• Education of Primary School Mathematics
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• v.27 no.2
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• pp.187-198
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• 2024

The addition and subtraction relationship and the multiplication and division relationship are explicitly dealt with in second and third grade mathematics textbooks. However, these relationships are not discussed anymore in the problem situations and activities in the 4th, 5th, and 6th grade mathematics textbooks. In this study, we investigate the calculation principles of subtraction and division in the elementary school mathematics textbooks. Based on our investigation, we justify the addition and subtraction relationship and the multiplication and division relationship at the level of children's understanding so that we discuss some problem situations and activities where the relationships can be applied to subtraction and division. In addition, we suggest educational implications that can be obtained from children's applying the relationships and the properties of equations to subtraction and division.

• Journal of Elementary Mathematics Education in Korea
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• v.3 no.1
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• pp.21-39
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• 1999

In this paper, we first exam the relation between Piaget's theory of cognitive development and cognitive constructivism. With it's outcome We find three principles of constructivist teaching-learning methods for primary mathematics These are as follows 1) active learning based on self-regulatory process 2) empirical learning by self initiated activities 3) individual learning derived from present cognitive structure and fits of new experiences. Finally we introduce several examples for classroom practice applied the above principles in primary mathematics.

• 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.

• 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.

• Communications of Mathematical Education
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• v.36 no.2
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• pp.229-252
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• 2022

This study analyzed the introduction of addition and subtraction, including the composition and decomposition of numbers in the Korean, Singaporean, American, and Japanese elementary mathematics textbooks. The analytic foci of this study included visual models and their connections with the given problem contexts, the introduction of addition/subtraction or addition/subtraction sentences and their connections with the visual models, and additional activities for students to develop a relational understanding of the equal sign. The results of the analysis demonstrated diverse connections, mainly because the problem contexts, visual models, and the introduction of addition/subtraction or addition/subtraction sentences were implemented differently for each textbook. There were differences among the textbooks in what order of problem contexts were presented. Regarding the use of visual models, two textbooks tended to use one model consistently, whereas the other textbooks used various models depending on the problem contexts. There were subtle but significant differences in introducing addition/subtraction or addition/subtraction sentences. For a relational understanding of the equal sign, all textbooks included activities emphasizing that both sides of the equal sign are equal. Based on the results of this study, this paper closes with several implications related to the problem contexts to introduce addition/subtraction and addition/subtraction sentences as well as the use of visual models, which can serve as a basis for a new unit for the subsequent textbook.

• Journal of the Korean School Mathematics Society
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• v.17 no.3
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• pp.409-435
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• 2014

This study examines relations between the 5th graders' fraction operation skills and error types on constructed-response items. As results, first, the participants have lower fraction operation skills on 'multiplication of fraction' than 'addition and subtraction of fraction'. Second, the participants have different error types depend on their constructed-response items. Most of error types which group with high ability made was 'leap of solving process', both groups error type with medium ability as well as low ability is 'misunderstanding of questions'. Third, the operation skills on 'addition and subtraction of fraction' have an influence on their operation skills on 'multiplication of fraction', and error types of 'understanding of questions' and 'understanding of solving process' have the most effects on the influence.

• The Mathematical Education
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• v.62 no.3
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• pp.341-362
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• 2023

This study analyzed student noticing in a lesson that emphasized relational understanding of equal signs for first graders from four aspects: centers of focus, focusing interactions, mathematical tasks, and nature of the mathematical activity. Specifically, the instructional factors that emphasize the relational understanding of equal signs derived from previous research were applied to a first-grade addition and subtraction unit, and then lessons emphasizing the relational understanding of equal signs were conducted. Students' noticing in this lesson was comprehensively analyzed using the focusing framework proposed in the previous study. The results showed that in real classroom contexts centers of focus is affected by the structure of the equation and the form of the task, teacher-student interactions, and normed practices. In particular, we found specific teacher-student interactions, such as emphasizing the meaning of the equals sign or using examples, that helped students recognize the equals sign relationally. We also found that students' noticing of the equation affects reasoning about equation, such as being able to reason about the equation relationally if they focuse on two quantities of the same size or the relationship between both sides. These findings have implications for teaching methods of equal sign.

• School Mathematics
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• v.13 no.4
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• pp.675-696
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• 2011

This study was designed to understand PCK to improve professionalism of teachers and derive implications about proper teachings methods. For achieving these research purposes, different PCK and teaching methods in class of three teachers were compared and analyzed targeting arithmetic operation unit of fraction. For this study, criteria of PCK analysis of teachers was set, PCK questionnaires were produced and distributed, teachers had interviews, PCK of teachers were analyzed, two times fraction class was observed and analyzed, and PCK of teachers and their classes were compared. Followings are results to analyze PCK of teachers about fraction. In relation to PCK of three teachers, first of all, A teacher accurately understood concepts of fraction and learners' errors that may occur when they study fraction. Also, he(she) proposed concrete teaching strategies for fraction based on manipulated materials. B teacher also understood concepts of fraction and learners' errors accurately too. On the other hand, C teacher laid stress on knowledge to stress principles and taught that they are bases for every class. These results mean that self-training and inservice- training should be efficiently upgraded to improve PCK of teachers.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.39-55
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• 2024

Recently, the 2022 revised mathematics curriculum has established achievement standards for equal sign and equality, and efforts have been made to examine teaching methods and student understanding of relational understanding of equal sign. In this context, this study conducted a lesson that emphasized relational understanding in an introduction to equal sign, and compared and analyzed the understanding of equal sign between the experimental group, which participated in the lesson emphasizing relational understanding and the control group, which participated in the standard lesson. For this purpose, two classes of students participated in this study, and the results were analyzed by administering pre- and post-tests on the understanding of equal sign. The results showed that students in the experimental group had significantly higher average scores than students in the control group in all areas of equation-structure, equal sign-definition, and equation-solving. In addition, when comparing the means of students by item, we found that there was a significant difference between the means of the control group and the experimental group in the items dealing with equal sign in the structure of 'a=b' and 'a+b=c+d', and that most of the students in the experimental group correctly answered 'sameness' as the meaning of equal sign, but there were still many responses that interpreted the equal sign as 'answer'. Based on these results, we discussed the implications for instruction that emphasizes relational understanding in equal sign introduction lessons.