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Using Multivariate Statistics

미국의 “전국 수학 교사 협의회”(National Council of Teachers of Mathematics, NCTM)는 1989년부터 〈학교 수학의 교육과정과 평가 규준〉(1989), 〈수학 가르침(교수)의 전문성 규준〉(1991), 〈학교 수학의 평가(시험) 규준〉(NCTM, 1995), 〈학교 수학의 원리와 규준〉(2000)을 출판하여 미국의 수학 교육 의 전망(목표, 나아갈 길)과 규준(실행 지침)을 제시하였다. 수학 교사들로 구성된 미국의 NCTM은 학생, 학부모, 학교 행정가 등 많은 사람들과 힘을 합하여 모든 학생들에게 수준 높은 수학 교육을 받을 수 있는 여건(환경, 기회)을 조성하는 데 구심점의 역할을 하였다. 한편 많은 관련 단체들은 여러 배경과 능력을 가진 학생들이 전문성을 지닌 교사(특수 교사를 일컫는 밀이 아니다. 수학 교과를 이해하고 수학의 전문성과 특수성을 가르칠 수 있는 일반 교사를 일컫는 말이다.)로부터 미래를 대비해 평등하고, 진취적이며, 지원이 잘 이루어지고, 공학 도구(IT)가 잘 갖춰진 환경에서 중요한 수학적 아이디어를 이해하면서 학습할 수 있는 수학 교실(미국에서는 우리나라처럼 수학 교사가 수학 시간에 학생의 방(교실: Homeroom)에 찾아가지 않고 학생들이 선생의 방(수학 교실: Classroom)을 찾아온다. 전형적인 수학 교실의 사진은 2쪽에 나와 있다.)을 만들기 위해 함께 힘썼다. NCTM에서 출간한 여러 규준들은 우리나라의 제6차와 제7차 교육과정에도 큰 영향을 미쳤다. 이 글에서는 NCTM(2000)에서 제시한 학습 원리를 간단히 살펴본 다음 이를 중심으로 현재 미국 수학 교육의 교수ㆍ학습 이론의 동향을 살펴본다.

미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론

The study reported here examines the English language knowledge and performance of bilingual school children of Middle School age in Britain, in particular their acquisition and use of vocabulary. One of the chief premises of the research is that pupils from bilingual minority ethnic backgrounds suffer a major disadvantage while learning from the National Curriculum because they lack the necessary richness of word knowledge, accompanied by the conceptual frameworks expected in learning subjects such as science and geography. Furthermore, it is believed that by raising awareness among teachers and by the adoption of appropriate methods of vocabulary teaching founded on research, the vocabulary learning of bilingual pupils can be greatly increased. The aim of the study is to identify, describe and evaluate methods of vocabulary instruction currently used and to provide recommendations for suitable methods to be introduced. By means of an action research methodology implemented in a middle school, and with the joint participation of some members of staff and some pupils, classroom data was collected over a two and a half year period from teachers of science, geography and English and their pupils, supplemented with semi-structured interviews with teachers and support staff and conversations with children. These data provided material for a detailed analysis of exactly how individual words develop from first introduction into the pupils’ active vocabulary.

Teaching and Learning Vocabulary

Sensorimotor synchronization (SMS), the rhythmic coordination of perception and action, occurs in many contexts, but most conspicuously in music performance and dance. In the laboratory, it is most often studied in the form of finger tapping to a sequence of auditory stimuli. This review summarizes theories and empirical findings obtained with the tapping task. Its eight sections deal with the role of intention, rate limits, the negative mean asynchrony, variability, models of error correction, perturbation studies, neural correlates of SMS, and SMS in musical contexts. The central theoretical issue is considered to be how best to characterize the perceptual information and the internal processes that enable people to achieve and maintain SMS. Recent research suggests that SMS is controlled jointly by two error correction processes (phase correction and period correction) that differ in their degrees of cognitive control and may be associated with different brain circuits. They exemplify the general distinction between subconscious mechanisms of action regulation and conscious processes involved in perceptual judgment and action planning.

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Sensorimotor synchronization: a review of the tapping literature.

As yet, there is no enactive account of social cognition. This paper extends the enactive concept of sense-making into the social domain. It takes as its departure point the process of interaction between individuals in a social encounter. It is a well-established finding that individuals can and generally do coordinate their movements and utterances in such situations. We argue that the interaction process can take on a form of autonomy. This allows us to reframe the problem of social cognition as that of how meaning is generated and transformed in the interplay between the unfolding interaction process and the individuals engaged in it. The notion of sense-making in this realm becomes participatory sense-making. The onus of social understanding thus moves away from strictly the individual only.

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Participatory sense-making

Past research has shown that interpersonal interactions are characterized by a tacit coordination of motor movements of the participants and has suggested that the emergent synchrony might be explained by a coupled oscillator dynamic. This study investigates whether unintended between-person coordination can be demonstrated in a laboratory task that will allow an evaluation of whether such dynamical processes are involved. Ten pairs of participants performed a simple rhythmic task in which they had visual information about each other's movements but had no goal to coordinate. A cross-spectral analysis of the movements revealed higher coherence and a distribution of relative phase angles that was dominated by values near 0 deg. and 180 deg. These results support the hypothesis that dynamical organizing principles are involved in natural interpersonal synchrony.

Evaluating the Dynamics of Unintended Interpersonal Coordination

This study examined the relative contributions of phonological awareness, orthographic pattern recognition, and rapid letter naming to fluent word and connected-text reading within a dyslexic sample of 123 children in second and third grades. Participants were assessed on a variety of fluency measures and reading subskills. Correlations and hierarchical multiple regression analyses were carried out to explore these relationships. The results demonstrate that phonological awareness, rapid letter naming, and orthographic pattern recognition contribute to word-reading skills. Furthermore, rapid naming, orthographic pattern recognition, and word reading fluency moderately predict different dimensions of connected-text reading (i.e., rate, accuracy, and comprehension) whereas phonological awareness contributes only to the comprehension dimension of connected-text reading. The findings support the multidimensional nature of fluency in which the whole is more than its parts.

Reading fluency: the whole is more than the parts.

This article details a study which predicted that across a wide range of print sizes dyslexic reading would follow the same curve shape as skilled reading, with constant reading rates across large print sizes and a sharp decline in reading rates below a critical print size. It also predicted that dyslexic readers would require larger critical print sizes to attain their maximum reading speeds, following the letter position coding deficit hypothesis. Reading speed was measured across twelve print sizes ranging from Snellen equivalents of 20/12 to 20/200 letter sizes for a group of dyslexic readers in Grades 2 to 4 (aged 7 to 10 years), and for non-dyslexic readers in Grades 1 to 3 (aged 6 to 8 years). The groups were equated for word reading ability. Results confirmed that reading rate-by-print size curves followed the same two-limbed shape for dyslexic and non-dyslexic readers. Dyslexic reading curves showed higher critical print sizes and shallower reading rate-by-print size slopes below the critical print size, consistent with the hypothesis of a letter-position coding deficit. Non-dyslexic reading curves also showed a decrease of critical print size with age. A developmental lag model of dyslexic reading does not account for the results, since the regression of critical print size on maximum reading rate differed between groups.

The effect of print size on reading speed in dyslexia

Reading speed is commonly used as an index of reading fluency. However, reading speed is not a consistent predictor of text comprehension, when speed and comprehension are measured on the same text within the same reader. This might be due to the somewhat ambiguous nature of reading speed, which is sometimes regarded as a feature of the reading process, and sometimes as a product of that process. We argue that both reading speed and comprehension should be seen as the result of the reading process, and that the process of fluent text reading can instead be described by complexity metrics that quantify aspects of the stability of the reading process. In this article, we introduce complexity metrics in the context of reading and apply them to data from a self-paced reading study. In this study, children and adults read a text silently or aloud and answered comprehension questions after reading. Our results show that recurrence metrics that quantify the degree of temporal structure in reading times yield better prediction of text comprehension compared to reading speed. However, the results for fractal metrics are less clear. Furthermore, prediction of text comprehension is generally strongest and most consistent across silent and oral reading when comprehension scores are normalized by reading speed. Analyses of word length and word frequency indicate that the observed complexity in reading times is not a simple function of the lexical properties of the text, suggesting that text reading might work differently compared to reading of isolated word or sentences.

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The role of reading time complexity and reading speed in text comprehension.

Advances in neuroimaging techniques and analytic methods have led to a proliferation of studies investigating the impact of bilingualism on the cognitive and brain systems in humans. Lately, these findings have attracted much interest and debate in the field, leading to a number of recent commentaries and reviews. Here, we contribute to the ongoing discussion by compiling and interpreting the plethora of findings that relate to the structural, functional, and connective changes in the brain that ensue from bilingualism. In doing so, we integrate theoretical models and empirical findings from linguistics, cognitive/developmental psychology, and neuroscience to examine the following issues: (1) whether the language neural network is different for first (dominant) versus second (nondominant) language processing; (2) the effects of bilinguals' executive functioning on the structure and function of the "universal" language neural network; (3) the differential effects of bilingualism on phonological, lexical-semantic, and syntactic aspects of language processing on the brain; and (4) the effects of age of acquisition and proficiency of the user's second language in the bilingual brain, and how these have implications for future research in neurolinguistics.

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Beth A. O'Brien

Papers

Evaluating the Dynamics of Unintended Interpersonal Coordination

Reading fluency: the whole is more than the parts.

The effect of print size on reading speed in dyslexia

The role of reading time complexity and reading speed in text comprehension.

Neurolinguistics: Structure, Function, and Connectivity in the Bilingual Brain