Do children learn the integers by induction?

According to one theory about how children learn the meaning of the words for the positive integers, they first learn that "one," "two," and "three" stand for appropriately sized sets. They then conclude by inductive inference that the next numeral in the count sequence denotes the size of sets containing one more object than the size denoted by the preceding numeral. We have previously argued, however, that the conclusion of this Induction does not distinguish the standard meaning of the integers from nonstandard meanings in which, for example, "ten" could mean set sizes of 10, 20, 30,... elements. Margolis and Laurence [Margolis, E., & Laurence, S. (2008). How to learn the natural numbers: Inductive inference and the acquisition of number concepts. Cognition, 106, 924-939] believe that our argument depends on attributing to children "radically indeterminate" concepts. We show, first, that our conclusion is compatible with perfectly determinate meanings for "one" through "three." Second, although the inductive inference is indeed indeterminate - which is why it is consistent with nonstandard meanings - making it determinate presupposes the constraints that the inference is supposed to produce.     

Children's Understanding of the Natural Numbers’ Structure

When young children attempt to locate numbers along a number line, they show logarithmic (or other compressive) placement. For example, the distance between “5” and “10” is larger than the distance between “75” and “80.” This has often been explained by assuming that children have a logarithmically scaled mental representation of number (e.g., Berteletti, Lucangeli, Piazza, Dehaene, & Zorzi, 2010 ; Siegler & Opfer, 2003 ). However, several investigators have questioned this argument (e.g., Barth & Paladino, 2011 ; Cantlon, Cordes, Libertus, & Brannon, 2009 ; Cohen & Blanc‐Goldhammer, 2011 ). We show here that children prefer linear number lines over logarithmic lines when they do not have to deal with the meanings of individual numerals (i.e., number symbols, such as “5” or “80”). In Experiments 1 and 2, when 5‐ and 6‐year‐olds choose between number lines in a forced‐choice task, they prefer linear to logarithmic and exponential displays. However, this preference does not persist when Experiment 3 presents the same lines without reference to numbers, and children simply choose which line they like best. In Experiments 4 and 5, children position beads on a number line to indicate how the integers 1–100 are arranged. The bead placement of 4‐ and 5‐year‐olds is better fit by a linear than by a logarithmic model. We argue that previous results from the number‐line task may depend on strategies specific to the task.     

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。     

抽象概念表征的具身认知观

抽象概念是否通过感知经验来表征以及如何被感知经验表征是具身认知面临的一大问题.在抽象概念表征是否具有感知经验基础的问题上,具身认知理论认为抽象概念通过情境模拟或隐喻与感知经验发生联系.在抽象概念如何与感知经验表征发生联系的问题上,概念模拟理论强调情景或运动模拟在抽象概念表征中的直接作用;概念隐喻理论则侧重具体经验或具体经验与抽象概念之间的共同结构关系在抽象概念表征中的间接作用.未来研究应改变概念表征的稳定的心理实体观,从语言和抽象表征的关系、正常儿童和特殊群体的抽象概念表征差异入手,整合不同的具身认知观点.     

Quine's Weak and Strong Indispensability Argument

Quine's views on indispensability arguments in mathematics are scrutinised. A weak indispensability argument is distinguished from a strong indispensability thesis. The weak argument is the combination of the criterion of ontological commitment, holism and a mild naturalism. It is used to refute nominalism. Quine's strong indispensability thesis claims that one should consider all and only the mathematical entities that are really indispensable. Quine has little support for this thesis. This is even clearer if one takes into account Maddy's critique of Quine's strong indispensability thesis. Maddy's critique does not refute Quine's weak indispensability argument. We are left with a weak and almost unassailable indispensability argument. This revised version was published online in August 2006 with corrections to the Cover Date.     

小学四年级数学诊断性测验的编制与研究

诊断性测验是诊断性评价的工具。本研究以教育测量与评价的基本原理为指导,按照诊断性测验编制的方法和步骤,在详细制定了小学四年级数学教学目标体系的基础上编制出《小学四年级数学诊断性测验》并获取了该测验的信度和效度证据。本研究对中小学各科诊断性测验的编制具有普遍的指导意义,所编测验对于诊断学生学习困难、弥补教学不足有实际应用价值。     

Content differences for abstract and concrete concepts

Concept properties are an integral part of theories of conceptual representation and processing. To date, little is known about conceptual properties of abstract concepts, such as idea. This experiment systematically compared the content of 18 abstract and 18 concrete concepts, using a feature generation task. Thirty-one participants listed characteristics of the concepts (i.e., item properties) or their relevant context (i.e., context properties). Abstract concepts had significantly fewer intrinsic item properties and more properties expressing subjective experiences than concrete concepts. Situation components generated for abstract and concrete concepts differed in kind, but not in number. Abstract concepts were predominantly related to social aspects of situations. Properties were significantly less specific for abstract than for concrete concepts. Thus, abstractness emerged as a function of several, both qualitative and quantitative, factors.     

Reasons and Value – in Defence of the Buck-Passing Account

In this article, I will defend the so-called buck-passing theory of value. According to this theory, claims about the value of an object refer to the reason-providing properties of the object. The concept of value can thus be analyzed in terms of reasons and the properties of objects that provide them for us. Reasons in this context are considerations that count in favour of certain attitudes. There are four other possibilities of how the connection between reasons and value might be formulated. For example, we can claim that value is a property that provides us with reasons to choose an option that has this property. I argue that none of these four other options can ultimately be defended, and therefore the buck-passing account is the one we ought to accept as the correct one. The case for the buck-passing account becomes even stronger, when we examine the weak points of the most pressing criticism against this account thus far.     

Simplified Models of the Relationship Between Health and Disease

The concepts of health and disease are crucial in defining the aim and the limits of modern medicine. Accordingly it is important to understand them and their relationship. However, there appears to be a discrepancy between scholars in philosophy of medicine and health care professionals with regard to these concepts. This article investigates health care professionals’ concepts of health and disease and the relationship between them. In order to do so, four different models are described and analyzed: the ideal model, the holistic model, the medical model and the disjunctive model. The analysis reveals that each model has its pros and cons, and that health care professionals appear to apply more than one models. Furthermore, the models and the way health care professionals’ use them may be helpful for scholars in philosophy of medicine with regard to developing theories and communicating them to health care professionals.