• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.851-858
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• 1999

A new problem of the theory of finite automata (Rabin-Scott's automata) is considered. So called basis automaton for the given regular language l is defined. this automaton is unique for the given L, it is defined by two au-tomata of canonical form: for L and for its inverse language LR. Some properties of basis automata are considered. Such properties make these automata most convenient for using in some special tasks dealing with the given regular language.

• Research in Mathematical Education
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• v.23 no.1
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• pp.13-22
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• 2020

The effectiveness of mathematics classroom teaching is directly affected by the teaching language. Comparing the teaching language of a novice teacher in algebra instruction with an expert teacher from the perspective of pragmatics, it comes to a conclusion that: both teachers attach great importance to the use of the teaching language, with the proportion of the teaching language time more than 50%; the novice teacher uses the affirmative language frequently, twice as often as the expert teacher; the declarative language the novice teacher uses in the exploration is mostly to repeat students' answer, which takes up a short time; the novice teacher uses the teaching language too much in the consolidation, which causes fewer opportunities for students to think. Then we get the following revelations: streamline the teaching language and control the time of the teaching language reasonably; make good use of the affirmative language to provide students hints and necessary time for thinking; avoid simple restatement of the student's answer and use the declarative language ingeniously to improve the feedback quality; use the teaching language appropriately to help students accumulate basic experience in mathematics activities.

• School Mathematics
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• v.5 no.3
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• pp.297-314
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• 2003

Mathematics students must appropriate their mathematical knowledge which has the definition and theorem of mathematics, algorithm, reasonable thought, heuristic, and mathematics language, and so on. That is, students should construct, use, and apply their own knowledge during learning. Appropriation of mathematical knowledge is practicable when mathematics language is in charge of many functions that Vygotsky cited. To reach the potential development level with mathematics language, students need the zones that they interact themselves and peers, as well as teacher. On that ground, this study presented the interactional zones of IZPD, ZPP, and ZAD, and modeled mathematics learning. By the case of 2 students, we found that ZPP and ZAD were necessary and important.

• Communications of Mathematical Education
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• v.36 no.3
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• pp.335-353
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• 2022

The purpose of this study is to identify the characteristics and types of errors in the conceptual image of Korean language learners according to the types of terms in mathematics that are the basis for solving mathematical word problems, and to prepare basic data for effective teaching and learning methods in solving the word problems of Korean language learners. To do this, a case study was conducted targeting four Korean language learners to analyze the specific conceptual images of terms registered in curriculum and terms that were not registered in curriculum but used in textbooks. As a result of this study, first, it is necessary to guide Korean language learners by using sufficient visualization material so that they can form appropriate conceptual definitions for terms in school mathematics. Second, it is necessary to understand the specific relationship between the language used in the home of Korean language learners and the conceptual image of terms in school mathematics. Third, it is necessary to pay attention to the passive term, which has difficulty in understanding the meaning rather than the active term. Fourth, even for Korean language learners who do not have difficulties in daily communication, it is necessary to instruct them on everyday language that are not registered in the curriculum but used in math textbooks. Fifth, terms in school mathematics should be taught in consideration of the types of errors that reflect the linguistic characteristics of Korean language learners shown in the explanation of terms. This recognition is expected to be helpful in teaching word problem solving for Korean language learners with different linguistic backgrounds.

• School Mathematics
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• v.9 no.2
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• pp.181-196
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• 2007

It would have a trouble to communicate mathematically without an appropriate use of mathematical language. Therefore it is necessary to form mathematics classroom culture to encourage students to use mathematical language precisely. A four-month teaching experiment in a 4th grade mathematics class was conducted focused the accurate use of mathematical language. In the course of the teaching experiment, children became more careful to use their language precisely. The use of demonstrative pronouns such as this or that as well as the use of inaccurate or wrong expressions was diminished. Children became to use much more mathematical symbols and terms instead of their imprecise expressions. The result of the experiment suggests that the culture that encourage students to use mathematical language precisely can be formed in elementary mathematics classroom.

• East Asian mathematical journal
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• v.40 no.3
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• pp.307-318
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• 2024

This paper explores the application of matrix factorization, specifically CUR decomposition, in the clustering of Korean language documents by topic. It addresses the unique challenges of Natural Language Processing (NLP) in dealing with the Korean language's distinctive features, such as agglutinative words and morphological ambiguity. The study compares the effectiveness of Latent Semantic Analysis (LSA) using CUR decomposition with the classical Singular Value Decomposition (SVD) method in the context of Korean text. Experiments are conducted using Korean Wikipedia documents and newspaper data, providing insight into the accuracy and efficiency of these techniques. The findings demonstrate the potential of CUR decomposition to improve the accuracy of document clustering in Korean, offering a valuable approach to text mining and information retrieval in agglutinative languages.

• Research in Mathematical Education
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• v.16 no.4
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• pp.265-276
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• 2012

These days, with the emphasis on statistical literacy, the importance of communication is the focus of attention. Communication about statistics is important since it is a way of describing the understanding of concepts and the interpretation of data. However, students usually have trouble with expressing what they understand, especially through writing. In this paper, we examined preservice teachers' difficulties when they wrote about statistical concepts. By comparing preservice teachers' written responses and interview transcripts of the variance concept task, we could find the missing information in their written language compared to their verbal language. From the results, we found that preservice teachers had difficulty in connecting terms contextually and conceptually, presenting various factors of the concepts that they considered, and presenting the problem solving strategies that they used.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.783-798
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• 1999

Nondeterministic finite Rabin-Scott's automata without initial and final states (2 $\omega$-FA) are considered. In this paper they are used to define so called sets of obstruction used also in various alge-braic systems and to consider similar problems for the formal languages theory. Thus we define sets of obstructions of languages(or, rather, 2$\omega$-languages) of such automata. We obtain that each 2$\omega$-language defined by 2 $\omega$-FA has the set of obstruction being a regular language. And vice versa for each regular language L(containing no proper subword of its another word) there exists a 2$\omega$ -FA having L as the set of obstructions.

• East Asian mathematical journal
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• v.31 no.2
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• pp.245-273
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• 2015

The purpose of this study is to investigate environmental factors that affect mathematics learning of students in multicultural families. For this study, as study subjects, eight elementary school students and one middle school student, who were born and grew up in multicultural families in Korea due to international marriage of Korean father and foreign mother, and their five mothers were selected. To examine factors affecting mathematics learning and interests of students in multicultural families, relationships with parents, friends, and teachers were surveyed, and mathematics attitude test was performed. After conducting one on one interview based on collected questionnaires and results of the attitude test, qualitative data analysis was performed. As a result of survey and interview, positive factors affecting mathematics learning of students in multicultural families included arousing interest in mathematics through mother's mathematics teaching in her mother language and direct teaching, good peer relation, teacher's compliment and encouragement, and lowering the burden of language in accordance with characteristics of mathematics course.

• Journal of the Korean School Mathematics Society
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• v.12 no.1
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• pp.115-129
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• 2009

The purpose of the study was to investigate the attitudes towards mathematics of high school students by comparing students of a general public school and a foreign language high school. The researchers were interested in how the two groups, middle or middle lower achievers and high achievers, showed their attitudes toward mathematics and where their attitudes were derived from. For the investigation, the researchers surveyed 121 students of general public high school and 64 students of a foreign language high school. Reliability, mean difference with t-test and frequency were analyzed. The results showed that many students from both groups had negative attitudes toward mathematics. However, the causes of the attitudes were different between the two groups. This implies that we need to reform the instructional methods and curricula of mathematics cources.