• The Mathematical Education
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• v.40 no.2
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• pp.195-215
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• 2001

The purpose of this paper is to present a specific set of home teaching methods in hopes to prevent slow learner of the elementary mathematics. This paper deals with the number and operations, one of five topics in the elementary mathematics A survey of two hundred elementary school teachers was made to see the teacher's opinions of the role of home studying and to concretize the contents of the research topics. There were asked which is the most essential contents for the concrete loaming and which is the most difficult monad that might cause slow leaner. And those were found to be; counting, and arithmetic operations(addition and subtraction) of one or two-digit numbers and multiplication and their concepts representations and operations(addition and subtraction) of fractions. The home teaching methods are based on the situated learning about problem solving in real life situations and on the active teaming which induces children's participation in the process of teaching and learning. Those activities in teaching each contents are designed to deal with real objects and situations. Most teaching methods are presented in the order of school curriculum. To teach the concepts of numbers and the place value, useful activities using manipulative materials (Base ten blocks, Unifix, etc.) or real objects are also proposed. Natural number's operations such as addition, subtraction and multiplication are subdivided into small steps depending upon current curriculum, then for understanding of operational meaning and generalization, games and activities related to the calculation of changes are suggested. For fractions, this paper suggest 10 learning steps, say equivalent partition, fractional pattern, fractional size, relationship between the mixed fractions and the improper fraction, identifying fractions on the number line, 1 as a unit, discrete view point of fractions, comparison of fractional sizes, addition and subtraction, quantitative concepts. This research basically centers on the informal activities of kids under the real-life situation because such experiences are believed to be useful to prevent slow learner. All activities and learnings in this paper assume children's active participation and we believe that such active and informal learning would be more effective for learning transfer and generalization.

• The Mathematical Education
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• v.61 no.1
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• pp.47-62
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• 2022

This study investigated the contents related to the plane figures in the geometry domains of Joseon-Sanhak in the late 18th century and focused on changes in explanations and calculation methods related to plane figures, the rigor of mathematical logic in the problem-solving process, and the newly emerged mathematical topics. For this purpose, We analyzed , and written in the late 18th century and and written in the previous period. The results of this study are as follows. First, an explanation that pays attention to the figures as an object of inquiry, not as a measurement object, and a case of additional presentation or replacing the existing solution method was found. Second, descriptions of the validity of calculations in some problems, explanations through diagrams with figure diagrams, clear perceptions of approximations and explanations of more precise approximation were representative examples of pursuing the rigor of mathematical logic. Lastly, the new geometric domain theme in the late 18th century was Palsun corresponding to today's trigonometric functions and example of extending the relationship between the components of the triangle to a general triangle. Joseon-Sanhak cases in the late 18th century are the meaningful materials which explain the gradual acceptance of the theoretical and argumentative style of Western mathematics

• Education of Primary School Mathematics
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• v.20 no.3
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• pp.205-224
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• 2017

A model method has been known as the main characteristic of Singaporean elementary mathematics textbooks. However, little research has been conducted on how the model method is employed in the textbooks. In this study, we extracted contents related to the model method in the Singaporean elementary mathematics curriculum and then analyzed the characteristics of the model method applied to the textbooks. Specifically, this study investigated the units and lessons where the model method was employed, and explored how it was addressed for what purpose according to the numbers and operations. The results of this study showed that the model method was applied to the units and lessons related to operations and word problems, starting from whole numbers through fractions to decimals. The model method was systematically applied to addition, subtraction, multiplication, and division tailored by the grade levels. It was also explicitly applied to all stages of the problem solving process. Based on these results, this study described the implications of using a main model in the textbooks to demonstrate the structure of the given problem consistently and systematically.

• Journal for History of Mathematics
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• v.25 no.1
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• pp.71-88
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• 2012

The purpose of this study is to find the way to build the concept image about natural logarithm and the method is using definite integral in calculus under GeoGebra environment. When the students approach to natural logarithm, need to use dynamic program about the definite integral in calculus. Visible reasoning process through using dynamic program(GeoGebra) is the most important part that make the concept image to students. Also, for understand mathematical concept to students, using GeoGebra environment in dynamic program is not only useful but helpful method of teaching and studying. In this article, about graph of natural logarithm using the definite integral, to explore process of understand and to find special feature under GeoGebra environment. And it was obtained from a survey of undergraduate students of mathmatics. Also, relate to this process, examine an aspect of students, how understand about connection between natural logarithm and the definite integral, definition of natural logarithm and mathematical link of e. As a result, we found that undergraduate students of mathmatics can understand clearly more about the graph of natural logarithm using the definite integral when using GeoGebra environment. Futhermore, in process of handling the dynamic program that provide opportunity that to observe and analysis about process for problem solving and real concept of mathematics.

• Journal of Information Technology Services
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• v.18 no.2
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• pp.143-159
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• 2019

Machine learning (ML) is a method of fitting given data to a mathematical model to derive insights or to predict. In the age of big data, where the amount of available data increases exponentially due to the development of information technology and smart devices, ML shows high prediction performance due to pattern detection without bias. The feature engineering that generates the features that can explain the problem to be solved in the ML process has a great influence on the performance and its importance is continuously emphasized. Despite this importance, however, it is still considered a difficult task as it requires a thorough understanding of the domain characteristics as well as an understanding of source data and the iterative procedure. Therefore, we propose methods to apply deep learning for solving the complexity and difficulty of feature extraction and improving the performance of ML model. Unlike other techniques, the most common reason for the superior performance of deep learning techniques in complex unstructured data processing is that it is possible to extract features from the source data itself. In order to apply these advantages to the business problems, we propose deep learning based methods that can automatically extract features from transaction data or directly predict and classify target variables. In particular, we applied techniques that show high performance in existing text processing based on the structural similarity between transaction data and text data. And we also verified the suitability of each method according to the characteristics of transaction data. Through our study, it is possible not only to search for the possibility of automated feature extraction but also to obtain a benchmark model that shows a certain level of performance before performing the feature extraction task by a human. In addition, it is expected that it will be able to provide guidelines for choosing a suitable deep learning model based on the business problem and the data characteristics.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.733-767
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• 2005

During the past decades, there has been a fundamental change in the objectives and nature of mathematics education, as well as a shift in research paradigms. The changes in mathematics education emphasize learning mathematics from realistic situations, students' invention or construction solution procedures, and interaction with other students of the teacher. This shifted perspective has many similarities with the theoretical . perspective of Realistic Mathematics Education (RME) developed by Freudental. The RME theory focused the guide reinvention through mathematizing and takes into account students' informal solution strategies and interpretation through experientially real context problems. The heart of this reinvention process involves mathematizing activities in problem situations that are experientially real to students. It is important to note that reinvention in a collective, as well as individual activity, in which whole-class discussions centering on conjecture, explanation, and justification play a crucial role. The overall purpose of this study is to examine the developmental research efforts to adpat the instructional design perspective of RME to the teaching and learning of differential equation is collegiate mathematics education. Informed by the instructional design theory of RME and capitalizes on the potential technology to incorporate qualitative and numerical approaches, this study offers as approach for conceptualizing the learning and teaching of differential equation that is different from the traditional approach. Data were collected through participatory observation in a differential equations course at a university through a fall semester in 2003. All class sessions were video recorded and transcribed for later detailed analysis. Interviews were conducted systematically to probe the students' conceptual understanding and problem solving of differential equations. All the interviews were video recorded. In addition, students' works such as exams, journals and worksheets were collected for supplement the analysis of data from class observation and interview. Informed by the instructional design theory of RME, theoretical perspectives on emerging analyses of student thinking, this paper outlines an approach for conceptualizing inquiry-oriented differential equations that is different from traditional approaches and current reform efforts. One way of the wars in which thus approach complements current reform-oriented approaches 10 differential equations centers on a particular principled approach to mathematization. The findings of this research will provide insights into the role of the mathematics teacher, instructional materials, and technology, which will provide mathematics educators and instructional designers with new ways of thinking about their educational practice and new ways to foster students' mathematical justifications and ultimately improvement of educational practice in mathematics classes.

• School Mathematics
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• v.13 no.4
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• pp.651-674
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• 2011

Functional thinking is a central topic in school mathematics and the purpose of teaching functional thinking is to develop student's functional thinking ability. Functional thinking which has to be taught in elementary school must be the thinking in terms of phenomenon which has attributes of 'connection'- assignment and dependence. The qualitative methods for evaluation of development of functional thinking can be based on students' activities which are related to functional thinking. With this purpose, teachers have to provide students with paradigm of the functional situation connected to the other subjects which have attributes of 'connection' and guide them by proper questions. Therefore, the aim of this study is to find teaching method for functional thinking by situation posing connected with other subject. We suggest the following ways for functional situation posing though the process of three steps : preparation, adaption and reflection of functional situation posing. At the first stage of preparation for functional situation, teacher should investigate student's environment, mathematical knowledge and level of functional thinking. With this purpose, teachers analyze various curriculum which can be used for teaching functional thinking, extract functional situation among them and investigate the utilization of functional situation as follows : ${\cdot}$ Using meta-plan, ${\cdot}$ Using mathematical journal, ${\cdot}$ Using problem posing ${\cdot}$ Designing teacher's questions which can activate students' functional thinking. For this, teachers should be experts on functional thinking. At the second stage of adaption, teacher may suggest the following steps : free exploration ${\longrightarrow}$ guided exploration ${\longrightarrow}$ expression of formalization ${\longrightarrow}$ application and feedback. Because we demand new teaching model which can apply the contents of other subjects to the mathematic class. At the third stage of reflection, teacher should prepare analysis framework of functional situation during and after students' products as follows : meta-plan, mathematical journal, problem solving. Also teacher should prepare the analysis framework analyzing student's respondence.

• Education of Primary School Mathematics
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• v.24 no.4
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• pp.189-202
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• 2021

The teacher's questions presented in the problem-solving situation stimulate students' mathematical thinking and lead them to find a solution to the given problem situation. In this research, the types and functions of questions presented in chapters of Pattern area of the 2015 revised elementary school mathematics textbooks were compared and analyzed by grade cluster. Through this, it was attempted to obtain implications for teaching and learning in identifying the characteristics of questions and effectively using the questions when teaching Pattern area. As a result of this research, as grade clsuter increased, the number of questions per lesson presented in Pattern area increased. Frequency of the types of questions in textbooks was found to be high in the order of reasoning questions, factual questions, and open questions in common by grade cluster. In chapters of Pattern area, relatively many questions were presented that serve as functions to help guess, invent, and solve problems or to help mathematical reasoning in the process of finding rules. It can be inferred that these types of questions and their functions are related to the learning content by grade cluster and characteristics of grade cluster. Therefore, the results of this research can contribute to providing a reference material for devising questions when teaching Pattern area and further to the development of teaching and learning in Pattern area.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.333-348
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• 2023

Clear analysis and diagnosis of various characteristic factors of individual students is the most important in order to realize individual customized teaching and learning, which is considered the most essential function of math artificial intelligence-based digital textbooks. In this study, analysis factors and tools for individual customized learning diagnosis and construction models for data collection and analysis were derived from mathematical AI digital textbooks. To this end, according to the Ministry of Education's recent plan to apply AI digital textbooks, the demand for AI digital textbooks in mathematics, personalized learning and prior research on data for it, and factors for learner analysis in mathematics digital platforms were reviewed. As a result of the study, the researcher summarized the factors for learning analysis as factors for learning readiness, process and performance, achievement, weakness, and propensity analysis as factors for learning duration, problem solving time, concentration, math learning habits, and emotional analysis as factors for confidence, interest, anxiety, learning motivation, value perception, and attitude analysis as factors for learning analysis. In addition, the researcher proposed noon data on the problem, learning progress rate, screen recording data on student activities, event data, eye tracking device, and self-response questionnaires as data collection tools for these factors. Finally, a data collection model was proposed that time-series these factors before, during, and after learning.

• Journal of Elementary Mathematics Education in Korea
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• v.5 no.1
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• pp.37-53
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• 2001

This paper tries to find out about organizational and managemental aspect of Korean curriculum through a comparison between Korea's 7th elementary mathematics curriculum and that of Japan's elementary mathematics curriculum, which will start in m2 through researching various literatures. The main characteristic of this elementary mathematics curriculum is that Korea has organized a teaming program that tended to individual differences, and focused on student-centered activities and communication based on constructivism. On the other hand, Japan reduced learning contents a lot by running 5-schooldays a week so that 80% of teaching time can be spent to help the students master mathematical contents of the textbook. This leaves 20％ of teaching time to be used for improving mathematical thinking power as a foundation of creativity through mathematical activities. Korea's teaching time spent for elementary mathematics is about 80％ of Japan's, which is also less than that of other country's. Less time in teaming mathematics will lead to decrease in teaming ability. Therefore, there is a need for increased teaching time in mathematics. Korea's revision of curriculum is about 5 years which is often compared to that of Japan's 10 years. Frequent revising is good in that it reflects the social demand, but it can cause much confusion and problems in accepting and applying its program in a real classroom setting, which is why it needs to be looked at again. The direction, objective and assesment of revision fits the demands of international trends and essentials of mathematics. Japan puts its emphasis on learning through repetition and Korea puts its emphasis on problem solving and communication. Regarding assesment, both Korea and Japan is looking for ways to find various assessing ways which will focus on mathematical process rather than the mathematical results, and also will put emphasis on criterion-directed assesment to measure goal achievements. However Japan emphasize on using report cards of assesment to help mathematics learning.