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.     

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.     

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。     

部总知识在解决加法文字题中的作用

探讨的问题是部总知识是否制约着算术文字题的解答过程。小学4年级学生(192人)和大学生(178人)被要求解答一步加法文字题。实验结果发现,正确列式方式受到已知客体集合具体特征的系统性影响,尤其是随着年龄的提高和练习程度的深入,这种影响越来越明显。这是部总知识作用假设所不能解释的。现根据集合在心理表征中的位置和表征强度解释结果,并在此基础上讨论了研究的实践意义。     

Lead exposure and child maltreatment as models for how to conceptualize early-in-life risk factors for violence

Although rates of violent crime have been on the decline in the United States for the past two decades, young people—and particularly young men—continue to commit and fall victim to alarmingly high rates of violence. Effective prevention requires data on what the determinants of violence are and when in the life course they emerge. The goal of this review was to identify early-in-life risk factors for violence and to describe (a) who is most affected and (b) effect mechanisms. I focus on abuse and neglect and exposure to lead as risk factors for violence that disproportionately affect young children and that are likely to have causal effects on development. I conclude with future directions for research and intervention.     

利用游戏log-file预测学生推理能力和数学成绩——机器学习的应用

以360名初中生为被试, 使用推箱子游戏, 结合游戏日志文件(log-file)和机器学习技术预测学生的推理能力和数学成绩。预测变量是从推箱子的过程数据中提取的一系列特征指标, 结果变量是瑞文推理测验成绩和数学成绩, 且均以25%为高低分组的临界值转换为二分变量。结果发现, 训练的模型预测推理能力最高能获得76.11%的查准率、65.72%的精确率、63.10%的查全率以及65.01%的F1得分; 预测数学成绩最高能获得83.07%的查准率、73.70%的精确率、73.33%的查全率以及75.57%的F1得分。研究结果说明, 机器学习建立的区分模型具有较好的预测效果, 利用log-file所记录的游戏过程数据可以对个体的能力进行有效预测。