• Title/Summary/Keyword: mathematical problem solving process

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An Analysis of Geometrical Differentiated Teaching and Learning Materials Using Inner Structure of Mathematics Problems (수학 문제의 내적구조를 활용한 기하 영역의 수준별 교수-학습 자료의 분석 연구)

  • Han, In-Ki
    • Communications of Mathematical Education
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    • v.23 no.2
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    • pp.175-196
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    • 2009
  • In this paper we analyze Ziv's geometrical differentiated teaching and learning materials using inner structure of mathematics problems. In order to analyze inner structure of mathematics problems we in detail describe problem solving process, and extract main frame from problem solving process. We represent inner structure of mathematics problems as tree including induced relations. As a result, we characterize low-level problems and middle-level problems, and find some differences between low-level problems and middle-level problems.

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An Analysis of Density Word Problem Solving Ability of Seventh Graders (중학교 1학년 학생들의 농도 문장제 해결력에 대한 분석)

  • Park, Jeong-Ah;Shin, Hyun-Yong
    • The Mathematical Education
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    • v.44 no.4 s.111
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    • pp.525-534
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    • 2005
  • The purpose of this study is to analyze difficulties in the density word problem solving process of seventh graders and to search for the way to increase their problem solving ability in the density word problem. The results of this study could help teachers diagnose students' difficulties involved in density word problem and remedy the understanding of the concept of density, algebraic expressions, and algebraic symbols.

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The Construction of an Abstract Schema in the Similar Mathematical Problem Solving Process (유사 문제 해결 과정에서 추상적 스키마 구성하기)

  • Kang, Jeonggi;Jun, Youngbae;Roh, Eunhwan
    • Journal of the Korean School Mathematics Society
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    • v.16 no.1
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    • pp.219-240
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    • 2013
  • It is the aim of this paper to suggest the method constructing abstract schema in similar mathematical problem solving processes. We analyzed closely the existing studies about the similar problem solving. We suggested the process designing a method for helping students construct an abstract schema. We designed the teaching method constructing abstract schema by appling this process to a group of similar problems chosen by researchers. We applied the designed method to a student. And we could check the possibility and practice of designed teaching method by observing the student's reaction closely.

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The Study on the analysis of Invariance Concept in Secondaty Mathematics Contents (불변성 개념에 관련된 중등학교 수학내용의 분석에 대한 연구)

  • Lee, Sang-Keun;Kim, Tae-Ho;Chung, Ki-Young;Lee, Chun-Goo
    • Communications of Mathematical Education
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    • v.20 no.4 s.28
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    • pp.603-619
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    • 2006
  • One of the most important aims in mathematics education is to enhance students' problem-solving abilities. To achieve this aim, in real school classrooms, many educators have examined and developed effective teaching methods, learning strategies, and practical problem-solving techniques. Among those trials, it is noticeable that Engel, Zeits, Shapiro and other not a few mathematicians emphasized 'Invariance Principle' as a mean of solving problems. This study is to consider the basic concept of 'Invariance Principle', analyze 'Invariance' concept in secondary Mathematics contents on the basis of framework of 'Invariance Principle' shown by Shapiro and discuss some instructional issues to occur in the process of it.

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The analysis of mathematics error type that appears from the process of solving problem related to real life (실생활 문장제의 해결과정에 나타나는 오류유형 분석)

  • Park, Jang Hee;Ryu, Shi Kyu;Lee, Joong Kwoen
    • Journal of the Korean School Mathematics Society
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    • v.15 no.4
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    • pp.699-718
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    • 2012
  • The purpose of mathematics eduction is to develop the ability of thinking mathematically. It informs method to solve problem through mathematical thinking that teach mathematical ability. Errors in the problem solving can be thought as those in the mathematical thinking. Therefore analysis and classification of mathematics errors is important to teach mathematics. This study researches the preceding studies on mathematics errors and presents the characteristic of them with analyzed models. The results achieved by analysis of the process of problem solving are as follows : ▸ Students feel much harder to solve words problems rather than multiple-choice problems. ▸ The length of sentence make some differences of understanding of the words problems. Students easy to understand short sentence problems than long sentence problems. ▸ If students feel difficulties on the pre-learned mathematical content, they feel the same difficulties on the words problems based on the pre-learned mathematics content.

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The Effect of Geometry Learning through Spatial Reasoning Activities on Mathematical Problem Solving Ability and Mathematical Attitude (공간추론활동을 통한 기하학습이 수학적 문제해결력과 수학적 태도에 미치는 효과)

  • Shin, Keun-Mi;Shin, Hang-Kyun
    • Journal of Elementary Mathematics Education in Korea
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    • v.14 no.2
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    • pp.401-420
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    • 2010
  • The purpose of this research is to find out effectiveness of geometry learning through spatial reasoning activities on mathematical problem solving ability and mathematical attitude. In order to proof this research problem, the controlled experiment was done on two groups of 6th graders in N elementary school; one group went through the geometry learning style through spatial reasoning activities, and the other group went through the general geometry learning style. As a result, the experimental group and the comparing group on mathematical problem solving ability have statistically meaningful difference. However, the experimental group and the comparing group have not statistically meaningful difference on mathematical attitude. But the mathematical attitude in the experimental group has improved clearly after all the process of experiment. With these results we came up with this conclusion. First, the geometry learning through spatial reasoning activities enhances the ability of analyzing, spatial sensibility and logical ability, which is effective in increasing the mathematical problem solving ability. Second, the geometry learning through spatial reasoning activities enhances confidence in problem solving and an interest in mathematics, which has a positive influence on the mathematical attitude.

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Primary Gifted Students' Mathematical Thinking and Attitude Related to Problem Solving of Triangular Array (삼각배열 문제해결과 관련된 초등영재의 수학적 사고와 태도)

  • Yim, Youngbin;Hong, Jin-Kon
    • School Mathematics
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    • v.17 no.3
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    • pp.377-390
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    • 2015
  • This study attempts to analyse mathematical thinking and attitude of students related to mathematization in the problem solving process and provide implication of teachers' roles. For this, this study analyses mathematical thinking and attitude by dividing the process of solving problems of triangular array into several steps. And it makes a proposal for teachers questioning which can help students according to steps. Therefore this study results students' mathematization needs various steps and compositive mathematical thinking and attitude when students solve even a problem. From the point of view of teachers who attempt to wean students on mathematization, it is necessary for teachers to observe and analyze how students have mathematical thinking and take a stand for mathematics in detail. It also indicates that it is desirable for students who can not move on next step to provide opportunities to learn on their own rather than simply providing students mathematical thinking directly. Students can derive pleasure from the process of solving difficult problems through this opportunity and realize usefulness of mathematics. Finally this experience can build mathematical attitude and prepare the ground to be able to think mathematically.

A Study on the Effect by Self-oriented Learning in Group for Improvement of Problem-solving Ability - Gentered to the 2nd Grade curriculum of Middle School - (수학과 그룹별 자기 주도 학습이 문제해결능력 신장에 미치는 영향 - 중학교 2학년 과정을 중심으로 -)

  • 오후진;김태흥
    • Journal of the Korean School Mathematics Society
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    • v.4 no.2
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    • pp.115-123
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    • 2001
  • In its seventh revision to start in 2001, mathematics will have a new emphasis in the middle school curriculum. Mathematics subject is now composed of practical things in the use of mathematics. Also, the future of new generation, which has been known as the information age, places much focus on problem-solving in order to collect, analyze, synthesize, and judge various kinds informations. This demand of problem-solving ability is not only related with mathematical education but, along the entire educational process, its related to actual life. With this change of social structure, the importance of school education is increasing rapidly. Therefore, in order to grow abilities and create new knowledge, adapted this new method of self-oriented learning in groups to middle school 2nd graders for one year, the results were as follows : 1. Students developed their ability of the use of mathematical terms and signs correctly. 2. Students' mathematical knowledge and problem-solving ability improved as they had increased interest in mathematics. 3. Students' peership was enhanced through their communication and cooperative activities in groups during the class. 4. Students themselves were more willing to volunteer and participate during the class.

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Design of the Mathematics Curriculum through Mathematical Modelling (수학적 모델링을 통한 교육과정의 구성원리)

  • 신현성
    • Journal of the Korean School Mathematics Society
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    • v.4 no.2
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    • pp.27-32
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    • 2001
  • The paper describes some principles how we design the mathematics curriculum through mathematical Modelling. since the motivation for modelling is that it give us a cheap and rapid method of answering illposed problem concerning the real world situations. The experiment was focussed on the possibility that they can involved in modelling problem sets and carry modelling process. The main principles could be described as follows. principle 1. we as a teacher should introduce the modelling problems which have many constraints at the begining situation, but later eliminate those constraints possibly. principle 2. we should avoid the modelling real situations which contain the huge data collection in the classroom, but those could be involved in the mathematics club and job oriented problem solving. principle 3. Analysis of modelling situations should be much emphasized in those process of mathematics curriculum principle 4. As a matter of decision, the teachers should have their own activities that do mathematics curriculum free. principle 5. New strategies appropriate in solving modelling problem could be developed, so that these could contain those of polya's heusistics

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The cognitive load of middle school students according to problem types in collaborative learning for solving the function problems (함수 영역 문제해결 협력학습 과정에서 문제 유형에 따른 중학생의 인지부하 분석)

  • Kim, Seong-Kyeong;Kim, Ji Youn;Lee, Sun Ji;Lee, Bongju
    • The Mathematical Education
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    • v.57 no.2
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    • pp.137-155
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    • 2018
  • From the assumption that an individual's working memory capacity is limited, the cognitive load theory is concerned with providing adequate instructional design so as to avoid overloading the learner's working memory. Based on the cognitive load theory, this study aimed to provide implications for effective problem-based collaborative teaching and learning design by analyzing the level of middle school students' cognitive load which is perceived according to the problem types(short answer type, narrative type, project) in the process of collaborative problem solving in middle school function part. To do this, this study analyzed whether there is a relevant difference in the level of cognitive load for the problem type according to the math achievement level and gender in the process of cooperative problem solving. As a result, there was a relevant difference in the task burden and task difficulty perceived according to the types of problems in both first and second graders in middle schools students. and there was no significant difference in the cognitive effort. In addition, the efficacy of task performance differed between first and second graders. The significance of this study is as follows: in the process of collaborative problem solving learning, which is most frequently used in school classrooms, it examined students' cognitive load according to problem types in various aspects of grade, achievement level, and gender.