Earticle

This study explored how three second-grade middle school students approached real-life contextual word problems, using Schoenfeld’s (1985) problem-solving framework of resources, heuristics, control, and beliefs. A qualitative case study design was adopted. The students’ problem-solving processes were video-recorded and analyzed through transcripts and follow-up interviews. Although all three students were aware of the mathematical knowledge needed to solve the problems, clear differences appeared in how they organized their knowledge, chose and applied strategies, monitored their work, and viewed problem solving. These differences became especially evident in a high-level task that required students to check and adjust their strategies. The findings suggest that success in solving real-life contextual word problems depends not only on what students know, but more importantly on how they use that knowledge. Heuristics guide the use of resources, control regulates the process, and beliefs support or constrain these actions. Therefore, students’ errors or unrealistic responses should not be seen simply as cognitive weaknesses, but as the result of interactions among these problem-solving components.

본 연구는 고위험 산모 시뮬레이션 교육을 받은 간호대학생의 메타인지, 학습몰입이 문제해결과정 에 미치는 영향을 파악하고자 하였다. 연구대상은 고위험 산모 시뮬레이션 교육을 경험한 간호학과 학생 125명을 대상자로 하였고 SPSS 29.0 프로그램을 사용하여 기술 통계, t-검정, 분산 분석, Pearson’s 상관 계수, 회귀 분석을 실시하였다. 연구 결과, 메타인지, 학습 몰입, 문제 해결 과정이 평균보다 높았으며, 메타인지는 학습몰입(r=.55, p<.001), 문제해결과정(r=.66, p<.001)과 유의한 상관 관계가 있었고 학습몰입과 문제해결과정도 유의한 정적 상관(r=.68, p<.001) 가 있었다. 문제해결과정에 영향을 미치는 요인은 메타인지, 학습몰입이었으며, 이들 변수의 총 설명력은 57.2 %로 나타났다. 결론적으로 간호대학생의 학습몰입과 메타인지를 강화하여 문제해결과정을 향상시킬 수 있을 것으 로 사료된다.

This study aimed to examine the effects of metacognition and learning flow on the problem-solving process among nursing students who received high-risk pregnancy simulation education. The participants were 125 nursing students who had experienced high-risk pregnancy simulation education. Data were analyzed using SPSS 29.0. and Descriptive statistics, independent t-tests, one-way analysis of variance (ANOVA), Pearson’s correlation coefficients, and regression analysis were conducted. The results showed that the levels of metacognition, learning flow, and problem-solving process were above average. Metacognition was significantly correlated with learning flow (r = .55, p < .001) and the problem-solving process (r = .66, p < .001). Learning flow was also significantly positively correlated with the problem-solving process (r = .68, p < .001). The factors influencing the problem-solving process were metacognition and learning flow, and these variables explained 57.2% of the variance. In conclusion, strengthening learning flow and metacognition may contribute to improving the problem-solving process among nursing students.

이 연구에서는 데이터를 기반으로 하여 대기대순환, 해류 순환에 관한 STEAM 교육프로그램을 제작하고 이 를 고등학교 1학년 106명을 대상으로 적용하여 그 효 과와 문제해결과정을 분석하고자 하였다. 이를 위해 데 이터를 수집, 정제, 시각화, 분석하고 이러한 결과를 기 반으로 의사소통 과정을 진행할 수 있도록 하는 프로그 램을 구성하였다. 이를 활용하여 일상생활에서의 순환 에서 전 지구적인 관점에서 나타나는 순환으로의 개념 을 확장하여 전 세계적으로 발생하는 순환에 관한 문제 를 확인할 수 있도록 하였다. 프로그램의 투입 결과 지식 정보처리역량과 그 하위 영역에서 유의미한 변화가 확인 되었으며. STEAM 핵심역량과 STEAM 핵심역량의 하위 영역인 융합, 창의 역량에서 유의미한 변화를 확인하였 다. 또한 학생들의 응답을 텍스트 네트워크의 형태로 분 석하여 데이터 기반 STEAM 교육에 대한 제안할 점을 얻고자 하였다.

In this study, STEAM program on the subject of ‘atmospheric circulation and surface current’ was produced based on data and applied to 106 first-year high school students to analyze its effect and problem-solving processes. This program was organized to collect, refine, visualize, and analyze data and to allow communication processes to proceed based on these results. Using this, the concept of circulation in daily life was expanded from a global perspective to identify problems about circulation around the world. As a result of the application of the program, significant changes were identified in knowledge information processing competency. Also, significant changes were made in terms of convergence and creativity, which are sub categories among STEAM core competencies. It also sought to obtain suggestions for data-based STEAM education by analyzing students' responses in the form of a Text network.

A creative innovation and an innovative problem-solving of industrial companies can be achieved by overcoming the challenges of technical and physical contradictions. The approaches to address conflicting and paradoxical problems, such as technical and physical contradictions have a crucial role in advancing the quality assessment for manufacturer and service provider. The term, technical contradiction, depicts the state that improvement of one ends of IFR (Ideal Final Result) leads to unfavorable condition of the other ends, and results in conflicting problem. Another type of contradictions that’s discussed in this study is a physical contradiction which is due to two mutually opposing states of the means of ends, and gives paradoxical situation. By integrating the means-ends chain perspectives, the physical contradiction that is a specifically root-causes, “means”, can be initially addressed to resolve the downstream problem of technical contradiction which represents a general and abstract goals, “ends”. This research suggests IFR resolution processes to handle both physical contradiction of means and technical contradiction of ends by employing causal relationship with IFR, effects and causes. In summary, the study represents three major processes that resolve such contradictions are demonstrated as follows: 1) Derivation of causal and hierarchical relationship among IFR, ends and means by considering CAED (Cause-And-Effect Diagram) and LT (Logic Tree). 2) Identification of causal relationship between physical contradiction and technical contradiction by using TPCT (TRIZ Physical Contradiction Tree) and TCD (Technical Contradiction Diagram). 3) Application of integrated TRIZ principles by classifying 40 inventive principles into 4 general conditions of the separation principle of mutually opposite states in space, in time, based on conditions, and between the parts and the whole. In order to validate the proof of proposed IFR resolution processes, the analysis of the TRIZ case studies from National Quality Circle Contest in the years, 2011 to 2014 have been proposed. The suggested guidelines that are built based on TRIZ principles can uniquely enhance the process of quality innovation and assessment for quality practitioners.

수학 문제해결 교육 연구에 있어서 문제해결 과정에 나타나는 인지적, 정의적 요소 의 상호작용 및 메타정의적 측면에 대한 연구의 비중이 점차 증가하고 있다. 이에 본 연구에서는 수학 학습 성취 수준에 따라 초등학생의 문제해결 과정에 작용하는 메타정의의 기능적 특성을 파악하기 위하여 빈도 분석과 사례 분석을 병행하였다. 수학 학습 성취 수준에 따라 협업적 문제해결 활동에서 나타나는 메타정의 출현 빈도, 메타정의 유형별 빈도, 메타정의의 메타적 기능 유형별 빈도를 비교 분석하 였다. 또한, 수학 학습 성취 수준별 메타정의의 메타적 기능 유형별 사례의 분석을 통하여 메타정의의 실제적인 작용 메카니즘을 파악하였다. 그 결과, 수학 학습 성 취 하 수준 집단의 문제해결 과정에서 상 수준 집단에 비해 메타정의의 출현 비율 이 상대적으로 높았으며, 상 수준 집단의 메타정의는 하 수준 집단에 비해 상대적 으로 다양한 유형의 메타적 기능으로 작용하였다. 이와 같은 연구 결과로부터 수학 문제해결 수업에 적용해 볼 수 있는 메타정의의 기능적 특성과 관련한 교육적 시 사점을 도출하였다.

Since the mathematics learning achievement level is closely related to problem-solving ability, it is necessary to understand the relationship between problem-solving ability and meta-affect ability from the point of view of general mathematics learning ability. In this study, we compared the frequency analysis and the case analysis of the functional aspects of the meta-affect in elementary school students' problem-solving processes according to mathematics learning achievement level in parallel with frequency analysis and case analysis. In other words, the frequency of occurrence of meta-affect, the frequency of meta-affective type, and the frequency of meta-functional types of meta-affect were compared and analyzed according to the mathematics learning achievement level in the collaborative problem-solving activities of small group members with similar mathematics learning achievement level. In addition, we analyzed the representative cases of meta-affect by meta-functional types according to the mathematics learning achievement level in detail. As a result, meta-affect in problem-solving processes of the upper level group acted as relatively various types of meta-functions compared to the lower level group. And, the lower level group, the more affective factors acted in the problem-solving processes.

교과서에서 사용되는 문제는 주로 정형화된 폐쇄형의 문제로 학생의 문제해결력을 육성하거나 학생의 자주적인 학습을 촉구하는데 제한적이다. 본 연구는 문제해결력을 육성하기 위해 개방형 문제를 해결해가는 과정을 폴리아의 문제해결단계를 따라 학생에게 나타나는 학습변화를 관찰하였다. 학생은 문제를 더욱 신중히 읽고 이해하는 과정에서 단순화하였고 계획수립과정에선 처음엔 익숙하지 않았지만 다양한 방법으로 해결하려는 시도와 체계적으로 되돌아보는 인지과정을 나타냈으며, 실행과정에서는 오류를 통한 계획수립의 재시도가 일어나 통제가 향상되는 과정을 보였다. 반성단계는 점검만하는 수준을 벗어나 다른 해결방법을 무엇인지 등의 반성단계의 필요성을 인식하였고 개방형문제의 실생활 적용과 일반화하는 과정을 통해 문제 해결력이 더욱 향상됨을 알 수 있었다.

This study is to investigate student's processes of problem solving using open-ended Geometric problems to understand student's thinking and behavior. One 8th grader participated in performing her learning in 5 lessons for June in 2006. The result of the study was documented according to Polya's four problem solving stages as follows: First, the student tended to neglect the stage of "understanding" a problem in the beginning. However, the student was observed to make it simplify and relate to what she had teamed previously Second, "devising a plan" was not simply done. She attempted to solve the open-ended problems with more various ways and became to have the metacognitive knowledge, leading her to think back and correct her errors of solving a problem. Third, in process of "carrying out" the plan she controled her solving a problem to become a better solver based on failure of solving a problem. Fourth, she recognized the necessity of "looking back" stage through the open ended problems which led her to apply and generalize mathematical problems to the real life. In conclusion, it was found that the student enjoyed her solving with enthusiasm, building mathematical belief systems with challenging spirit and developing mathematical power.

이 연구의 목적은 CPS에서 사용되고 있는 발산 행위와 수렴 행위 테크닉을 PR 기획 과정에 활용하여 그 효과를 실험을 통해 검증하고자 하는 것이다. 실험을 위해 CPS 테크닉을 활용한 PR 기획 과정을 개발하여 D대학교에서 한 학기 동안 “PR 캠페인” 과목을 수강하는 학생들을 대상으로 실험하였다. 연구 결과에 의하면 CPS 테크닉을 활용한 PR 기획 과정은 참가자들의 PR 문제 발견 능력, PR 문제 해결을 위한 아이디어 생성 능력, PR 문제 해결 능력 증진에 효과가 있는 것으로 나타났고, 참가자들의 만족도 향상에도 효과가 있는 것으로 나타났다. CPS 테크닉인 발산 행위와 수렴 행위를 활용한 PR 기획 과정은 각 단계별 목표를 달성하기 위한 의사 결정 과정이 포함되어 있어 PR 실무자들이 PR 프로그램 및 캠페인을 위한 효과적인 PR 기획을 하는 데 도움이 될 것이며, 이 분야에 대한 지속적인 연구가 요구된다.

The purpose of the study is to test effects of public relations planning processes using creative problem solving (CPS) techniques, divergent and convergent activities. A public relations planning process was developed and tested to students who took a public relations planning course titled, “Public Relations Campaign.” The results of the research indicated that the PR planing process using CPS techniques was effective in improving participants' PR problem finding ability, idea generation ability, PR problem solving ability, and satisfaction levels. Therefore, if public relations practitioners were to apply these CPS techniques to their PR planning as decision procedures, the effects of their public relations programs and campaigns could be increased.

This paper presents a critical overview of some recent attempts at building formal models of organizations as information-processing and problem-solving entities. We distinguish between two classes of models according to two distinct objects of analysis. The first class includes models mainly addressing information processing and learning; the second class includes models focusing upon the relationship between the division of cognitive labor and search process in some problem-solving space. The results begin to highlight important comparative properties regarding the impact on problem-solving efficiency and learning of different forms of hierarchical governance, the dangers of lock-in associated with specific forms of adaptive learning, the relative role of “online” vs. “offline” learning, the impact of the “cognitive maps” which organizations embody, the possible trade-offs between accuracy and speed of convergence associated with different “decomposition schemes,” the (ambiguous) role of organizational memory in changing environments.

학생들의 실생활 문제 해결력을 향상시키는 시도의 일부로써, 비구조화된 문제 상황에서 문제발견과 문제해결을 경험하고 학습하게 할 필요가 있다. 선행연구에서 문제발견에 대한 여러 변인 사이의 관계를 분석하였는데, 비구조화된 문제 상황에서 문제발견 활동의 지도를 위해서는 이러한 연구뿐만 아니라, 실생활 상황에서 과학적 문제발견 과정에 대한 연구가 필요하다. 이 연구에서는 수행 평가를 통해서 비구조화된 문제 상황에서 문제를 발견하고 해결한 경험을 가진 고등학생들 중 6명을 심층 면담한 결과를 분석하였다. 학생들은 비구조화된 문제 상황에서 문제발견과 문제해결을 위해 정보를 탐색하는 작업을 반복적으로 수행하였다. 이러한 과정에서 학생들은 신뢰할 수 있고 적합한 자료 선별에 어려움을 느꼈다. 따라서 교사가 비구조화된 과학적 문제 상황에서 문제발견과 해결에 대한 안내를 할 때, 학생이 어렵게 느끼는 정보 선별에 대한 연구가 필요하다.

The purpose of this study was to analyze the steps of process, in which high school students did the problem-finding and problem-solving under ill-structured scientific problem situation. Most situations of daily life are ill-structured. Therefore, it is necessary to investigate how the students take an approach for scientific problems and solve the problems in the ill-structured situations. In this study, the problem-finding and problem-solving processes were analyzed by high school students under the ill-structured situations based on the qualitative approach. One task of scientific problem finding in the ill-structured problem situation was assigned to 208 high school students; later, 6 of them participated in the research through interviews. Results indicated that the students searched for the information repeatedly in order to do the problem-finding and problem-solving under the ill-structured problem situations, in which they had difficulty selecting reliable and appropriate information.

본 연구는 유아 수학 문장제 문제해결 과정에서 유아가 사용하는 문제해결 전략 및 오류유형이 관련 변인들(성별, 연령, 언어능력, 연산능력)에 따라 차이가 있는지를 살펴보는데 목적이 있다. 이를 위하여 D광역시와 G도의 유치원과 어린이집에 다니는 만 4∼6세 유아 346명을 대상으로 연구를 실시하였다. 연 구결과 첫째, 연령과 성별에 따른 수학 문장제 문제해결 전략은 덧셈과 뺄셈 모두에서 유의미한 차이가 있었으며, 오류유형은 성별은 뺄셈에서, 연령은 덧셈과 뺄셈 모두에서 유의미한 차이가 있었다. 둘째, 언 어능력과 연산능력에 따른 문제해결 전략은 덧셈과 뺄셈 모두에서 유의미한 차이가 나타났으며, 언어능 력과 연산능력에 따른 오류유형도 덧셈과 뺄셈 모두에서 유의미한 차이가 있었다. 유아가 수학 문장제 문 제를 해결하는 과정에서 나타나는 문제해결 전략과 오류유형의 정보를 제공하는 본 연구결과는 개별 유 아의 발달에 적합한 수학 문장제 학습 방안과 지도방법 모색의 기초 자료를 제공한다.

The purpose of this study was to examine children’s mathematical word problem solving processes according to the affecting variables (gender, age, language abilities, and computation abilities). The participants of this study were 346 children aged four through six, enrolling day-care centers or kindergartens in D or G cities. The study results were as follows. First, children’s mathematical word problem solving strategies used in subtraction questions showed significant differences according to age and gender. Significant differences were also observed in error types according to gender as were in all types of addition and subtraction questions according to age. Second, both children’s mathematical word problem solving strategies and error types showed significant differences in solving all types of addition and subtraction questions according to language abilities and computation abilities.

본 연구에서는 '힘과 운동'에 관한 문제들을 충동성-사려성의 인지양식을 가진 해결자가 어떻게 해결하는가를 해결과정분석을 통해 비교해보고자 하였다. 여자고등학교 1학년 학생을 대상으로 1학기 성적이 상위 10%에 들어가고 역학문제 성취도가 높고, 인지양식검사에서 충동성과 사려성이 강하게 나타나는 학생들 8명을 선정하였다. 학생들에게 발성사고법을 연습시키고, 해당내용을 복습하게 한 다음, 여섯 문제를 풀게 하였다. 마지막 만남에서는 회상적 면담을 하였고, 해답에 대한 자신감, 문제의 친밀도와 선호도를 조사하였다. 연구 결과, 더 풍부한 물리적 지식을 보유하고 있는 충동적인 학생들이 그렇지 못한 사려적인 학생들 보다 더 많이 문제해결에 성공하였고, 사려적인 학생들은 천천히 주의 깊게 수행하였으므로 문제해결에 더 많은 시간이 걸렸다. 특히 이해, 실행, 검증 단계에 더 많은 시간을 사용하였다. 그리고, 문제해결에 있어서 단계를 반복하는 것은 충동적인 학생에게서 더 많이 나타났다. 그들은 첫 번째 아이디어에 집착하는 경향이 있었다. 충동적인 학생들은 사려적인 학생들보다 문제를 더 생소해 했으나, 자신감이나 선호도에는 차이가 없었다.

The purpose of this study was to analyze physics problem solving processes according to students' cognitive style in the area of 'Force and Motion' at high school level. Students who have already learned t e area of 'Force and Motion' during the first semester of the 10th grade have taken physics test and cognitive style test to choose students who have basic knowledge of physics and reflective or impulsive style. Four students who got over 19 points in the cognitive style test were selected as reflective students, and another four students who got below 12 points were selected as impulsive students. After explaining the purpose and procedure of this study, think-aloud method was introduced to the students, and the students practiced it. After that, the students solved three quantitative and qualitative problems each. Then, the questionnaire on the belief system on physics and physics problem solving and prerequisite knowledge test were also administered. By recording the students' problem solving processes, protocol was made and analyzed. After solving the problems, the students expressed their confidence, intimacy, and preference on each problem by the five point Likert scale. Impulsive students tended to succeed in solving more problems, less intimate, and more spontaneous and positive in seeking alternative solution when confronted with unacquainted problems. On the other hand, reflective students used more time in executing the problems even without planning, and used more time in solving problems and verification. Whether making effective plan or not was important rather than how much time they used in the planning step. In addition, repeating steps were more likely shown to impulsive students; they tended to be attached to their first idea.

본 연구는 '힘과 운동'에 관한 정량적, 정성적 문제에 따른 문제해결과정을 분석하여 어떤 차이가 있는지를 알아보고자 실시되었다. 본 연구의 대상은 여자고등학교 1학년 학생 8명이었다. 이들은 문제해결에 필요한 내용지식을 보유하고 있는 학생들이었다. 선행 지식검사와 정량적 문제 3개와 정성적 문제 3개로 구성된 본검사를 사용하였다. 연구결과, 정량적 문제에서는 계획단계의 시간비율이 정성적 문제에 비해 더 높고 총 소요시간도 길게 나타났으며, 해결단계의 반복횟수도 더 많았다. 정량적 문제에서 해결에 성공하는 정도는 정성적 문제에서 별 차이가 없었고, 전략사용에도 차이가 없었다. 학생들은 평소 물리학습에서 정량적 문제를 많이 접하므로 수식과 공식을 사용하여 문제 푸는 일에 익숙해 있고, 수식과 공식에 의한 결과를 더 신뢰해서 정성적 문제를 정량적으로 해결하려는 경향이 있었으며, 정성적 문제 보다 정량적 문제를 더 선호하였다.

The purpose of this study was to analyze physics problem solving processes to qualitative and quantitative problems in the area of 'Force and Motion' in high school science. The students who have already learned the area of 'Force and Motion' during the first semester of 10th grade have taken physics test to choose students who have basic knowledge of physics. Eight students were selected. After explaining the purpose and the procedure of this study, think-aloud method was instructed to the students, and the students practiced it. After that, the students solved three problems in each quantitative and qualitative type. Then, the questionnaire of belief system on physics and physics problem solving and the prerequisite knowledge test were administered. By recording the students' solving processes, protocol was made and analyzed. After solving problems, the students expressed their confidence, intimacy, and preference. Quantitative problems needed much time at planning step than qualitative problems did. Moreover, solving time was longer and repeating frequency was more than those of qualitative problems. It seemed because even though the students qualitatively knew the answer, they should determine the given quantitative conditions, consider formulae, and recall the specific numbers. Since the students usually got access to many quantitative items in their physics study, they were accustomed to solve problems by using formulae. In addition, they put confidence in formulae, so they tended to solve problems quantitatively. As the result, they preferred quantitative problems to qualitative problems.

This study analyzed the interaction types exhibited by science education experts while utilizing generative AI, ChatGPT-4, to solve tasks, and explored the characteristics of human-AI interactions based on these findings. The research employed grounded theory methodology to examine interaction data generated during the development of conceptual frameworks for socio-scientific issue learning. Through analyzing the progression of interactions, key features were identified. The findings revealed eight distinct interaction types: Simple Information Request, Simple Task Instruction, Judgment and Selection Request, Product Revision Request, Application and Example Request, Iterative Refinement Request, Insightful Thinking Question, and Context-Driven Task Instruction. Among these, Iterative Refinement Requests and Application and Example Requests were the most frequently used. The study further observed that experts engaged in repetitive and cyclical processes to refine and enhance the outputs generated by the AI. This research highlights the potential of AI as a collaborative partner, transcending its role as a mere information provider. These findings offer a theoretical foundation for refining and systematically utilizing human-AI interactions and are expected to contribute to the development of effective collaboration strategies between humans and AI for more efficient and meaningful outcomes.

Purpose: The aim of this study was to find the effect of collaborative learning on problem-solving processes according to the level of metacognition, after adopting collaborative learning to clinical practice of nursing management. Method: Senior college students participated in this study. 90 students who was involveled in high level metacognitive group and another 88 students in low level metacognitive group. The data was collected from 2003 to 2005. The process of collaborative learning was categorised in 4 steps. The data were analyzed using t-test, ANCOVA, paired t-test. Results: 'There will be a distinction between the low and high metacognition groups after application of collaborative learning' was rejected. 'In the high level metacognitive group, the problem-solving ability will also increase after application of collaborative learning than before application' was supported. 'In the low level metacognitive group, the problem-solving ability will increase after application of collaborative learning than before application' was supported. Conclusion: The results showed that with collaborative learning, the problem-solving ability of learners with different levels of metacognition is improved.

본 연구는 유아가 수학 문장제를 해결하는 과정을 의사결정나무(decision tree) 방법을 통하여 살펴보는 것에 목적이 있다. 연구 참여자는 D광역시와 G도의 유치원과 어린이집의 만 4세에서 6세까지의 유아 186명으로, 어떠한 의사결정 행동이 나타나게 되는 인지적 과정에 관심을 가지는 연구방법인 의사결정나무 방법을 사용하였다. 본 연구결과 문장제 덧셈에서 수학 문장제 문제해결력 상수준의 남·여의 연령은 6년 0개월∼6년 6개월이며 언어·연산능력이 모두 상집단 유아들로 자동인출 전략을 사용하여 정답에 도달하였고, 문제해결력이 하수준의 남·여의 연령은 4년 6개월∼4년 11개월로 언어·연산능력이 모두 하집단 이었다. 한편, 문장제 뺄셈에서 수학 문장제 문제해결력 상수준의 남·여의 연령은 6년 0개월∼6년 6개월로 언어·연산능력이 모두 상집단으로 남아는 자동인출 전략을, 여아는 자동인출과 덜어내기 전략을 사용하여 정답을 맞혔고, 문제해결력 하수준인 남·여의 연령은 4년 6개월∼4년 11개월로 언어·연산능력이 모두 하집단으로 무반응으로 문제해결에 실패하였다. 유아들이 수학 문장제 문제를 성공적으로 해결할 수 있도록 교사는 관련 변인, 전략, 오류유형을 미리 파악하고 이를 보완할 수 있는 적극적인 지원이 필요함을 제안하였다.

The purpose of this study was to examine children‘s mathematical word problem solving processes according to the affecting variables on them, especially by using decision tree analysis. The participants of this study were 346 children aged four through six, enrolling day-care centers or kindergartens in D or G cities. Study findings were as follow. In terms of the addition, both male and female children - aged six years through six years and six months, with high level of word problem solving abilities and language abilities - answered the questions correctly by using a direct-retrieval strategy. In contrast, male and female children - aged four years and six months through four years and 11 months, with both low level of word problem solving abilities and language abilities - reached correct answers by using a counting all strategy. In terms of the subtraction, among the children with high level of language and computation abilities, aged six years through six years and six months, male children solved the problems successfully by using a direct-retrieval strategy, while female children by a direct-retrieval and separate from strategy. Among the children with low level of language and computation abilities, aged four years through four years and 11 months, both male and female children failed to solve the problems by using a no response strategy. These findings suggested that children should be provided with educational environments with a variety of mathematical experiences and therefore they could naturally improve and expand their mathematical abilities and solving strategies through the experiences.

During problem solving, "mathematical thought process" is a systematic sequence of thoughts triggered between logic and insight. The test questions are formulated into several areas of questioning-types which can reveal rather different result. The lower level questions are to investigate individual ability to solve multiple mathematical problems while using "mathematical thought." During problem solving, "mathematical thought process" is a systematic sequence of thoughts triggered between logic and insight. The scope of this case study is to present a desirable model in solving mathematical problems and to improve teaching methods for math teachers.

본 연구의 목적은 학생들의 수학적 사고 스타일에 따른 문제해결과정에서 나타나는 특징을 발견함으로써 교사가 학생에게 다양한 표상을 제공하는 방법론에 대한 시사점을 주는 것이다. 이러한 특징들을 분석하기 위해서 대학교 1학년 학생 202명에게 지필검사를 실시한 후 수학적 사고 스타일을 고려한 4개 그룹으로 분류하여 그룹별로 두 명씩 총 8명에 대해 인터뷰를 실시하였다. 그 결과, 수학적 사고 스타일은 수학적 개념 정의방법, 표상에 대한 문제해결, 표상 간의 번역능력과 관계가 있다고 결론지을 수 있었다. 이러한 결과를 토대로 Dienes의 지각적 다양성의 원리를 구체화하여 향후 교수학습에서 다양한 표상을 제시하는 방법론에 대한 시사점을 줄 것으로 기대할 수 있다.

The purpose of this study is to investigate characteristics of students' problem solving processes based on their mathematical thinking styles and thus to provide implications for teachers regarding how to employ multiple representations. In order to analyze these characteristics, 202 university freshmen were recruited for a paper-and-pencil survey. The participants were divided into four groups on a mathematical-thinking-style basis. There were two students in each group with a total of eight students being interviewed. Results show that mathematical thinking styles are related to defining a mathematical concept, problem solving in relation to representation, and translating between mathematical representations. These results imply methods of utilizing multiple representations in learning and teaching mathematics by embodying Dienes' perceptual variability principle.

본 연구는 시선추적 기법을 활용하여 문제 해결 과정에서 한국어 학습자들의 수준별 읽기 양상을 살펴보는 데에 궁극적인 목적을 두었다. 문제 해결 과정에서 한국어 학습자들의 수준별 읽기 양상은 정의적 차원과 인지적 차원으로 살펴보았다. 정의적 차원에서는 과제집착력을 제시하여 살펴보았고 인지적 차원에서는 문제 해결 과정에서 사용하는 읽기 전략을 살펴보았다. 문제 해결 과정에서 시선추적 기법으로 수준별 한국어 학습자들의 읽기 양상을 살펴본 결과는 다음과 같다. 우선 정의적 측면에서 분석한 결과 텍스트를 꼼꼼히 읽은 집단의 이해도가 꼼꼼히 읽지 않은 집단보다 높은 것으로 나타났다. 즉 이해도가 높은 집단일수록 과제집착력 또한 높은 경향을 보이고 있음을 확인할 수 있었다. 그리고 인지적 측면에서 분석한 결과 한국어 수준이 낮은 학습자일수록 상향적 읽기 전략을 높은 빈도로 사용하고 있었고, 한국어 수준이 높은 학습자일수록 하향식 읽기 전략을 높은 빈도로 사용하고 있는 것으로 나타났다. 초인지 전략 또한 수준이 높은 학습자일수록 높은 빈도로 사용하고 있음을 확인하였다.

The purpose of this study is to investigate the reading patterns of Korean learners in the problem-solving process using eye-tracking technology. This study examined the reading patterns in problem-solving process in terms of the definitional dimension, task-commitment and the cognitive dimension of reading strategies depending on the Korean learner’s levels. The results of the eye-tracking study on the reading behavior of Korean learners at different levels during the problem-solving process are as follows. First, we analyzed the definitional aspect and found that the comprehension level of the group that read the text carefully was higher than the group that did not read the text carefully. In other words, the group with higher comprehension level tends to have higher task- commitment. Second, we analyzed the cognitive aspect and found that the low-level Korean learners used the bottom-up reading strategy more frequently, while the high-level learners used the top-down reading strategy more frequently. The meta-cognitive strategies were also found to be used more frequently by higher-level learners.

The purpose of this study was to analyze the elementary students' mathematical thinking, which is found during mathematical problem solving processes based on mathematical knowledge, heuristics, control, and mathematical disposition. The participants were 8 fifth grade elementary students in Seoul. A qualitative case study was used for investigating the students' mathematical thinking. The data were coded according to the four components of the students' mathematical thinking. The results of the analyses concerning mathematical thinking of the elementary students were as follows: First, in terms of mathematical knowledge, the elementary students frequently used conceptual knowledge, procedural knowledge and informal knowledge during problem solving processes. Second, students tended not to find new heuristics or apply new one, but they only used the heuristics acquired from the experiences of the class and prior experiences. Third, control was found while students were solving problems. Last, mathematical disposition influenced on the mathematical problem solving processes. Teachers need to in-depth observations on the problem solving processes of students, which leads to teachers'effective assistance on facilitating students' problem solving skills.