• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.77-93
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• 2011

Jisuguimundo(地數龜文圖) is a magic hexagon created by Suk-Jung Choi in his book about three hundreds years ago in Korea. Recently attention is focused on jisuguimundo, and it is known that jisuguimundos exist when magic number is from 77 to 108, however a general method making jisuguimundos is not known so far. Up to now, methods of making jisuguimundos using computers are known. In this study, a method making jisuguimundos is suggested using pairs of two numbers with sum p and q ($p{\neq}q$) alternately when magic number is from 88 to 92, and from 94 to 98, without using computer in elementary math class as a task for problem solving. Mathematical theory is introduced for this method, and jisuguimundos are presented which are found out through this method. Elementary students are expected to make their own jisuguimundo using this method.

• School Mathematics
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• v.14 no.3
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• pp.357-375
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• 2012

This research intends to examine how 6th graders (age 12) generalize various increasing patterns. In this research, 6 problems corresponding to the ax, x+a, ax+c, ax2, and ax2+c patterns were given to 290 students. Students' generalization methods were analysed by the generalization level suggested by Radford(2006), such as arithmetic and algebraic (factual, contextual, and symbolic) generalization. As the results of the study, we identified that students revealed the most high performance in the ax pattern in the aspect of the algebraic generalization, and lower performance in the ax2, x+a, ax+c, ax2+c in order. Also we identified that students' generalization methods differed in the same increasing patterns. This imply that we need to provide students with the pattern generalization activities in various contexts.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.719-745
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• 2012

This research is a study on student's understanding fundamental conception of mathematical curriculum, especially in geometry domain. The goal of researching is to analyze student's wrong conception about that domain and get the mathematical teaching method. We developed various questions of descriptive assessment. Then we set up the term, procedure of research for the understanding student's knowledge of geometry. And we figured out the student's understanding extent through analysing questions of descriptive assessment in geometry. In this research, we concluded that most of students are having difficulty with defining the fundamental conception of mathematics, especially in geometry. Almost all the students defined the fundamental conceptions of mathematics obscurely and sometimes even missed indispensable properties. Prior to this study, we couldn't identify this problem. Here are some suggestions. First, take time to reflect on your previous mathematics method. And then compile some well-selected questions of descriptive assessment that tell us more about student's understanding in geometry.

• Education of Primary School Mathematics
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• v.21 no.2
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• pp.131-150
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• 2018

The structure of a mathematics task shapes the aspects of learning of those who solve the task. This study explores the process of understandings on the statistical variability of primary school students. Students were given two problems with different degrees of structuring - a well-structured problem (WSP) and an ill-structured problem (ISP) - and discussed in a group to solve each task. The highest level of development achieved in both cases appeared to be similar. However, when given the ISP, students dynamically proposed ideas and justified the conclusion based on their hypothesis. Furthermore, all students actively participated in solving the ISP until the end whereas some students were marginalized while solving the WSP. This discrepancy results from the difference in the degrees of task structuring.

• School Mathematics
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• v.5 no.3
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• pp.385-399
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• 2003

In our present elementary mathematics curriculum, natural numbers are taught by using the a method of one-to-one correspondence or counting operation which are not related to measurement, and fractional numbers are taught by using a method which is partially related to measurement. The most serious limitation of these teaching methods is that natural numbers and fractional numbers are separated. To overcome this limitation, Dewey and Davydov insisted that the natural number and the fractional number should be taught by measurement of quantity. In this article, we suggested a method of teaching the natural number and the fractional number by measurement of quantity based on the claims of Dewey and Davydov, and compare it with our current method. In conclusion, we drew some educational implications of teaching the natural number and the fractional number by measurement of quantity as follows. First, the concepts of the natural number and the fractional number evolve from measurement of quantity. Second, the process of transition from the natural number to the fractional number became to continuous. Third, the natural number, the fractional number, and their lower categories are closely related.

• School Mathematics
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• v.18 no.2
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• pp.323-348
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• 2016

The 2009 revised national mathematics curriculum have inserted mathematical 'linking cube' activities in the 6th grade math classes to improve students' spatial problem solving abilities and communication skills. However, we found that it was hard for teachers to teach problem solving and communication skills due to the absence of mathematical way of representing linking cubes in the classroom. In this paper, we propose 3D 'turtle representation system' as teaching and learning tools for linking cube activities. After using turtle representation system for linking cube activities, teachers responded that turtle representation system is a valuable problem solving and communication tools for the linking cube mathematics classes. We conclude that turtle representation system is a well designed teaching and learning tools for linking cube activities, and there are lots of educational meanings in the 3D turtle representation system.

• The Mathematical Education
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• v.48 no.3
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• pp.329-352
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• 2009

The purpose of this study was to investigate the effects of small group cooperative communicative activities on the strategies for estimating measurement. To do this, two research questions were set as follow: First, are there any differences between strategies employed by students in the experimental group and the control group before and after the estimating measurement activities? Second, are there any differences between strategies employed by students in different ability levels(upper, middle, lower) of pre-estimating measurement test in the experimental group? The research results were drawn from the investigation as below: First, the strategical change of before and after the estimating measurement tasks in the experimental group was quite noticeable. Unlike the small strategical change in the control group, small group cooperative communicative learning resulted in a decrease of simple memorization and guessing strategies and an increase of refined strategies such as the standard strategy, clustering, unit load and so on. Second, mathematical communicative activities in a small group cooperative learning showed that the students in the upper level of pre-estimating measurement test used more refined strategies and the students in the lower level used simple memorization and guessing strategy more frequently. And through interaction in small group, students could have chances to recognize error of strategies and to modify and learn strategies. In conclusion, small group cooperative activities allowed students to have chances to communicate mathematically and it is a efficient way of helping students learn estimating measurement strategies.

• Communications of Mathematical Education
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• v.32 no.4
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• pp.455-475
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• 2018

The purpose of this study is to investigate characteristics of pre-service teachers' cognition about learning through the use of technology by employing a teacher education program in the use of technology-friendly flipped classroom. For this purpose, 45 pre-service teachers participated in the study and they completed both pre- and post-surveys including questions about Technology Adopter Category Index(TACI) and Technological Pedagogical Content Knowledge(TPACK). They were also asked to write self-reflections on mathematics softwares(Geometer's Sketch Pad(GSP), Geogebra, Cabri 3D). Results show that the teacher education program in the use of technology-friendly flipped classroom affected pre-service teachers' cognitions of TACI and TPACK, and they perceived that technology integration helped students' mathematics learning process. Findings from this study indicate that ideas about how to develop a technology-friendly teacher education program are more specified..

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.475-496
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• 2018

Although the multiplication of decimal fractions is expected to be easy for students to understand because of the similarity to natural numbers multiplication in computing methods, students show many errors in the multiplication of decimal fractions. This is a result of the instruction focused more on skill mastery than conceptual understanding. This study is a basic study for effectively developing a unit of multiplication of decimal fractions. For this purpose, we analyzed the curriculums' performance standards, significance in teaching-learning and evaluation, contents and methods for teaching multiplication of decimal fractions from the 7th curriculum to the revised curriculum of 2015 and the textbooks' activities and lessons. Further, we analyzed preceding studies and introductory books to suggest effective directions for developing teaching unit. As a result of the analysis, three implications were obtained: First, a meaningful instruction for estimation is needed. Second, it is necessary to present a visual model suitable for understanding the meaning of decimal multiplication. Third, the process of formalizing an algorithms for multiplying decimal fractions needs to be diversified.

• The Mathematical Education
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• v.60 no.1
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• pp.1-19
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• 2021

This study investigates students' conceptions of fractions from a measurement approach while providing a technological environment designed to support students' understanding of the relationships between quantities and adjustable units. 13 third-graders participated in this study and they were involved in a series of measurement tasks through task-based interviews. The tasks were devised to investigate the relationship between units and quantity through manipulations. Screencasting videos were collected including verbal explanations and manipulations. Drawing upon the theory of semiotic mediation, students' constructed concepts during interviews were coded as mathematical words and visual mediators to identify conceptual profiles using a fine-grained analysis. Two students changed their strategies to solve the tasks were selected as a representative case of the two profiles: from guessing to recursive partitioning; from using random units to making a relation to the given unit. Dragging mathematical objects plays a critical role to mediate and formulate fraction understandings such as unitizing and partitioning. In addition, static and dynamic representations influence the development of unit concepts in measurement situations. The findings will contribute to the field's understanding of how students come to understand the concept of fraction as measure and the role of technology, which result in a theory-driven, empirically-tested set of tasks that can be used to introduce fractions as an alternative way.