• Title/Summary/Keyword: mathematical problem solving

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Analyses on the reasoning in primary mathematics textbooks (초등 수학 교재에서 활용되는 추론 분석)

  • 서동엽
    • Journal of Educational Research in Mathematics
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    • v.13 no.2
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    • pp.159-178
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    • 2003
  • This study analyzes on the reasoning in the process of justification and mathematical problem solving in our primary mathematics textbooks. In our analyses, we found that the inductive reasoning based on the paradima-tic example whose justification is founnded en a local deductive reasoning is the most important characteristics in our textbooks. We also found that some propositions on the properties of various quadrangles impose a deductive reasoning on primary students, which is very difficult to them. The inductive reasoning based on enumeration is used in a few cases, and analogies based on the similarity between the mathematical structures and the concrete materials are frequntly found. The exposition based en a paradigmatic example, which is the most important characteristics, have a problematic aspect that the level of reasoning is relatively low In Miyazaki's or Semadeni's respects. And some propositions on quadrangles is very difficult in Piagetian respects. As a result of our study, we propose that the level of reasoning in primary mathematics is leveled up by degrees, and the increasing levels are following: empirical justification on a paradigmatic example, construction of conjecture based on the example, examination on the various examples of the conjecture's validity, construction of schema on the generality, basic experiences for the relation of implication.

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The Variation of Emotions in Mathematical Problem Solving (수학 문제 해결 과정에서 학생들의 감정 변화에 대한 사례 연구)

  • Ahn, Yoon-Kyeong;Kim, Sun-Hee
    • Journal of Educational Research in Mathematics
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    • v.21 no.3
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    • pp.295-311
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    • 2011
  • The importance of problem solving in mathematics education has been emphasized and many studies related to this issue have been conducted. But, studies of problem solving in the aspect of affect domain are lacked. This study found the changing pattern of emotions that occur in process of a problem solving. The results are listed below. First, students experienced a lot of change of emotions and had a positive emotion as well as negative emotion during solving problems. Second, students who solved same problems through same methods experienced different change patterns of emotions. The reason is that students have different mathematical beliefs and think differently about a difficulty level of problem. Third, whether students solved problems with positive emotion or negative emotion depends on their attitude of mathematics. Fourth, students who thought that a difficulty level of problem was relatively high experienced more negative affect than students who think a difficulty level of problem is low experienced.

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The Effects of Reflective Problem Posing Activities on Students' Problem Solving Ability and Attitudes toward Mathematics (반성적 문제 만들기 활동이 초등학생들의 문제해결력 및 수학적 태도에 미치는 영향)

  • Bae, Jun-Hwan;Park, Mangoo
    • Journal of Elementary Mathematics Education in Korea
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    • v.20 no.2
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    • pp.311-331
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    • 2016
  • The purpose of this study was to analyze mathematical errors and the effects of reflective problem posing activities on students' mathematical problem solving abilities and attitudes toward mathematics. We chose two 5th grade groups (experimental and control groups) to conduct this research. From the results of this study, we obtained the following conclusions. First, reflective problem posing activities are effective in improving students' problem solving abilities. Students could use extended capability of selecting a condition to address the problem to others in the activities. Second, reflective problem posing activities can improve students' mathematical willpower and promotes reflective thinking. Reflective problem posing activities were conducted before and after the six areas of mathematics. Also, we examined students' mathematical attitudes of both the experimental group and the control group about self-confidence, flexibility, willpower, curiosity, mathematical reflection, and mathematical value. In the reflective problem posing group, students showed self check on their problems solving activities and participated in mathematical discussions to communicate with others while participating mathematical problem posing activities. We suggested that reflective problem posing activities should be included in the development of mathematics curriculum and textbooks.

The Effect of the Estimation Strategy on Placing Decimal Point in Multiplication and Division of Decimals (어림하기를 통한 소수점 찍기가 소수의 곱셈과 나눗셈에 미치는 효과)

  • Lee, Youn-Mee;Park, Sung-Sun
    • Journal of Elementary Mathematics Education in Korea
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    • v.15 no.1
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    • pp.1-18
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    • 2011
  • The purpose of this study was to investigate the effects of estimation strategy on placing decimal point in multiplication and division of decimals. To examine the effects of improving calculation ability and reducing decimal point errors with this estimation strategy, the experimental research on operation with decimal was conducted. The operation group conducted the decimal point estimation strategy for operating decimal fractions, whereas the control group used the traditional method with the same test paper. The results obtained in this research are as follows; First, the estimation strategy with understanding a basic meaning of decimals was much more effective in calculation improvement than the algorithm study with repeated calculations. Second, the mathematical problem solving ability - including the whole procedure for solving the mathematical question - had no effects since the decimal point estimation strategy is normally performed after finishing problem solving strategy. Third, the estimation strategy showed positive effects on the calculation ability. Th Memorizing algorithm doesn't last long to the students, but the estimation strategy based on the concept and the position of decimal fraction affects continually to the students. Finally, the estimation strategy assisted the students in understanding the connection of the position of decimal points in the product with that in the multiplicand or the multiplier. Moreover, this strategy suggested to the students that there was relation between the placing decimal point of the quotient and that of the dividend.

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The Issues of the Elementary School Teacher Recruitment Examination (교대 수학심화과정에서 본 초등교원 임용고사의 문제점)

  • Lee, Eui-Won
    • Journal of Elementary Mathematics Education in Korea
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    • v.14 no.3
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    • pp.659-680
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    • 2010
  • Under the banner "Toward Global Excellence in Teacher Education", Daegu National University of Education has strived for the single aim of excellence in pre-service and in-service for over fifty years. Specially the department of Mathematics education aims to develope students' mathematical power which is related to elementary school mathematical concepts & theories. However not a few of the students seem to have test-anxiety which is relate to teacher recruitment examination. In these view, we conclude that students must have been suffered from test anxiety. Consequently the results of the study are follow. $\cdot$ 2nd paper-pencil test of the elementary school teacher recruitment(2010) has been emphasized on statement of examinee logocal thought about all 10 subjects. $\cdot$ 3rd test of the elementary school teacher recruitment(2010) has been focused on only speaking english of examinee. Thus we conclude that these Recruitment Examination(2010) couldn't minimize the test anxiety of the students. Therefore next test of the elementary school Teacher Recruitment should contain on mathematical problem-solving in elementary school mathematics textbooks.

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A Classroom Activities of the Problem Solving Using Visualized Materials In Pre-service Mathematics Teacher's Education (예비 수학 교사 교육에서 시각적 자료를 이용한 문제 해결 지도 사례)

  • Kim, Nam-Hee
    • School Mathematics
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    • v.12 no.4
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    • pp.493-506
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    • 2010
  • In this study, we conducted classroom activities that are exploring and explaining visualized materials for problem solving of school mathematics with pre-service teachers in 2007~2009. After finishing these classroom activities, pre-service teachers recorded an afternote that includes changes of their thinking about mathematics and mathematics education through these activities in this study. We collected various opinions of pre-service mathematics teachers. From the analysis these data, we searched educational effects of our classroom activities. Through conducting the practice like these classroom activities of our study, pre-service mathematics teachers will have an opportunity of a practical training that supports the teaching of mathematical problem-solving. Moreover their PCK will be enhanced. Also, They will learn a good way to realize the aim of school mathematics curriculum.

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A Study on the 6th Graders' Use of Visual Representations in Mathematical Problem Solving (수학 문제 해결과정에서 초등학교 6학년 학생들의 시각적 표현에 관한 연구)

  • Hwang, Hyun-Mi;Pang, Jeong-Suk
    • Education of Primary School Mathematics
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    • v.12 no.2
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    • pp.81-97
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    • 2009
  • Visual representations play an important role for students to understand the meaning of a given problem, devise problem-solving approaches, and implement them successfully. The purpose of this study was to investigate how 6th graders would use visual representations in solving mathematical problems and in what ways such use might affect successful problem solving. The results showed that many students preferred numerical expressions to visual representations. However, students who used visual representations, specifically schematic representations, performed better than those who employed numerical representations. Given this, this paper includes instructional implications to nurture students' use of visual representations in a way to increase their problem solving ability.

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The Comparison of Students Grade Level on the Integrated Learning Program for Mathematical Problem Solving using EPL (EPL을 활용한 수학문제해결 통합교육프로그램의 학년 수준 비교)

  • Han, Seon-Kwan;Kim, Soo-Hwan
    • Journal of The Korean Association of Information Education
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    • v.14 no.3
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    • pp.311-318
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    • 2010
  • In this paper, we proposed the integrated education program of informatics and math for solving problem using EPL. We applied a integrated math curriculum with EPL and analyzed mathematical thinking and attitude to the 3rd and 5th students. We used mathematical thinking test, mathematical attitude test and interview through student review. We also analyzed data of observers who are elementary school teachers. The results of test are as follows; First, we found effective points of meta-cognition and visualization of thought in solving the mathematical problem using Scratch. Second, mathematical thinking and attitude showed the result that 3rd grade students are more increased than 5th grade students in pre and post t-test of the mathematical. Consequently, we expect that the integrated education program of informatics and math using EPL can be applied to solve problem in math effectively.

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A Study of the Potentials of Math Based Convergence Instructional Model (수학 기반 융합 수업 모형의 가능성 탐색)

  • Kim, YuKyung;Pang, JeongSuk
    • Education of Primary School Mathematics
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    • v.18 no.2
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    • pp.107-122
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    • 2015
  • This research aims to suggest a math-based convergence instructional model. The convergence instructional model with emphasis on problem solving ability was developed based on each subject and the STEAM model. Then, the appropriateness and limit of the classroom model were investigated, through examining the aspects of its realization in each stage of the class instruction model while enacting a four part lesson on 6th graders. As a result, each stage of the classroom instruction model influenced in helping the students discover various problem solving skills, critically examine the process of the solving, and attain positive perspectives on the classroom instruction. However, appropriate intervention of the teacher was needed to lead the students to further synthesize the explored issues in mathematics and to expand the scope of their emotional experience. This paper closes with suggestions in implementing math based convergence lessons.

Effects of Mathematical Justification on Problem Solving and Communication (수학적 정당화가 문제 해결과 의사소통에 미치는 영향)

  • Jeong, In Su
    • Education of Primary School Mathematics
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    • v.16 no.3
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    • pp.267-283
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    • 2013
  • Mathematical justification is the process through which one's claim is validated to be true based on proper and trustworthy data. But it serves as a catalyst to facilitate mathematical discussions and communicative interactions among students in mathematics classrooms. This study is designed to investigate the effects of mathematical justification on students' problem-solving and communicative processes occurred in a mathematics classroom. In order to fulfill the purpose of this study, mathematical problem-solving classes were conducted. Mathematical justification processes and communicative interactions recorded in problem understanding activity, individual student inquiry, small and whole group discussions are analyzed. Based on the analysis outcomes, the students who participated in mathematical justification activities are more likely to find out various problem-solving strategies, to develop efficient communicative skills, and to use effective representations. In addition, mathematical justification can be used as an evaluation method to test a student's mathematical understanding as well as a teaching method to help develop constructive social interactions and positive classroom atmosphere among students. The results of this study would contribute to strengthening a body of research studying the importance of teaching students mathematical justification in mathematics classrooms.