A model for residence time in concurrent variable interval performance

A component-functions model of choice behavior is proposed for performance on interdependent concurrent variable-interval (VI) variable-interval schedules based on the product of two component functions, one that enhances behavior and one that reduces behavior. The model is the solution to the symmetrical pair of differential equations describing behavioral changes with respect to two categories of reinforcers: enhancing and reducing, or excitatory and inhibitory. The model describes residence time in interdependent concurrent VI VI schedules constructed from arithmetic and exponential distributions. The model describes the data reported by Alsop and Elliffe (1988) and Elliffe and Alsop (1996) with a variance accounted for of 87% compared to 64% accounted for by the Davison and Hunter (1976) model and 42% by Herrnstein's (1970) hyperbola. The model can explain matching, undermatching, and overmatching in the same subject under different procedures and has the potential to be extended to performance on concurrent schedules with more than two alternatives, multiple schedules, and single schedules. Thus, it can be considered as an alternative to Herrnstein's quantitative law of effect.     

CONSTRUCTING AND DERIVING RECIPROCAL TRIGONOMETRIC RELATIONS: A FUNCTIONAL ANALYTIC APPROACH

Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed by tests of novel relations. Experiment 2 addressed training in accordance with frames of coordination (same as) and frames of opposition (reciprocal of) followed by more tests of novel relations. All assessments of derived and novel formula‐to‐graph relations, including reciprocal functions with diversified amplitude and frequency transformations, indicated that all 4 participants demonstrated substantial improvement in their ability to identify increasingly complex trigonometric formula‐to‐graph relations pertaining to same as and reciprocal of to establish mathematically complex repertoires.     

情绪的数学公式

综合经验事实,提出对于同一个受试者和同一种呈现事件,近似描述情绪体验强度与客观呈现事件数量之间的一个数学公式.     

Recognition failure of recallable words: problems of mathematical constraint and dependence

The graph space of P ( RN | RL ) vs. P ( RN ), probabilities of recognition given recall and overall recognition, is the setting for the Tulving-Wiseman (TW) function of recognition failure research. According to Hintzman (1991, 1992), the moderate scatter of data points about the TW curve is an artefactual regularity caused by a mathematical constraint when P ( RN ) < P ( RL ). However, both constrained and unconstrained (when P ( RN ) ≥ P ( RL )) points conform equally well to the TW function, consistent with the unobserved fact that the location of both kinds of points is determined by the same mathematical rule. Hintzman's claim that there is no regularity in the data plot when P ( RN ) < P ( RL ) other than that produced by the constraint is not supported by this study. He based his claim on an incorrect use of the measure of dependence (association) called gamma. The graph space corresponding to gamma is that of P ( RN | RL ) vs. P ( RN | nRL ), as shown by using the Bayes function (Bayes' theorem). The margin-free measure gamma is a function of two thetas, theta being a margin-sensitive measure of dependence that is the parameter of the Bayes function. The variance of gamma reflects the fact that it is compounded of the theta variances, so a margin-free measure is obtained at the expense of greater variability.     

Departure from normal assumptions: A promise for future psychometrics with substantive mathematical modeling

Normal assumptions have been used in many psychometric methods, to the extent that most researchers do not even question their adequacy. With the rapid advancement of computer technologies in recent years, psychometrics has extended its territory to include intensive cognitive diagnosis, etcetera, and substantive mathematical modeling ha become essential. As a natural consequence, it is time to consider departure from normal assumptions seriously. As examples of models which are not based on normality or its approximation, the logistic positive exponent family of models is discussed. These models include the item task complexity as the third parameter, which determines the single principle of ordering individuals on the ability scale.     

小学生近似数量系统敏锐度的发展趋势及其与数学能力的关系：抑制控制的中介作用

采用测量法和问卷法考察了172名小学生近似数量系统敏锐度的发展,以及抑制控制在近似数量系统敏锐度与数学能力关系中的中介效应。结果表明：(1)随着年龄增长,小学生的近似数量系统敏锐度逐渐提高;(2)近似数量系统敏锐度(负相关序列中的韦伯系数)和抑制控制均能显著正向预测小学生的数学能力;(3)抑制控制在小学生近似数量系统敏锐度(负相关序列中的韦伯系数)与数学能力的关系中起部分中介作用。     

学校氛围对学生数学成绩影响的跨文化比较:基于多水平分析的结果

学校氛围是学校中被成员所体验并对其行为产生影响的、相对持久而稳定的学校环境特征。它以成员的共同行为感知为基础,对学校和学生的发展具有重要作用。以PISA2003测试的数据为基础,采用多水平线性模型,考察了中国香港、日本、美国和土耳其的15岁学生及其所在学校的校长知觉的学校氛围对学生数学成绩的影响。结果显示:(1)学生知觉的师生关系、数学课堂秩序,校长知觉的学生士气、学校消极行为对数学成绩的显著预测作用具有较高的跨文化一致性;(2)数学课堂上的教师支持、教师负面状态、数学教师间的共识能显著预测部分国家/地区的学生数学成绩;(3)学生知觉的对学校的看法、校长知觉的教师士气对四个国家/地区的学生数学成绩均无显著预测作用。     

The Revival of Rejective Negation

Whether assent (acceptance) and dissent (rejection) are thought of as speech acts or as propositional attitudes, the leading idea of rejectivism is that a grasp of the distinction between them is prior to our understanding of negation as a sentence operator, this operator then being explicable as applying to A to yield something assent to which is tantamount to dissent from A. Widely thought to have been refuted by an argument of Frege"s, rejectivism has undergone something of a revival in recent years, especially in writings by Huw Price and Timothy Smiley. While agreeing that Frege"s argument does not refute the position, we shall air some philosophical qualms about it in Section 5, after a thorough examination of the formal issues in Sections 1–4. This discussion draws on – and seeks to draw attention to – some pertinent work of Kent Bendall in the 1970s.