• School Mathematics
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• v.9 no.3
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• pp.427-445
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• 2007

This study presents the results of a case study that investigated a seventh grader's fractional reasoning related to multiplicative reasoning. In addition, by employing domain analysis and taxonomic analysis for analyzing qualitative data, I show how a qualitative methodology was used for the data collected by teaching experiment methodology. The study identifies three distinct issues that emerged as the student engaged in solving fraction problems: a view of fractions as operations vs. results, the issue of units, and mixed numbers vs. improper fractions. These three issues have instructional implications in that each of them is critical in developing multiplicative reasoning and investigating how they relate to each other suggests a way to improve multiplicative reasoning in fractional contexts.

• Journal of the Korean School Mathematics Society
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• v.13 no.3
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• pp.381-395
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• 2010

The purpose of this paper is to examine the competence and the methods of problem solving in four operations word problems based on the informal knowledges by five-year-old children. The numbers which are contained in problems consist of the numbers bigger than 5 and smaller than 10. The subjects were 21 five-year-old children who didn't learn four operations. The interview with observation was used in this research. Researcher gave the various materials to children and permitted to use them for problem solving. And researcher read the word problems to children and children solved the problems. The results are as follows: five-year-old children have the competence of problem solving in four operations word problems. They used mental computation or counting all materials strategy in addition problem. The methods of problem solving were similar to that of addition in subtraction, multiplication and division, but the rate of success was different. Children performed poor1y in division word problems. According to this research, we know that kindergarten educators should be interested in children's informal knowledges of four operations including shapes, patterns, statistics and probability. For this, it is needed to developed the curriculum and programs for informal mathematical experiences.

• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.227-246
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• 2003

In this paper, some terms of high school mathematics which read Chinese characters phonetically in Hangul are studied semantically. Nowadays, most terms of high school mathematics are terms of Chinese characters given the reading of them in Hangul alphabet. In such terms of Chinese characters, there are many loan-words from daily life and newly coined terms. Some such terms are examined in respect of meaningfulness and rule-ness. The degree of meaningfulness and rule-ness of loan-words from daily life are relative. Students seems familiar to loan-words usually, but it is difficult to know whether students seems to be familiar to loan-words or not. Degree of familiarity to a certain loan-word must be relative. In loan-words, there are such terms whose mathematical meaning is different from daily life meaning. Such terms are strong in rule-ness. Newly coined terms are strong in rule-ness. Students are not familiar to newly coined terms which are not used in daily life and have only mathematical meaning. In coining new terms using Chinese character, unit characters are related directly or indirectly to concept which unit characters want to express. So, It is possible to guess something unit characters want to express by investigating them. According to Vinner(1991), images can be evoked. But in case of reading Chinese characters phonetically in Hangul, it can not be guaranteed for Hangul mathematical terms to evoke images which the original mathematical terms evoked. To solve such problems semantic investigation of mathematical terms has been suggested. Through this process, transplanting images which the original mathematical terms evoked into Hangul terms are planned.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.59-75
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• 2012

This study aims to find whether the solutions for well-structured problems learned in school can be transferred to the moderately-structured problem and ill-structured problem. For these purpose, research questions were set up as follows: First, what are the patterns of changes in strategies used in solving the mathematics problems with different level of structuredness? Second, From the group using and not using proportion algorithm strategy in solving moderately-structured problem and ill-structured problem, what features were observed when they were solving that problems? Followings are the findings from this study. First, for the lower level of structuredness, the frequency of using multiplicative strategy was increased and frequency of proportion algorithm strategy use was decreased. Second, the students who used multiplicative strategies and proportion algorithm strategies to solve structured and ill-structured problems exhibited qualitative differences in the degree of understanding concept of ratio and proportion. This study has an important meaning in that it provided new direction for transfer and analogical problem solving study in mathematics education.

• Journal of Science Education
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• v.43 no.1
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• pp.17-42
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• 2019

This study, as an attempt to integrate mathematics and information for convergence education, was conducted to develop teaching-learning materials on mathematics education combined with coding education, which has recently been emphasized. We chose the subject of digital signature for coding education, and used SageMath as a coding program. In this study, we overview mathematics used in the elliptic curve digital signature algorithm, one of the many methods for digital signature, and developed the teaching-learning materials on the algorithm for mathematics education integrated with information education based on coding. The elliptic curve digital signature algorithm utilized in transactions of Bitcoin, which many people recently are interested in, is a good example, showing students that mathematics is applied to problem-solving in the real world and provides an optimal environment for implementation by coding. Accordingly, we expect that a class on algorithm will provide a specific teaching-learning program to achieve the goal of integrated mathematics education. By comprehensively considering the opinions of mathematicians, mathematics teachers and mathematics education experts, we expect that the teaching-learning program will be realized as a meaningful class in science high schools, high school's math clubs, and 'number theory' class in colleges.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.4
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• pp.383-403
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• 2019

The purpose of this study was to examine how students' perception of their mathematics teachers' instructional practices is associated with students' attitude toward mathematics, taking into account their self-efficacy in mathematics. The sample contained 4669 Korean fourth graders who participated in Trends in International Mathematics Science Study 2015. We used exploratory factor analysis and confirmatory factor analysis to explore the factor structure of three latent variables and conducted structural equation modeling to examine the hypothesized model. The results revealed that when students positively perceived their teachers' instructional practices, they tended to have a positive attitude toward mathematics. We also found that students' self-efficacy beliefs in mathematics positively mediated the relationship between perceived teachers' instructional practices and personal attitude toward mathematics. We discuss the practical and methodological implications of these findings and offer directions for future studies.

• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.447-462
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• 2003

The purpose of this study was to Investigate the preservice elementary teachers' pedagogical content knowledge of addition and subtraction. The subjects for data collection were 29 preservice elementary teachers and data were collected through open ended problems. The findings imply that the preservice elementary teachers show low level of understanding of addition and subtraction such as the word problem posing and the contexts of part-part-whole and compare. The research results indicate that the preservice elementary teachers possess primarily a procedural knowledge of pedagogical content knowledge and don't understand relationship with real-world situation. This study provide the information available on developing program for preservice elementary teachers.

• The Mathematical Education
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• v.59 no.3
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• pp.271-294
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• 2020

The purpose of this study was to explore the possibility of digital simulation by which pre-service teachers (PSTs) can approximate the core teaching practice of eliciting student thinking. This study examined PSTs' questions to elicit student thinking, their use of "pause" session and peer feedback, and their reflections on doing a digital simulation. We analyzed a two-hour digital simulation session with 13 PSTs who enrolled in the elementary mathematics methods course. The results showed that PSTs shifted their general questions to more content-specific questions throughout the simulation and made a quick transition to comparing students' strategies. The number of lead PST-initiated "pause" ranged one to four times for various reasons. Their peer-coaches did not voluntarily "pause" the simulation session but actively shared what they noticed from the student work samples and suggested the next teaching moves. Without utilizing the pause session, the dramatic improvement of questioning was not observed. Even though the PSTs felt overwhelmed with interacting with the student-avatars in real-time, they highlighted the benefits of simulations, appreciated the opportunity to learn the core teaching practice, and viewed this digital simulation as "real" and "authentic" experience. The findings of this study provide implications for re-designing a practice-based teacher education program.

• The Mathematical Education
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• v.61 no.4
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• pp.559-579
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• 2022

Research on lexicon and language provides insights into the interests, values and practices of a community where individuals use the language. The International Classroom Lexicon Project, in which ten countries participated, identified own country's mathematics teaching and learning lexicons by investigating mathematics classroom instruction from teachers' perspectives in a speaking-oriented community. This study, as an extension of the International Classroom Lexicon Project research, investigated pedagogical lexicons used in 「Mathematics and Education」 journals specialized for Korean professional mathematics teachers published by the Korean Society of Teachers of Mathematics. Using the text mining approach, we also traced how these pedegogical lexicons have changed quantitatively over the past 10 years with a diachronic perspective. As a results, several novel terms were found in the writing-oriented community, which were not identified in the speaking-oriented community. In addition, we could discover some pedagogical lexicons have increased statistically significantly and some lexicons appeared(increased) rapidly across years. This implies the teacher community's values and zeitgeist by reflecting these changes in the sociocultural, incidental and social changing (i.e., periodical change) contexts. This study has value as a first step in understanding zeitgeist for mathematics education in Korean mathematics teacher community according to changes of times over the past 10 years. Also, this study contributes to the methodological insights: the text mining technique provides a methodological contribution to researching changes in interests, values and zeitgeist according to these changes in the times.

• Journal of The Korean Association For Science Education
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• v.40 no.4
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• pp.359-374
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• 2020

This study is a complex type consisting of survey study and self-study. The former investigated elementary teachers' epistemological beliefs on convergence knowledge and teaching. As a representative of the result of survey study I, as a teacher as well as a researcher, was the participant of the self-study, which investigated my epistemological belief on convergence knowledge and teaching and my execution of convergent science teaching based on family resemblance of mathematics, science, and physical education. A set of open-ended written questionnaires was administered to 28 elementary teachers. Participating teachers considered convergent teaching as discipline-using or multi-disciplinary teaching. They also have epistemological beliefs in which they conceived convergence knowledge as aggregation of diverse disciplinary knowledge and students could get it through their own problem solving processes. As a teacher and researcher I have similar epistemological belief as the other teachers. During the self-study, I tried to apply convergence knowledge system based on the family resemblance analysis among math, science, and PE to my teaching. Inter-disciplinary approach to convergence teaching was not easy for me to conduct. Mathematical units, ratio and rate were linked to science concept of velocity so that it was effective to converge two disciplines. Moreover PE offered specific context where the concepts of math and science were connected convergently so that PE facilitated inter-disciplinary convergent teaching. The gaps between my epistemological belief and inter-disciplinary convergence knowledge based on family resemblance and the cases of how to bridge the gap by my experience were discussed.