• Title/Summary/Keyword: mathematical problem solving

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The Function of Meta-affect in Mathematical Problem Solving (수학 문제해결에서 메타정의의 기능)

  • Do, Joowon;Paik, Suckyoon
    • Journal of Elementary Mathematics Education in Korea
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    • v.20 no.4
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    • pp.563-581
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    • 2016
  • Studies on meta-affect in problem solving tried to build similar structures among affective elements as the structure of cognition and meta-cognition. But it's still need to be more systematic as meta-cognition. This study defines meta-affect as the connection of cognitive elements and affective elements which always include at least one affective element. We logically categorized types of meta-affect in problem solving, and then observed and analyzed the real cases for each type of meta-affect based on the logical categories. We found the operating mechanism of meta-affect in mathematical problem solving. In particular, we found the characteristics of meta function which operates in the process of problem solving. Finally, this study contributes in efficient analysis of meta-affect in problem solving and educational implications of meta-affect in teaching and learning in problem solving.

The Influences of Experiences of Productive Failures on Mathematical Problem Solving Abilities and Mathematical Dispositions (문제해결에서 생산적 실패의 경험이 초등학생의 수학적 문제해결력 및 수학적 성향에 미치는 영향)

  • Park, Yuna;Park, Mangoo
    • Education of Primary School Mathematics
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    • v.18 no.2
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    • pp.123-139
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    • 2015
  • The purpose of this study was to investigate the effects of the experiences of productive failures on students' mathematical problem solving abilities and mathematical dispositions. The experiment was conducted with two groups. The treatment group was applied with the productive mathematics failure program, and the comparative group was taught with traditional mathematics lessons. In this study, for quantitative analysis, the students were tested their understanding of mathematical concepts, mathematical reasoning abilities, students' various strategies and mathematical dispositions before and after using the program. For qualitative analysis, the researchers analyzed the discussion processes of the students, students's activity worksheets, and conducted interviews with selected students. The results showed the followings. First, use of productive failures showed students' enhancement in problem solving abilities. Second, the students who experienced productive failures positively affected the changes in students' mathematical dispositions. Along with the more detailed research on productive mathematical failures, the research results should be included in the development of mathematics textbooks and teaching and learning mathematics.

An effect coming to the problem solving ability from the problem posing activity by presenting the problem situation (문제 상황 제시에 따른 문제만들기 활동이 문제해결력에 미치는 영향)

  • Kim Jun Kyum;Lim Mun Kyu
    • Journal of Elementary Mathematics Education in Korea
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    • v.5 no.1
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    • pp.77-98
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    • 2001
  • This study has a purpose to find out how the problem posing activity by presenting the problem situation effects to the mathematical problem solving ability. It was applied in two classes(Experimental group-35, Controlled group-37) of the fourth grade at ‘D’ Elementary school in Bang Jin Chung nam and 40 Elementary school teachers working in Dang Jin. The presenting types of problem situation are the picture type, the language type, the complex type(picture type+ language type), the free type. And then let them have the problem posing activity. Also, We applied both the teaching-teaming plan and practice question designed by ourself. The results of teaching and learning activities according to the type of problem situation presentation are as follows; We found out that the learning activity of the mathematical problem posing was helpful to the students in the development of the mathematical problem solving ability. Also, We found out that the mathematical problem posing made the students positively change their attitude and their own methods for mathematical problem solving.

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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 Effect of the Belief Systems on the Problem Solving Performance of the Middle School Students (중학생의 신념체계가 수학적 문제해결 수행에 미치는 영향)

  • Kwon Se Hwa;Jeon Pyung Kook
    • The Mathematical Education
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    • v.31 no.2
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    • pp.109-119
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    • 1992
  • The primary purpose of the present study is to provide the sources to improve the mathematical problem solving performance by analyzing the effects of the belief systems and the misconceptions of the middle school students in solving the problems. To attain the purpose of this study, the reserch is designed to find out the belief systems of the middle school students in solving the mathematical problems, to analyze the effects of the belief systems and the attitude on the process of the problem solving, and to identify the misconceptions which are observed in the problem solving. The sample of 295 students (boys 145, girls 150) was drawn out of 9th grade students from three middle schools selected in the Kangdong district of Seoul. Three kinds of tests were administered in the present study: the tests to investigate (1) the belief systems, (2) the mathematical problem solving performance, and (3) the attitude in solving mathematical problems. The frequencies of each of the test items on belief systems and attitude, and the scores on the problem solving performance test were collected for statistical analyses. The protocals written by all subjects on the paper sheets to investigate the misconceptions were analyzed. The statistical analysis has been tabulated on the scale of 100. On the analysis of written protocals, misconception patterns has been identified. The conclusions drawn from the results obtained in the present study are as follows; First, the belief systems in solving problems is splited almost equally, 52.95% students with the belief vs 47.05% students with lack of the belief in their efforts to tackle the problems. Almost half of them lose their belief in solving the problems as soon as they given. Therefore, it is suggested that they should be motivated with the mathematical problems derived from the daily life which drew their interests, and the individual difference should be taken into account in teaching mathematical problem solving. Second. the students who readily approach the problems are full of confidence. About 56% students of all subjects told that they enjoyed them and studied hard, while about 26% students answered that they studied bard because of the importance of the mathematics. In total, 81.5% students built their confidence by studying hard. Meanwhile, the students who are poor in mathematics are lack of belief. Among are the students accounting for 59.4% who didn't remember how to solve the problems and 21.4% lost their interest in mathematics because of lack of belief. Consequently, the internal factor accounts for 80.8%. Thus, this suggests both of the cognitive and the affective objectives should be emphasized to help them build the belief on mathematical problem solving. Third, the effects of the belief systems in problem solving ability show that the students with high belief demonstrate higher ability despite the lack of the memory of the problem solving than the students who depend upon their memory. This suggests that we develop the mathematical problems which require the diverse problem solving strategies rather than depend upon the simple memory. Fourth, the analysis of the misconceptions shows that the students tend to depend upon the formula or technical computation rather than to approach the problems with efforts to fully understand them This tendency was generally observed in the processes of the problem solving. In conclusion, the students should be taught to clearly understand the mathematical concepts and the problems requiring the diverse strategies should be developed to improve the mathematical abilities.

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The Effects of the FOCUS Problem Solving Steps on Mathematical Problem Solving Ability and Mathematical Attitudes (FOCUS 문제해결과정이 수학 문제해결력 및 수학적 태도에 미치는 영향)

  • Lee, Yeon Joo;Ryu, Sung Rim
    • Journal of Elementary Mathematics Education in Korea
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    • v.21 no.1
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    • pp.243-262
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    • 2017
  • This study has its purpose on improving mathematic education by analyzing the effects of the teaching and learning process which adopted 'FOCUS Problem Solving Steps' on student's mathematical problem solving ability and their mathematical attitude. The result is as follows. First, activities through FOCUS Problem Solving Steps showed positive effect on students' problem solving ability. Second, among mathematical attitudes, mathematical curiosity, reflection and value are proved to have statistically meaningful effect and from the result that analyzed changes of subject students, we could suppose that all 6 elements of mathematical attitude had positive effect. Third, by solving questions through FOCUS steps, students felt satisfaction when they success by themselves. If projects which adopted FOCUS Problem Solving Steps take effect continuously by happiness from the process of reviewing and reflecting their own fallacy and solving that, we might expect meaningful effect on students' problem solving ability. Through this study, FOCUS Problem Solving Steps had positive effect not only on students' mathematical problem solving ability but also on formation of mathematical attitude. As a result, it implies that FOCUS Problem Solving Steps need to be applied to other grades and fields and then studied more.

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Students' Field-dependency and Their Mathematical Performance based on Bloom's Cognitive Levels

  • Alamolhodaei, Hassan;Hedayat Panah, Ahmad;Radmehr, Farzad
    • Research in Mathematical Education
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    • v.15 no.4
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    • pp.373-386
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    • 2011
  • Students approach mathematical problem solving in fundamentally different ways, particularly problems requiring conceptual understanding and complicated strategies. The main objective of this study is to compare students' performance with different thinking styles (Field-dependent vs. Field independent) in mathematical problem solving. A sample of 242 high school males and females (17-18 years old) were tested based on the Witkin's cognitive style (Group Embedded Figure Test) and by a math exam designed in accordance with Bloom's Taxonomy of cognitive level. The results obtained indicated that the effect of field dependency on student's mathematical performance was significant. Moreover, field-independent (FI) students showed more effective performance than field-dependent (FD) ones in math tasks. Male students with FI styles achieved higher results compared to female students with FD cognitive style. Moreover, FI students experienced few difficulties than FD students in Bloom's Cognitive Levels. The implications of these results emphasize that cognitive predictor variables (FI vs. FD) could be challenging and rather distinctive factor for students' achievement.

An Analysis of Third Graders' Representations and Elaborating Processes of Representations in Mathematical Problem Solving (초등학교 3학년 학생의 수학적 문제 해결에서의 표상과 표상의 정교화 과정 분석)

  • Lee, Yang-Mi;Jeon, Pyung-Kook
    • The Mathematical Education
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    • v.44 no.4 s.111
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    • pp.627-651
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    • 2005
  • This study was conducted to attain an in-depth understanding of students' mathematical representations and to present the educational implications for teaching them. Twelve mathematical tasks were developed according to the six types of problems. A task performance was executed to 151 third graders from four classes in DaeJeon and GyeongGi. We analyzed the types and forms of representations generated by them. Then, qualitative case studies were conducted on two small-groups of five from two classes in GyeongGi. We analyzed how individuals' representations became elaborated into group representation and what patterns emerged during the collaborative small-group learning. From the results, most students used more than one representation in solving a problem, but they were not fluent enough to link them to successful problem solving or to transfer correctly among them. Students refined their representations into more meaningful group representation through peer interaction, self-reflection, etc.. Teachers need to give students opportunities to think through, and choose from, various representations in problem solving. We also need the in-depth understanding and great insights into students' representations for teaching.

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An Analysis on the Effect by the Characteristics of Intuition of Elementary Students in Mathematical Problem Solving Process (초등학생들의 문제해결 과정에서 직관의 특징에 의한 영향 분석)

  • Lee, Dae-Hyun
    • Journal of Elementary Mathematics Education in Korea
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    • v.14 no.2
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    • pp.197-215
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    • 2010
  • Intuition plays an important role in the mathematical education as well as the process of invention in mathematics. And many mathematics educators became interested in intuition in mathematics education. So we need to analyze the effect of the characters of intuition of elementary students. In this study, the questionnaire and the interview were used. The subjects were 6 grade-103 students in the questionnaire. They were asked to solve the problems in the questionnaire which was designed by the researcher and to describe the reasons why they answered like that. Students are effected directly by the characters of intuition, ie self-evidence, intrinsic certainty, implicitness, etc. And the effect come from intuitive and ordinary experiences and the results of previous learning. In conclusion, we have to be interested in teaching via intuition and to control the effect of the characters of intuition.

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The History of Mathematical Problem Solving and the Modeling Perspective (수학 문제 해결의 역사와 모델링 관점)

  • Lee Dae Hyun;Seo Kwan Seok
    • Journal for History of Mathematics
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    • v.17 no.4
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    • pp.123-132
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    • 2004
  • In this paper, we reviewed the history of mathematical problem solving since 1900 and investigated problem solving in modeling perspective which is focused on the 21th century. In modeling perspective, problem solvers solve the realistic problem which includes contextualized situations in which mathematics is useful. In this case, the problem is different from the traditional problems which are routine, close, and words problem, etc. Problem solving in modeling perspective emphasizes mathematizing. Most of all, what is important enables students to use mathematics in everyday problem solving situation.

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