• Journal of Educational Research in Mathematics
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• v.22 no.3
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• pp.311-329
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• 2012

This study analyzed third graders' understanding on the part-whole fraction concept in both the continuous and the discrete contexts. A set of problems were developed as an equivalent form to compare and contrast students' understanding of fraction in the two contexts. Unexpectedly, the results of this study showed that students' performance in the continuous contexts was slightly lower than their performance in the discrete contexts. Students tended to use different strategies depending on the contexts and they had difficulties in applying what they knew in the new contexts. On the basis of the detailed analyses about students' difficulties and their sources, this paper provides information on how to construct curricular materials and how to teach the basic concepts related to the part-whole fraction.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.159-170
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• 2012

Many obstacles have been found in the learning of ratio and rate. The types of epistemological obstacles concern 'terms', 'calculations' and 'symbols'. It is important to identify the epistemological obstacles that students must overcome to understand the learning of ratio and rate. In this respect, the present study attempts to figure out what types of epistemological obstacles emerge in the area of learning ratio and rate and where these obstacles are generated from and to search for the teaching implications to correct them. The research questions were to analyze this concepts as follow; A. How do elementary students show the epistemological obstacles in ratio and rate? B. What is the reason for epistemological obstacles of elementary students in the learning of ratio and rate? C. What are the teaching implications to correct epistemological obstacles of elementary students in the learning of ratio and rate? In order to analyze the epistemological obstacles of elementary students in the learning of ratio and rate, the present study was conducted in five different elementary schools in Seoul. The test was administered to 138 fifth grade students who learned ratio and rate. The test was performed three times during six weeks. In case of necessity, additional interviews were carried out for thorough examination. The final results of the study are summarized as follows. The epistemological obstacles in the learning of ratio and rate can be categorized into three types. The first type concerns 'terms'. The reason is that realistic context is not sufficient, a definition is too formal. The second type of epistemological obstacle concerns 'calculations'. This second obstacle is caused by the lack of multiplication thought in mathematical problems. As a result of this study, the following conclusions have been made. The epistemological obstacles cannot be helped. They are part of the natural learning process. It is necessary to understand the reasons and search for the teaching implications. Every teacher must try to develop the teaching method.

• School Mathematics
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• v.11 no.3
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• pp.479-496
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• 2009

Some children can construct a basic concept of addition and subtraction during the preschool years. Children start to experience mathematics via numbers and their of operations and contact with various contexts of addition and subtraction. In special, word problems reflect mathematics which is appliable to real life. In this paper, I analyse the types of word problems in text book and its students' responses. First, I analyse the types of addition word problems which consist of change add-into situations and part-part-whole situations. Second, I analyse the types of subtraction word problems which consist of change take-away situations, compare situations and equalize situations. Third, I analyse the students' responses by the types of word problems in addition and subtraction. And 115 2nd grade elementary school students participated in this survey. The following results have been drawn from this study. First, the proposition of word problems of part-part-whole situations is higher than that of change add-into situations and the proposition of word problems of take-away situations is higher than that of compare situations and equalize situations. According to the analysis about students' responses, It is no difference between change add-into situations and part-part-whole situations. But the proposition of word problems of take-away situations is higher than that of compare situations and equalize situations. This results from word problems which contain unnecessary information in problem. So, we have to present the various word problems to students.

• Education of Primary School Mathematics
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• v.25 no.2
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• pp.161-178
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• 2022

Korean uses a dual numeral system consisting of native and Chinese words. This dual numerical system is customarily selected in real life, mixed with two methods, or irregularly transformed. Therefore, the burden on both students and teachers is increased in the learning guidance process of numeral. This study recognized the need to improve the difficulty of learning guidance due to the dual numeral system. To this end, the context in which the numeral system method is selected, various modified cases, and related guidance contents of the current curriculum and textbooks were analyzed and organized. As a result of the analysis, there were characteristics of the selection and deformation of the numeral system method, which appears according to the actual situation using numerical. However, the criteria for characteristics were ambiguous and there were no specific guidance guidelines in the curriculum and textbooks. In this case, since the role of the teacher is more important, the teacher should be aware of the detailed characteristics of the actual situation related to the dual numeral system and let the student understand through experience and practice on various aspects of the use of the dual numeral system.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.655-676
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• 2016

The purpose of this study is to examine the effects of teaching on functional thinking, one of the algebraic thinking in sixth grade students level. For this study, we developed functional thinking based-teaching through analyzing mathematical curriculum and preceding research, which consisted of 12 classes, and we investigated the effects of teaching through quantitative and qualitative analysis. In the results of this study, functional thinking based-teaching was statistically proven to be more effective in improving algebraic reasoning skills and lower elements which is an algebraic reasoning as generalized arithmetic and functional thinking, compared to traditional textbook-centered lessons. In addition, the functional thinking based-teaching gave a positive impact on the functional thinking level. Thus functional thinking based-teaching provides guidance on the implications for teaching and learning methods and study of the functional thinking in the future, because of the significant impact on the mathematics learning in six grade students.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.635-652
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• 2023

This study conducts a comprehensive analysis of the curricular progression of the concepts and learning sequences of 'lines', specifically, 'line segments', 'straight lines', and 'rays', at the elementary school level. By examining mathematics curricula and textbooks, spanning from 2nd to 7th and 2007, 2009, 2015, and up to 2022 revised version, the study investigates the timing and methods of introducing these essential geometric concepts. It also explores the sequential delivery of instruction and the key focal points of pedagogy. Through the analysis of shifts in the timing and definitions, it becomes evident that these concepts of lines have predominantly been integrated as integral components of two-dimensional plane figures. This includes their role in defining the sides of polygons and the angles formed by lines. This perspective underscores the importance of providing ample opportunities for students to explore these basic geometric entities. Furthermore, the definitions of line segments, straight lines, and rays, their interrelations with points, and the relationships established between different types of lines significantly influence the development of these core concepts. Lastly, the study emphasizes the significance of introducing fundamental mathematical concepts, such as the notion of straight lines as the shortest distance in line segments and the concept of lines extending infinitely (infiniteness) in straight lines and rays. These ideas serve as foundational elements of mathematical thinking, emphasizing the necessity for students to grasp concretely these concepts through visualization and experiences in their daily surroundings. This progression aligns with a shift towards the comprehension of Euclidean geometry. This research suggests a comprehensive reassessment of how line concepts are introduced and taught, with a particular focus on connecting real-life exploratory experiences to the foundational principles of geometry, thereby enhancing the quality of mathematics education.

• School Mathematics
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• v.4 no.4
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• pp.633-642
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• 2002

This paper focuses on the concepts of a value of ratio and a rate in elementary school mathematics. Although the concept of a value of ratio can be distinguished meaningfully from that of a rate by phenomenological analyses, this distinction is impossible at the elementary school level. Two concepts tend to be treated as identical, therefore they need to be classified by the other methods. By analyzing the series of mathematics textbooks from the first curriculum to the present 7th curriculum, this paper investigated how two concepts have been transposed into the products of school mathematics. In addition, we discussed how the difference of two concepts in the changing process of definitions have been presented clearly to the students. As a result, this paper concluded that the difference of two concepts has not been developed clearly for elementary students in general, except the textbook by the 7th curriculum. The definitions of two concepts were described obscurely so that the students may confuse the concept of a value of ratio with that of a rate. The role of a value of ratio needs to be reconsidered when it is applied to set proportional expressions. Therefore, this paper suggests not adhering to the terminology ‘value of ratio’ to present the ratio as a quotient or the rate as a fractional representation in school mathematics.

• Communications of Mathematical Education
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• v.36 no.3
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• pp.335-353
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• 2022

The purpose of this study is to identify the characteristics and types of errors in the conceptual image of Korean language learners according to the types of terms in mathematics that are the basis for solving mathematical word problems, and to prepare basic data for effective teaching and learning methods in solving the word problems of Korean language learners. To do this, a case study was conducted targeting four Korean language learners to analyze the specific conceptual images of terms registered in curriculum and terms that were not registered in curriculum but used in textbooks. As a result of this study, first, it is necessary to guide Korean language learners by using sufficient visualization material so that they can form appropriate conceptual definitions for terms in school mathematics. Second, it is necessary to understand the specific relationship between the language used in the home of Korean language learners and the conceptual image of terms in school mathematics. Third, it is necessary to pay attention to the passive term, which has difficulty in understanding the meaning rather than the active term. Fourth, even for Korean language learners who do not have difficulties in daily communication, it is necessary to instruct them on everyday language that are not registered in the curriculum but used in math textbooks. Fifth, terms in school mathematics should be taught in consideration of the types of errors that reflect the linguistic characteristics of Korean language learners shown in the explanation of terms. This recognition is expected to be helpful in teaching word problem solving for Korean language learners with different linguistic backgrounds.

• Journal of the Korean Society of Earth Science Education
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• v.16 no.2
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• pp.291-301
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• 2023

In this study, the STEAM elements and convergence types which appeared in the creative and convergent activities in authorized elementary school science textbooks for 5^th and 6^th graders were analyzed. For this study, creative and convergence activities presented in 9 different science textbooks for 5^th and 6^th graders were selected and the STEAM elements and convergence types were analyzed by each publisher, grade-semester, and science field. The results of this study are as follows. First, there was a large variation by publisher in the total frequency of STEAM elements and the frequency of each element in creative and convergence activities. Second, the ratio of convergence type consisting of two elements was very high, and the higher the number of fused elements, the lower the ratio appeared in overall. Third, the art (A) element had the highest frequency in all grade-semesters, and the technology (T), engineering (E), mathematics (M) elements differed in the distribution of frequency by grade-semesters. Fourth, the engineering (E) element in the 'integration' field, and the art (A) element in the fields of 'movement and energy', 'material', 'earth and universe', and 'life' had the highest frequency.

• Education of Primary School Mathematics
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• v.24 no.2
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• pp.103-114
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• 2021

In this study I recognized the problems with the use of the terms 'quotient' and 'reminder' in the division of decimal and explored ways to improve them. The prior studies and current textbooks critically analyzed because each researcher has different views on the use of the terms 'quotient' and 'reminder' because of the same view of the values in the division calculation. As a result of this study, I proposed to view the result 'q' and 'r' of division of decimals by division algorithms b=a×q+r as 'quotient' and 'reminder', and the amount equal to or smaller to q the problem context as a final 'result value' and the residual value as 'remained value'. It was also proposed that the approximate value represented by rounding the quotient should not be referred to as 'quotient'.