수학 학습장애 위험 아동의 수학 능력 발달 특성에 관한 연구: 수학 문장제 해결 능력과 인지 변인 간의 관계를 중심으로

학위논문 (박사)-- 서울대학교 대학원 : 협동과정 특수교육전공, 2013. 2. 김동일.Although many students show proficiency on assessments of general mathematics skills, many of them experience difficulties in solving word problems in mathematics. This may be attributed to a lack of the required skills necessary for the solution of these word problems. In order for students to be able to solve these problems, they first have to be able to read and understand the problem. Next, they must have the ability to translate the texts of the problem described in natural language into arithmetic operations expressed in mathematical language. Finally, they should be able to compute the equations without any error and to check that their calculations and computations are correct. In other words, word problem solving in mathematics requires the integration of computation and application knowledge with basic reading skills in terms of language comprehension. Students with certain learning disabilities are especially less successful in word problem solving in mathematics compared to other students without learning disabilities. The former group has difficulty understanding word problems because of the fact that they lack the basic reading and computation skills, coupled usually with the condition of diminished working memory. Specifically, they are not capable of representing the relationship in the problem to some comprehensible form which can lead them to solve the problem mathematically. Moreover, students with learning disabilities use even more inefficient strategies for problem solving than typically achieving students. The notion of learning disabilities has traditionally indicated unexpected underachievement due to a disorder in one or more of the basic psychological process or processes. This notion has been ratified within an intrinsic processing deficits model and has been used as an indicator for identifying learning disabilities. This model attempts to evaluate psychological process or capacity weakness directly, because these two variables form the basis on which learning problems are determined. Although the intrinsic processing deficits model provides the primary criterion for identifying learning disabilities, and although it is a direct approach to characterize and measure learning disabilities as opposed to the indirect methods using exclusionary clauses, it has not been a mandatory requirement for identification of learning disabilities in South Korea. That is not only because theoretical and empirical support for the notion of psychological process deficits and its influence on learning is still vague, but also because there is no agreement as to how to accurately measure cognitive ability This renders results acquired through this test invalid at best. This research attempts to explore in a defined heterogeneous population whether students difficulties in learning mathematics is based on their growth patterns and/or cognitive abilities. The research attempts this by, first of all, exploring the possibility that students' growth trajectories might be a determinant of the mathematical learning problem as it pertains to solving word problems. . Then, the cognitive predictors of group membership are identified and the similarities and differences in the cognitive characteristics by subtypes among students with mathematical difficulties are determined. For these purposes, the following research questions were established: 1) Are there any identifiable groups within the given population whose mathematical word problem solving ability show correlation with those students growth patterns (intercept and slope) 2) Given that there are multiple growth patterns, what are the effects of students' cognitive abilities on their growth patterns in terms of word problem solving in mathematics? 3) Do cognitive abilities differ among students with mathematical difficulties identified by their growth patterns, depending on whether there is an accompanying problem in computation, in reading, in both computation and in reading, or in neither computation or reading? The implications in conjunction with the interventions, as well as some of the limitations of the study, are discussed at the end of this study. Research Question 1 was used to examine identifiable subgroups based on growth patterns of word problem solving in mathematics. In order to explore the heterogeneity in growth trajectories of students repeatedly measured data, latent class growth analysis (LCGA) was conducted. As a result of LCGA, four distinct classes emerged based on characteristics of growth patterns (i.e. performance levels and growth rates). Class 1 (15.2%) was characterized as high intercept and slow progress. Class 2 (25.6%) was characterized as average intercept and fast progress. Class 3 (43.1%) was characterized as low intercept and slow progress. Class 4 (16.1%) was characterized as lowest intercept and little progress. The four groups classified by exploratory methods were labeled as high achieving students (HAS), average and fast growing students (AFG), low but steadily growing students (LSG), and students with mathematics difficulties (SDD) respectively. Research Question 2 was used to examine the relationship between growth patterns of word problem solving and cognitive abilities in mathematics. To investigate this relationship between students' learning progress in word problem solving and their cognitive abilities, a growth mixture modeling approach was used. In the case of setting up a HAS group as a reference, the lower the students' working memory ability is, the higher the possibility for students to be categorized into an AFG group (odds ratio=0.570) and a LSG group (0.582). Also, when the values of a processing speed and a language decrease (odds ratio=0.344 and 0.477, respectively), the probability of being in a SDD group increases. If the AFG group is set up as a reference, the lower the students' processing speed (odds ratio=0.664), the higher the possibility for students to be classified into a LSG group. The estimates of the multinomial logistic regression show that the probability of being in a SDD group increases as the values of a processing speed and a language decreasing (odds ratio=0.340 and 0.540, respectively). When a LSG group is the reference group, having lower processing speed (odds ratio=0.513) and language (odds ratio=0.640) increased the estimated odds of being a SDD group student compared to other groups. When a SDD group is set up as a reference, when the values of a processing speed (odds ratio=1.950) and a language (odds ratio=1.562) increase, the probability that students belong to a LSG group increases. Attention and nonverbal reasoning are not related to group contrasts. In research Question 3, the different growth patterns and cognitive abilities among subtypes of students with difficulties in word problem solving were explored. Based on the hypothesis that students would have different cognitive characteristics depending on whether they have difficulties in computation, in reading, in both computation and reading, or in neither computation nor reading, multivariate analysis of variance (MANOVA) was used to explore their differences on cognitive abilities. For group formation, 25th percentile and 40th percentile were selected as cutoffs and four subgroups were identified by difficulty status – word problem solving difficulty (PD), computational difficulty with word problem solving difficulty (CPD), reading difficulty with word problem solving difficulty (RPD), computational and reading difficulty with word problem solving difficulty (CRPD). Observed mean trajectories revealed CPD, RPD, and CRPD showed significantly lower growth levels compared to PD. CRPD showed the lowest growth levels among the four groups. Significant differences between PD and RPD were found in working memory, processing speed, language, and nonverbal reasoning. Working memory, processing speed, and language between PD and CRPD, and working memory and language between CPD and RPD/CRPD were significantly different. No difference in attention was found in any contrast. In neither PD versus CPD, nor RPD versus CRPD, were cognitive profile differences found.I. INTRODUCTION 1 1.Statements of Purpose 1 2.Research Questions 14 3.Definition of Terminology 15 II. LITERATURE REVIEW 18 1.Cognitive abilities related to mathematics learning and mathematics learning disabilties 18 2.Cognitive abilities involved in word problem solving 26 3.Prospective approach to identification of learning disabilties: The intrinsic processing deficit model 32 III. METHODOLOGY 36 1.Subjects 36 2.Measures 39 3.Procedure 47 4.Data Analysis 50 IV. RESULTS 60 1.Descriptive Statistics 60 2.Preliminary anlayses: Normality test and analysis of overall growth pattern of word problem solving skills 62 3.Research question 1: Identifiable subgroups based on growth patterns 65 4.Research question 2: Relationship between growth patterns and cognitive abilities 75 5.Research question 3: Cognitive characteristics of students with difficulties in word problem solving 83 V. DISCUSSION 94 1. General Discussion 96 2. Limitations 108 VI. REFERENCES 111 국 문 요 약 142Docto

Measuring Number Sense for Early Identification of Learning Disabilities in Math: A Review of Literature

수학학습에서의 심각한 문제를 예방하기 위해서 수학학습장애 위험아동을 조기 판별하여 적절한 조기 중재를 제공하고 형성평가를 통해 진전도를 모니터링 하는 것이 필요하다. 최근 수학학습장애 조기 판별 관련 연구에서는 수감각을 주요한 변인으로 다루고 있다. 이는 수감각이 수학학습장애 위험아동을 선별할 수 있는 기준으로 사용될 수 있다는 여러 연구 결과에 기초한 것이며, 이를 바탕으로 수감각을 기반으로 하는 다양한 검사가 개발되었다. 수감각의 정의에 대해서는 연구자들마다 의견이 다르지만, 수감각이 무엇이고 어떤 특성이 수감각을 이루고 있는지에 대해서는 점차 의견의 일치를 이루고 있다. 이에 본 연구에서는 선행 연구에서 제시된 수감각의 정의 및 특징을 살펴보고, 이를 바탕으로 개발된 여러 가지 수감각 검사들을 분석하여 우리나라 교육 현장에서 유용하게 사용될 수 있는 수감각 검사의 개발 필요성 및 활용 방안에 대해 탐색해 보고자 한다. Although the ability of mathematics has been emphasized during the last two decades, a number of children still struggle with math problems in school. Since the math ability develops hierarchically, early identification of at risk children is important to prevent severe failure later on. For early identification of at risk children in mathematics, we need to examine informal knowledge, such as early numeracy. These early numeracy skills are often represented as number sense. Many researchers reveal that the outcome of informal early mathematics instruction is number sense. Although there are some disagreements among researchers about the conceptual definition of number sense, number sense is understood as skills that provide a foundation for the acquisition of later mathematical abilities, and are resulted from experiences acquired prior to school entry. Thus, there are some measurements of number sense, but still these instruments have problems of administrating to children and identifying at risk children with learning difficulties. In present study, we reviewed literatures for investigating what the number sense is and which tests are developed and used for children. Throughout literature reviews, we revealed what characteristics of the measurement are for identifying at risk children with learning difficulties in math. These characteristics could be a foundation of developing test for early identification and intervention in Korea. Key words: Mathematics, Learning Disabilities, Early Identification, Measurement, Number Sens

Comorbidity of Attention-Deficit/Hyperactivity Disorder(ADHD) and Learning Disabilities(LD): The Present and The Future

논문 요약본 연구는 교육현장에서 관심이 증대되고 있는 주의력결핍과잉행동장애(ADHD)와 학습장애의 공존장애에 관한 연구가 어떻게 진행되어 오고 있는지를 살펴보고자 하였다. 먼저, ADHD/학습장애 공존장애의 특성, 예후, 원인에 대해 살펴보았고, 공존장애집단을 ADHD나 학습장애 단독집단과 구분하여 판별해야할 필요성을 논의하였다. 다음으로, ADHD와 학습장애 및 ADHD/학습장애 공존장애 평가 및 판별체계의 문제점을 논의하였고, 공존장애집단을 일차적으로 판별하고 이들의 어려움을 근거리에서 중재할 수 있는 일차적인 현장인 공교육 현장에서 ADHD/학습장애 공존장애 평가 및 판별을 통한 연구가 이루어지지 않고 있다는 문제점을 제기하였다. 이후 공교육현장에서 활용될 수 있도록 ADHD/학습장애 공존장애에 대한 다면적인 평가체계에 대한 필요성을 제기하였으며, 마지막으로 중재, 판별 및 진단, 연구방법 등 후속 연구에 대한 시사점을 논의하였다. This study attempts to grasp the progress of the rising topic in a public school setting, the comorbidity of Attention-Deficit/Hyperactivity Disorder(ADHD) and Learning Disabilities(LD). First, we examined the characteristics, prognosis and cause of comorbidity of ADHD/LD, then we discussed the need that the comorbidity group should be identified with ADHD or Learning Disability in separate group. Afterwards, we debated about the problems of assessment and identification system on ADHD, Learning Disabilities and comorbidity of ADHD/LD, specifically focusing on lack of researches in regard to assessment and identification of comorbidity of ADHD/LD in a public school setting where is the very first place to identify the group of comorbidity of ADHD/LD and to mediate the students suffering from ADHD and learning disabilities in comorbidity group together. Finally, we suggested need for the multimodal assessment system of comorbidity of ADHD/LD that can be used in a public school setting, and then the future directions for following research concerning the diagnosis, identification, intervention and methods for research are suggested.The work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (No. R01-2008-000-20528-0

The Exploratory Study for Screening and Identification Processes of Learning Disabilities at Special Education Support Center: Focused on Current Condition and Improvement Method

최근 학습장애 선정 조건 및 절차(교육과학기술부 특수교육지원과-2677)가 2010년 5월에 각급 학교로 전 달된 것은 우리나라에서도 학습장애를 선별, 진단함에 있어 RTI가 도입됨을 의미하나 실제 현장에서 RTI 모델 이 적용가능한가에 대한 많은 의문점이 제기되고 있다. 본 연구에서는 11개 지역 교육청 특수교육지원센터를 대상으로 한 설문 조사를 통해, 2010년 이후로 현 지침을 시행하는 데 있어 어려움과 개선점을 파악하였다. 1단 계에서는 중재반응 평가결과 및 증빙자료의 신뢰성 문제, 소집단 교수 불명확성, 학습장애 위험아동 상시의뢰과 정 필요성, 특수교사와 일반교사의 협력 문제, 2단계에서는 한정된 진단검사도구, 일선학교와 특수교육지원센터 간 협력체계, 특수교육운영위원회의 역할규명 문제가 제기되었다. 이를 위해 충분한 교사 및 전문가 교육, 효과 적인 증거기반 중재 프로그램의 개발 및 제공, 일선학교 교사들과의 협조 및 검사도구의 확대 보급이 필요하다. In recent years, document containing identification conditions and procedures for decision making of learning disabilities (LDs) within a Response to Intervention (RTI) framework has been delivered to schools. In this study, we examined difficulties and things to be improved with respect to the guidelines on the identification of LDs, based on the questionnaire answers of teachers at the center for special education support. As for the difficulties, reliability of assessment data result as well as proof documents, uncertainty about the small group instructions, the need of direct referral procedure for children at risk, and the cooperation of general and special educators were raised for the step 1, while limited assessment tools, cooperating system between schools and the support center, and the role examination of the steering committee for the special education were proposed for the step 2. Based on these problems, the support center personnels argued these things to be improved: 1) teacher and specialist training to get accustomed to the assessment and the identification process, 2) developing and providing the effective intervention programs to deliver the evidence-based practices, and 3) cooperation with teachers at school.본 연구는 2011년도 정부(교육과학기술부, 기초연구지원 인문사회 일반연구)의 재원으로 한국연구재단의 지원을 받아 연구되었음(NRF-2011-32A-B00194)

Validation of Global Talent Indicator (GTI) for Adolescents II : Testing of Group Invariance Between Male and Female Students

본 연구는 청소년 GTI(Global Talent Indicator) 검사의 타당성을 확보하기 위하여, 하위 요인인 개인내 역량 요인과 개인간 역량 요인의 상관을 가정하여 분석하였으며, 남녀집단간 동등성을 검증하였다. 연구 결과 검사의 두 하위 요인인 개인내역량과 개인간역량은 서로 유의한 상관을 가지고 있었다. 또한 요인 구조 및 부하량, 측정 변수 절편, 잠재변수 공분산 검증에서 남녀 집단간 동등성을 수용할 수 있었다. 이는 GTI 검사의 요인구조와 부하량, 측정변수 절편은 남녀 집단간 안정적으로 동등하게 나타나기 때문에 남녀 간 공통 규준을 사용할 수 있다는 실제적인 의의가 있다. The purpose of this study was to validate the Global Talent Indicator. For this purpose, a strong relationship between inter-individual competence and intra-individual competence was proposed and tested through a confirmatory factor analysis. In addition, multi-group confirmatory factor analysis was performed to test factor invariance, metric invariance, scalar invariance and invariance of structural covariance across female and male students. The results indicated followings. First of all, a correlation of inter-individual competence and intra-individual competence was high(.93) and the new model's fit index was appropriate. Second, a result of multi-group confirmatory factor analysis showed factor invariance, metric invariance, scalar invariance and invariance of structural covariances across female and male students. It indicated when using norm and interpreting test results, common norm and factor structure could be applied to both female and male.본 연구는 서울대학교 산학협력연구 (700-20100008)에 의하여 수행되었습니다

Validation of Global Talent Indicator (GTI) for Adolescents

본 연구는 글로벌 인재역량 (Global Talent)의 특성을 확인하고, 글로벌 인재의 구성요소를 추출한 후, 이를 이용하여 초기 청소년기의 글로벌 인재 역량을 탐색하기 위한 목적으로 수행되었다. 이러한 연구목적을 달성하기 위하여 글로벌 인재 역량의 정의를 제안하고 검사를 개발하며, 개발한 검사를 타당화 하였다. 먼저 문헌분석을 통해서 글로벌 인재의 관련 개념을 확인하고, 구인을 확인한 후, 초등학교 4, 5, 6 학년, 중학교 1, 2학년까지 의 초기 청소년기의 학생을 대상으로 자료를 수집한 후 타당화 작업을 수행하였다. 연구 결과에 따르면, 글로벌 인재 역량의 구인은 비전, 자기주도성, 창의성, 시민의식, 감성지능, 문화지능, 대인관계능력으로 확인되었다. 신뢰도 분석과 상관관계 분석 및 구조방정식을 이용한 타당도 분석에 따르면 글로벌 인재역량 검사는 초기 청소년들의 글로벌 역량 특성을 합당하게 반영하는 것으로 밝혀졌다. 또한, 이러한 결과를 바탕으로 향후 글로벌 인재 역량에 대한 후속 연구의 가능성과 사회적 함의를 제시하였다. The purpose of this study was to define and extract components of Global Talent, and to develop and validate the Global Talent Indicator. For this purpose, preliminary concepts were reviewed and derived from the previous studies. Two pilot studies were conducted. Through the pilot studies, the items were revised. Exploratory factor analysis was executed and identified 8 factors. The validation study was conducted with 1,855 students ranging from 4th to 8th graders. The validities of the GTI was examined through correlation, reliability, and confirmatory factor analysis. The Global Talent Indicator consisted of 8 factors. The factors were Vision, Self-Leadership, Creativity, Citizenship, Emotional intelligence, Cultural intelligence, Interpersonal competence, and Cognitive abilities. Lastly, implications for further research on Global Talent Model were discussed. Key words: Global Talent, Vision, Self-Leadership, Creativity, Citizenship, Emotional intelligence, Cultural intelligence, Interpersonal competence, and Cognitive abilitie

Learning Disabilities in Korea: A Synthesis of Researches from 1999 to 2008

본 연구는 국내의 학습장애 연구에 대한 문헌분석을 통해 현재 국내 학습장애의 전반적인 연구 동향을 파악하고, 이에 따른 시사점을 제공하며, 향후 연구에 대한 방향을 모색해보고자 하였다. 이를 위해 1999년부터 2008년까지 발표된 연구 총 289편을 분석하였다. 국내 학습장애 연구의 분석결과를 요약하면 다음과 같다. 첫째, 특성에 관한 연구는 학습장애와 읽기장애의 특성, 특히 그 인지적 특성에 관한 연구에 편중되어 이루어져왔다. 둘째, 정의와 진단 및 판별에 있어 대부분의 연구들이 학습장애의 정의와 진단 및 판별과 관련하여 이루어졌으며, 연구들은 주로 현재의 정의와 진단 및 판별에 있어서의 문제를 지적하고 새로운 대안을 제시하고 있다. 셋째, 학습장애와 관련하여 중재 영역의 연구가 가장 많이 이루어졌으나 세부 영역별로 편중되어 있고, 개별 중재에 대해 반복 연구가 부족한 경향을 나타내었다. 넷째, 이 밖에 학습장애와 관련한 연구로는 학습장애에 대한 인식 및 해외의 학습장애와 관련한 사례를 제시하고 있는 논문들이 있었다. 논의에서는 이러한 분석결과에 대한 제언을 포함, 2년 단위로 한 연구 경향 분석을 제시하였다. 그 결과, 2000년대 초반까지는 주로 학습장애의 특성, 정의와 진단 및 판별, 중재 및 치료에 관한 연구가 활발하게 이루어진 반면, 2000년대 후반에 접어들면서 그 경향이 완만한 하향세를 띄며, 생물학적 연관성이나 기타의 측면에 대한 관심이 차츰 생겨나고 있음을 알 수 있었다. 그리고 학습장애의 하위 영역 중 비언어적 학습장애, 학습장애 공존장애, 학습장애 영재에 대한 연구가 좀 더 수행될 필요성에 대해서 언급하였다. The purpose of this study was to find out the recent trends of researches in Korea by synthesizing findings of students with learning disabilities, in order to provide implications for future directions. 289 studies published between 1999 and 2008 were examined. The results of the present study were as follows. First, studies on characteristics of learning disabilities have been mostly conducted in conjunction with reading disabilities, specially focusing on cognitive characteristics of reading disabilities. Second, studies on definition, diagnosis and identification of learning disabilities point out problems of these areas and propose the alternatives. Third, it was found that the majority of research on learning disabilities in Korea has been dedicated to examine the effects of an intervention on students with learning disabilities. However, studies on intervention of learning disabilities have been conducted under a biased towards specific area, and showed the lack of replication studies on each intervention. Fourth, additionally there were studies on awareness on learning disabilities and foreign case studies. As the results, while studies on characteristic, definition, diagnosis/identification, intervention/treatment of learning disabilities until early 2000's were mainly conducted, it showed a tendency to decrease in late 2000's and interests on the biological and other aspects start to increase. It was suggested the future directions for research toward nonverbal learning disabilities, comorbidity of learning disabilities, and the gifted learning disabilities