Enhancing probabilistic reasoning: The role of causal graphs, statistical format and numerical skills

Research on the counterintuitive Monty Hall dilemma (MHD) and analogous problems has shown that correct reasoning is rarely observed, even with the help of certain hints. Making the causal structure explicit or presenting probabilities by means of natural frequencies seem to enhance performance, but only to a moderate degree. The present experiments aimed to analyze the usefulness of these hints for solving an analogous MHD in more detail. Results showed that, compared to relative frequencies, natural frequencies improved reasoning, but this effect depended on previous numerical skills. On the other hand, a graph representing the causal structure had no effect, suggesting that numerical representations are more critical for solving the dilemma. Furthermore, success in solving the dilemma strongly correlated with participants’ skill in representing probabilities. Hence, an adequate numerical representation seems to be particularly relevant for understanding counterintuitive probabilistic problems.     

概率统计思想与方法在实际问题中的应用

随着科学技术的不断发展,概率统计在人们生活和工作中的运用越来越广泛,但是,概率统计思想方法之间存在的内在联系并没有完全被人们掌握,因而我们研究的概率统计思想方法很多时候还只是停留在学术表面,而没有真正将概率统计思想方法应用到实际之中。为了能够将概率统计思想方法灵活的运用到实际当中,对其进行相应的研究就具有举足轻重的意义。     

A longitudinal perspective on inductive reasoning tasks. Illuminating the probability of change

Cognitive scientists have studied internal cognitive structures, processes, and systems for decades in order to understand how they function in human learning. Nevertheless, questions concerning the diagnosis of changes in these cognitive structures while solving inductive reasoning tasks are still being scrutinized. This paper reports findings from an experimental study in which 64 participants in three experimental groups solved tasks at ten measurement points. We were able to illuminate changes of cognitive structures and found significant differences between the treatments. The results also indicate that supportive information is an important aid for developing cognitive structures while solving inductive reasoning tasks.     

Children's and adults' knowledge and models of reasoning about the ozone layer and its depletion

A model giving the main domains of ‘process knowledge’ in solving problems in physics is proposed. In the framework of this model the strategies and results of using thinking‐aloud experiments to obtain the elements of ‘process knowledge’ in the problem‐solving activity in physics are discussed.

     

Relative expertise in an everyday reasoning task: Epistemic understanding, problem representation, and reasoning competence

Experts in cognitive domains differ from non-experts in how they represent problems and knowledge, and in their epistemic understandings of tasks in their domain of expertise. This study investigates whether task-specific epistemic understanding also underlies the representation of knowledge on an everyday reasoning task on which the competent reasoners have neither expert domain knowledge nor training. 180 people on jury duty were assessed for epistemological understanding about the nature of knowledge and knowing in general, understanding of the specific task of the juror, and level of argument skill and evidence representation on two jury cases. Epistemic construal of the juror task and task-specific competent reasoning was found related to general epistemology, argument skills, and representation of the evidence. Additionally, estimations of the possibility of certainty in general and in a juror task predicted the participants' expressed certainty about their verdict choices. Implications for developing everyday reasoning competence are discussed.     

条件概率公式在一类马尔科夫报酬模型上的计算

在马尔科夫报酬模型上,把条件概率算子引入连续随机报酬逻辑中,以此表达更为丰富的性质。在harmony假设下,路径的报酬限制可以转化成时间限制,从而将连续随机报酬逻辑中的路径公式转化为连续随机逻辑中的路径公式。再由已知的参数化乘积连续时间马尔科夫链的方法,建立起高效的检测算法。     

Proportional reasoning and the linguistic abilities required for hypothetico-deductive reasoning

The hypothesis is advanced that a necessary, though not sufficient, condition for the acquisition of proportional reasoning during adolescence is the prior internalization of key linguistic elements of argumentation, essentially those used in hypothetico-deductive reasoning. This hypothesized internalization, which does not occur in all individuals, results in some who have acquired the ability to reflect upon the correctness of self-generated answers in a hypothetico-deductive manner, and others who have not. As an initial test of the hypothesis, 46 subjects (Ss) (mean age = 21.03 years) were classified into additive, transitional, or proportional reasoning categories based upon responses to a proportions task. Group differences were found in which proportional Ss performed better than transitional Ss who in turn performed better than additive Ss on a number of items testing Ss' abilities to identify, generate, and use the linguistic elements of argumentation. Further it was found that some Ss who were successful on the linguistic items failed the proportions task, but no Ss who were successful on the proportions task failed the linguistic items. This result supports the hypothesis that the internalization of linguistic elements of argumentation is a prerequisite for proportional reasoning and by inference other advanced reasoning schemata as well. Implications for science instruction are drawn.     

Socioscientific issues in science education: labels, reasoning, and transfer

This paper provides a critical analysis of some of the issues raised in Simonneaux and Simonneaux’s analysis of socioscientific reasoning among a group of university level students negotiating three socioscientific issues. I first discuss the labels used to reference approaches in science education that prioritize socially relevant issues and the science related to these issues. I draw distinctions between approaches labeled science-technology-society (STS), the socioscientific issues framework, and les questions socialement vives (socially acute questions), which Simonneaux and Simonneaux introduce. Next, I discuss ways in which Simonneaux and Simonneaux’s use socioscientific reasoning as an analytic construct varies with respect to its initial conceptualization. The primary distinctions include linguistic inconsistencies and the conceptual differences these language choices confer, expansion of the construct to subsume a broader range of practices, and issues related to unit of analysis (i.e., applying socioscientific reasoning as an analytic resource for assessing individual practice vs. group patterns). Finally, the issue of transfer of socioscientific reasoning is addressed. When considering the extent to which and how students leverage experiences and practice relative to the exploration of one socioscientific issue to inform their negotiation of another, I suggest that researchers and practitioners consider the distinction between the content of arguments advanced and underlying reasoning patterns. The tension between embedding science in meaningful, specific contexts and promoting forms of scientific literacy applicable to diverse, socially-relevant issues emerges as an important point of emphasis for educators interested in the socioscientific issues (or socially acute questions) movement.

Measurement,Sampling, and Equating Errors in Large-Scale Assessments

In large-scale assessments, such as state-wide testing programs, national sample-based assessments, and international comparative studies, there are many steps involved in the measurement and reporting of student achievement. There are always sources of inaccuracies in each of the steps. It is of interest to identify the source and magnitude of the errors in the measurement process that may threaten the validity of the final results. Assessment designers can then improve the assessment quality by focusing on areas that pose the highest threats to the results. This paper discusses the relative magnitudes of three main sources of error with reference to the objectives of assessment programs: measurement error, sampling error, and equating error. A number of examples from large-scale assessments are used to illustrate these errors and their impact on the results. The paper concludes by making a number of recommendations that could lead to an improvement of the accuracies of large-scale assessment results.     

5ayes统计中两种抽样法的比较分析

拒绝性抽样法和重要性抽样法是贝叶斯统计中两种重要的产生模拟样本的方法．两种方法之间存在一些关联,拒绝性抽样法在做一些形式上的转变后可以看作一种特殊的重要性抽样法．此外,如果将拒绝性抽样法中的包络函数作为重要性抽样法中的提议密度函数,这样新形成的抽样法会比原本的拒绝性抽样法更为有效．     

Development of reasoning associated with pictographs: Representing, interpreting, and predicting

A developmental model involving four response levels is proposed concerning how students arrange pictures to represent data in a pictograph, how they interpret these pictographs, and how they make predictions based on these pictographs. The model is exemplified by responses from three related interview-based studies. In Study 1, examples of each response level are provided from 48 preparatory- to tenth-grade students. Students from higher grades were more likely to respond at higher levels. In Study 2, 22 students were interviewed longitudinally after a three-year interval; many improved in response level over time, although a few responded at lower levels. In Study 3, 20 third-grade students were interviewed and then prompted with conflicting responses of other students on video; many improved their initial responses to higher levels after exposure to the conflicting prompts. Associations among levels of representing, interpreting, and predicting were explored. Educational implications are discussed concerning reasonable expectations of students and suggestions to develop these skills in students at different grades. This revised version was published online in July 2006 with corrections to the Cover Date.     

Field independence,task ambiguity,and performance on a proportional reasoning task

This study investigated the proportional reasoning abilities of 35 college science students. Using a projection of shadows problem, proportional reasoning was assessed under one of two experimental conditions corresponding to the type of information presented: (a) relevant only, or (b) relevant and irrelevant. Subjects were also measured on the cognitive style of field independence. Results showed that subjects in the relevant only condition performed significantly better than those in the relevant-irrelevant condition. Degree of field independence was related to performance only in the relevant-irrelevant condition. These results indicated an interaction between type of information presented in a task and cognitive style.     

审美直觉与合情推理

论述了审美直觉与合情推理及其之间的关系，重点阐述了审美直觉强化合情推理的可靠性、审美直觉调控合理推理的方向性。     

Conditional reasoning with false premises facilitates the transition between familiar and abstract reasoning

Abstract reasoning is critical for science and mathematics, but is very difficult. In 3 studies, the hypothesis that alternatives generation required for conditional reasoning with false premises facilitates abstract reasoning is examined. Study 1 (n = 372) found that reasoning with false premises improved abstract reasoning in 12- to 15-year-olds. Study 2 (n = 366) found a positive effect of simply generating alternatives, but only in 19-year-olds. Study 3 (n = 92) found that 9- to 11-year-olds were able to respond logically with false premises, whereas no such ability was observed in 6- to 7-year-olds. Reasoning with false premises was found to improve reasoning with semiabstract premises in the older children. These results support the idea that alternatives generation with false premises facilitates abstract reasoning.