• Education of Primary School Mathematics
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• v.22 no.4
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• pp.281-294
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• 2019

The purpose of this study is to analyze errors and treatment behavior during the course of mathematics learning of academic achievement by applying reflective activities in the second semester of the third year of elementary school. The study participants are students from two classes, 21 from the third-grade S elementary school in Seoul and 20 from the comparative class. In the case of the experiment group, the multiplication unit was reconstructed into a mathematics class that applied reflective activities. They were pre-post-test to examine the changes in students' mathematics performance, and mathematical communication was recorded and analyzed for the focus group to analyze the patterns of learners' error handling in the reflective activities. In addition, they recorded and analyzed students' activities and conversations for error type and error handling. As a result of the study, the student's mathematics achievement was increased using reflective activities. When learning double digit multiplication, the error types varied. It was also confirmed that the reflective activities helped learners reflect on the multiplication algorithm and analyze the error-ridden calculations to reflect on and deal with their errors.

• East Asian mathematical journal
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• v.25 no.3
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• pp.321-341
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• 2009

The purpose of this study was to examine the effect of the manipulative materials in the Australian Maths 300 program by applying it to Korean Elementary Mathematics Education - based on parts of 'Probability and Statistics', and 'Symbol and Expression'. In order to this purpose, we select appropriate Maths 300's manipulate materials that could be used to obtain learning objectives within class time for each part, four lessons with the materials were taught at to third, fourth, and fifth grade students of elementary School. The effect of the teaching was analyzed by videotape and student opinion. The results of this study are the following: First, the manipulative tools were almost entirely lacking for the 'Probability and Statistics' section without a 'number of cases' unit. The tools presented in the 'Symbol and Expression' section were helpful in the games that were used for checking preceding learning. Second, the results of using the Math 300 manipulative materials in class showed that the students were eager to be involved in the activities using those materials and to find their own solutions in problem-solving questions that were suited to them; these led to them making their own questions. In response to questioning about the use of the manipulative materials, the students stated that it was easy and fun for them to use the manipulative materials, to solve the problems for themselves, and that they would like to continue practicing the activities in the future. Finally, Studies on the presentation of a variety of manipulative materials including those in this study that can used in problem-solving learning and other learning fields, and the methodology for the use of manipulative materials can be enhanced through further studies.

• Korean Chemical Engineering Research
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• v.61 no.2
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• pp.226-233
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• 2023

To create an environmentally sustainable fuel with a low sulfur concentration, requires alternative sulfur removal methods. During the course of this study, a high surface gamma alumina-supported ZnO nanocatalyst with a ZnO/-Al₂O₃ ratio of 12% was developed and tested for its ability to improve the activity of the oxidative desulfurization (ODS) process for the desulfurization of kerosene fuel. Scanning electron microscopy (SEM) and Brunauer-Emmett-Teller (BET) were used to characterize the produced nanocatalyst. In a digital batch baffled reactor (20~80 min), the effectiveness of the synthesized nanocatalyst was tested at different initial concentrations of dibenzothiophene (DBT) of 300~600 ppm, oxidation temperatures (25~70 ℃), and oxidation periods (0.5, 1, and 2 hours). The baffles included in the digital baffled batch reactor resist the swirling of the reaction mixture, thus facilitating mixing. The ODS procedure yielded the maximum DBT conversion (95.5%) at 70 ℃ with an 80-minute reaction time and an initial DBT level of 600 ppm. The most precise values of kinetic variables were subsequently determined using a mathematical modelling procedure for the ODS procedure. The average absolute error of the simulation findings was less than 5%, demonstrating a good degree of agreement with the experimental results acquired from all runs. The optimization of the operating conditions revealed that 99.1% of the DBT can be removed in 140 minutes.

• Communications of Mathematical Education
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• v.37 no.1
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• pp.47-64
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• 2023

The current elementary mathematics curriculum does not include intensive quantity. However, other subjects also deal with intensive quantity. In order to find a solution to this problem from a pedagogical point of view, the curriculum of mathematics, science, social studies, and elementary textbooks were compared and analyzed, focusing on intensive quantity. As a result of the analysis, the learning contents of intensive quantity were not explicitly presented or the term was not used in the elementary mathematics curriculum. However, intensive quantity was used as a material of activity and word problems in elementary mathematics textbooks. In science and social studies, it was also found that the learning order and content did not match, such as calculating the intensive quantity. For effective learning, it is necessary to consider presenting intensive quantity in elementary mathematics, and to be careful in the composition of learning order and content.

• School Mathematics
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• v.4 no.3
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• pp.375-399
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• 2002

When a curriculum change is being an issue, the editorships and the promotive directions reflect to supplement the social requests. However it is often criticized that such changes in the textbook itself are not satisfactory enough as to coherent to the editoships. And we set the following research questions; (1) One of the most important changes in the new 7th curriculum is to encourage the students' activities. We checked if it is well suited in the new textbooks. (2) Often textbook itself is not important In class, while instructor or students want something else other than the one suggested in the textbook. We asked 187 teachers how they use the textbooks in class. To answer (1), we checked up the introductory - activity - contents with 7 categories, which are ${\circled1}$ of real life sources ${\circled2}$ in use of concrete manipulative ${\circled3}$ in use of computers or calculators ${\circled4}$ in use of historical resources ${\circled5}$ stimulating to recall a relevant previous knowledges ${\circled6}$ of coherence between the activity and the exploratory contexts. ${\circled2}$ were increased, rewarding to the decrease of ${\circled5}$, in the new textbooks, while changes in ${\circled3}$ and ${\circled4}$ were not enough to talk about increments. Especially slight decrease in ${\circled6}$ were detected and it seemed to attribute to the unmatchable use of ${\circled1}$ and ${\circled2}$ with the explanation of mathematical subjects, which also implies how difficult to match ${\circled1}$ and ${\circled2}$ with ${\circled6}$. Analyzing the reponses of (2), about 70% of the teachers used the introductory activities in the textbook, which led better attention of sudents, while 30% of teachers do not use it because they felt that its inroductory activities had not been adequate for their purposes. Teachers counted inadequacy reasons for not being helpful in class, lack of time or lack of support of students, etc. Those teachers use introductory activities invented of their own for classes. As some results of the study, we suggest firstly that authors of textbooks have to get more informations to provide ways to entcourage students' interest in mathematics classes. The ways must be practical and brain storming as well as More use of computers and calculators and mathematical history are expected. Secondly, we are emphasizing the feedbacks between the textbook authors and the users(teachers and students) through internet. Which, we anticipate, will get better communications between them and be a good foundations of continuous modifications of textbooks.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.363-384
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• 2001

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them and to make suggestions for definition - teaching as a mathematising activity, Definitions used in academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. And in school mathematics textbooks there are definitions which carry out special functions in mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. In this thesis we investigated the cases in school mathematics textbooks, when such functions of definition are accompanied. With the result of this investigation we tried to make suggestions for definition-teaching as an intellectual activity. To begin with we considered definition from two aspects, methods of definition and functions of definition. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics and search for a method for definition-teaching through mathematization. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. Functions of definition are classified as, description-function, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about levels of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics. And as a result of analysing functions of definition we found that functions of definition appear more often in geometry than in algebra or analysis and that improvement-function, demonstration-function appear regularly after demonstrative geometry while other functions appear before demonstrative geometry. Also, we found that generally speaking, the functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding. And the mathematics teachers should be aware of the functions of definitions. As mentioned above, in this thesis we analysed definitions in school mathematics, identified various types of didactical transformations of definitions, and presented a basis for future researches on definition teaching in school mathematics.

• Journal of the Korean School Mathematics Society
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• v.5 no.2
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• pp.1-15
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• 2002

The purpose of this study came to start to be helpful in that the teachers in field produced evaluation subject about the mathematics and applied by analyzing the performance capacity for the students about the subject developed through the application of subject about the teaching-learning model that can utilize the learners' learning experience and the development of items that can evaluate it by utilizing various and concrete operational materials as an object of the first year at the middle schools. The concrete purpose of realizing it is as follows. 1. This study is to develop the teaching-learning model centered on activities adequate to utilize various and concrete operational materials. 2. This study is to develop evaluation data for utilizing the concrete operational materials by making construction through the application of developed teaching-learning model as possible. 3. This study is to present standards initiative for reliable and fair marking about the evaluation data and to analyze the students' practice capacity by using it effectively. For accomplishing the purpose of this research, this study is the work-oriented teaching and learning model using learning data that can be easily found around the surroundings and 8 evaluation programs in order that the experience-oriented learning based on circumstances learning among the learning models of constructivism. Also, it is to examine the result after applying that on a basis of 25 students, consisted of only on class in a year, in the first year at the small size of agricultural middle schools. The result of this study from this research is as follows. First, as a result of frequency survey, of response about the developed evaluation data it showed positive response more than 80% of all the items. The atmosphere of self-directed learning was produced because the developed evaluation data could induce activity-based learning naturally by stimulating the students' curiosity and promoting interest. Second, this study executed t-test for the result of questionnaire about the mathematics propensity, and there were significant differences in 19 items among 25 items. It presented that the application of data about the teaching-learning and evaluation directly using concrete operational materials to the constructional learning by level might have desirable affect on the students' mathematical propensity. It came to be a motive that could increase value recognition and interest on the subject of mathematics by investigating a mathematical principle rule and confirming it through activity learning using the concrete operational materials.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.24 no.5
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• pp.315-326
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• 1991

This study was tried for a mathematical approaches related to daily fluctuations in the stomach fullness of Agrammus agrammus. The specimen was collected by angling and gill net from September 1984 to August 1985 off Shinsudo, Samchonpo. Fullness of the stomachs was increased in the early morning and the late afternoon, decreased in the late morning, at noon, and during the night. That is, feeding activity of the fish was more intense at sunrise and sunset. Daily feeding activity of the fish in a day was divided into the time period of gastric evacuation and both feeding and gastric evacuation. Stomach fullness with the lapse of time in the time period of gastric evacuation was geometrically decreased. Stomach fullness in the time period of both feeding and gastric evacuation was affected by gastric evacuation rates, feeding rates, and maximum fullness of the stomach. These parameters were able to estimate from the method estimating the regression coefficient in the relationship between the time(t) and the stomach fullness$(F_t)$, or between stomach fullness at the time t and $t+\Deltat$. The rates of feeding and gastric evacuation were the highest in spring and the lowest in winter. The relationships between time(t) and stomach fullness$(F_t)$ in the time period of gastric evacuation and both feeding and gastric evacuation induced from hypotheses were respectively as follows. $$F_t=F_{to}e^{-r(t-to)}$$, $$F_t=F\infty-(F\infty-F_{to})e^{-(p+r)(t-{to})}$$

• Communications of Mathematical Education
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• v.34 no.3
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• pp.235-256
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• 2020

The purpose of this study was to investigate the experience of pre-service mathematics teachers who attended at a university course combined with teaching practicum based on design thinking process to identify the change of their awareness of its activities. For the research, 8 pre-service mathematics teachers participated in a mathematics major course, consisting of 5 phases of design thinking formed by Stanford d.school. In the end of the course, qualitative data were collected through individual and focus group interviews and the course activities. By data analysis, the results of this study were as follows. Firstly, the participants' perspectives of design thinking activities were changed from the difficulty and ambiguity of its activity in the beginning of the process to positiveness with competence of solving authentic problem in terms of teaching practicum over time. Secondly, the participating pre-service teachers emphasized that design thinking activities helped them prepare well teaching practicum and raise understanding of students they met in the school fields. Thirdly, some research participants went through the difficulty in utilizing their products drawn from 4th phase (prototyping) of design thinking process depending on the acceptance of their guidance teachers. Fourthly, the research participants also pointed out that the design thinking was a significant activity in that they learned how to understand and communicate with their students and how to collaborate with team members and it gave an insight about the preparation for a class. Through these results, this study identified the possibility of using the design thinking process for pre-service mathematics teachers' teaching practicum. In addition, the research put forward some implications for better use of design thinking in teacher education.

• The Mathematical Education
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• v.61 no.4
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• pp.539-557
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• 2022

A research field develops by experiencing several turns of paradigms. Mathematics education research have experienced those turns as well. Still, the dominant perspective is that mathematics education research should be scientific and objective. In this article, I suggest that this need not to be the prime rule to follow and that the mathematics education field will fertile by discussing extraordinary cases which may seem controversal to be recognized as valid research work. To this end, I first briefly describe the necessity of open discussions among researchers for a field to develop. Then, I introduce fiction writing, a resesarch method derived from arts-based research, as an extraordinary case for open discussions. The benefit of Arts-based research is on that it takes an holistic approach to how we know by embracing emotion and emphathy as means for knowing. Because of this trait, arts-based research holds a powerful potential for influencing a wide range of people, both inside and outside of the resesarch field. Following this, I present a fiction about a prospective teacher who participated in an activity for designing educative curriculum materials. By doing so, I sought to provoke discussions among mathematics education researchers about what to include as a valid research work, possible standards for reviewing arts-based resesarch.