• Title/Summary/Keyword: mathematical problem solving

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A Review of the Neurocognitive Mechanisms of Number Sense (수 감각의 인지신경학적 기반에 관한 연구 개관)

  • Cho, Soohyun
    • Korean Journal of Cognitive Science
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    • v.24 no.3
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    • pp.271-300
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    • 2013
  • Human and animals are born with an intuitive ability to determine approximate numerosity. This ability is termed approximate number sense (hereafter, number sense). Evolutionarily, number sense is thought to be an essential ability for hunting, gathering and survival. According to previous research, children with mathematical learning disability have impaired number sense. On the other hand, individuals with more accurate number sense have higher mathematical achievement. These results support the hypothesis that number sense provides a basis for the development of mathematical cognition. Recently, researchers have been examining whether number sense training can lead to enhancement in mathematical achievement and changes in brain activity in relation to mathematical problem solving. Numerosity which basically represents discontinuous quantity is expected to be closely related to continuous quantity such as representations of space and time. A theory of magnitude (ATOM) states that processing of number, space and time is based on a common magnitude system in the posterior parietal cortex, especially the intraparietal sulcus. The present paper introduces current literature and future directions for the study of the common magnitude system.

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A Study of Story-Shell Applied to Mathematical Communication (이야기 틀을 활용한 수학 수업에 나타난 의사소통 활동 분석)

  • Kim Young Ok;Paik Seok Yoon
    • Journal of Elementary Mathematics Education in Korea
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    • v.8 no.1
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    • pp.1-21
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    • 2004
  • The purpose of this study is analyzing phenomenon of mathematical communication by students applied story shell. Also, this study is obtained teaching indicated in early standardized mathematics classes. It is served we realize the purpose of study and set study subject to be as follows. First, it finds out how to be described activities of students' mathematical communication in the mathematics class applied story shell. Second, it finds out what phenomenon is observed in a behavior side of the mathematics class applied story shell. It is developed 7 story shells for the 6th grade of the elementary school for about 4 months and when applying mathematics classes, it is analyzed the notes and recorded data to get in an each class and when applying mathematics classes. It is analyzed the notes and recorded data to get in an each class. The result of this study is as follows: First, in a mathematics class which applies story shell, students concentrate on the class when hearing and reading mathematics problem. So, they are able to understand a mathematical language included in the problem. Second, in a mathematics class which applies story shell, students participate actively at the mathematics class. And in complicate situation among the students it is served they justify own opinion and persuaded logically. The point which study hints to see such a result is as follows: First, in a mathematics class which applies story shell students have answered more quickly than the old times as hearing and reading the problem in a picture. Second, in a mathematics class which applies story shell, students were used to being the mathematics language intimately and there was to observe to express it by an equation. Third, in a mathematics class which applies story shell students attend to study activity with interest. Forth, in situation of complicate thought, students are persuading and explaining their opinions for the purpose of justification.

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The Effects of STEAM-based Mathematics Class in the Mathematical Problem-solving Ability and Self-efficacy (STEAM 기반 수학 수업이 문제해결력과 자기효능감에 미치는 영향)

  • Lee, GaEun;Choi, JaeHo
    • Journal of Elementary Mathematics Education in Korea
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    • v.21 no.4
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    • pp.663-686
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    • 2017
  • The purpose of this study was to identify the effects of convergent approach of mathematics education on students' problem-solving ability and self-efficacy by designing and applying mathematics curriculum based on STEAM. The results are as follows. First, the test results between the two groups did not show any statistically significant difference in terms of problem solving ability, but the experimental group showed a higher average score than the comparative group. Compared with the standard deviation of the experimental group, It can be seen that the level of difference between students is great. This suggests that STEAM-based mathematics lessons have a positive effect on the problem solving ability of low-level students. Second, the results of the self-efficacy t-test of STEAM-based mathematics class showed statistically significant results at a 5% significance level. In the sub-domain, the preference for the difficulty of the mathematics task, except math self-confidence and the math self-regulation efficacy, were statistically significant at a 5% significance level. This study shows that STEAM-based mathematics classes have a positive effect on the students' positive aspects. Through the STEAM program, students learn that mathematics is connected with other fields, and it provides an opportunity to explore on their own, and they more became interested, motivated, and achievement. Also, through the results of the STEAM-based mathematics class, it can be seen that the expressive power and self-confidence are increased by using the non-formal representation outside of the existing formal representation center. The result of this study can be summarized as follows: A STEAM-based mathematics class has a positive effect on problem solving ability and self-efficacy. Therefore, it is interpreted that the application of the STEAM program focusing on mathematics accounts for education effectives.

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An Analysis on the Elementary Preservice Teachers' Problem Solving Process in Intuitive Stages (직관적 수준에서 초등 예비교사들의 문제해결 과정 분석)

  • Lee, Dae Hyun
    • School Mathematics
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    • v.16 no.4
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    • pp.691-708
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    • 2014
  • In general, the intuitive knowledge that can use in mathematics problem solving is one of the important knowledge to teachers as well as students. So, this study is aimed to analyze the elementary preservice teachers' intuitive knowledge in relation to intuitive and counter-intuitive problem solving. For this, I performed survey to use questionnaire consisting of problems that can solve in intuitive methods and cause the errors by counter-intuitive methods. 161 preservice teachers participated in this study. I got the conclusion as follows. preservice teachers' intuitive problem solving ability is very low. I special, many preservice teachers preferred algorithmic problem solving to intuitive problem solving. So, it's needed to try to improve preservice teachers' problem solving ability via ensuring both the quality and quantity of problem solving education during preservice training courses. Many preservice teachers showed errors with incomplete knowledges or intuitive judges in counter-intuitive problem solving process. For improving preservice teachers' intuitive problem solving ability, we have to develop the teacher education curriculum and materials for preservice teachers to go through intuitive mathematical problem solving. Add to this, we will strive to improve preservice teachers' interest about mathematics itself and value of mathematics.

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A Case Study on Instruction for Mathematically Gifted Children through The Application of Open-ended Problem Solving Tasks (개방형 과제를 활용한 수학 영재아 수업 사례 분석)

  • Park Hwa-Young;Kim Soo-Hwan
    • Communications of Mathematical Education
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    • v.20 no.1 s.25
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    • pp.117-145
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    • 2006
  • Mathematically gifted children have creative curiosity about novel tasks deriving from their natural mathematical talents, aptitudes, intellectual abilities and creativities. More effect in nurturing the creative thinking found in brilliant children, letting them approach problem solving in various ways and make strategic attempts is needed. Given this perspective, it is desirable to select open-ended and atypical problems as a task for educational program for gifted children. In this paper, various types of open-ended problems were framed and based on these, teaming activities were adapted into gifted children's class. Then in the problem solving process, the characteristic of bright children's mathematical thinking ability and examples of problem solving strategies were analyzed so that suggestions about classes for bright children utilizing open-ended tasks at elementary schools could be achieved. For this, an open-ended task made of 24 inquiries was structured, the teaching procedure was made of three steps properly transforming Renzulli's Enrichment Triad Model, and 24 periods of classes were progressed according to the teaching plan. One period of class for each subcategories of mathematical thinking ability; ability of intuitional insight, systematizing information, space formation/visualization, mathematical abstraction, mathematical reasoning, and reflective thinking were chosen and analyzed regarding teaching, teaming process and products. Problem solving examples that could be anticipated through teaching and teaming process and products analysis, and creative problem solving examples were suggested, and suggestions about teaching bright children using open-ended tasks were deduced based on the analysis of the characteristic of tasks, role of the teacher, impartiality and probability of approaching through reflecting the classes. Through the case study of a mathematics class for bright children making use of open-ended tasks proved to satisfy the curiosity of the students, and was proved to be effective for providing and forming a habit of various mathematical thinking experiences by establishing atypical mathematical problem solving strategies. This study is meaningful in that it provided mathematically gifted children's problem solving procedures about open-ended problems and it made an attempt at concrete and practical case study about classes fur gifted children while most of studies on education for gifted children in this country focus on the studies on basic theories or quantitative studies.

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An Analysis of Representation Usage Ability and Characteristics in Solving Math Problems According to Students' Academic Achievement (수학 문제 해결에서 학업성취도에 따른 표상 활용 능력과 특징 분석)

  • Kim, Min-Kyung;Kwean, Hyuk-Jin
    • Communications of Mathematical Education
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    • v.24 no.2
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    • pp.475-502
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    • 2010
  • In this paper, the ability to use mathematical representations in solving math problem was analyzed according to student assessment levels using 113 first-year high school students, and the characteristics of their representation usage according to student assessment levels were also examined. For this purpose, problems were presented that could be solved using various mathematical representations, and the students were asked to solve them using a maximum of three different methods. Also, based on the comparative analysis results of a paper evaluation, six students were selected and interviewed, and the reasons for their representation usage differences were analyzed according to their student assessment levels. The results of the analysis show that over 50% of high ranking students used two or more representations in all questions to solve problems, but with middle ranking students, there were deviations depending on the difficulty of the questions. Low ranking students failed to use representation in diverse ways when solving problems. As for characteristics of symbol usage, high ranking students preferred using formulas and used mathematical representations efficiently while solving problems. In contrast, middle and low ranking students mostly used tables or pictures. Even when using the same representations, high ranking students' representations were expressed in a more structurally refined manner than those by middle and low ranking students.

Analysis on Connection of Curriculum and Textbooks in Elementary School Mathematics : Focused on 1~2 Grades (초등학교 수학과 교육과정과 교과서의 연계 분석 - 2009 개정 교육과정 초등학교 1~2학년군을 중심으로 -)

  • Chang, Hyewon;Kim, Dongwon;Lee, Hwanchul
    • School Mathematics
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    • v.15 no.4
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    • pp.759-783
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    • 2013
  • Both curriculum and textbooks play an important role in the process of didactical transposition from mathematics as a science to school mathematics. The 2009 revised national curriculum for mathematics introduced the system of grade-band, so its achievement criteria for mathematical contents tend to be addressed more and less generally in the curriculum. We need to investigate whether the achievement criteria were applied meaningfully in elementary textbooks for mathematics. This study aims to recognize the connection between the curriculum and the textbooks and make a suggestion for composing the following curriculum and its textbooks. To do this, we analyzed the mathematics textbooks for 1~2 grades in relation to the mathematical contents as per reconstructed one of curriculum achievement criteria, the mathematical terms and symbols, and the mathematical processes -mathematical problem solving, mathematical reasoning, mathematical communication. Based this analysis, futhermore, this study includes some didactical discussions and implications for development of mathematics textbooks in 3~4 and 5~6 grade-bands.

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The Effects of Metacognitive Training in Math Problem Solving Using Smart Learning System (스마트 러닝 시스템을 활용한 수학 문제 풀이 맥락에서 메타인지 훈련의 효과)

  • Kim, Sungtae;Kang, Hyunmin
    • The Journal of the Convergence on Culture Technology
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    • v.8 no.1
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    • pp.441-452
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    • 2022
  • Training using metacognition in a learning environment is one of the topics that have been continuously studied since the 1990s. Metacognition can be broadly divided into declarative metacognitive knowledge and procedural metacognitive knowledge (metacognitive skills). Accordingly, metacognitive training has also been studied focusing on one of the two metacognitive knowledge. The purpose of this study was to examine the role of metacognitive skills training in the context of mathematical problem solving. Specifically, the learner performed the prediction of problem difficulty, estimation of problem solving time, and prediction of accuracy in the context of a test in which problems of various difficulty levels were mixed within a set, and this was repeated 5 times over a total of 5 weeks. As a result of the analysis, we found that there was a significant difference in all three predictive indicators after training than before training, and we revealed that training can help learners in problem-solving strategies. In addition, we analyzed whether there was a difference between the experiment group and control group in the degree of test anxiety and math achievement. As a result, we found that learners in the experiment group showed less emotional and relationship anxiety at 5 weeks. This effect through metacognitive skill training is expected to help learners improve learning strategies needed for test situations.

An Analysis on the Mathematical Problem Solving Strategies of Ordinary Students, Gifted Students, Pre-service Teachers, and In-service Teachers (일반학생, 영재학생, 예비교사, 현직교사의 다전략 수학 문제해결 전략 분석)

  • Park, Mangoo
    • Journal of the Korean School Mathematics Society
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    • v.21 no.4
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    • pp.419-443
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    • 2018
  • The purpose of this study was to analyze the problem solving strategies of ordinary students, gifted students, pre-service teachers, and in-service teachers with the 'chicken and pig problem,' which has multiple strategies to obtain the solution. For this study, 98 students in the 6th grade elementary schools, 96 gifted students in a gifted institution, 72 pre-service teachers, and 60 in-service teachers were selected. The researcher presented the "chicken and pig" problem and requested them the solution strategies as many as possible for 30 minutes in a free atmosphere. As a result of the study, the gifted students used relatively various and efficient strategies compared to the ordinary students, and there was a difference in the most used strategies among the groups. In addition, the percentage of respondents who suggested four or more strategies was 1% for the ordinary students, 54% for the gifted students, 42% for the pre-service teachers, and 43% for the in-service teachers. As suggestions, the researcher asserted that various kinds of high-quality mathematical problems and solving experiences should be provided to students and teachers and have students develop multi-strategy problems. As a follow-up study, the researcher suggested that multi-strategy mathematical problems should be applied to classroom teaching in a collaborative learning environment and reflected them in teacher training program.

Aspects of Meta-affect According to Mathematics Learning Achievement Level in Problem-Solving Processes (문제해결 과정에서의 수학 학습 성취 수준에 따른 메타정의의 기능적 특성 비교 분석)

  • Do, Joowon;Paik, Suckyoon
    • Journal of Elementary Mathematics Education in Korea
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    • v.22 no.2
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    • pp.143-159
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    • 2018
  • Since the mathematics learning achievement level is closely related to problem-solving ability, it is necessary to understand the relationship between problem-solving ability and meta-affect ability from the point of view of general mathematics learning ability. In this study, we compared the frequency analysis and the case analysis of the functional aspects of the meta-affect in elementary school students' problem-solving processes according to mathematics learning achievement level in parallel with frequency analysis and case analysis. In other words, the frequency of occurrence of meta-affect, the frequency of meta-affective type, and the frequency of meta-functional types of meta-affect were compared and analyzed according to the mathematics learning achievement level in the collaborative problem-solving activities of small group members with similar mathematics learning achievement level. In addition, we analyzed the representative cases of meta-affect by meta-functional types according to the mathematics learning achievement level in detail. As a result, meta-affect in problem-solving processes of the upper level group acted as relatively various types of meta-functions compared to the lower level group. And, the lower level group, the more affective factors acted in the problem-solving processes.

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