• The Mathematical Education
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• v.56 no.3
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• pp.301-318
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• 2017

This paper explores students' question generation process and their study in small group discussion. The research is based on Anthropological Theory of the Didactic developed by Chevallard. He argues that the savior (knowledge) we are dealing with at school is based on a paradigm that we prevail over whether we 'learn' or 'study' socially. In other words, we haven't provided students with autonomous research and learning opportunities under 'the dominant paradigm of visiting works'. As an alternative, he suggests that we should move on to a new didactic paradigm for 'questioning the world a question', and proposes the Study and Research Courses (SRC) as its pedagogical structure. This study explores the SRC structure of small group activities in solving ill-structured problems. In order to explore the SRC structure generated in the small group discussion, one middle school teacher and 7 middle school students participated in this study. The students were divided into two groups with 4 students and 3 students. The teacher conducted the lesson with ill-structured problems provided by researchers. We collected students' presentation materials and classroom video records, and then analyzed based on SRC structure. As a result, we have identified that students were able to focus on the valuable information they needed to explore. We found that the nature of the questions generated by students focused on details more than the whole of the problem. In the SRC course, we also found pattern of a small group discussion. In other words, they generated questions relatively personally, but sought answer cooperatively. This study identified the possibility of SRC as a tool to provide a holistic learning mode of small group discussions in small class, which bring about future mathematics classrooms. This study is meaningful to investigate how students develop their own mathematical inquiry process through self-directed learning, learner-specific curriculum are emphasized and the paradigm shift is required.

• Communications of Mathematical Education
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• v.31 no.3
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• pp.241-255
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• 2017

The 4th industrial revolution is coming. In order to prepare for the new learning environment with it, we may need digital mathematics textbooks that fully utilize all possible technologies. So various attempts have been made in elementary and middle school mathematics education. However, despite the importance of higher mathematics, we haven't seen a best possible math digital textbooks yet in Korea. In this paper, we introduce our new model of interactive math digital textbook about Linear Algebra/ Calculus/ Differential Equations/ Statistics/ Engineering Math. Especially, this manuscript focuses on our experience of using digital contents and interactive labs for developing a new model for linear algebra digital textbook. We introduce our works on linear algebra digital textbooks which include pdf e-book, web contents, video clips of lectures, interactive lab. Using this linear algebra digital textbook, students can freely use any mobile devices to access diverse learning materials, lessons, and hands-on exercises without any limitations. Also, times saved in the computation, coding, and typing process can be used to have more discussions for deeper understanding of mathematical concepts. This type of linear algebra digital textbook, which contains all interactive free cyber-lab with codes and all lectures for each sections, can be considered as a new model for the next generation of math digital textbook.

• Education of Primary School Mathematics
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• v.17 no.3
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• pp.265-276
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• 2014

In this study, we aim to search the utilization plan of primary 3-4 mathematics textbooks for 'Flipped Classroom' practice. In the flipped classroom, students are required to manipulate more rigorous concepts, deal with realistic problems and various activities, and discussions. Researcher analyzed the new mathematics textbooks of primary 3-4 grade that is applied 2014. The criteria of analysis was made of the instructional model for 'Flipped Classroom' that was set up by previous researcher. To practice the flipped classroom, teachers need to design their classes carefully for using selectively many materials of the textbooks to make students participate discussion in the classroom actively and to consider their interests and levels.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.11
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• pp.1548-1562
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• 2003

This paper is the first of several companion papers which compare the methods of Air-fuel ratio determination. There are many methods which calculate Air-Fuel ratio from exhaust emission. Most of them are based on the simple chemical equations, which use balance of atom, and the error of the calculation is negligible as far as the instrumentation accuracy is guaranteed. They assume homogeneous mixture and complete combustion to the extent of oxygen availability. Because of these simple assumptions, they cannot offer the information about the fuel distribution state and the malfunction of instrument. For these limitations, Eltinge offered new one based on stricter mathematical model. This result coincides with the others very well and gives more information about the mixture state and instrumentation. Consequently this might be a general solution for Air-fuel ratio determination and exhaust composition. The objects of the calculation, however, were not commercial fuels except gasoline and the compensation method of unburned hydrocarbon was not appropriate to recent analyzer. Moreover he did not consider the fuel which contains oxygen, such as methanol, ethanol and blend of gasoline-alcohol. In this paper, Eltinge chart is expanded to the arbitrary fuel composition as the reference exhaust compositions for the purpose of further discussions about Air-fuel ratio determination methods and the charts fur gasoline, diesel, methanol, M85, liquefied petroleum gas(LPG), natural gas(NG), propane, butane are illustrated.

• Education of Primary School Mathematics
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• v.13 no.1
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• pp.13-24
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• 2010

Mathematics educators oriented to reform-based curricular have asserted that mathematics teachers should lead instructions where all students in their classrooms are able to participated. In this paper, some practices for them to implement it are discussed. Before explaining them, some discussions are made about students ability to construct knowledge. One of them is that teachers should know different learners construct different understandings because of their differences of prior knowledge and reasoning ability. Also, it was discussed that teachers consider classroom environments, assigning children's sitting and tasks in the light of learning. The reason to state them is that perspectives of them should be changed. Finally, "Teacher's careful listening to learners' responses", "Why do think in that way?, How do you know?, What is it meant?", "accepting ideas from all learners", "no supporting a particular idea", "utilizing waiting time", and "teacher's responses to learner's errors and mistakes" are discussed as practices for letting all learners be participated in the mathematics instruction.

• School Mathematics
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• v.15 no.3
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• pp.633-650
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• 2013

The aim of this paper is to explore and understand, using in-depth interviews, the participant's interests and discourse analytic expressions in studying the notion of infinity and limit. In addition we tried to understand how the participant's ways of dealing with math and thinking patterns on the polygons whose boundary is infinite but area is finite as they brought up such examples. Further follow-up questions are posed on the infinite sum of a smallest number close to 0 and the sum of infinite sets of different smallest numbers close to 0. Larger aspects of two pre-service teachers' subjective thinking patterns and colloquial discourses were sketched by contrasting the three posed tasks. Cross case discussions are provided with several suggestions for the future research directions.

• Journal of the Korean School Mathematics Society
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• v.4 no.1
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• pp.91-101
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• 2001

Nowadays the number of students that is losing their interest as well as learning desire in mathematics is increasing because of lack of logical thought creative power and abstract expression that present-day mathematics requires by reason of discrepancy of extreme scholastic ability by speciality of mathematics. In these conditions, we reduce the number of learning depression by bringing about learning desire or learning interest on mathematics, and students learn effective learning methods to be voluntary learning of discovery themselves that studies basic concepts, principles, rules through logical thought of students to solve difference of scholastic ability, thus we assumed that debate studies through small group activities in ability group would be one of ways to improve learning power, so the results of our research are as follows; 1. Debate studies through small group activities were very effective because of reinforcing the achivement level of students. 2. By this learning method, an individual or cooperrative learning was fostered, and lively discussions were accomplished. And learning attitudes of students were changed by the extension of cooperative learning abilities through advices or by themselves. 3. A personal opinion is payed regard by accepting an individual idea in the process of making questions. Learners can correct wrong concepts in the process of correcting wrong answers. So if we apply above-mentioned studies with easy contents from the lower grades, the effectiveness would increase as learners go to the higher grade. According to the results of various researches as follows; "The teaching-learning method oriented coopperative debate studies is effective to find solutions to mathematical problems." If small group activities are applied in the educational situation to search the course of a desirable cooperation learning through small group activities to improve scholastic abilities for a discoverable problem-solving power. I think that the teaching-learning method oriented cooperative debate studies is one of the most desirable methods to increase the problem-solving ability.

• School Mathematics
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• v.18 no.3
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• pp.733-747
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• 2016

To describe mathematics learning relying on a priori assumptions about the learners has a risk of assuming the learners as well-prepared subjects. In this study we investigate the epistemological perspective of Gilles Deleuze which is expected to give overcome this risk. Then we analyze the constructivist's epistemology and prior discussions about learning mathematics in the preceding studies accordingly. As a result, a priori assumption on which students are regarded as well-prepared for learning mathematics is reconsidered and we propose a new model of thought to highlight the involuntary aspect of the occurrence of thinking facilitated by the encounter with mathematical signs. This perspective gives a new vision on involuntary aspects of mathematics learning and the learner's confusion or difficulty at the starting point of learning.

• Education of Primary School Mathematics
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• v.22 no.3
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• pp.149-166
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• 2019

The purpose of this study is to analyze the statistical literacy in elementary school students when they beginning inference. Picto-graphs provide statistical information and often data-related arguments they certainly qualify as objects for interpretation, for critical evaluation, and for discussion or communication of the conclusions presented. For research, the inference from pictograph task was designed and statistical literacy standards for evaluating the student's level was presented based on prior studies. Evaluating student's statistical literacy is meaningful in that it can check their current level. To know the student's current level can help them achieve a higher level of performance. The outcomes of this research indicate that pictograph can provide a basis for rich tasks displaying not only student's counting skills but also their appreciation of variation and uncertainty in prediction. Raising statistical thinking by students is an important goal in statistical education, and the experience of informal statistical reasoning can help with formal statistical reasoning that will be learned later. Therefore, the task about the inference from a pictograph, discussions on statistical learning of elementary school children are expected to present meaningful implications for statistical education.

• Journal of Radiation Protection and Research
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• v.49 no.3
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• pp.102-113
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• 2024

Diffusing alpha-emitters radiation therapy (DaRT) represents a groundbreaking development in cancer therapy, offering a solution to the limitations of conventional radiation therapy. By deploying ²²⁴Ra embedded seeds, DaRT achieves targeted delivery of high-dose alpha particles directly to tumor sites, showing considerable efficacy in tumor control and minimal damage to adjacent healthy tissues. This comprehensive review analyzes the published literature regarding mechanisms, seed production, dose calculation, measurement, and biological experiments related to DaRT. It includes in-depth discussions on mathematical models, Monte Carlo simulations for dose distribution, real-time in vivo dosimetry developments, and biological experiments both in vitro and in vivo. Clinical trial outcomes are also examined to evaluate the therapy's effectiveness in various cancer types. DaRT utilizes ²²⁴Ra-labeled seeds, using the decay chain of ²²⁴Ra to deliver alpha particles effectively within a tumor. Several asymptotic diffusion-leakage models were developed to calculate the alpha dose distribution of DaRT. In vivo dosimetry techniques have been developed for real-time monitoring. Biological experiments demonstrated the cytotoxic effects of DaRT across various cancer cells, with varying radiosensitivity. Additionally, the enhanced effects of combined therapy with chemotherapy and immunotherapy were suggested by many in vivo studies. Clinical trials have shown high complete response rate in squamous cell carcinoma, with minimal side effects, suggesting DaRT's feasibility and safety. DaRT emerges as a highly localized cancer treatment method with minimal side effects compared to traditional radiation therapy. It directly ablates tumors and potentially enhances immune responses, indicating a significant advance in cancer therapy. Future research and ongoing clinical trials will further elucidate its efficacy across different cancer types and in combination with other treatments.