风险决策价值函数的数学公式

本文提出风险决策价值函数的一个数学公式,定量描述决策者对价值的主观感受与收益及损失之间的关系。     

Interpretation(s) of elasticity in operant demand

This brief report provides an account of varying interpretations of elasticity (η ) in the operant demand framework. General references to “demand elasticity” have existed since the Exponential model of operant demand was proposed by Hursh and Silberberg (2008). This term has been used interchangeably with Essential Value (EV), P_MAX, and the rate of change constant α . This report provides an in-depth account of η and the various ways in which this metric has been used to interpret fitted demand functions. A review of relevant mathematic terms, operations associated with differentiating parameters, and worked solutions for η are provided for linear and nonlinear demand functions. The relations between η and EV, P_MAX, and α are described and explained in terms of their mathematical bases and recommendations are provided regarding their individual interpretation. This report concludes with recommendations for providing additional mathematical detail in published works and emphasizing a consistent use of terms when describing aspects of operant demand.     

小学低年级儿童的计算流畅性与数学焦虑:基于变量为中心与个体为中心的分析

为考察计算流畅性对小学低年级儿童数学焦虑的影响及作用机制,对592名小学二年级儿童的计算流畅性、数学学习兴趣、教师支持和数学焦虑进行测查。结果发现:(1)计算流畅性不仅通过数学学习兴趣间接影响数学焦虑,也可通过数学学习兴趣进而通过教师支持间接影响数学焦虑;(2)对计算流畅性和数学学习兴趣得分进行潜剖面分析,可将儿童区分为三种类型:低能力-低兴趣型、高能力-高兴趣型和低能力-高兴趣型;(3)低能力-低兴趣型儿童的数学焦虑得分显著高于其他两类,而低能力-高兴趣型和高能力-高兴趣型儿童的数学焦虑得分则无显著差异。上述结果表明计算流畅性、数学学习兴趣和教师支持在预防和干预小学低年级儿童的数学焦虑中具有重要作用。     

Editorial: The role of reasoning in mathematical thinking

ABSTRACT

Research into mathematics often focuses on basic numerical and spatial intuitions, and one key property of numbers: their magnitude. The fact that mathematics is a system of complex relationships that invokes reasoning usually receives less attention. The purpose of this special issue is to highlight the intricate connections between reasoning and mathematics, and to use insights from the reasoning literature to obtain a more complete understanding of the processes that underlie mathematical cognition. The topics that are discussed range from the basic heuristics and biases to the various ways in which complex, effortful reasoning contributes to mathematical cognition, while also considering the role of individual differences in mathematics performance. These investigations are not only important at a theoretical level, but they also have broad and important practical implications, including the possibility to improve classroom practices and educational outcomes, to facilitate people's decision-making, as well as the clear and accessible communication of numerical information.     

The Contingency of Creation and Modern Science

The Bible reveals a free, contingent act of the triune, personal God as the origin of the world. This paper explores the fruitfulness of taking the contingency of creation as the starting-point for our thinking about the natural world. We will see that the contingency of creation implies a conception of the natural order which is in harmony with modern science. It is the foundation for the experimental method and the use of mathematics, provides an understanding of contingent laws of nature, shows that natural order is open to historical evolution, and makes room for chance and novelty.     

Differences in mathematical reasoning between typically achieving and gifted children

Mathematical giftedness refers to mastery in a specific mathematical domain at an earlier than expected age. The present study examined which cognitive processes accounted for differences in mathematical reasoning between gifted children (MRG) and their typically achieving peers (TA). Naming speed, phonological awareness, short-term memory, executive functioning, and working memory were examined in 51 children aged approximately 7 years. A series of stepwise regression models, using a contrast variable to capture differences in mathematical reasoning between MRG and TA children, were created to examine which cognitive domains accounted for differences in mathematical reasoning. Short-term memory (r²?=?.08) and visual-spatial working memory (r²?=?.39) emerged as the only cognitive predictors within a model that included gender, age, and fluid intelligence. This model captured all of the variance distinguishing mathematics reasoning between MRG and TA children, explaining an overall contribution of 70% of the variance in mathematical reasoning.     

Glivenko Type Theorems for Intuitionistic Modal Logics

In this article we deal with Glivenko type theorems for intuitionistic modal logics over Prior's MIPC. We examine the problems which appear in proving Glivenko type theorems when passing from the intuitionistic propositional logic Intto MIPC. As a result we obtain two different versions of Glivenko's theorem for logics over MIPC. Since MIPCcan be thought of as a one-variable fragment of the intuitionistic predicate logic Q-Int, one of the versions of Glivenko's theorem for logics over MIPCis closely related to that for intermediate predicate logics obtained by Umezawa [27] and Gabbay [15]. Another one is rather surprising.     

Penrose's New Argument

It has been argued, by Penrose and others, that Gödel's proof of his first incompleteness theorem shows that human mathematics cannot be captured by a formal system F: the Gödel sentence G(F) of F can be proved by a (human) mathematician but is not provable in F. To this argment it has been objected that the mathematician can prove G(F) only if (s)he can prove that F is consistent, which is unlikely if F is complicated. Penrose has invented a new argument intended to avoid this objection. In the paper I try to show that Penrose's new argument is inconclusive.