• The Mathematical Education
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• v.38 no.2
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• pp.145-157
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• 1999

Ability diagnosis is similar to medical diagnosis from a number of perspectives. However, a medical diagnosis is carried out by a direct observation through medical apparatuses, while an ability diagnosis is made by an indirect observation in the from of testing. In this respect, ability diagnosis is more difficult than medical diagnosis. Confined to middle school 1st year Mathematics, we collected survey data in 1996 from monthly tests. The data consist of student responses to diagnosis results on their abilities and of the effects of catch-up guidances for individual students which are provided based on their ability diagnosis outcomes. We analyzed the data and summarized the result in the paper. One of the main results is that the ability diagnosis as used in the paper has a very positive effect on catch-up study. But it is important to note that the effects vary across the ability groups, the effect appearing weaker in the lower ability group than in the higher ability group. This calls our attention to the need that the ability diagnosis and guidance for the catch-up study be differentiated among ability groups.

• Journal of Educational Research in Mathematics
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• v.12 no.3
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• pp.409-424
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• 2002

The historico-genetic principle has been advocated continuously, as an alternative one to the traditional deductive method of teaching and learning mathematics, by Clairaut, Cajori, Smith, Klein, Poincar$\'{e}$, La Cour, Branford, Toeplitz, etc. since 18C. And recently we could find various studies in relation to the historico-genetic principle. Lakatos', Freudenthal's, and Brousseau's are representative in them. But they are different from the previous historico- genetic principle in many aspects. In this study, the previous historico- genetic principle is called as classical historico- genetic principle and the other one as modern historico-genetic principle. This study shows that the differences between them arise from the historical views of mathematics and the development of the theories of mathematics education. Dewey thinks that education is a constant reconstruction of experience. This study shows the historico-genetic principle could us embody the Dewey's psycological method. Bruner's discipline-centered curriculum based on Piaget's genetic epistemology insists on teaching mathematics in the reverse order of historical genesis. This study shows the real understaning the structure of knowledge could not neglect the connection with histogenesis of them. This study shows the historico-genetic principle could help us realize Bruner's point of view on the teaching of the structure of mathematical knowledge. In this study, on the basis of the examination of the development of the historico-genetic principle, we try to stipulate the principle more clearly, and we also try to present teaching unit for the logarithm according to the historico- genetic principle.

• The Mathematical Education
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• v.44 no.2 s.109
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• pp.159-167
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• 2005

As the 7th mathematics curriculum reform in Korea was implemented with its goal based on Freudenthal's perspectives on mathematization theory, the research on the effect of mathematization has been become more significant. The purpose of this thesis is not only to find whether this foreign theory would be also applied effectively into our educational practice in Korea, but also to investigate how much important role teachers should play in their teaching students, in order that students accomplish the process of mathematization more effectively. Two case studies were carried out with two groups of middle-school students using qualitative-research method with the research instrument designed by the researcher. It was found that we could get the possibility of being able to apply effectively this theory even to our educational practice since the students engaged in their mathematization using the horizontal mathematization and the vertical mathematization in geometry. Also, it was mentioned that teachers' role was so important in guiding students' processes of mathematization, although mathematization is the teaching-learning theory, stimulating students' activities. Since the Freudenthal's mathematization applied in the thesis is so meaningful in our educational practice, we need more various research about this theory that helps students develope their mathematical thinking.

• Journal of Educational Research in Mathematics
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• v.13 no.1
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• pp.77-94
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• 2003

This study attempts to compare the topic "approximate value" in mathematics text-books of the 2nd year of South Korean junior high schools and that of the 3rd year of North Korean high schools. In addition, a survey questionnaire was distributed to junior and senior high school students as well as to mathematics teachers in South Korea. Based on the results of the survey, this study attempts to uncover the issues within the current teaching methods of "approximate value" and proposes the directions in which the teaching of approximate value should go in order to enhance mathematical thinking power and creativity of the students. First, it Is necessary to teach students how an error applies to the real world. To accomplish this end, it may be worthwhile to consider introducing the relative errors with more seriousness. Second, it is more important to teach the way of thinking which is concealed in the background of the calculation methods of approximate values than to simply teach mere calculation methods. Third, it is necessary to teach the calculation of approximate value with more realistic examples. Fourth, It is needed to teach students what the differences are when the terminology of "approximately" and "about" is used in real life and in mathematics.

• School Mathematics
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• v.8 no.2
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• pp.215-237
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• 2006

In this study, we research distinctive features of geometry problem solving of middle school students whose mathematical achievement levels are distinguished by National Assessment of Educational Achievement. We classified 9 students into 3 groups according to their level : advanced level, proficient level, basic level. They solved an atypical geometry problem while all their problem solving stages were observed and then analyzed in aspect of development of geometrical concepts and access to the route of problem solving. As those analyses, we gave some suggestions of teaching on mathematics as students' achievement level.

• School Mathematics
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• v.12 no.1
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• pp.27-43
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• 2010

In this article the conceptual meaning of expression, equation and identity used in Korean mathematics textbooks and American mathematics textbooks is compared and discussed. For this purpose definitions and examples in several mathematics textbooks which are used in Korean elementary school, the 1st grade of middle school and American middle school are investigated. It is founded out that at first there are some parts that give rise to misunderstanding and then there are differences between the Korean terminologies and their corresponding English counterparts. The definitions of expression, equation and identity are advised to examine in the view of middle mathematics curriculum.

• Communications of Mathematical Education
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• v.30 no.3
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• pp.281-294
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• 2016

This study deals with the content that was developed by the authors and the utilization of the 'Interactive Engineering Math Laboratory (IEmath Lab).' IEmath Lab provides online review lectures as well as a wide range of examples and exercises from the curriculum of engineering mathematics courses. The lectures come with pre-coded Python-based SageMath cells through which students can run and modify the code directly from this free laboratory. IEmath Lab is accessible via mobile devices so that the students can use it anywhere, anytime for maximum learning effectiveness and achievement. IEmath Lab would be an ideal tool for the effective learning and teaching of engineering mathematics, which combines theory and practice.

• Journal of Educational Research in Mathematics
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• v.16 no.1
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• pp.79-94
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• 2006

The purpose of this study is to find out the characteristics of the types(levels) of justification which are appeared by elementary mathematically gifted students in solving the tasks of plane division and spatial division. Selecting 10 fifth or sixth graders from 3 different groups in terms of mathematical capability and letting them generalize and justify some patterns. This study analyzed their responses and identified their differences in justification strategy. This study shows that mathematically gifted students apply different types of justification, such as inductive, generic or formal justification. Upper and lower groups lie in the different justification types(levels). And mathematically gifted children, especially in the upper group, have the strong desire to justify the rules which they discover, requiring a deductive thinking by themselves. They try to think both deductively and logically, and consider this kind of thought very significant.

• School Mathematics
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• v.19 no.1
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• pp.95-116
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• 2017

Through the teaching experiments, we investigated a series of processes for obtaining the differential coefficient at x=0 of the exponential function $y=2^x$ based on the process of constructing the natural constant e and the understanding of it. and all of the students who participated in this study were students who had no experience of calculating the derivative of the exponential function. The purpose of this study was not to generalize the responses of students but to suggest implications for mathematical concept mapping related to calculus by analyzing various responses of students participating in experiments. It is expected that the accumulation of research data derived in this kind of research on the way of understanding and composition of learners will be an important basic data for presenting the learning model related to calculus.

• Journal of the Korean School Mathematics Society
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• v.14 no.3
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• pp.295-323
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• 2011

This study is based on the recognition that teacher educators have to focus their attention on developing pre-service teachers' statistical reasoning for statistics education of school mathematics. This paper investigated knowledge on pre-service teachers' statistical reasoning. Statistical Reasoning Assessment (SRA) is performed to find out pre-service teachers' statistical reasoning ability. The research findings are as follows. There was meaningful difference in the statistical area of statistical reasoning ability with significant level of 0.05. This proved that 4 grades pre-service teachers were more improve on statistical reasoning than 2 grades pre-service teachers. Even though most of the pre-service teachers ratiocinated properly on SRA, half of pre-service teachers appreciated that small size of sample is more likely to deviate from the population than the large size of sample. A few pre-service teachers have difficulties in understanding "Correctly interprets probabilities(be able to explain probability by using ratio" and "Understands the importance of large samples(A small sample is more likely to deviate from the population)".