Productive struggle is a student's persevering effort to understand mathematical concepts and solve challenging problems that are not easily solved, but the problem can lead to curiosity. Productive struggle is a key component of students' learning mathematics with a conceptual understanding, and supporting it in learning mathematics is one of the most effective mathematics teaching practices. In comparison to research on students' productive struggles, there is little research on preservice mathematics teachers' productive struggles. Thus, this study focused on the productive struggles that preservice mathematics teachers face in solving a non-routine mathematics problem. Polya's four-step problem-solving process was used to analyze the collected data. Examples of preservice teachers' productive struggles were analyzed in terms of each stage of the problem-solving process. The analysis showed that limited prior knowledge of the preservice teachers caused productive struggle in the stages of understanding, planning, and carrying out, and it had a significant influence on the problem-solving process overall. Moreover, preservice teachers' experiences of the pleasure of learning by going through productive struggle in solving problems encouraged them to support the use of productive struggle for effective mathematics learning for students, in the future. Therefore, the study's results are expected to help preservice teachers develop their professional expertise by taking the opportunity to engage in learning mathematics through productive struggle.
Journal of Elementary Mathematics Education in Korea
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v.21
no.4
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pp.663-686
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2017
The purpose of this study was to identify the effects of convergent approach of mathematics education on students' problem-solving ability and self-efficacy by designing and applying mathematics curriculum based on STEAM. The results are as follows. First, the test results between the two groups did not show any statistically significant difference in terms of problem solving ability, but the experimental group showed a higher average score than the comparative group. Compared with the standard deviation of the experimental group, It can be seen that the level of difference between students is great. This suggests that STEAM-based mathematics lessons have a positive effect on the problem solving ability of low-level students. Second, the results of the self-efficacy t-test of STEAM-based mathematics class showed statistically significant results at a 5% significance level. In the sub-domain, the preference for the difficulty of the mathematics task, except math self-confidence and the math self-regulation efficacy, were statistically significant at a 5% significance level. This study shows that STEAM-based mathematics classes have a positive effect on the students' positive aspects. Through the STEAM program, students learn that mathematics is connected with other fields, and it provides an opportunity to explore on their own, and they more became interested, motivated, and achievement. Also, through the results of the STEAM-based mathematics class, it can be seen that the expressive power and self-confidence are increased by using the non-formal representation outside of the existing formal representation center. The result of this study can be summarized as follows: A STEAM-based mathematics class has a positive effect on problem solving ability and self-efficacy. Therefore, it is interpreted that the application of the STEAM program focusing on mathematics accounts for education effectives.
Journal of the Korea Academia-Industrial cooperation Society
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v.12
no.4
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pp.1786-1795
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2011
The trajectory control for omni-directional mobile robot is not easy. Especially, the tracking control which system uncertainty problem is included is much more difficult. This paper develops trajectory controller of 3-wheels omni-directional mobile robot using fuzzy multi-layered algorithm. The fuzzy control method is able to solve the problems of classical adaptive controller and conventional fuzzy adaptive controllers. It explains the architecture of a fuzzy adaptive controller using the robust property of a fuzzy controller. The basic idea of new adaptive control scheme is that an adaptive controller can be constructed with parallel combination of robust controllers. This new adaptive controller uses a fuzzy multi-layered architecture which has several independent fuzzy controllers in parallel, each with different robust stability area. Out of several independent fuzzy controllers, the most suited one is selected by a system identifier which observes variations in the controlled system parameter. This paper proposes a design procedure which can be carried out mathematically and systematically from the model of a controlled system; related mathematical theorems and their proofs are also given. Finally, the good performance of the developed mobile robot is confirmed through live tests of path control task.
The activity of finding rules is useful for enhancing the algebraic thinking of elementary school students. This study analyzed the pattern activities of a finding rules unit in 10 different government-authorized mathematics curricular materials for fourth graders aligned to the 2015 revised national mathematics curriculum. The analytic elements included three main activities: (a) activities of analyzing the structure of patterns, (b) activities of finding a specific term by finding a rule, and (c) activities of representing the rule. The three activities were mainly presented regarding growing numeric patterns, growing geometric patterns, and computational patterns. The activities of analyzing the structure of patterns were presented when dealing mainly with growing geometric patterns and focused on finding the number of models constituting the pattern. The activities of finding a specific term by finding a rule were evenly presented across the three patterns and the specific term tended to be close to the terms presented in the given task. The activities of representing the rule usually encouraged students to talk about or write down the rule using their own words. Based on the results of these analyses, this study provides specific implications on how to develop subsequent mathematics curricular materials regarding pattern activities to enhance elementary school students' algebraic thinking.
The purposes of this study were to analyze the levels of cognitive demand and questioning types in tasks of 'Data and Chance' presented in elementary mathematics textbooks in Korea, the United States, and Australia. The levels of cognitive demand of textbook tasks were analyzed according to the knowledge and process and thinking types required in the tasks. The tasks were also analyzed for questioning types, answer types, and response types. As a result, in terms of knowledge and process and thinking types in tasks, all three countries had something in common: the percentage of tasks requiring 'representation' and process was the highest, and the percentage of tasks requiring 'basic application of skill/concept' was also the highest. From a thinking types perspective, differences were found between textbook tasks in the three countries in graph and chance learning. The results of analyzing questioning types showed that in all three textbooks, the percentage of observational reasoning questions was highest, followed by the percentage of factual questions. The proportions and characteristics of the constructing questions included in the U.S. and Australian textbooks differed from those in the Korean textbooks. Based on these results, this study presents implications for constructing elementary mathematics textbook tasks in 'Data and Chance.'
This study noted that a survey of teachers in a leading study conducted in Korea during the Pandemics period pointed out that the "real-time interactive" classes account for a significantly small portion of the remote class format. Contentually, the study reported cases of developing and applying "real-time interactive" class materials based on "planar decision requirements" of high school mathematics subject geometry. The teacher who participated in the development was a math teacher who worked at a Seoul-based high school with 28 years of high school teaching experience, and a teacher who was in charge of geometry in the math department in 2020. The development teacher decided to develop real-time interactive classes. In particular, the materials were developed by organizing the class guidance plan in four stages: 'Meeting and Class Guidance', 'Giving motivation', 'Suggesting tasks', 'Individual Investigative Activities and Teacher Feedback' and 'Reflection and Evaluation' which were selected through the process of selecting the class contents and selecting online class tools. At this time, the development teacher produced and presented about five minutes of video material using the videooscribe, a whiteboard animation program. And in case of task number 8, it consisted of recording the students' free thoughts after class, which served as a role of assessment by students themselves and providing feedback to their teachers. This study is a case study that introduces a series of courses in which field teachers develop class materials, and in addition to presenting class materials that can be applied directly to classes, is a result of a study that focuses on the role of presenting samples for future class data development. The materials developed were verified as class materials based on the opinions of the students who participated in the class and the results of the evaluation commissioned by the three math teachers.
Journal of Korean Home Economics Education Association
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v.33
no.4
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pp.85-101
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2021
The purpose of this study was to make suggestions for improvement by analyzing the activity tasks in the clothing life area in middle school 「Technology & Home Economics」 textbooks of the 2015 revised curriculum. For this purpose, the multiple intelligence teaching-learning strategy analysis criteria were reconstructed and used for analysis. The activity tasks of the clothing life area of 「Technology & Home Economics I」 textbooks from 12 different publishers were analyzed based on the reconstructed analysis criteria, and the content validity was verified by 11 experts. The content validity, assessed by CVI was 0.94. According to the results, the logical·mathematical intelligence accounted for the highest proportion with 31.02%, followed by linguistic intelligence(23.81%), visual/spatial intelligence(17.08%), intrapersonal intelligence(14.71%), interpersonal intelligence(5.79%), bodily/kinesthetic intelligence(5.22%), naturalistic intelligence(2.37%), and musical intelligence(0.00%). The results showed that the teaching-learning strategies most frequently implemented in clothing life area were logical/mathematical intelligence, linguistic intelligence, visual/spatial intelligence, and intrapersonal intelligence. On the other hand, teaching-learning strategies related to interpersonal intelligence, bodily/kinesthetic intelligence, and naturalistic intelligence were used at a relatively low proportion. Therefore, it is recommended to expand the teaching-learning strategies of interpersonal, bodily/kinesthetic, naturalistic and musical intelligence, for a more balanced intelligence development of students.
Potential economic impact of a hypothetical severe accident at a nuclear power plant(Uljin units 3/4) was estimated by applying the Delphi method, which is based on the expert judgements and opinions, in the process of quantifying uncertain factors. For the purpose of this study, it is assumed that the radioactive plume directs the inland direction. Since the economic risk can be divided into direct costs and indirect effects and more uncertainties are involved in the latter, the direct costs were estimated first and the indirect effects were then estimated by applying a weighting factor to the direct cost. The Delphi method however subjects to risk of distortion or discrimination of variables because of the human behavior pattern. A mathematical approach based on the Bayesian inferences was employed for data processing to improve the Delphi results. For this task, a model for data processing was developed. One-dimensional Monte Carlo Analysis was applied to get a distribution of values of the weighting factor. The mean and median values of the weighting factor for the indirect effects appeared to be 2.59 and 2.08, respectively. These values are higher than the value suggested by OECD/NEA, 1.25. Some factors such as small territory and public attitude sensitive to radiation could affect the judgement of panel. Then the parameters of the model for estimating the direct costs were classified as U- and V-types, and two-dimensional Monte Carlo analysis was applied to quantify the overall economic risk. The resulting median of the overall economic risk was about 3.9% of the gross domestic products(GDP) of Korea in 2006. When the cost of electricity loss, the highest direct cost, was not taken into account, the overall economic risk was reduced to 2.2% of GDP. This assessment can be used as a reference for justifying the radiological emergency planning and preparedness.
This study investigated the relationship between the cutflow of rural population and agricultural policy by using time series method. For the analytical tools, decomposition time series methods and regression technique were employed in computing seasonal fluctuation and cyclical fluctuation of population migration. Also, this study predicted farmhouse, rural population till the 2000's by means of the mathematical methods. The analytical forms employed in forecasting farmhouse, rural population were Exponential curve, Gompertz curve and Transcendental form. The major findings of this study were identified as follows: 1) Rural population and farmhouse population began to decrease from 1965 and hastily went down since 1975. Rural population which accounted for 36.4 percent, 35.6 percent of national population respectively in 1960 diminished about two times: 17.5 percent, 17.1 percent respectively. 2) The rapid decreasing of the rural population was caused because of the outflow of rural people to the urban regions. Of course, that was also caused from the natural decreases but the main reason was heavily affected more the former than the latter. In the outflowing course shaped from rural to the urban regions, rural people concentrated on such metropolis as Seoul, Pusan, Keanggi. But these trends were diminishing slowly. On the other hand, compared with that of the 1970's the migration to Keanggi was still increasing in the 1980's. That is, people altered the way of migration from the migration to Seoul, Pusan to the migration to the out-skirts of Seoul. 3) The seasonal fluctuation index of population migration has gone down since the June which the request of agricultural labor force increases and has turned to be greatly wanted in the March as result of decomposition time series method. As result of cyclical analysis, the cyclical patterns of migration have greatly 7 cycle. 4) As result of forecasting the rural and farmhouse population, rural and farmhouse population in the 2000 will be about 9,655(thousand/people) and 4,429(thousand/people) respectively. Thus, it is important to analyze the probloms that rural and farmhouse population will decrease or increase by the degree. But fairly defining the agricultural into a industry that supply the food, this problem - how much our nation need the rural and farmhouse population - is greatly significant too. Therefore, the basic problems of the agricultural including the outflows of rural people are the earning differentials between rural and urban regions. And we should regard the problems of the gap of relative incomes between rural and urban regions as the main task of the agricultural policy and treat the agricultural policy in the viewpoint of developing economic equilibrium than efficiency by using actively the natural resources of the rural regions.
Journal of the Korea Organic Resources Recycling Association
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v.17
no.1
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pp.58-72
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2009
In this study, the organic matter and biomass was characterized by using respirometry based on ASM No.2d (Activated Sludge Model No.2d). The activated sludge models are based on the ASM No.2d model, published by the IAWQ(International Association on Water Quality) task group on mathematical modeling for design and operation of biological wastewater treatment processes. For this study, OUR(Oxygen Uptake Rate) measurements were made on filtered as well as non-filtered wastewater. Also, GC-FID and LC analysis were applied for the estimation of VFAs(Volatile Fatty Acids) COD(S_A) in slowly bio-degradable soluble substrates of the ASM No.2d. Therefore, this study was intended to clearly identify slowly bio-degradable dissolved materials(S_S) and particulate materials(X_I). In addition, a method capable of determining the accurate time to measure non-biodegradable COD(S_I), by the change of transition graphs in the process of measuring microbial OUR, was presented in this study. Influent fractionation is a critical step in the model calibrations. From the results of respirometry on filtered wastewater, the fraction of fermentable and readily biodegradable organic matter(S_F), fermentation products(S_A), inert soluble matter(S_I), slowly biodegradable matter(X_S) and inert particular matter(X_I) was 33.2%, 14.1%, 6.9%, 34.7%, 5.8%, respectively. The active heterotrophic biomass fraction(X_H) was about 5.3%.
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