Provability logics for natural turing progressions of arithmetical theories

Provability logics with many modal operators for progressions of theories obtained by iterating their consistency statements are introduced. The corresponding arithmetical completeness theorem is proved.     

Independence of uniphasic and biphasic audiogenic seizure progressions in mice

DBA/2J mice were monaurally or binaurally tested for susceptibility to sound-induced seizure. Two seconds following the beginning of running, one group of binaurally tested mice had acoustic stimulation interrupted for 15 s. These mice later seized when the stimulation was readministered. Their seizure progression closely resembled the behavior exhibited by noninterrupted binaurally stimulated mice and did not shift to the biphasic motor pattern of monaurally stimulated subjects. We conclude that the single burst of running of a binaurally tested mouse is qualitatively different from either of the two bursts of running exhibited by monaurally tested mice.     

Learning without representational change: development of numerical estimation in individuals with Williams syndrome

Experience engenders learning, but not all learning involves representational change. In this paper, we provide a dramatic case study of the distinction between learning and representational change. Specifically, we examined long‐ and short‐term changes in representations of numeric magnitudes by asking individuals with Williams syndrome (WS) and typically developing (TD) children to estimate the position of numbers on a number line. As with TD children, accuracy of WS children's numerical estimates improved with age (Experiment 1) and feedback (Experiment 2). Both long‐ and short‐term changes in estimates of WS individuals, however, followed an atypical developmental trajectory: as TD children gained in age and experience, increases in accuracy were accompanied by a logarithmic‐to‐linear shift in estimates of numerical magnitudes, whereas in WS individuals, accuracy increased but logarithmic estimation patterns persisted well into adulthood and after extensive training. These findings suggest that development of numerical estimation in WS is both arrested and atypical.     

Mediatory cue proximity and mental subnormality in the perception of rectilinear dot progressions

This study investigated the relationship between illusory displacement of sequentially presented light stimuli and their proximity to mediatory cues. Twenty-four retardates, 24 equal CA normals, and 24 equal MA normals were tested to determine the relative stabilizing effects of four different frame conditions on these groups. Illusory displacement decreased from least to most proximate cue condition, was least for the MA group, and was most for retardates It was concluded that interstimulus mediation referents, rather than restricted eye movement, facilitated veridical perception of successive light positions. nt]mis|The author extends sincere appreciation to Dr. Ralph Osborne, superintendent of the Hamilton Township school system, Mr. George Murphy, principal of Hamilton High School West, and Mrs. Isabel Robinson, principal of Kuser School, for their generous cooperation in providing students and testing space for this experiment.     

心理测量学模型在学习进阶中的应用:理论、途径和突破

学习进阶是对学生在一段时间内,关于某一主题连续发展、逐渐复杂思维的描述,它的建立是以假设性学习进阶为起点到收集证据验证假设性学习进阶不断迭代的过程。心理测量学模型能够使学习进阶与评价结合起来,既为验证学习进阶的有效性提供证据,又能对学生做出诊断,当前应用到学习进阶中的心理测量学模型有单维项目反应模型、多维项目反应模型和认知诊断模型。学习进阶还能为垂直量尺化、自适应学习提供新的研究视角,但应注意项目功能差异等问题。     

Radicalizing numerical cognition

In recent decades, non-representational approaches to mental phenomena and cognition have been gaining traction in cognitive science and philosophy of mind. In these alternative approach, mental representations either lose their central status or, in its most radical form, are banned completely. While there is growing agreement that non-representational accounts may succeed in explaining some cognitive capacities (e.g. perception), there is widespread skepticism about the possibility of giving non-representational accounts of cognitive capacities such as memory, imagination or abstract thought. In this paper, I will critically examine the view that there are fundamental limitations to non-representational explanations of cognition. Rather than challenging these arguments on general grounds, I will examine a set of human cognitive capacities that are generally thought to fall outside the scope of non-representational accounts, i.e. numerical cognition. After criticizing standard representational accounts of numerical cognition for their lack of explanatory power, I will argue that a non-representational approach that is inspired by radical enactivism offers the best hope for developing a genuine naturalistic explanatory account for these cognitive capacities.

     

Playing linear numerical board games promotes low-income children's numerical development

The numerical knowledge of children from low-income backgrounds trails behind that of peers from middle-income backgrounds even before the children enter school. This gap may reflect differing prior experience with informal numerical activities, such as numerical board games. Experiment 1 indicated that the numerical magnitude knowledge of preschoolers from low-income families lagged behind that of peers from more affluent backgrounds. Experiment 2 indicated that playing a simple numerical board game for four 15-minute sessions eliminated the differences in numerical estimation proficiency. Playing games that substituted colors for numbers did not have this effect. Thus, playing numerical board games offers an inexpensive means for reducing the gap in numerical knowledge that separates less and more affluent children when they begin school.     

Heterogeneity impairs numerical matching but not numerical ordering in preschool children

Do preschool children appreciate numerical value as an abstract property of a set of objects? We tested the influence of stimulus features such as size, shape, and color on preschool children's developing nonverbal numerical abilities. Children between 3 and 5 years of age were tested on their ability to estimate number when the sizes, shapes, and colors of the elements in an array were varied (heterogeneous condition) versus when they did not vary (homogeneous condition). One group of children was tested on an ordinal task in which the goal was to select the smaller of two arrays while another group of children was tested on a match‐to‐sample task in which the goal was to choose one of two visual arrays that matched the sample in number. Children performed above chance on both homogeneous and heterogeneous stimuli in both tasks. However, while children showed no impairment on heterogeneous relative to homogeneous arrays in the ordering task, performance was impaired by heterogeneity in the matching task. We suggest that nonverbal numerical abstraction occurs early in development, but specific task objectives may prevent children from engaging in numerical abstraction.     

Implicit Learning and Concept Learning

In Experiments 1 and 2, subjects were exposed to letter strings that followed a pattern—the second letter was always the same. This exposure was disguised as a test of immediate memory. Following this training, subjects could discriminate new letter strings following the pattern from letter strings not following the pattern more often than would be expected by chance, which is the traditional evidence for concept learning. Discrimination was also better than would be predicted from subjects' explicit report of the pattern, demonstrating the co-occurrence of concept learning and implicit learning. In Experiment 3, rules were learned explicitly. Discrimination was worse than would be predicted from subjects' explicit report, validating the implicit learning paradigm. In Experiment 4, deviations from a prototypical pattern were presented during training. In the test of discrimination, prototypes were as familiar as old deviations and more familiar than new deviations, even when considering only implicit knowledge. Experiment 5 found implicit knowledge of a familiar concept. These results are consistent with the hypothesis that the distinguishing features of a concept can be learned implicitly, and that one type of implicit learning is concept learning.     

From Sole Learning to Soul Learning

Abstract. Is it effective or even possible to teach an introductory course in religious studies that not only provides first‐year university students with the fundamental vocabulary, concepts, and critical tools of religious inquiry but also invites and stimulates the transformation of the religious imagination? In what kind of teaching and learning method could the process of personal transformation occur and how might one assess it? These are the questions that led to an experiment in teaching religion the objective of which was to prepare beginning students for the academic approach to religion and, at the same time, transmit the experience of learning as an embodied process that engages personal narrative within a community context. This essay is based on a three‐year project that has made considerable progress in meeting these goals and answering these questions. (Supplementary materials for this essay are available on the Wabash Center for Teaching and Learning in Theology and Religion web site http://www.wabashcenter.wabash.edu/journal/baldwin.html .)     

Across-notation automatic numerical processing

In this article, the authors explored the existence of across-notation automatic numerical processing using size comparison and same-different paradigms. Participants were Arabic speakers, who used 2 sets of numerical symbols -- Arabic and Indian. They were presented with number pairs in the same notation (Arabic or Indian) or in different ones (Arabic and Indian). In the size comparison paradigm, 2 digits differing both numerically and physically were compared on the physical dimension. Nevertheless, there was evidence that participants automatically processed the irrelevant numerical dimension in different notation pairs. In the same-different paradigm, 2 digits were presented either in the same or in different notations. Participants had to indicate whether the 2 digits were physically the same. The results again showed evidence for the automatic processing of numerical magnitude for pairs in different notations. Findings of both experiments suggest that numbers in different notations are automatically translated into a common representation of magnitude, in line with M. McCloskey's (1992) abstract representation model.     

Young children's numerical competence

In their analysis of numerical competence, Creeno, Riley, and Gelman 1984 distinguish between conceptual, procedural, and utilization competence. Principled knowledge about a domain, for example, counting, serves as the basis of conceptual competence. Conceptual competence does not provide recipes for procedures but does set constraints on the class of procedures that procedural competence can generate. The ability to assess a task correctly (utilization competence) influences performance because it, too, sets constraints on procedure generation. These distinctions allow one to classify the source of erroneous or variable performances on different number tasks. Our hypothesis that early counting behavior is guided by counting principles, despite the child's limited skill, is tested in four experiments with children ranging in age from 3 to 5 years old. The experiments focus on knowledge of the order-irrelevance and cardinal count principles; children either discriminate between erroneous and correct counting efforts of a puppet, assess the effect of counting the same array in different orders, or solve a counting task that has a constraint. The results of these studies allow us to reinterpret evidence others cite against the principle-first hypothesis, and conclude that much development takes place in the name of procedural and utilization competence.     

The development of numerical estimation: evidence for multiple representations of numerical quantity

Abstract - We examined children's and adults' numerical estimation and the representations that gave rise to their estimates. The results were inconsistent with two prominent models of numerical representation: the logarithmic-ruler model, which proposes that people of all ages possess a single, logarithmically spaced representation of numbers, and the accumulator model, which proposes that people of all ages represent numbers as linearly increasing magnitudes with scalar variability. Instead, the data indicated that individual children possess multiple numerical representations; that with increasing age and numerical experience, they rely on appropriate representations increasingly often; and that the numerical context influences their choice of representation. The results, obtained with second graders, fourth graders, sixth graders, and adults who performed two estimation tasks in two numerical contexts, strongly suggest that one cause of children's difficulties with estimation is reliance on logarithmic representations of numerical magnitudes in situations in which accurate estimation requires reliance on linear representations.     

类别学习中分类学习与推理学习的对比研究

本研究对类别学习中分类学习与推理学习进行了对比.实验中要求被试从成对呈现的项目中选择一个更典型的A,并且要求被试将典型的A和典型的B画出来.测试中所呈现项目诊断性程度或典型性程度不同.研究结果表明,分类学习者主要受诊断性信息的影响,而推理学习者主要受典型性信息的影响.即,分类学习者关注类别间信息,而推理学习者关注类别内信息.     

学习策略教学对学习动机的影响研究

在当今教育领域越来越重视如何教学生学会学习的问题之际,学习动机对学生学习的影响日益受到普遍关注。许多研究者从不同角度对它们进行了研究。如家庭资源对学习不良儿童的学习动机影响是非常重要的(俞国良等,1998);外部奖赏在一定条件下会削弱内在动机(吴增强,1995);教学中不同的目标结构会导致学生形成不同的学习动机(郭德俊等,1994)。而对学习策略是否影响学习动机?及如何影响学习动机的研究尚不多见。本研究运用教学实验、问卷等方法,探讨了学习策略对学习动机的影响,这对提高教与学的质量具有非常重要的理论及实践意义。     

Representations for biased numerical judgments

Models are presented that introduce bias parameters into the numerical representations for ratio and interval judgments. An interval bias model is considered that has the capability of accounting for both interval and ratio judgments. A contrasting ratio bias model—a simple generalization of the classical model that accepts ratio judgments at face value—is also considered, and both models are tested with brightness data. The ratio estimation data lead to the conclusion that the constraints placed on the structure of the data by the classical model are too strong. In terms of goodness-of-fit and certain theoretical criteria, the interval bias model accounts for the ratio estimation data better than the ratio bias model. The interval estimation data are supportive of recent efforts directed toward the development of direct interval scaling theory.     

A Learning Abilities Program for Learning Disabled Students

This report describes a treatment program for learning disabled soldiers who have completed their basic training and are experiencing academic difficulties as they begin their Advanced Individual Training. Rationale for the evaluation/treatment techniques used as well as suggested class room modifications are described.