高考数学试卷多维项目反应理论的分析及应用

高考数学学科试卷的试题综合性较强,一道试题通常考查多种能力属性,而基于单维性假设下的经典测量理论和传统的项目反应理论无法完成该种情形下试卷测量性能分析和考生作答表现分析.本文以MIRT理论为基础,使用CONQUEST软件为工具进行分析,可以获得试卷内部不同能力维度之间的相关以及考生不同维度的能力参数,为提升命题质量和改进教学提供了依据,表明MIRT具有很好的应用前景.由于MIRT理论的复杂性以至于目前分析软件的不足制约其进一步的深入应用,这是今后应该深入研究的问题.     

Introduction to special issue on contributions of mathematical psychology to clinical science and assessment

Evolution of clinical mathematical psychology, exemplifying integrative, translational psychological science, is considered in light of target, idealized scientific systems. It is observed that mutual benefits to psychological clinical science, and quantitative theory, potentiated through their interlacing as exemplified in this special issue, stand to parallel the historical symbiosis between older disciplines and mathematics. Enumerated are the range of psychological processes and clinical groups addressed, forms of modeling implemented, and clinical issues engaged, the latter ranging from intervention, to elucidation of deviant basic processes. A denouement comprising cogent quotations from historical figures in science concludes this Introduction.     

Working memory resources in young children with mathematical difficulties

Kyttälä, M., Aunio, P. & Hautamäki, J. (2010). Working memory resources in young children with mathematical difficulties. Scandinavian Journal of Psychology, 51 , 1–15.
Working memory (WM) ( Baddeley, 1986, 1997 ) is argued to be one of the most important cognitive resources underlying mathematical competence ( Geary, 2004 ). Research has established close links between WM deficits and mathematical difficulties. This study investigated the possible deficits in WM, language and fluid intelligence that seem to characterize 4- to 6-year-old children with poor early mathematical skills before formal mathematics education. Children with early mathematical difficulties showed poor performance in both verbal and visuospatial WM tasks as well as on language tests and a fluid intelligence test indicating a thoroughly lower cognitive base. Poor WM performance was not moderated by fluid intelligence, but the extent of WM deficits was related to language skills. The educational implications are discussed.     

THE DYNAMICS OF THE LAW OF EFFECT: A COMPARISON OF MODELS

Dynamical models based on three steady‐state equations for the law of effect were constructed under the assumption that behavior changes in proportion to the difference between current behavior and the equilibrium implied by current reinforcer rates. A comparison of dynamical models showed that a model based on Navakatikyan's (2007) two‐component functions law‐of‐effect equations performed better than models based on Herrnstein's (1970) and Davison and Hunter's (1976) equations. Navakatikyan's model successfully described the behavioral dynamics in schedules with negative‐slope feedback functions, concurrent variable‐ratio schedules, Vaughan's (1981) melioration experiment, and experiments that arranged equal, and constant‐ratio unequal, local reinforcer rates.     

Mathematical psychology: Prospects for the 21st century: A guest editorial

The twenty-first century is certainly in progress by now, but hardly well underway. Therefore, I will take that modest elasticity in concept as a frame for this essay. This frame will serve as background for some of my hopes and gripes about contemporary psychology and mathematical psychology’s place therein. It will also act as platform for earnest, if wistful thoughts about what might have (and perhaps can still) aid us in forwarding our agenda and what I see as some of the promising avenues for the future. I loosely structure the essay into a section about mathematical psychology in the context of psychology at large and then a section devoted to prospects within mathematical psychology proper. The essay can perhaps be considered as in a similar spirit, although differing in content, to previous editorial-like reviews of general or specific aspects of mathematical psychology such as [Estes, W. K. (1975). Some targets for mathematical psychology. Journal of Mathematical Psychology, 12, 263-282; Falmagne, J. C. (2005). Mathematical psychology: A perspective. Journal of Mathematical Psychology, 49, 436-439; Luce, R. D. (1997). Several unresolved conceptual problems of mathematical psychology. Journal of Mathematical Psychology, 41, 79-87] that have appeared in this journal.     

数学能力与决策的关系：个体差异的视角

即便在相同的情形中, 每个人所做的决策也有千差万别, 导致决策个体差异的因素之一就是数学能力。文章综述了算术能力、数量表征、概率推理能力以及数学认知启发式对各种决策的影响。目前这方面的研究或者采用相关范式将数学能力作为决策的外部关联因素, 或者采用成分范式确定决策过程所需要的特定数学认知成分; 观点上的主要争论在于是一般认知能力还是数学能力在预测决策表现, 以及数学能力是否总是对决策有积极作用; 此外, 双系统模型和模糊痕迹理论有望为决策的个体差异提供理论解释。今后研究应该澄清上述争论, 确定合适的研究范式和结果解释框架, 并探讨更多提高决策能力的措施。     

西方数学学习困难研究的综述

近十年来,西方心理学界对数学学习困难(MD)的研究不断地增加。本文阐述了MD研究的几个主要的方面：MD界定与鉴别的复杂性、工作记忆各个成分对MD的影响、MD数概念与计数知识的发展、MD算术策略的特征及发展。并在此基础上提出几点对MD研究的思考。     

The Uses of Argument in Mathematics

Stephen Toulmin once observed that ‘it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate’ [Toulmin et al., 1979, An Introduction to Reasoning, Macmillan, London, p. 89]. Might the application of Toulmin’s layout of arguments to mathematics remedy this oversight? Toulmin’s critics fault the layout as requiring so much abstraction as to permit incompatible reconstructions. Mathematical proofs may indeed be represented by fundamentally distinct layouts. However, cases of genuine conflict characteristically reflect an underlying disagreement about the nature of the proof in question.     

小学生数学问题解决中视觉空间表征的研究

本研究区分了两类数学应用题:非视觉化题目与视觉化题目,采用数学测验与个别访谈相结合的方法,考察了54名小学四、五、六年级不同学业水平学生的视觉空间表征。结果表明:图式表征在非视觉化题目与视觉化题目上都极大地促进了问题解决,图像表征妨碍非视觉化题目的解决但与视觉化题目的解决无关,并提出图式表征和图像表征在两类题目上有不同的含义。六年级学生的解题成绩及图式表征有显著的提高,但图像表征与年级因素无关。差生的图式表征能力很差,而在视觉化题目上使用图像表征显著地多于优生及中等生。在非视觉化题目的非视觉空间表征与图式表征之间的转换灵活性上,优生表现了明显的优势。     

小学数学教师职业知识的结构与内在关系

本研究以小学数学分数起始教学为媒介,通过自编的小学数学教师职业知识测验,考察了162名小学数学教师在学科知识、一般教育学知识和教育实践知识等三类知识上的表现,并据此探讨了这三类职业知识间的相互关系。研究结果表明,自编的小学数学职业知识测验具有良好的信度和结构效度,教师的学科知识和一般教育学知识能显著地预测其教育实践知识。