• The Mathematical Education
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• v.57 no.4
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• pp.371-391
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• 2018

The purpose of this study is to analyze manifestation examples and effects of group creativity in mathematical modeling and to discuss teaching and learning methods for group creativity. The following two points were examined from the theoretical background. First, we examined the possibility of group activity in mathematical modeling. Second, we examined the meaning and characteristics of group creativity. Six students in the second grade of high school participated in this study in two groups of three each. Mathematical modeling task was "What are your own strategies to prevent or cope with blackouts?". Unit of analysis was the observed types of interaction at each stage of mathematical modeling. Especially, it was confirmed that group creativity can be developed through repetitive occurrences of mutually complementary, conflict-based, metacognitive interactions. The conclusion is as follows. First, examples of mutually complementary interaction, conflict-based interaction, and metacognitive interaction were observed in the real-world inquiry and the factor-finding stage, the simplification stage, and the mathematical model derivation stage, respectively. And the positive effect of group creativity on mathematical modeling were confirmed. Second, example of non interaction was observed, and it was confirmed that there were limitations on students' interaction object and interaction participation, and teacher's failure on appropriate intervention. Third, as teaching learning methods for group creativity, we proposed students' role play and teachers' questioning in the direction of promoting interaction.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.23-28
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• 2019

In this paper, we consider an interaction energy with attractive-repulsive potential. We survey recent results on the structure of global minimizers for the mildly repulsive interaction energy. We introduce a theorem which is important to the proof of the above results, and give a detailed proof of the theorem.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.31-50
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• 1999

We revisit the problems of testing three-factor classifica-tion models with a single observation per cell. A common approach in analyzing such nonreplicated data is to omit the highest order in-teraction and regard it as error. This paper discusses the use of a multiplicative model(See and Smith 1996 and 1998) which is applied on residuals in order to separate the variablility due to three-factor interaction from what is counted as random error. in particualr to test the significance of the interaction term we derived an approxi-mated distribution of the likelihood ratio test statistic based on the quadrilinear model known as Tucher's three-mode principal compo-nent model. The derivation utilizes the distribution of the eignevalues of the Wishart matrix.

• The Mathematical Education
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• v.41 no.3
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• pp.329-339
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• 2002

This study analyzes the epistemological meaning of‘social construction’in mathematical instruction. The perspective that consider the cognition of mathematical concept as a social construction is explained by a cyclic scheme of an academic context and a school context. Both of the contexts require a public procedure, social conversation. However, there is a considerable difference that in the academic context it is Lakatos' ‘logic of mathematical discovery’In the school context, it is Vygotsky's‘instructional and learning interaction’. In the situation of mathematics education, the‘society’which has an influence on learner's cognition does not only mean‘collective members’, but‘form of life’which is constituted by the activity with purposes, language, discourse, etc. Teachers have to play a central role that guide and coordinate the educational process involving interactions with learners in this context. We can get useful suggestions to mathematics education through this consideration of the social contexts and levels to form didactical situations of mathematics.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1017-1031
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• 2009

The problem of interaction of surface water waves by small undulation at the bottom of a laterally unbounded sea is treated on the basis of linear water wave theory for both normal and oblique incidences. Perturbation analysis is employed to obtain the first order corrections to the reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom undulation. Fourier transform method and residue theorem are applied to obtain these coefficients. As an example, a patch of sinusoidal ripples is considered in both the cases as the shape function. The principal conclusion is that the reflection coefficient is oscillatory in the ratio of twice the surface wave number to the wave number of the ripples. In particular, there is a Bragg resonance between the surface waves and the ripples, which is associated with high reflection of incident wave energy. The theoretical observations are validated computationally.

• Journal of Educational Research in Mathematics
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• v.12 no.3
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• pp.371-388
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• 2002

The purpose of this study is to analyze the effects of interaction based on contingent regulation between teacher and underachiever in elementary mathematics. For this purpose, research questions are established as follows; (1) Is there any difference between contingent regulation and natural regulation in mathematics achievement\ulcorner (2) Is there any difference between contingent regulation and natural regulation in affectionate perspective\ulcorner (3) Is there any difference between contingent regulation and natural regulation in adult regulation\ulcorner Two classes of fifth grade Children(10 children) were sampled from an elementary school in city of Daegu. One of them was assigned to the contingent regulation group and the other to natural regulation group. An experiment was conducted for 7 weeks. Two kinds of test instruments were used : pre-test and post-test. The pre-test scores guaranteed that both groups were homogeneous. Post-test was used to identify two effects(research questions (1) & (2)) and the post-test scores were analyzed by t-test. The results were as follows. (1) There was significant difference between contingent regulation and natural regulation in mathematics achievement. This means that experiment group was higher than control group and the interaction effect of contingent regulation was higher in post-test. The self-control indicated in experiment group. (2) There was slightly significant difference between contingent regulation and natural regulation in affectionate perspective. This means that experiment group turned to slightly positioner in post-test. (3) There was significant difference between contingent regulation and natural regulation in adult regulation. In other words, level of contingent regulation changed depending on underachievers' ability but level of natural regulation didn't change. Therefore, I suggest that contingent regulation based on Vygotsky theory would provide effective mathematics education for underachievers in elementary mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.1
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• pp.1-22
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• 2010

The purpose of this study was to examine the relationship between teacher's role and interaction patterns in mathematics classrooms. Teacher's role was divided into usual practices with students, usual practices with content and usual practices with students and contents, and interaction patterns were classified into report, inquiry and discussion. The subjects in this study were teachers and students in three fourth- grade classes in T elementary school located in Seoul. After the classes of every math teacher were observed, three teachers who played distinctively unique roles were selected in accordance with the results of the first-semester autonomous supervision, of open class for parents and of the instructional observation. Thus, there was a close relationship between the teacher roles and interaction patterns. And it's concluded that students are able to have a more discussion on each other's ideas in the student-centered classroom, and that teachers should perform active roles in that process. Given the findings of the study, there are some suggestions: First, the teachers appeared to fulfill consistent roles when their videotaped classes, study aids and performance assessment materials were analyzed, and they should play more active roles in mathematics class. Second, they should try to create the kinds of climate that encourages students to come up with ideas in an active manner. Third, earlier studies had focused on student-teacher interaction patterns, but this study found that the roles of the teachers depended on interaction with not only students but study aids and performance assessment materials, and that the interaction patterns hinged on their roles as well. Therefore more profound research efforts should be directed into this issue.

• Journal of Educational Research in Mathematics
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• v.10 no.2
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• pp.279-300
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• 2000

This research investigated students' interaction in the environment with dynamic geometry software such as Cabri II, and GSP in order to understand and analyze why computer environment is a richer interaction field for developing children's explorative ability than other traditional paper-and-pencil environments. This research focused on 5th graders' interaction with topics of transformational geometry and similar figure and analyzed children's learning process and their interview results gotten through audio and video recording. Computer exploration with a dynamic software seems to be very helpful for elementary students to learn geometry. However, the effectiveness of the computer should be discussed with respected to its methodological validity of teachers to guide students' explorative activities with a dynamic software.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.147-169
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• 2012

We introduce a Heaviside-function formulation of the interaction between incompressible two-phase fluid and a non-deformable solid. Fluid and solid interact in two ways : fluid satises the Dirichlet boundary condition imposed by the velocity field of solid, and solid is accelerated by the surface traction exerted by fluid. The two-way couplings are formulated by the Heaviside function to the interface between solid and fluid. The cumbersome treatment of interface is taken care of by the Heaviside function, and the interaction is discretized in a simple manner. The discretization results in a stable and accurate projection method.

• Education of Primary School Mathematics
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• v.5 no.1
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• pp.13-20
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• 2001

Interaction through communication plays critical role in the mathematics learning in the sociocultural perspectives. The communication make the students construct shared knowledge, and also plays a role of mediation in making meaning. So, we have to consider sociocultural eprspectives in design of the mathematics leaning using computer. While Computer Assisted Instruction was the one-directional teaching program which proceed from computer to students, mathematics leaning using computer in the sociocultural perspectives have to consider two-directional instruction that proceed from computer to students as well as from students to computer. This interactional activity is the critical thing in the mathematics learning using computer.