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.     

Multidimensional adaptive testing

Maximum likelihood and Bayesian procedures for item selection and scoring of multidimensional adaptive tests are presented. A demonstration using simulated response data illustrates that multidimensional adaptive testing (MAT) can provide equal or higher reliabilities with about one-third fewer items than are required by one-dimensional adaptive testing (OAT). Furthermore, holding test-length constant across the MAT and OAT approaches, substantial improvements in reliability can be obtained from multidimensional assessment. A number of issues relating to the operational use of multidimensional adaptive testing are discussed.     

先天模块与后天文化资源的相互作用论——B.Butterworth的"数字模块"理论述评

从理论假设、概念体系和研究方法三个方面对B.Butterworth的“数字模块”理论进行了介绍和评价。该理论假定人类数学能力是先天的“数字模块”与后天的拓展模块功能的“概念工具”相互作用的产物。其概念体系涉及“数字模块”的定义、功能、结构及模块与文化资源间的相互作用。其方法以认知神经心理学为主,兼及跨文化、灵长目认知的研究和基因学的证据。     

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.     

Translation of first order formulas into ground formulas via a completion theory

A translation technique is presented which transforms a class of First Order Logic formulas, called Restricted formulas, into ground formulas. For the formulas in this class the range of quantified variables is restricted by Domain formulas.If we have a complete knowledge of the predicates involved in the Domain formulas their extensions can be evaluated with the Relational Algebra and these extensions are used to transform universal (respectively existential) quantifiers into finite conjunctions (respectively disjunctions).It is assumed that the complete knowledge is represented by Completion Axioms and Unique Name Axioms à la Reiter. These axioms involve the equality predicate. However, the translation allows to remove the equality in the ground formulas and for a large class of formulas their consequences are the same as the initial First Order formulas. This result open the door for the design of efficient deduction techniques.