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How do one expert mathematics teacher in China implement deep teaching in problem-solving and problem-posing classroom: A case study

  • Yanhui Xu
    • Research in Mathematical Education
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    • v.27 no.1
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    • pp.1-24
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    • 2024
  • In this paper, the author analyzed characteristics of deep mathematics learning in problem solving and problem-posing classroom teaching. Based on a simple wrong plane geometry problem, the author describes the classroom experience how one expert Chinese mathematics teacher guides students to modify geometry problems from solution to investigation, and guides the students to learn how to pose mathematics problems in inquiry-based deep learning classroom. This also demonstrates how expert mathematics teacher can effectively guide students to teach deep learning in regular classroom.

An Analysis on the Characteristics of Problem-Finding and the Aspects of Using Science and Technology of Undergraduate Students' Convergence Problem Solving Activity (대학생들의 융합형 문제 해결 활동에서 문제발견 및 과학기술 분야 활용 양상 분석)

  • Baek, Jongho
    • Journal of The Korean Association For Science Education
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    • v.36 no.6
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    • pp.867-876
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    • 2016
  • In accordance with the changing of society, remarkable increase in knowledge and information, the competencies to choose and use proper information in various domains are considered as an important skill. As one of the methods in developing these competencies, it is emphasized that a problem-based learning can make student understand and use knowledge by solving the contextualized problem. However, it is skeptical of learner's development of competencies to use knowledge by solving well-defined given problem. Therefore it is required that students be allowed to develop the competency to find problem through experiences to determine and evaluate the purpose of the problem and method. The purpose of this study is to understand how undergraduate students use science or technology in finding a problem. In this line, this study articulated four cases conducted by participants who engaged in convergence teaching-learning program. And this study investigated the participants' process of problem-finding, method and reason to apply science or technology. The results were drawn by analyzing interviews and written data, including their proposal, a poster, and final reports. Participants changed the form of problem from initial ill-structured one into a concrete one, where the participant could derive a detailed solution. Science or technology applied as the detailed example to convert problem into a concrete form, or as the analyzing tool or theoretical background of problem to make a link with other domain. Their reason of applying science or technology could be summarized in 'personal interest based on prior experience' and 'alternatives to resolve a dissatisfaction.' Based on the result, this study suggests holistic approach that is included in both intuitive thinking and logical thinking and metacognitive regulation to stimulate problem-finding in problem-based learning program.

A Study on the Pattern of usage of Problem Solving Strategy according to Its Presentation (협력 학습을 통한 문제 해결에서 해결 전략의 사용형태에 관한 대화 분석)

  • 정민수;신현성
    • Journal of the Korean School Mathematics Society
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    • v.4 no.2
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    • pp.135-142
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    • 2001
  • The selected questions for this study was their conversation in problem solving way of working together. To achieve its purpose researcher I chose more detail questions for this study as follows. $\circled1$ What is the difference of strategy according to its level \ulcorner $\circled2$ What is the mathematical ability difference in problem solving process concerning its level \ulcorner This is the result of the study $\circled1$ Difference in the strategy of each class of students. High class-high class students found rules with trial and error strategy, simplified them and restated them in uncertain framed problems, and write a formula with recalling their theorem and definition and solved them. High class-middle class students' knowledge and understanding of the problem, yet middle class students tended to rely on high class students' problem solving ability, using trial and error strategy. However, middle class-middle class students had difficulties in finding rules to solve the problem and relied upon guessing the answers through illogical way instead of using the strategy of writing a formula. $\circled2$ Mathematical ability difference in problem solving process of each class. There was not much difference between high class-high class and high class-middle class, but with middle class-middle class was very distinctive. High class-high class students were quick in understanding and they chose the right strategy to solve the problem High class-middle class students tried to solve the problem based upon the high class students' ideas and were better than middle class-middle class students in calculating ability to solve the problem. High class-high class students took the process of resection to make the answer, but high class-middle class students relied on high class students' guessing to reconsider other ways of problem-solving. Middle class-middle class students made variables, without knowing how to use them, and solved the problem illogically. Also the accuracy was relatively low and they had difficulties in understanding the definition.

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A Study of Husband's Problem Drinking on the Wife's Problem Drinking -Focused on the mediating Effect of Spouse Abuse- (남성가구주의 음주가 배우자 음주에 미치는 영향 -배우자 폭력의 매개효과-)

  • Yoon, Myeong-Sook;Cho, Hye-Chung
    • Korean Journal of Social Welfare
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    • v.64 no.2
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    • pp.111-131
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    • 2012
  • Research has consistently reported a strong association between spouse abuse and problem drinking. The primary aim of this study was to examine the role of spouse abuse as mediator between the husband's problem and wife's problem drinking. Data from 1st year Korea Welfare Panel were used for the analysis. Subjects in this study consisted of 3,284 male household who aged between 19 years old and 64 years old. The statistical significance was tested by SPSS 18.0, AMOS 18.0. The findings of the study were as follows: First, husband's problem drinking were significantly affected to the wife's problem drinking. Second, there was a strong association between husband's problem drinking and spouse abuse. Third, spouse abuse worked as mediators between the husband's problem and wife's problem drinking. Based upon these findings we suggest to develop an integrated substance abuse-domestic violence treatment program. The implications and limitations of these findings were discussed, and directions for future studies were also proposed.

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A Comparison of Students' Reasoning Shown in Solving Open-Ended and Multiple-Choice Problems (개방형 문제와 선택형 문제 해결에 나타난 학생의 추론 비교)

  • Lee, Myoung Hwa;Kim, Sun Hee
    • School Mathematics
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    • v.19 no.1
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    • pp.153-170
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    • 2017
  • This study conducted an analysis of types of reasoning shown in students' solving a problem and processes of students' reasoning according to type of problem by posing an open-ended problem where students' reasoning activity is expected to be vigorous and a multiple-choice problem with which students are familiar. And it examined teacher's role of promoting the reasoning in solving an open-ended problem. Students showed more various types of reasoning in solving an open-ended problem compared with multiple-choice problem, and showed a process of extending the reasoning as chains of reasoning are performed. Abduction, a type of students' probable reasoning, was active in the open-ended problem, accordingly teacher played a role of encouragement, prompt and guidance. Teachers posed a problem after varying it from previous problem type to open-ended problem in teaching and evaluation, and played a role of helping students' reasoning become more vigorous by proper questioning when students had difficulty reasoning.

An Analysis of Similarities that Students Construct in the Process of Problem Solving (중학생들이 수학 문장제 해결 과정에서 구성하는 유사성 분석)

  • Park Hyun-Jeong;Lee Chong-Hee
    • Journal of Educational Research in Mathematics
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    • v.16 no.2
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    • pp.115-138
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    • 2006
  • The purpose of this paper is to investigate students' constructing similarities in the understanding the problem phase and the devising a plan phase of problem solving. the relation between similarities that students construct and how students construct similarities is researched through case study. Based on the results from the research, authors reached a conclusion as following. All of two students constructed surface similarities in the beginning of the problem solving process and responded to the context of the problem information sensitively. Specially student who constructed the similarities and the difference in terms of a specific dimension by using diagram for herself could translate the equation which used to solve the base problem or the experienced problem into the equation of the target problem solution. However student who understood globally the target problem being based on the surface similarity could not translate the equation that she used to solve the base problem into the equation of target problem solution.

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Reconsideration of Teaching Mathematics Problem Solving in Elementary School (초등학교 수학과 문제해결 교육 재고)

  • Jeong, Eun-sil
    • Journal of Elementary Mathematics Education in Korea
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    • v.19 no.2
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    • pp.123-141
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    • 2015
  • The purpose of this study is to reconsider of teaching mathematics problem solving in Korea's elementary school through an analysis of mathematics curricula and mathematics textbooks of the elementary school. As a result, it is found that the problem solving had been emphasized continually from the 4th curriculum to the 2009 revised curriculum. However, contents in their textbooks did not reflect the intent of the mathematics curricula properly. And amount of contents related to teaching about problem solving in the textbooks reached the peak in the 6th mathematics curriculum. Then teaching about problem solving had been weakened gradually. And it is also revealed that there had been a movement to change to teaching for problem solving in the textbooks of the 2007 and 2009 revised curricula. Teaching via problem solving had not been carried out appropriately so far.

Simple Solution for Multi-commodity Transportation Problem (복합상품 운송 문제의 간단한 해법)

  • Lee, Sang-Un;Choi, Myeong-Bok
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.13 no.5
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    • pp.173-181
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    • 2013
  • This paper proposes a heuristic optimal solution of multicommodity transportation problem. The proposed algorithm has 3 steps. First the proposed algorithm transforms multicommodity transshipment problem to a general transportation problem, but if the problem is a multicommodity transportation problem, it is not transformed. And the multicommodity is disassembled to a single commodity. Second if it is a multicommodity transportation problem, the algorithm selects the minimum cost according to commodity, on the other hand if it is a multicommodity transshipment problem, the algorithm directly selects the minimum cost based on demand area. And the algorithm assigns carloadings to be satisfied the supply and demand quantity. The algorithm repeats these processes until a given demand quantity is satisfied. Last if it has a condition that is able to reduce the transportation expense, the proposed algorithm controls the assignment quantity of the initial value that got from the step 2. The proposed algorithm was applied to two multicommodity transportation problem and three multicommodity transshipment problem and it got more good result than an existing linear programming method.

An Experiment,11 Study on Implementation of Problem-Oriented Nursing Record (문제제시 간호기록 방법이 간호기록 행위에 미치는 효과에 대한 실험적 연구)

  • 강윤희
    • Journal of Korean Academy of Nursing
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    • v.7 no.1
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    • pp.1-9
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    • 1977
  • Primary function of health record is that as tool of communication between the health processionals with the mutual goal, the promotion of health care standard. Studies have been carried out world over oil tile subject, among those, Weed's Problem-Oriented Health Record is considered a paramount achievement. This study was designed to assess tile possibility of implementing tile problem-oriented health record system through ail experiment in order to provide data for nurse administrators infiltrating reformation of recording system and format. Record of 29 patients admitted at Korea University Hospital, Seoul, from March through June, 1976 for 4 to 14 days were sampled. Nursing notes were recorded by research assistants; senior nursing student trailed extensively by the researcher oil Problem-Oriented Records, oil Problem Oriented Nursing Record format (experimental group) and analysis were carried out comparative, with that of traditional nursing records noted by other nursing personnel (control group) on the same patient. Attitude towards Problem Oriented Nursing Record system and format were attained through questionaries responded by the 51 research assistants. Results are as fellows: Comparative analysis revealed that: 1. Assessment of patients' health problems recorded significantly more in traditional records. 2. Focus of health Problem differed; traditional records slowed significantly higher frequency in medical and procedure as focus while problem oriented records on nursing focus problems. 3. Problem- Oriented records were better organized, Mean value scores of attitude towards Problem- Oriented Records revealed that: Positive value scores on all 4 categories: 1) Assessment of nursing needs, 2) Nursing care planning 3) Patient progress assessment and 4) Tool of teaching and learning revealed that the Problem-Oriented Nursing Record is positively accepted by tile respondents. Recommendation Further experiments on implementation of Problem- Oriented Health Record are recommended: experiment involving all health professionals, in larger scope and longitudinal.

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A Study on Problem-Solving Ability and Classification of Mathematical Problems. (문제 해결력과 수학문제의 분류 관점에 관한 연구)

  • Kim Cheol Hwan;Park Bae Hun;Jung Chang Hyun
    • The Mathematical Education
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    • v.26 no.2
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    • pp.9-13
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    • 1988
  • Mathematics education is generally to cultivate mathematical thought. Most meaningful thought is to solve a certain given situation, that is, a problem. The aim of mathematies education could be identified with the cultivation of mathematical problem-solving ability. To cultivate mathematical problem-solving ability, it is necessary to study the nature of mathematical ability and its aspects pertaining to problem-solving ability. The purpose of this study is to investigate the relation between problem-solving ability and classficational viewpoint of mathematical verbal problems, and bet ween the detailed abilities of problem-solving procedure and classificational viewpoint of mathematical verbal problems. With the intention of doing this work, two tests were given to the third-year students of middle school, one is problem-solving test and the other classificational viewpoint test. The results of these two tests are follow ing. 1. The detailed abilities of problem-solving procedure are correlated with each other: such as ability of understanding, execution and looking-back. 2. From the viewpoint of structure and context, students classified mathematical verbal problems. 3. The students who are proficient at problem-solving, understanding, execution, and looking-back have a tendency to classify mathematical verbal problems from a structural viewpoint, while the students who are not proficient at the above four abilities have a tendency to classify mathematical verbal problems from a contextual viewpoint. As the above results, following conclusions can be made. 1. The students have recognized at least two fundamental dimensions of structure and context when they classified mathematical verbal problems. 2. The abilities of understanding, execution, and looking- back effect problem-solving ability correlating with each other. 3. The instruction emphasizing the importance of the structure of mathematical problems could be one of the methods cultivating student's problem-solving ability.

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