• Title/Summary/Keyword: mathematical problem solving

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An Analysis on the Mathematical Problem Solving via Intuitive Thinking of the Korean and American 6th Grade Students (한국과 미국 6학년 학생들의 직관적 사고에 의한 수학 문제해결 분석)

  • Lee, Dae Hyun
    • The Mathematical Education
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    • v.55 no.1
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    • pp.21-39
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    • 2016
  • This research examined the Korean and American $6^{th}$ grade students' mathematical problem solving ability and methods via an intuitive thinking. For this, the survey research was used. The researcher developed the questionnaire which consists of problems with intuitive and algorithmic problem solving in number and operation, figure and measurement areas. 57 Korean $6^{th}$ grade students and 60 American $6^{th}$ grade students participated. The result of the analysis showed that Korean students revealed a higher percentage than American students in correct answers. But it was higher in the rate of Korean students attempted to use the algorithm. Two countries' students revealed higher rates in that they tried to solve the problems using intuitive thinking in geometry and measurement areas. Students in both countries showed the lower percentages of correct answer in problem solving to identify the impact of counterintuitive thinking. They were affected by potential infinity concept and the character of intuition in the problem solving process regardless of the educational environments and cultures.

Identification and Selection the Mathematically Gifted on the Elementary School (초등 수학 영재의 판별과 선발)

  • Song Sang-Hun
    • Proceedings of the Korean Society for the Gifted Conference
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    • 2001.05a
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    • pp.43-72
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    • 2001
  • Identification and discrimination the mathematical giftedness must be based on it's definition and factors. So, there must be considered not only IQ or high ability in mathematical problem solving, but also mathematical creativity and mathematical task commitment. Furthermore, we must relate our ideas with the programs to develop each student's hidden potential not to settle only. This study is focused on the discrimination of the recipients who would like to enter the elementary school level mathematical gifted education program. To fulfill this purpose, I considered the criteria, principles, methods, tools and their application. In this study, I considered three kinds of testing tools. The first was KEDI - WISC personal IQ test, the second is mathematical problem solving ability written test(1st type), and the third was mathematical creativity test(2nd type) which were giving out divergent products. The number of the participant of these tests were 95(5-6 grade). According to the test, students who had ever a prize in the level of national mathematical contest got more statistically significant higher scores on 1st and 2nd type than who had ever not, but they were not prominent on the phases of attitude, creative ability or interest and willing to study from the information of the behavior characteristics test. Using creativity test together with the behavior characteristics test will be more effective and lessen the possibility of exclusion the superior.

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Insight into an Structural Similarity in Stage of Similar Mathematical Problem Solving Process (유사 문제 해결에서 구조적 유사성의 인식)

  • Jun, Young-Bae;Roh, Eun-Hwan;Kang, Jeong-Gi
    • The Mathematical Education
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    • v.50 no.1
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    • pp.1-12
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    • 2011
  • It is the aim of this paper to study the target problem solving process in reference to the base problem. We observed closely how students solve the target problem in reference to the base problem. The students couldn't solve the target problem, although they succeed to find the base problem. This comes from failing to discover the structural similarity between the target problem and the base problem. Especially it is important to cognize the proper corresponding of primary components between the base problem and target problem. And there is sometimes a part component of the target problem equivalent to the base problem and the target problem can't be solved without the insight into this fact. Consequently, finding the base problem fail to reach solving the target problem without the insight into their structural similarity. We have to make efforts to have an insight into the structural similarity between the target problem and the base problem to solve the target problem.

A study on the improvement of ability of a creative solving mathematical problem (수학문제의 창의적 해결력 신장에 관한 연구 -농어촌 중학교 수학영재를 중심으로-)

  • 박형빈;서경식
    • Journal of the Korean School Mathematics Society
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    • v.6 no.1
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    • pp.1-17
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    • 2003
  • In this paper, we study the methods of improving an ability of a creative solving mathematical problem belonging to an educational system which every province office of education has adopted for the mathematically talented students. Especially, we give an attention on a preferential reaction in teaching styles according to student's LQ., the relationship between student's LQ. and an ability of creative solving mathematical problems, and seeking for an appropriative teaching methods of the improvement ability of a creative solving problem. As results, we have the followings; 1. The group having excellent students who have a higher intelligential ability prefers inquiry learning which is composed of several sub-groups to a teacher-centered instruction. 2. The correlation coefficient between student's LQ. and an ability creative solving of mathematical is not high. 3. Although the contents and the model of thematic inquiry learning don't have a great influence on the divergent thinking (ex. fluency, flexibility, originality), they affect greatly the convergent thinking - a creative mathematical - problem solving ability. Accordingly, our results show that we should use a variety of mathematical teaching materials apart from our regular textbooks used in schools to improve a creative mathematical problem solving ability in the process of thematic inquiry learning. Also we can see that an inquiry learning which stimulates student's participation and discussion can be a desirable model in the thematic mathematical classroom activities.

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Instrument Development and Analysis of Secondary Students' Mathematical Beliefs (우리나라 중.고등학생의 수학적 신념 측정 및 특성 분석)

  • Kim, Bu-Mi
    • Journal of Educational Research in Mathematics
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    • v.22 no.2
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    • pp.229-259
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    • 2012
  • The purpose of the present study is to develop instrument of mathematical belief of middle school and high school students and to analysis results of test using the instrument. Based on the results of literature review, mathematical belief is the cumulative effects of self-assessment and self-concept in mathematical learning and achievement experience. Four sub-components of mathematical belief is identified belief of school mathematics, belief of mathematical problem solving, mathematical self-concept, belief of mathematical teaching and learning. The instrument was developed to investigate mathematical belief by reflecting Korean middle school and high school students' psychological characters. To develop the appropriate items for the mathematical belief, after reviewing literature thoroughly, first version of the instrument was developed and exploratory factor analysis and confirmatory factor analysis were conducted. Then, to reduce the effect of the gender difference and achievement level difference, Correlation Analysis and 1-way ANOVA was performed. Also, using multiple group confirmatory factor analysis, this instrument was investigated to see whether this can be used for both middle school and high school. The final items for middle school students is consisted 7 items of belief of school mathematics, 9 items of belief of mathematical problem solving, 11 items of mathematical self-concept, 10 items of belief of mathematical teaching and learning. Instrument of mathematical belief for high school students is consisted 9 items of belief of school mathematics, 9 items of belief of mathematical problem solving, 11 items of mathematical self-concept, 11 items of belief of mathematical teaching and learning. This study examined the differences about mathematical belief's sub-factors shown by three groups of mathematics achievement level. Students of higher achievement level showed that the degree of most factors ware the highest excepting stereotype of belief of school mathematics. Also, Male students preferred more positive in mathematics belief than female students.

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A case study on the mathematical problem solving performance of simultaneous equations for the students from a remedial course (특별보충과정 학생들의 문제해결수행에 대한 사례연구)

  • Ko, Sang-Sook;Lee, Sang-Hui
    • Journal of the Korean School Mathematics Society
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    • v.9 no.1
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    • pp.105-120
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    • 2006
  • The Seventh Curriculum makes sure that those students who don't have a proper understanding of contents required at a certain stage take a remedial course. But a trend contrary to the intention is formed since there is no systematic education for such a course and thus more students get to fall into the group of low achievement. In particular, solving a simultaneous equation in a rote way without understanding influences negatively students' achievement. Schoenfeld introduced the basic elements of one's own mathematical problem solving process and behavior, referred to Polya's. Employing Schoenfeld's strategy, this study aimed to induce students' active participation in math classes, as well as to focus on a mathematical problem solving process during the study. Two students were selected from a remedial course at 00 Middle School and administered with a qualitative case study method over 17 lessons, each of which lasted for 30 minutes. In the beginning, they used such knowledge as facts and definitions a lot. There was a tendency of their resorting to intuitive knowledge more when they lacked basic knowledge or met with a difficult question. As the lessons were given, however, they improved their ability to implement algorithm procedures and used more familiar ones with the developed common procedures in the area of resources.

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Analyzing Errors Made by Eighth-Grade Students in Solving Geometrical Problems

  • Huang, Xingfeng;Cheng, Longhai
    • Research in Mathematical Education
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    • v.15 no.4
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    • pp.357-371
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    • 2011
  • In mathematical problem solving, students may make various errors. In order to draw useful lessons from the errors, and then correct them, we surveyed 24 eighth-grade students' performances in geometrical problem solving according to Casey's hierarchy of errors. It was found that: 1. Students' effect can lead to errors at the stage of "comprehension", "strategy selection", and "skills manipulation"; and 2. Students' geometric schemas also influenced their strategy selection".

The Effects of Mathematical Problem Posing Activities by the Fourth Graders (4학년 아동들의 수학적 문제 설정 활동의 효과)

  • 조제호;신인선
    • Education of Primary School Mathematics
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    • v.2 no.2
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    • pp.133-144
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    • 1998
  • We examined two kinds of problem posing, 'problem making' and 'problem modifying' to find which one is more effective for improving mathematical problem solving ability according to the student's learning-levels and sexes. The results showed that 'problem making' is more effective for high and middle-level groups than 'problem modifying'. There was no big difference according to the sexes. These facts implies that making a problem when a situation was presented is more effective to develop problem solving ability than modifying a problem : modifying some conditions and contents of given problem.

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Analysis of the Mathematical Processes in Mathematical Essay Lessons : Focused on the Probability and Statistics Domain (수학논술을 활용한 수업에서 나타나는 수학적 과정 분석: 확률과 통계 영역을 중심으로)

  • Kim, Kyu-Sang;Lee, Jae-Hak;Lee, Kwang-Ho
    • School Mathematics
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    • v.16 no.3
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    • pp.543-565
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    • 2014
  • The purpose of this study is investigating the various properties related with mathematical processes in the mathematical essay lessons, analyzing the positive changes of students, and proposing an example that the mathematical essay lessons can be a model for changing traditional mathematical lessons. To carry out the research, mathematical essay questions were developed based upon the high school mathematics curriculum in probability and statistics domain. Eight 12th graders were participated for the research. Variety of properties related mathematical problem solving, reasoning, and communication in the lessons were appeared. The research conclude that mathematical essays are helpful not only appearance of general properties related mathematics process, but also appearance of properties that would be low chance of developed.

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Applying the Mathematical Processes to an Elementary School Class for Mathematics (초등 수학 수업을 위한 수학적 과정의 적용)

  • Chang, Hyewon;Kim, Minseon
    • Journal of Elementary Mathematics Education in Korea
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    • v.17 no.1
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    • pp.19-37
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    • 2013
  • 2009 revised national curriculum for mathematics emphasizes the mathematical processes which consist of mathematical problem solving, mathematical reasoning, and mathematical communication. This study focused on applying these processes to an elementary school class for mathematics. Even though they say that it is desirable that the mathematical processes are realized in every mathematics class, any vague intention for their application without specific plans is apt to be apart from meaningful practice. Therefore this study proposed a lesson plan about the characteristics and the comparison of bar graphs and line graphs for 4th grade students based on the mathematical processes. And we applied it to 27 subjects. By observing and analyzing their activities and communications, we discussed about the guidelines of applying the mathematical processes to elementary school classes for mathematics.

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