了显著的抑制作用(实验三)：当两者之间是同音关系时,前者对后者产生了显著的促进作用。这一结果表明,对于中国的英语学习者来说,他们的第二语言只能借助其汉语对译词的词汇表征通达其语义概念表征,实验结果在一定程度上支持了Mroll(1994)的层次模型。     

言语理解中的知觉符号表征与命题符号表征

采用移动窗口技术探讨言语理解中信息表征的方式。被试为华南师范大学本科生96名。实验材料按照探测图画中物体的形状跟先前阅读的句子中描述的物体的隐含形状的关系总体上分为两类,一类是匹配版本,一类是不匹配版本。采用相关样本t检验分别对两种条件下图画再认的反应时间和正确率进行统计分析。实验1中被试读完句子以后马上进行图画探测任务,结果表明这时被试头脑中进行的是知觉符号表征。实验2中被试的阅读任务难度增大,结果表明这时被试头脑中进行的是命题符号表征。实验3中被试阅读的关键信息进入长时记忆以后再进行图画探测任务,结果表明这时被试头脑中进行的也是命题符号表征。总的实验结果表明言语理解中既存在知觉符号表征,也存在命题符号表征,知觉符号表征是信息表征的一种早期状态,人类头脑中最终的信息表征形式主要是命题符号表征。     

From children's hands to adults' ears: gesture's role in the learning process

Children can express thoughts in gesture that they do not express in speech--they produce gesture-speech mismatches. Moreover, children who produce mismatches on a given task are particularly ready to learn that task. Gesture, then, is a tool that researchers can use to predict who will profit from instruction. But is gesture also useful to adults who must decide how to instruct a particular child? We asked 8 adults to instruct 38 third- and fourth-grade children individually in a math problem. We found that the adults offered more variable instruction to children who produced mismatches than to children who produced no mismatches--more different types of instructional strategies and more instructions that contained two different strategies, one in speech and the other in gesture. The children thus appeared to be shaping their own learning environments just by moving their hands. Gesture not only reflects a child's understanding but can play a role in eliciting input that could shape that understanding. As such, it may be part of the mechanism of cognitive change.     

Primacy effects in self-attribution of ability1

Primacy effects in self-attribution of ability were investigated in an experiment. Subjects' performance on a 30-item test was experimentally manipulated to reflect one of three patterns: ascending, descending, or random success. It was predicted that there would be a primacy effect in self-attribution of ability regarding the task when subjects had no previous expectation or anchor to which performance could be assimilated, but that the primacy effect would be attenuated when a previous anchor existed. The presence or absence of a prior anchor was manipulated by describing the task as either a test related to intelligence or a test of an unsual ability, unrelated to previous experience. Results supported the hypothesis that there is a primacy effect in self-attribution of ability, and that this effect occurs most strongly where an individual has no prior anchor or expectation regarding his ability.     

An investigation of the relationships between problem solving strategies, representation and memory

There has been considerable debate in recent years about the status of “imagery” in problem solving. The present experiment attempts to show that while subjects may employ representational strategies when they first encounter a class of problems, they abandon such strategies as they gain experience with the problems. It does this by asking subjects to answer unexpected questions which are based upon the information which they have just used to solve a problem. The hypothesis, which is supported by the results, is that increasing experience with problems will be paralleled by a decreasing ability to answer unexpected questions. The experiment also shows that such effects are not attributable to a build-up in proactive interference.     

Stacking of irregularly shaped blocks in chimpanzees (Pan troglodytes) and young humans (Homo sapiens)

Stacking blocks provides a way to evaluate cognitive development in humans and other species using the same comparative measures. The present study used regular cubic blocks as well as cubic blocks with bumps on two sides. The bumps changed the physical properties of the blocks and increased the difficulty involved in stacking them. Subjects were required to choose the appropriate orientation for stacking the blocks. Three juvenile chimpanzees and 14 human children (aged 2–3 years) were tested under identical task settings in a face-to-face situation. The goal of a trial was to stack up four blocks (two cubic blocks and two cubic blocks with bumps). The results showed initial difficulty in stacking the blocks with bumps in both chimpanzees and humans. Experienced juvenile chimpanzees and humans older than 3 years became proficient at solving the task. Behavioral strategies adopted to succeed in the task were common to both species. The subjects spontaneously adopted a strategy of stacking as the last block of the tower a block with a bump facing upwards. The subjects also showed active change in the orientation of the blocks when necessary, although correct orientation changes were infrequent especially during the early phases of experiment. The results are discussed in the context of the underlying cognitive development in the domain of physical understanding in both species.     

Dilemmatics in Public Sector Assessment: A Framework for Developing and Evaluating Selection Systems

This research examined the effects of a break (incubation) on solutions to a geometric insight problem. Experiment 1 showed that subjects receiving an analogical hint during incubation obtained more solutions than continuously working controls. Experiment 2 tested the hypothesis that incubation effects are due to the total time (including intermittant problem solving during incubation) spent on a problem. Subjects given relaxation instructions and no task during a problem-solving break were more successful than those who worked continuously for 20 min or were given demanding mental work as an intervening task. Self-report data supported the explanation that incubation effects are a result of covert effort and that the effectiveness of an analogical hint depends on the solver's ability to relate it to the problem.     

Abilities and strategies of blind and sighted subjects in visuo-spatial imagery

An active visuo-spatial memory task was used in order to determine the characteristics of mental imagery in subjects with and without visual experience. Subjects were instructed to generate a mental representation of verbally presented 2D patterns that were placed in a grid and to indicate how many pattern elements were in corresponding positions in the two halves of the grid according to a specific grid axis (vertical or horizontal). Unexpectedly, results showed a similar performance in early blind, late blind and sighted subjects. However, subjects' debriefing showed that the three groups used different strategies. The sighted and the late blind subjects took advantage of a visuo-spatial strategy. They generated a mental image of the matrix and they simplified this image to maintain only the relevant information in memory. In contrast, the early blind subjects encoded each pattern element by its location in a (X,Y) coordinate system without visual representation. This indicates that both early and late blind subjects are able to perform an active visuo-spatial imagery task as well as sighted subjects although they use different strategies.