• The Mathematical Education
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• v.63 no.2
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• pp.319-334
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• 2024

The purpose of this study was to reveal the discursive constructs of AI-based mathematical objects by analyzing how concrete objects used in the optimization content of AI mathematics textbooks are transformed into discursive objects through naming and discursive operation. For this purpose, we extracted concrete objects used in the optimization contents of five high school AI mathematics textbooks and developed a framework for analyzing the discursive constructs and discursive operations of AI-based mathematical objects that can analyze discursive objects. The results of the study showed that there are a total of 15 concrete objects used in the loss function and gradient descent sections of the optimization content, and one concrete object that emerges as an abstract d-object through naming and discursive operation. The findings of this study are not only significant in that they flesh out the discursive construction of AI-based mathematical objects in terms of the written curriculum and provide practical suggestions for students to develop AI-based mathematical discourse in an exploratory way, but also provide implications for the development of effective discursive construction processes and curricula for AI-based mathematical objects.

• School Mathematics
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• v.7 no.2
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• pp.123-137
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• 2005

Elementary combinatorial problem may be classified into three different combinatorial models(selection, distribution, partition). The main goal of this research is to determine the effect of type of combinatorial operation and implicit combinatorial model on problem difficulty. We also classified errors in the understanding combinatorial problem into error of order, repetition, permutation with repetition, confusing the type of object and cell, partition. The analysis of variance of answers from 339 students showed the influence of the implicit combinatorial model and types of combinatorial operations. As a result of clinical interviews, we particularly noticed that some students were not able to transfer the definition of combinatorial operation when changing the problem to a different combinatorial model. Moreover, we have analysed textbooks, and we have found that the exercises in these textbooks don't have various types of problems. Therefore when organizing the teaching , it is necessary to pose various types of problems and to emphasize the transition of combinatorial problem into the different models.

• Journal of the Korean earth science society
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• v.41 no.3
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• pp.261-272
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• 2020

The purpose of this study was to compare the earth science curriculums of South Korea and North Korea. Aspects such as the content of the curriculums and the timing of learning were analyzed, in order to provide basic data that can be used to design a revised and integrated Korean curriculum. The objects of this study were South Korean Science textbooks from grades 5-9, and the high school Unity of Science and Earth Science I and II textbooks. Additionally, from North Korea, the junior middle school Natural Science 1 and 2 textbooks and the senior middle school Chosun Geography 2 and Geography 1 textbooks were analyzed. The results of this study obtained through an analysis that used the Trends in International Mathematics and Science Study (TIMSS 2019) grade 8 earth science assessment framework were as follows. First, South Korea needs to adopt iterative learning. Repetitive learning, which is effective for understanding what is being learned, is applied to only 1 by 8th grade. Second, South Korea needs to adjust the time when certain content is learned. This is because there is a disparity between when content is learned in comparison to North Korea, and the timing of learning of about 50% of the TIMSS standards have not been followed. Third, it is necessary to reflect the content present within the TIMSS that have not been learned. This can be a way to increase the nations' educational competitiveness in the international community. This paper proposed a comparative analysis of South korean and North Korean approaches to the earth science curriculum and conducted practical research to facilitate the construction of an integrated curriculum.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.287-314
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• 2010

The algorithm is a chain of mechanical procedures, capable of solving a problem. In modern mathematics educations, the teaching algorithm is performing an important role, even though contracted than in the past. The conspicuous characteristic of current elementary mathematics textbook's manner of manipulating multiplication algorithm is exceeding converge to 'standard algorithm.' But there are many algorithm other than standard algorithm in calculating multiplication, and this diversity is important with respect to didactical dimension. In this thesis, we have reconstructed the experimental learning and teaching plan of multiplication algorithm unit by making the best use of diversity of multiplication algorithm. It's core contents are as follows. Firstly, It handled various modified algorithms in addition to standard algorithm. Secondly, It did not order children to use standard algorithm exclusively, but encouraged children to select algorithm according to his interest. As stated above, we have performed teaching experiment which is ruled by new lesson design and analysed the effects of teaching experiment. Through this study, we obtained the following results and suggestions. Firstly, the experimental learning and teaching plan was effective on understanding of the place-value principle and the distributive law. The experimental group which was learned through various modified algorithm in addition to standard algorithm displayed higher degree of understanding than the control group. Secondly, as for computational ability, the experimental group did not show better achievement than the control group. It's cause is, in my guess, that we taught the children the various modified algorithm and allowed the children to select a algorithm by preference. The experimental group was more interested in diversity of algorithm and it's application itself than correct computation. Thirdly, the lattice method was not adopted in the majority of present mathematics school textbooks, but ranked high in the children's preference. I suggest that the mathematics school textbooks which will be developed henceforth should accept the lattice method.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.443-465
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• 2014

Mathematics subject has been recognized as a subject in which we resolve some problematic situations through the logical and mathematical thinking according to mathematical concepts, principles, and rules. So we has focused on cultivating logical and mathematical thinking abilities when teaching and learning mathematics. However according to Bruner, we can use the narrative mode of thought which supplements the logical and scientific mode of thought when we think about logical and scientific matters, and we could make meanings by doing so. On the other hand, the Ministry of Education has announced recently that it would develope the textbooks of storytelling type of mathematics, and then many people have been interested in using stories in mathematics subject. The purposes of this article are to investigate the effects and the defects of using stories in mathematics subject, to probe the narrative characteristics of mathematics, and to inquire how using mathematics narrative can make students to make meaning about mathematics which compensates the defects of using stories in mathematics subject. And the main purpose is to inquire the implications of using mathematics narrative in teaching and learning mathematics.

• Communications of Mathematical Education
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• v.32 no.3
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• pp.407-433
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• 2018

In order to analyze textbooks from a discursive approach, the purpose of this study is to structuralize an analytic framework based on previous literature review and apply it to analyzing the meanings and their syntheses developed by words and visual mediators appeared in the definition of graph in first-year middle school textbooks. The discursive approach consists of the communicational approach developed by Sfard(2008) and the systemic functional linguistics developed by Halliday(1985/2004). In this study, ideational meta-functions for ideational meanings and interpersonal meta-functions for interpersonal meanings were employed to analyze the meanings produced by words and visual mediators in textbooks, whereas textual meta-functions for textual meanings were used for analyzing the synthesized relationships between words and visual mediators. Results show that first, density in mathematical discourse was very high and subjects in mathematical activities were ambiguous in the ideational meanings of words, and behavior aspect was more emphasized than thinking aspect in the interpersonal meanings of words which request student participations. In the case of ideational meanings of visual mediators, there was a lack of narrative diagrams, whereas there were qualitative differences in the case of offer. Second, there was a need for promoting a wide range of diverse synthetic relationships between words and visual mediators for developing enriched mathematical meanings through the varying uses like specification, explanation, similarity, and complement. These results are so important that they provide a new analytic framework from a discursive approach to textbook analysis because not only words, but also visual mediators are analyzed as tools for producing meanings in mathematics textbooks and their synthetic relationships are also examined.

• Journal of Korea Multimedia Society
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• v.24 no.4
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• pp.569-582
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• 2021

Education emphasizes problem-solving skills based on convergent thinking power in an era of rising uncertainty and rapid progress. This paper proactively designed e-Learning team teaching convergence liberal arts courses for prospective teachers by these social needs. It analyzed the empirical effects on the operation of the subjects to foster future talent who can converge and apply knowledge in various fields. The curriculum consisted of professors of mathematics, practical Arts, computer, and education, and was operated to convey convergent knowledge of information technology and humanities, and consisted of 15 liberal arts courses at J University. Besides, textbooks and teaching materials were also developed by the faculty. As a result of the primary research, prospective teachers who took the course generally showed high satisfaction with the class, especially for the faculty. The students' overall convergent thinking ability has increased to a statistically significant level (p<.01), and the students' major has been found to be irrelevant. On the other hand, it can be seen that communication, content convergence, and caring factors, excluding creativity factor, have all risen to a significant level.

• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.327-344
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• 2011

This study is the first step for us toward improving high school students' capability of statistical inferences, such as obtaining and interpreting the confidence interval on the population mean that is currently learned in high school. We suggest 5 underlying concepts of 'discretion of contingency and inevitability', 'discretion of induction and deduction', 'likelihood principle', 'variability of a statistic' and 'statistical model', those are necessary to appreciate statistical inferences as a reliable arguing tools in spite of its occasional erroneous conclusions. We assume those 5 concepts above are to be gradually developing in their school periods and Korean mathematics textbooks of grades 1-12 were analyzed. Followings were found. For the right choice of solving methodology of the given problem, no elementary textbook but a few high school textbooks describe its difference between the contingent circumstance and the inevitable one. Formal definitions of population and sample are not introduced until high school grades, so that the developments of critical thoughts on the reliability of inductive reasoning could not be observed. On the contrary of it, strong emphasis lies on the calculation stuff of the sample data without any inference on the population prospective based upon the sample. Instead of the representative properties of a random sample, more emphasis lies on how to get a random sample. As a result of it, the fact that 'the random variability of the value of a statistic which is calculated from the sample ought to be inherited from the randomness of the sample' could neither be noticed nor be explained as well. No comparative descriptions on the statistical inferences against the mathematical(deductive) reasoning were found. Few explanations on the likelihood principle and its probabilistic applications in accordance with students' cognitive developmental growth were found. It was hard to find the explanation of a random variability of statistics and on the existence of its sampling distribution. It is worthwhile to explain it because, nevertheless obtaining the sampling distribution of a particular statistic, like a sample mean, is a very difficult job, mere noticing its existence may cause a drastic change of understanding in a statistical inference.

• School Mathematics
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• v.8 no.4
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• pp.379-396
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• 2006

The purpose of this study is to analyze characteristics of problem solving in mathematics for gifted students through case study on solving the mathematical problem for gifted students, and to investigate what are relationships with the cognitive and affective characteristics. To this end, this study was to analyze the characteristics on the problem solving in mathematics by using qualitative research method after it selected two students who had specific education for brilliant students. As a result, this study has shown that it had high preference for question with clear answer, high preference for individual inquiry learning, high adhesion to answer for question, and high adhesion for assignment on characteristics of process of problem solving, but there was much difference in spirit of competition. As to the characteristics of thoughts in problem solving, this study has shown that it had high grasp capacity, intuitive insight, and capacity for visualization, but there were differences in capacity for generalization and adaptability. However, both two students had low values in deductive thought. In addition, as to the home environment and cognitive and affective characteristics, they were not related to the characteristics on problem solving directly, but it has shown that it affected each other indirectly. As to the conclusion of this study, this researcher thinks that it will be valuable documentation in order to improve curriculum, development of textbooks, and teaching method for special education for the gifted students and education for secondary mathematics.

• School Mathematics
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• v.11 no.3
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• pp.463-477
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• 2009

Decimal Fraction with a significant meaning is being treated for long periods, from elementary school to high school. It is necessary to consider in a course of guidance about various aspects of decimal Fraction first of all in order that student understand well about the concert of it. If you overlook guidance of various means of decimal Fraction, Previously learned number system is limited understand of Decimal Fraction concept or meaning of Decimal Fraction limited to the one is difficult to calculate the Decimal Fraction, even can weaken understand of Real Number. Accordingly, in this study, we would like to separate meanings of the Decimal Fraction, focusing on the role and function of the Decimal Fraction in various situations used the Decimal Fraction. Based on this, we analyzed and criticized how to introduce the Decimal Fraction in elementary school textbooks according to the 7th curriculum.