Developing Model‐Based Reasoning

Key elements of the structure and function of models in mathematics and science are identified. These elements are used as a basis for discussing the development of model‐based reasoning. A microgenetic study examines the beginnings of model‐based reasoning in a pair of fourth‐ and fifth‐grade children who solved several problems about chance and probability. Results are reported in the form of a cognitive model of children's problem‐solving performance. The cognitive model explains a transition in children's reasoning from tacit reliance on empirical regularity to a form of model‐based reasoning. Several factors fostering change in children's thinking are identified, including the role of notations, peer interaction, and teacher assistance. We suggest that model‐based reasoning is a slowly‐developing capability that emerges only with proper contextual and social support and that future study should be carried out in classrooms, where these forms of assistance can also be part of the object of study.

Model‐based reasoning is a significant intellectual milestone because it bridges the worlds of personal, intuitive knowledge, on the one hand, and mathematical‐scientific theory, on the other. However, across disciplines, consensus is still forming about what model‐based reasoning comprises, and there is little knowledge about its ontogenetic origins or how it develops. We consider analogy as the core of modeling, because in model‐based reasoning a system in one domain is used to understand a system in another. To understand how models come to play a role in reasoning, it is important to initiate study of their origins. Accordingly, we report a microgenetic study examining the beginnings of model‐based reasoning in a pair of young children solving problems about chance and probability. In this study we are engaged in the enterprise of modeling the development of modeling. That is, we report our results in the form of a cognitive model of children's problem‐solving performance that explains a transition in reasoning from a tacit reliance on empirical regularity to a form of model‐based reasoning. It is important to note the two distinct meanings for the term model used in this article. The first describes how children come to understand and appropriate a system of reasoning exemplified in practices of modeling. The second describes a research tool, a model of human reasoning—specifically, how children in this study began to use models of probability to reason about uncertain events. In this report, we use the terms model or model‐based reasoning to refer to the former interpretation, whereas references to a cognitive model denote the simulation of children's thinking—in this case, implemented as a computer program.

Before describing the empirical work, we first identify some key elements of the structure and function of models. Next, these elements of modeling are used as the basis for generating some conjectures about the development of model‐based reasoning. We describe a task that we used as a window to understanding progression in student reasoning toward reliance on models as tools for thought. We present our rationale for developing cognitive models of student performance and explain some choices concerning the implementation of the cognitive model reported here. Finally, we turn to the children's performance on chance and probability tasks and explain how that performance illuminates both what children do not understand about models and the kinds of relevant knowledge that they are acquiring.     

数学建模的几种基本预测方法的探讨

针对学生在建立预测模型时不能准确判别使用合适的预测模型,归纳了几种使用较多的预测方法:微分方程模型、时间序列方法、灰色预测和BP神经网络。对每种预测模型做了简单的介绍分析和适当地对某些模型进行了改进,总结了相应的优缺点以及各自适用的预测范围。     

Effects of sample size,estimation methods,and model specification on structural equation modeling fit indexes

A Monte Carlo simulation study was conducted to investigate the effects on structural equation modeling (SEM) fit indexes of sample size, estimation method, and model specification. Based on a balanced experimental design, samples were generated from a prespecified population covariance matrix and fitted to structural equation models with different degrees of model misspecification. Ten SEM fit indexes were studied. Two primary conclusions were suggested: (a) some fit indexes appear to be noncomparable in terms of the information they provide about model fit for misspecified models and (b) estimation method strongly influenced almost all the fit indexes examined, especially for misspecified models. These 2 issues do not seem to have drawn enough attention from SEM practitioners. Future research should study not only different models vis‐à‐vis model complexity, but a wider range of model specification conditions, including correctly specified models and models specified incorrectly to varying degrees.     

Thinking about Art: Could Elementary Textbooks Serve as Models of Practice to Help New Teachers and Non‐Specialists Support Reasoning in Art?

Some primary school teachers may neglect reasoning about art. Models of practice can exemplify classroom teaching and, to some extent, a textbook for children can be seen as a model of practice. Can those in art serve as models of practice and help teachers foster reasoning? This study examined 19 art textbooks intended for use by Key Stage 2 children (7–11 years old) to see to what extent they might direct a teacher's attention to reasoning in art. Some gave no attention to reasoning but some were found to have the potential to do that, at least in connection with evaluating the art of others. In this respect, they might serve as models of practice. Nevertheless, the teachers most likely to benefit from such models may not recognise a good one, be proficient in using it productively, be able to develop thinking about the art of others further or extrapolate thinking to the child's own art. Consequently, knowing what counts in art education and using models of practice to good effect could be an important part of training courses.     

A More Flexible Bayesian Multilevel Bifactor Item Response Theory Model

Multilevel bifactor item response theory (IRT) models are commonly used to account for features of the data that are related to the sampling and measurement processes used to gather those data. These models conventionally make assumptions about the portions of the data structure that represent these features. Unfortunately, when data violate these models' assumptions but these models are used anyway, incorrect conclusions about the cluster effects could be made and potentially relevant dimensions could go undetected. To address the limitations of these conventional models, a more flexible multilevel bifactor IRT model that does not make these assumptions is presented, and this model is based on the generalized partial credit model. Details of a simulation study demonstrating this model outperforming competing models and showing the consequences of using conventional multilevel bifactor IRT models to analyze data that violate these models' assumptions are reported. Additionally, the model's usefulness is illustrated through the analysis of the Program for International Student Assessment data related to interest in science.     

Financing Higher Education According to Performance Parameters: The Rhineland-Palatinate

In the 1990s, two models for the financing of higher education were introduced in Rhineland- Palatinate. In 1993, a special system for distributing the budget was established (Mittelbemes sungsmodell) . According to this model, [euro]35 million is given to eleven universities annually. In 1998, a second model, called Personalbemessungskonzept, was implemented. Here the personnel costs for approximately 7,000 academic and non-academic members are distributed amongst the universities. This article describes these two models in some detail and gives some information about the performance parameters used.     

Intercultural Education and the Professional Knowledge of Teachers

The theme is the in‐service training of teachers, but it may be that the ideas apply equally to pre‐service work. The concerns are professional rather than academic: the aim is to find ways of changing, and of improving, what teachers do in schools. In order to effect such change we require models of the ways in which teachers make decisions about practice; we also need to find models which will be relevant to our own practice as teachers of teachers. This paper seeks to set out a model of professional knowledge and to explore ways in which that model might help towards an understanding of some of the processes involved in courses for teachers on intercultural issues.     

稀疏过程在一类相依多险种风险模型中的应用

将汽车保险中的一类相依两险种风险模型扩展到相依三险种风险模型，用对齐次poisson过程的稀疏与分解将该模型转化为古典风险模型，并证明了转化的合理性，进而给出破产概率的一般表达式及其一个上界估计．这种转化的方法对类似的多险种相依情形同样适用．     

Secondary Students' Dynamic Modeling Processes: Analyzing,Reasoning About,Synthesizing, and Testing Models of Stream Ecosystems

In this paper, we explore dynamic modeling as an opportunity for students to think about the science content they are learning. We examined the Cognitive Strategies for Modeling (CSMs) in which students engaged as they created dynamic models. We audio- and videotape-recorded eight pairs of ninth grade science students and analyzed their conversations and actions. In analyzing appropriate objects and factors for their model, some students merely enumerated potential factors whereas others engaged in rich, substantial, mindful analysis. In reasoning about their models, students discussed relationships in depth, concentrated only on the most important key relationships, or encountered difficulty distinguishing between causal and correlational relationships. In synthesizing working models, students mapped their model to aid visualization, focused on their goal, or talked about their model's appearance or form. Students attempted to articulate explanations for their relationships, but sometimes their explanations were shallow. In testing their models, some students tested thoroughly but only a few persisted in debugging their model's behavior so that it matched their expectations. In our conclusion we suggest that creating dynamic models has great potential for use in classrooms to engage students in thought about science content, particularly in those thinking strategies best fostered by dynamic modeling: analysis, relational reasoning, synthesis, testing and debugging, and making explanations.     

工作流响应时间概率分布分析

提出了一种基于流体随机Petri网的工作流响应时间概率分布计算方法.首先讨论了利用随机工作流网建模的一些相关问题,然后描述了如何将随机工作流网模型转化为流体随机Petri网模型,最后给出了该种流体随机Petri网模型的动态方程,说明工作流响应时间的概率分布可直接由流体随机Petri网模型的暂态解得到.该方法对工作流模型的结构没有提出任何限制,且工作流任务的处理时间可取任意概率分布,通过递归地使用网化简技术可有效地处理大型工作流模型.     

Doctoral student supervision in a managerial climate

Prevailing clinical and educational models of dyslexia have focused on effective ways of addressing the proposed core deficits such as poor phonological skills. These models have been helpful in guiding intervention and bringing about some improvements in children's literacy performance (Hatcher, 1994). From a social model of disability perspective these models have not considered sufficiently how cultural factors such as specified school literacy standards can transform the impairments that some children have into disabilities. The underlying tenet of inclusion is that the school should adapt its practice to accommodate the child (Clark et al, 1995; Jenkinson, 1997). This would suggest that an examination of the social model of disability perspective may have a role to play in future school policy and practice across Europe in respect to literacy.     

Optimal Identification of Mismeasured Individuals

Optimal appropriateness measurement statistically provides the most powerful methods for identifying individuals who are mismeasured by a standardized psychological test or scale. These methods use a likelihood ratio test to compare the hypothesis of normal responding versus the alternative hypothesis that an individual's responses are aberrant in some specified way. According to the Neyman-Pearson Lemma, no other statistic computed from an individual's item responses can achieve a higher rate of detection of the hypothesized measure- ment anomaly at the same false positive rate. Use of optimal methods requires a psychometric model for normal responding, which can be readily obtained from the item response theory literature, and a model for aberrant responding. In this article, several concerns about measurement anomalies are described and transformed into quantitative models. We then show how to compute the likeli- hood of a response pattern u* for each of the aberrance models.     

Cognitive diagnostic model of best choice: a study of reading comprehension

Abstract

The present study compared the performance of six cognitive diagnostic models (CDMs) to explore inter skill relationship in a reading comprehension test. To this end, item responses of about 21,642 test-takers to a high-stakes reading comprehension test were analyzed. The models were compared in terms of model fit at both test and item levels, classification consistency and accuracy, and proportion of skill mastery profiles. The results showed that the G-DINA performed the best and the C-RUM, NC-RUM, and ACDM showed the closest affinity to the G-DINA. In terms of some criteria, the DINA showed comparable performance to the G-DINA. The test-level results were corroborated by the item-level model comparison, where DINA, DINO, and ACDM variously fit some of the items. The results of the study suggested that relationships among the subskills of reading comprehension might be a combination of compensatory and non-compensatory. Therefore, it is suggested that the choice of the CDM be carried out at item level rather than test level.     

Another Perspective on Assessing the Significance of Information Technology in Education

Summary

The significance of information technology in education is usually assessed or evaluated on terms of some measures of effectiveness. In different school settings the effectiveness is operationalized in different ways, and in the literature various methods of determining the effectiveness have been discussed (e.g., Secretary's Conference on Educational Technology 1999). In this article, models for assessing the significance of information technology in education based on the teachers' subjective perspective are introduced. Theoretical backgrounds of the models are based on methods developed in information management science to assess the impact of information technology (IT) in industry and business. The first model is comprised of categorizing the rationales for using IT in education, the second model assesses the strategic impact of existing IT applications on one hand and of future IT applications on the other on education, and the third model assesses the roles of applications of IT in teaching. Also, the empirical findings of a small scale test of the two latter models in the Teacher Training School in Rauma (TTSR), a primary school in Finland with about 260 pupils and 19 teachers, are introduced.     

CSR Model Implementation From School Stakeholder Perspectives

Despite comprehensive school reform (CSR) model developers' best intentions to make school stakeholders adhere strictly to the implementation of model components, school stakeholders implementing CSR models inevitably make adaptations to the CSR model. Adaptations are made to CSR models because school stakeholders internalize CSR model practices in their own ways. This article focuses on how teachers and school leaders internalize CSR model practices by examining their perceptions of the components of CSR models as well as perceptions of CSR across grades and classrooms. Schools were found to be acquainted, informed, knowledgeable, and fully articulate about their CSR models. Contextual factors, such as teacher turnover, principal leadership, and school priorities, as well as developer supports, accounted for differing perceptions about CSR.     

Pendula,Models, Constructivism and Reality

It is argued that Galileo made an important breakthroughin the methodology of science by considering idealizedmodels of phenomena such as free fall, swinging pendulaand the like, which can conflict with experience. Theidealized models are constructs largely by our reasoningprocesses applied to the theoretical situation at hand. Onthis view, scientific knowledge is not a construction out ofexperience, as many constructivists claim about both themethods of science and about the learning of science. Infact Galileo's models can, depending on their degree ofidealization or concretization, be at variance with experience.This paper considers what is meant by idealization andconcretization of both the objects and properties that makeup theoretical models, and the ideal laws that govern them.It also provides brief illustrations of ideal laws and how theymay be made more concrete, and briefly considers howtheories and models might be tested against what we observe.Finally some difficulties are raised for a radical constructivistapproach to both science and learning in the light of Galileo'smethodological approach. The upshot is that both the dialoguestructure of Galileo's writings and his method of model buildingprovide a rich resource for science education that rivals that of thestandard varieties of constructivism, and at the same time gives amuch better picture of the actual procedures of science itself.     

Predicting people’s environmental behaviour: theory of planned behaviour and model of responsible environmental behaviour

Using different measures of self-reported and other-reported environmental behaviour (EB), two important theoretical models explaining EB – Hines, Hungerford and Tomera’s model of responsible environmental behaviour (REB) and Ajzen’s theory of planned behaviour (TPB) – were compared regarding the fit between model and data, predictive ability, solidarity of the model structure and model modifications. Results of structural equation modelling revealed that the predictors in the TPB model explained much more variance in behavioural intention than those in the REB model (approximately 69 vs. 37%) but the two models differed little in explaining the variance in EB (about 75% with self-reported measure and 26% with other-reported measure). In addition, both suffered weakness of ineffective paths in the model structure. It was found that the operationalizations of the variables in the models might affect the results of the tests of these models and some adjustments and examinations were suggested. Although the REB model was shown to be imperfect in many aspects, it should be evaluated from a different viewpoint and was encouraged to be applied and tested in the context of environmental education.     

Predictions of Individual Change Recovered With Latent Class or Random Coefficient Growth Models

Popular longitudinal models allow for prediction of growth trajectories in alternative ways. In latent class growth models (LCGMs), person-level covariates predict membership in discrete latent classes that each holistically define an entire trajectory of change (e.g., a high-stable class vs. late-onset class vs. moderate-desisting class). In random coefficient growth models (RCGMs, also known as latent curve models), however, person-level covariates separately predict continuously distributed latent growth factors (e.g., an intercept vs. slope factor). This article first explains how complex and nonlinear interactions between predictors and time are recovered in different ways via LCGM versus RCGM specifications. Then a simulation comparison illustrates that, aside from some modest efficiency differences, such predictor relationships can be recovered approximately equally well by either model—regardless of which model generated the data. Our results also provide an empirical rationale for integrating findings about prediction of individual change across LCGMs and RCGMs in practice.     

中小城市中学教师运用情感教学模式的调查——以江苏宜兴地区为例

情感教学模式要求在关注学生认知发展的基础上,同时关注学生的情感发展。研究显示,该模式在上海等大城市的中小学教学中已被广泛应用,但在中小城市的应用情况尚缺乏数据支持。本研究以江苏宜兴地区为例,调查情感教学模式在中小城市中学教学中的运用情况,结果显示：（1）大部分教师认为在中学教学中应当重视情感因素;（2）仅有约一半的被调查教师（54．8％）总是或经常考虑学生的情感需要;（3）仅有约一半（52．2％）的被调查教师在教学中经常考虑并尝试应用情感教学的方法;（4）绝大多数被调查教师认为这是源于应试的压力,其次是缺乏理论指导和缺乏方法指导。可见,中小城市的中学教学中,情感因素越来越受到重视,但在实际的教学实践中仍存一些问题。     

What Teachers of Science Need to Know about Models: An overview

The purpose of this article is to provide an overview of the nature of models and their uses in the science classroom based on a theoretical review of literature. The ideas that science philosophers and science education researchers have in common about models and modelling are scrutinised according to five subtopics: meanings of a model, purposes of modelling, multiplicity of scientific models, change in scientific models and uses of models in the science classroom. First, a model can be defined as a representation of a target and serves as a ‘bridge’ connecting a theory and a phenomenon. Second, a model plays the roles of describing, explaining and predicting natural phenomena and communicating scientific ideas to others. Third, multiple models can be developed in science because scientists may have different ideas about what a target looks like and how it works and because there are a variety of semiotic resources available for constructing models. Fourth, scientific models are tested both empirically and conceptually and change along with the process of developing scientific knowledge. Fifth, in the science classroom, not only teachers but also students can take advantage of models as they are engaged in diverse modelling activities. The overview presented in this article can be used to educate science teachers and encourage them to utilise scientific models appropriately in their classrooms.