Patterns of abduction

This article describes abductions as special patterns of inference to the best explanation whose structure determines a particularly promising abductive conjecture (conclusion) and thus serves as an abductive search strategy (Sect. 1). A classification of different patterns of abduction is provided which intends to be as complete as possible (Sect. 2). An important distinction is that between selective abductions, which choose an optimal candidate from given multitude of possible explanations (Sects. 3–4), and creative abductions, which introduce new theoretical models or concepts (Sects. 5–7). While selective abduction has dominated the literature, creative abductions are rarely discussed, although they are essential in science. The article introduces several kinds of creative abductions, such as theoretical model abduction, common cause abduction and statistical factor analysis, and illustrates them by various real case examples. It is suggested to demarcate scientifically fruitful abductions from purely speculative abductions by the criterion of causal unification (Sect. 7.1).     

教师资格和职业发展因素对学生数学成绩的影响：一个跨文化比较

采用TIMSS2003中的数据,应用混合模型,比较香港、日本、瑞典和美国四个国家(地区)教师资格因素和职业发展因素对其学生数学学业成绩的影响。结果发现香港教师高学历和常有其他教师听课提高了学生成绩;瑞典教师的性别、专业和参加数学教学方法方面的职业发展活动,以及美国教师的专业和听其他教师讲课显著影响其学生成绩;日本教师资格和职业发展因素对其学生成绩没有影响。     

The Materiality of the Abstraction Voice

The comment on Bertau's paper underlines the importance of the internally social character of the dialogical self, which is not trivial and can not be taken for granted. A consistent theory of this internal character demands specific theoretical means native to a tradition of Leibniz' philosophy. In consequence the concept of dialogical self is presented as a non-empirical one based in an ethos. We, and not nature, are responsible for the modes of conceptualising.     

Number words in young children's conceptual and procedural knowledge of addition, subtraction and inversion

Three studies addressed children's arithmetic. First, 50 3- to 5-year-olds judged physical demonstrations of addition, subtraction and inversion, with and without number words. Second, 20 3- to 4-year-olds made equivalence judgments of additions and subtractions. Third, 60 4- to 6-year-olds solved addition, subtraction and inversion problems that varied according to the inclusion of concrete referents and number words. The results indicate that number words play a different role in conceptual and procedural development. Children have strong addition and subtraction concepts before they can translate the physical effects of these operations into number words. However, using number words does not detract from their calculation procedures. Moreover, consistent with iterative relations between conceptual and procedural development, the results suggest that inversion acquisition depends on children's calculation procedures and that inversion understanding influences these procedures.     

The Development of Infants' Spatial Categories

ABSTRACT— Early theories of how infants develop spatial concepts focused on the perceptual and cognitive abilities that contribute to this ability. More recent research, however, has centered on whether experience with spatial language might also play a role. The present article reviews how infants learn to form spatial categories, outlining the perceptual and cognitive abilities that drive this learning, and examines the role played by spatial language. I argue that infants' spatial concepts initially are the result of nonlinguistic perceptual and cognitive abilities, but that, as infants build a spatial lexicon, spatial language becomes an important tool in the spatial categories infants learn to form.     

HIERARCHIES: THE CORE ARGUMENT FOR A NATURALISTIC CHRISTIAN FAITH

This article takes on a perhaps impossible task: not only to reconstruct the core argument of Arthur Peacocke's program in science and religion but also to evaluate it in two major areas where it would seem to be vulnerable, namely, more recent developments in systems biology and the philosophy of mind. If his theory of hierarchies is to be successful, it must stand up to developments in these two areas and then be able to apply the results in a productive way to Christian theological reflection. Peacocke recognized that one's model of the mind‐body relation is crucial for one's position on the God‐world relation and divine action. Of the three models that he constructed, it turns out that only the third can serve as a viable model for theology if it is to be more than purely deistic or metaphorical.     

Supporting the formal verification of mathematical texts

The formal verification of mathematical texts is one of the most interesting applications for computer systems. In fact, we argue that the expert language of mathematics is the natural choice for achieving efficient mathematician–machine interaction. Our empirical approach, the analysis of carefully authored textbook proofs, forces us to focus on the language and the reasoning pattern that mathematician use when presenting proofs to colleagues and students. Enabling a machine to understand and follow such language and argumentation is seen to be the key to usable and acceptable math assistant systems. In this paper, we first perform an analysis of three textbook proofs by hand; we then describe a computational framework that aims at mechanising such an analysis. The resulting proof-of-concept implementation is capable of processing simple textbook proofs and constitutes promising steps towards a natural mathematician–machine interface for proof development and verification.     

小学生数学应用题解题水平影响因素的研究——视空间能力、认知方式及表征方式的影响

研究采用3(年级)×2(场认知方式)×2(视空间能力水平)×3(问题表征方式)四因素混合实验设计,探讨了这四种因素对小学生数学应用题解题水平的影响。结果表明:年级、认知方式、空间能力以及问题表征方式均是影响小学生应用题解决水平的关键因素;问题表征方式、认知方式、空间能力以及年级四个因素对小学生解题水平存在交互作用,其中图形提示有利于场依存性学生解题水平的提高,低空间-场依存型的学生更适合图形提示;高空间-场依存型的学生随年级升高解题能力发展较快,而低空间-场依存型的学生解题水平提高较慢;随着年级的升高,图式表征对小学生问题解决的促进作用增强。     

How Do You Say Nature?: Opening the Design Space with a Knowledge Environment

In this paper, we describe a design study on how families in Los Angeles experience nature, with a particular focus on how using alternative formats for research analysis and presentation can enrich a design research inquiry. Conducted in Pasadena, CA as a part of Super Studio, the year-long design research class emphasized knowledge building and sharing through design methods of analysis, exhibition, and concept prototypes. After conducting interviews and engaging participants with probes, the class built the results into an open-ended knowledge environment. The main observation from the exhibition – that Angelenos have a limited vocabulary for describing nature and their interaction with it – helped to define the opportunity for design intervention that created connection points between Angelenos and nature. There are few attempts to describe how probe returns evolve into design concepts. Showcased is a process that depends on the unique affordances of design as the vehicle for discovery and invention.     

From grammatical number to exact numbers: early meanings of 'one', 'two', and 'three' in English, Russian, and Japanese

This study examined whether singular/plural marking in a language helps children learn the meanings of the words 'one,' 'two,' and 'three.' First, CHILDES data in English, Russian (which marks singular/plural), and Japanese (which does not) were compared for frequency, variability, and contexts of number-word use. Then young children in the USA, Russia, and Japan were tested on Counting and Give-N tasks. More English and Russian learners knew the meaning of each number word than Japanese learners, regardless of whether singular/plural cues appeared in the task itself (e.g., "Give two apples" vs. "Give two"). These results suggest that the learning of "one," "two" and "three" is supported by the conceptual framework of grammatical number, rather than that of integers.