• School Mathematics
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• v.12 no.3
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• pp.411-424
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• 2010

The fractional concept consists of various meaning, so that it is difficult to understand in primary school mathematics. In this article, we intend to analyze the cognition of 54 pre-service elementary teachers about the operations of partitioning and iterating that are based on Steffe's fraction schemes. The following fraction problem is used in this analysis: If the bar $\Box$ represent 3/8, then create a bar that is equivalent to 4/3. In our analysis, the 43% of pre-service elementary teachers can be well to treat the operations of partitioning and iteration. The 33% are use the equivalent fractions. But the 19% is not good. From the our analysis, it is important that pre-service elementary teachers must be have experimental(operational) thinking as the science education. And in this study we apply the operations of partitioning and iterating to the fraction activity of textbooks.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.769-789
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• 2016

Pattern activities are useful to develop functional thinking of young students, but there has been lack of research on how to teach patterns. This study explored teaching methods of geometric patterns for developing functional thinking of elementary school students, and then analyzed the lessons in which such methods were implemented. For this, three classrooms of fourth grades in elementary schools were selected and three teachers taught geometric patterns on the basis of the same lesson plan. The lessons emphasized noticing the commonality of a given pattern, expanding the noti ce for the commonality, and representing the commonality. The results of this study showed that experience of analyzing the structure of a geometric pattern had a significant impact on how the fourth graders reasoned about the generalized rules of the given pattern and represented them in various methods. This paper closes with several implications to teach geometric patterns in a way to foster functional thinking.

• Journal of Educational Research in Mathematics
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• v.15 no.2
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• pp.131-145
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• 2005

This study intends to analyze didactically on triangle-determining conditions and triangle-congruence conditions. The result of this study revealed the followings: Firstly, many pre-service mathematics teachers and secondary school students have insufficient understanding or misunderstanding on triangle-determining conditions and triangle-congruence conditions. Secondly, the term segment instead of edge may show well the concern of triangle-determining conditions. Thirdly, when students learn the method of finding six elements of triangle using the law of sines and cosines in high school, they should be given the opportunity to reflect the relation and the difference between triangle-determining situation and the situation of finding six elements of triangle. Fourthly, accepting some conditions like SSA-obtuse as a triangle-determining condition or not is not just a logical problem. It depends on the specific contexts investigating triangle-determining conditions. Fifthly, textbooks and classroom teaching need to guide students to discover triangle-deter-mining conditions in the process of inquiry from SSS, SSA, SAS, SAA, ASS, ASA, AAS, AAA to SSS, SAS, ASA, SAA. Sixthly, it is necessary to have students know the significance of 'correspondence' in congruence conditions. Finally, there are some problems of using the term 'correspondent' in describing triangle-congruence conditions.

• Journal of the Korean School Mathematics Society
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• v.16 no.2
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• pp.459-478
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• 2013

Didactic transposition refers to an adaptive treatment of mathematical knowledge into knowledge to be taught. This study intends to investigate how mathematical knowledge was modified in mathematics textbooks and lessons. This study identified examples of didactic transposition in mathematics textbooks and lessons in Korea and those in the U.S., The examples identified were FOIL method, trigonometry using s, c, t in writing style, order of operations(PEMDAS), area of a circle and circumference, order of prefixes in the metric system, trigonometry(SOH, CAH, TOA), operations on integer, and regular polyhedra. These examples were classified into the two categories, one for mnemonics, and one for concreteness and intuitiveness. Then a survey was conducted for in-service teachers in Korea and those in the U.S. to evaluate the appropriateness and the necessity of didactic transposition. Lastly, the potential didactic phenomena, meta-cognitive shift which may occur with these examples were discussed.

• School Mathematics
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• v.18 no.3
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• pp.479-501
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• 2016

This study was conducted as a learning project for 20 pre-third graders in high school by means of math textbooks, G+, and sample questions from previous CSAT as learning tools for 9 weeks from Dec. 24, 2015. The purpose of the study was to develop 'math textbook project learning(MtPL)', a mixed learning method combined on-line with off-line, and analyze the effects of MtPL on the affective domain of high school students. As a result of the study, it was found that MtPL had positive effects on self-efficacy and self-confidence of students, while the collaborative learning using a textbook and teacher's role worked as instrumental motivation in mathematics learning. The result also implies that the perception of high school students, who think to resolve more difficult math problems to succeed in CSAT, about mathematics learning method has to be modified. Furthermore, it is shown that the preparation of CSAT by utilizing textbook and the use of textbook in math learning have been worked positively for the students.

• School Mathematics
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• v.15 no.4
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• pp.801-818
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• 2013

The purpose of this study is to investigate the relation between major subjects of industrial circle high school and mathematics matched with present 2007 revision curriculum. We compare and analyze learning contents in industrial circle's math education via various aspects including methods of explanations, contents domains, and contents levels. The analysis followed by the research study performed with literature study of curriculums and text books. Our research indicates that school curriculum should be reflected relation between industrial high school's each major course and mathematics, so each major course curriculum should be different. Many contents beyond high school mathematics were founded. Hence suitable mathematical maturity and levels within standard high school math curriculum should be considered when one make text books of major course in industrial circle high school.

• Communications of Mathematical Education
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• v.38 no.1
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• pp.69-92
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• 2024

This study analyzed students' mathematical noticing in high school sequence classes based on students' two perceptions of sequence. Specifically, mathematical noticing was analyzed in four aspects: center of focus, focusing interaction, task features, and nature of mathematics activities, and the following results were obtained. First of all, the change pattern of central of focus could not be uniquely described by any one component among 'focusing interaction', 'task features', and 'the nature of mathematical activities'. Next, the interactions between the components of mathematical noticing were identified, and the teacher's individual feedback during small group activities influenced the formation of the center of focus. Finally, students showed two different modes of reasoning even within the same classroom, that is, focusing interaction, task features, and nature of mathematics activities that resulted in the same focus. It is hoped that this study will serve as a catalyst for more active research on students' understanding of sequence.

• Journal of Families and Better Life
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• v.31 no.5
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• pp.97-108
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• 2013

The purpose of this study was to investigate what variables have a significant effect on child care center teachers' mathematics teaching efficacy among teachers' individual variables, mathematics activity variables, and teachers' awareness variables, and also whether these results are different for teachers of 0 to 2-year-olds when compared to teachers of 3 to 5-year-olds. The subjects consisted of 438 teachers from child care centers located in D city and K province of Korea. The results of this study were as follows: First, mathematics activity variables had a significant effect on the mathematics teaching efficacy of both teacher groups. Second, teachers' awareness of the environment of mathematics education had a significant influence on the mathematics teaching efficacy of both teacher groups, and for teachers of 0 to 2-year-olds, that influence was the greatest among all of the variables. Third, teachers' awareness of the purpose of mathematics education had a significant effect on the mathematics teaching efficacy of only teachers of 0 to 2-year-olds. Lastly. teachers' awareness of the mathematics education curriculum had a significant influence on the mathematics teaching efficacy of only teachers of 3 to 5-year-olds, and that influence was the greatest. These results were discussed in terms of different types of support for each teacher group to improve the quality of mathematics education.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.33-55
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• 2011

This study explores the characteristics of calculus students' and instructors' discourses on the derivative using a communicational approach to cognition. The data were collected from surveys, classroom observations, and interviews. The results show that the instructors did not explicitly address some aspects of the derivative such as the relationship between the derivative function (f'(x)) and the derivative at a point (f'(a)), and f'(x) as a function, and that students incorrectly described or used these aspects for problem solving. It is also found that both implicitness in the instructors' discourse, and students' incorrect descriptions were closely related to their use of the word, "derivative" without specifying it as "the derivative function" or "the derivative at a point." Comparison between instructors' and students' discourses suggests that explicit discussion about the derivative including exact use of terms will help students see the relationship that f'(a) is a number, a point-specific value of f'(x) that is a function, and overcome their mixed and incorrect notion "the derivative" such as the tangent line at a point.

• Journal of Elementary Mathematics Education in Korea
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• v.2 no.1
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• pp.1-14
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• 1998

Nowadays there are presented various educational methods based on Constructivism which is regarded as newest epistemological paradigm about Knowledge and knowing, but none which is dramatically new. The educational methods proposed by the advocates of Constructivism are already put in practice by the teachers that are interested. Following this, we will interpret R. Skemp's theory about educational methods based on Constructivism. Here we will introduce various play activities for building number concepts.