• Journal of Gifted/Talented Education
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• v.15 no.2
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• pp.59-76
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• 2005

We examined the relations between the score of the divergent thinking in mathematical (Mathematical Creative Problem Solving Ability Test; MCPSAT: Lee etc. 2003) and non-mathematical situations (Torrance Test of Creative Thinking Figural A; TTCT: adapted for Korea by Kim, 1999). Subjects in this study were 213 eighth grade students(129 males and 84 females). In the analysis of data, frequencies, percentiles, t-test and correlation analysis were used. The results of the study are summarized as follows; First, mathematically gifted students showed statistically significantly higher scores on the score of the divergent thinking in mathematical and non-mathematical situations than regular students. Second, female showed statistically significantly higher scores on the score of the divergent thinking in mathematical and non-mathematical situations than males. Third, there was statistically significant relationship between the score of the divergent thinking in mathematical and non-mathematical situations for middle students was r=.41 (p<.05) and regular students was r=.27 (p<.05). A test of statistical significance was conducted to test hypothesis. Fourth, the correlation between the score of the divergent thinking in mathematical and non-mathematical situations for mathematically gifted students was r=.11. There was no statistically significant relationship between the score of the divergent thinking in mathematical and non-mathematical situations for mathematically gifted students. These results reveal little correlation between the scores of the divergent thinking in mathematical and non-mathematical situations in both mathematically gifted students. Also but for the group of students of relatively mathematically gifted students it was found that the correlations between divergent thinking in mathematical and non-mathematical situations was near zero. This suggests that divergent thinking ability in mathematical situations may be a specific ability and not just a combination of divergent thinking ability in non-mathematical situations. But the limitations of this study as following: The sample size in this study was too few to generalize that there was a relation between the divergent thinking of mathematically gifted students in mathematical situation and non-mathematical situation.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.651-662
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• 1998

Mathematics is means for making sense of one's experiential world and products of human activities. A usefulness of mathematics is derived from this features of mathematics. Keeping the meaning of situations during the mathematizing of situations. However, theories about the development of mathematical concepts have turned mainly to an understanding of invariants. The purpose of this study is to show the possibility of computer in representing situation and phenomena. First, we consider situated cognition theory for looking for the relation between various representation and situation in problem. The mathematical concepts or model involves situations, invariants, representations. Thus, we should involve the meaning of situations and translations among various representations in the process of mathematization. Second, we show how the process of computational mathematization can serve as window on relating situations and representations, among various representations. When using computer software such as ALGEBRA ANIMATION in mathematics classrooms, we identified two benifits First, computer software can reduce the cognitive burden for understanding the translation among various mathematical representations. Further, computer softwares is able to connect mathematical representations and concepts to directly situations or phenomena. We propose the case study for the effect of computer software on practical mathematics classrooms.

• Research in Mathematical Education
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• v.10 no.2 s.26
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• pp.103-113
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• 2006

The mathematics instructional beliefs of a teacher include the exterior mathematics instructional beliefs and the internal mathematics instructional beliefs. These two kinds of beliefs are formed in two kinds of different situations. The situated theory thinks that beliefs are related with the situations; so, the two kinds of beliefs are showed in the different situations. The internal instructional mathematics beliefs effect on the actual mathematics instruction, they ought to be noticeable.

• School Mathematics
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• v.1 no.2
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• pp.417-431
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• 1999

In this study, I consider Brousseau's theory of didactical situation focused on 'the development process of situations', and analyze some examples of didactical situation related to instruction of 'decimal' concept. To elaborate situations which really make a mathematical notion function, we have to analyze the essence of the notion, and to construct the situation which can be developed to situations of 'action-formulation-validation - institutionalization'. From this view, it can be said that the instruction of decimal concept in our country mainly lies in the situations of 'action' and 'institutionalization'. we have to provide more situations of 'formulation' and 'institutionalization' which can connect 'action' and 'institutionalization'.

• East Asian mathematical journal
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• v.31 no.4
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• pp.569-585
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• 2015

Many mathematics teachers in characterization high schools have been troubled to teach students because most of the students have weak interests in mathematics and they are also lack of preliminary mathematical knowledges. Currently many of mathematics teachers in such schools teach students using worksheets owing to the situation that proper textbooks for the students are not available. In this study, we referred to Chevallard's didactic transposition theory based on Brousseau's theory of didactical situations for mathematical teaching and learning. Our lessons utilizing worksheets necessarily entail encouragement of students' self-directed activities, active interactions, and checking the degree of accomplishment of the goal for each class. Through this study, we recognized that the elaborate worksheets considering students' level, follow-up auxiliary materials that help students learn new mathematical notions through simple repetition if necessary, continuous interactions in class, and students' mathematical activities in realistic situations were all very important factors for effective mathematical teaching and learning.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.883-898
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• 2013

The purpose of this study is to examine that high school students recognize mathematical situation when they are requested for changing identical mathematics situations into different situations. The results of the study are followings. First, percentage of correct answers to the questions of turning equal mathematical situation into function is higher than the one of turning equal mathematical situation into equation and inequality. As a result of individual interview for comprehensibility of the students on these relations, it is found that if degree goes up and there is different expressions of questionaries although mathematical situation is identical, it affects comprehensibility of the subjects. Second, we found that they cannot understand identical mathematics situations because they have trouble in drawing graph or applying to get the answer while many students understand a point of intersection on the graph as a correct answer. Third, As a result of individual interview for comprehensibility of the students on relation between equation, inequality and function, we found that students manage to get correct answer even without perfect comprehensibility on this relation.

• Honam Mathematical Journal
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• v.14 no.1
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• pp.99-106
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• 1992

• School Mathematics
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• v.7 no.4
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• pp.427-444
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• 2005

The Purpose of this study is to explore he mathematical discovery and justification of six 10th grade students through mathematical modeling activities in spreadsheet environments. The students investigated problem situations with a spreadsheet, which seem to be difficult to solve in paper and pencil environment. In spreadsheet environments, it is easy for students to form a data table and graph by inputting and copying spreadsheet formulas, and to make change specific variable by making a scroll bar. In this study those functions of spreadsheet play an important role in discovery and justification of mathematical rules which underlie in the problem situations. In modeling activities, the students could solve the problem situations and find the mathematical rules by using those functions of spreadsheets. They used two types of trial and error strategies to find the rules. The first type was to insert rows between two adjacent rows and the second was to make scroll bars connecting specific variable and change the variable by moving he scroll bars. The spreadsheet environments also help students to justify their findings deductively and convince them that their findings are true by checking various cases of the Problem situations.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2001.01a
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• pp.410-420
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• 2001

A primitive conceptualization is defined as the set of all intended situations. A non-primitive conceptualization is defined as the set of all the pairs every of which consists of an intended knowledge system and the set of all the situations admitted by the knowledge system. The reality of a domain is considered as the set of all the situation which have ever taken place in the past, are taking place now and will take place in the future. A conceptualization is defined as precise if the set of intended situations is equal to the domain reality. The representation of various elements of a domain ontology in a model of the ontology is considered. These elements are terms for situation description and situations themselves, terms for knowledge description and knowledge systems themselves, mathematical terms and constructions, auxiliary terms and ontological agreements. It has been shown that any ontology representing a conceptualization has to be non-primitive if either (1) a conceptualization contains intended situations of different structures, or (2) a conceptualization contains concepts designated by terms for knowledge description, or (3) a conceptualization contains concept classes and determines properties of the concepts belonging to these classes, but the concepts themselves are introduced by domain knowledge, or (4) some restrictions on meanings of terms for situation description in a conceptualization depend on the meaning of terms for knowledge description.

• East Asian mathematical journal
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• v.32 no.4
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• pp.443-464
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• 2016

The purpose of ths study is to compare and analyze the sequence of teaching multiplication facts in the elementary school mathematics. Generally, the multiplication in the elementary school mathematics is composed of the followings; concepts of multiplication, situations involving multiplication, didactical models for multiplication, and multiplication strategies for teaching multiplication facts. This study is focusing to multiplication facts, especially to the sequence of teaching and multiplication strategies. The method of this study is a comparative and analytic method. In order to compare textbooks, we select the Korean elementary mathematics textbooks(1st curriculum~2009 revised curriculum) and the 9 foreign elementary mathematics textbooks(Japan, China, Germany, Finland, Hongkong etc.). As results of comparative investigation, the sequence of teaching multiplication facts is reconsidered on a basis of elementary students' mathematical thinking. And the connectivity of multiplication facts is strengthened in comparison with the foreign elementary mathematics textbooks. Finally multiplication strategies for teaching multiplication facts are discussed for more understanding and reasoning the principles of multiplication facts in the elementary school mathematics.