循环系统的数学模型及仿真实验

循环系统建立数学模型与计算机仿真是一种新型研究方法。它将有关循环系统的生理和物理学知识整合起来 ,构成数学模型 ,然后进行计算机仿真研究。这种方法已应用于研究循环系统的生理及病理机制、疾病治疗手段和超常环境下循环障碍及其防护措施     

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。     

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。     

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。     

学科领域知识和学业成绩对工作记忆广度的影响

引入Alexander领域知识概念形成数学学科领域知识,以七年级有理数单元为研究材料,编写问卷和E-Prime实验程序,筛选60名初中生为被试,考察数学学科领域知识和学业成绩对工作记忆广度的影响。研究发现:(1)学优生的认知过程知识和问题条件知识显著高于学困生,而学理内容知识差异不显著;(2)在简单加工任务上,学优生和学困生工作记忆广度差异不显著。在复杂任务上,学优生的工作记忆广度都显著高于学困生;(3)当工作记忆广度任务中存储部分的词语和数学学科领域知识相关时,问题条件知识分数和认知过程分数能够显著地预测工作记忆广度。而不相关时,仅问题条件知识分数能够显著地预测工作记忆广度。     

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.