• The Mathematical Education
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• v.46 no.2 s.117
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• pp.207-226
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• 2007

The purpose of this study was to design and develop the processes of tasks and assessment rubrics of open-ended tasks, and those for the 5th graders of elementary school mathematics. 7 tasks were finally developed, and 'problem understanding', 'problem solving process', 'communication' were selected as the criteria for assessment rubrics. The result was that the ability of mathematical power covering problem understanding ability, problem solving ability and mathematical communication ability was low. Specifically, problem understanding ability was the highest, problem solving ability was middle, and mathematical communication ability was the lowest.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.129-144
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• 2009

The purpose of the study was to investigate the effects of the use of RNP curriculum based on Lesh translation model on third grade students' understandings of fraction concepts and problem solving ability. Students' conceptual understandings of fractions and problem solving ability were improved by the use of the curriculum. Various manipulative experiences and translation processes between and among representations facilitated students' conceptual understandings of fractions and contributed to the development of problem solving strategies. Expecially, in problem situations including fraction ordering which was not covered during the study, mental images of fractions constructed by the experiences with manipulatives played a central role as a problem solving strategy.

• Journal of The Korean Association For Science Education
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• v.22 no.3
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• pp.411-421
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• 2002

This study investigated small group processes in paired think-aloud problem solving. Two high school chemistry classes were assigned to St-SL group (using Strategy-Solve Listener) and SL group (Solver Listener), and their small-group behaviors were audio/video taped. Verbal behaviors of solver and listener in respect to 4 problem-solving stages and performance levels at each stage were analyzed. At the understanding stage, listeners in the St-SL group exhibited more behaviors of agreement to solver's understanding processes about given and goal of problem. As regards recalling a related law at the planning stage, solvers in the St-SL group exhibited more behaviors of modification based on listener's questions or pointing out. These verbal interactions seemed to have a positive effect on students' deriving the physical quantity with the proper laws. Few in both SL and St-SL groups exhibited the behaviors regarding setting up subgoals. No verbal behavior was observed in the SL group at the reviewing stage, and solvers in the St-SL group tended to ask for listener's agreement. However, only few performed the strategy explaining the meaning of answer at the molecular level correctly through the interactions. The St-SL group perceived that the understanding stage was the most helpful and that the planning or reviewing stages were difficult to apply.

• The Mathematical Education
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• v.31 no.2
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• pp.109-119
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• 1992

The primary purpose of the present study is to provide the sources to improve the mathematical problem solving performance by analyzing the effects of the belief systems and the misconceptions of the middle school students in solving the problems. To attain the purpose of this study, the reserch is designed to find out the belief systems of the middle school students in solving the mathematical problems, to analyze the effects of the belief systems and the attitude on the process of the problem solving, and to identify the misconceptions which are observed in the problem solving. The sample of 295 students (boys 145, girls 150) was drawn out of 9th grade students from three middle schools selected in the Kangdong district of Seoul. Three kinds of tests were administered in the present study: the tests to investigate (1) the belief systems, (2) the mathematical problem solving performance, and (3) the attitude in solving mathematical problems. The frequencies of each of the test items on belief systems and attitude, and the scores on the problem solving performance test were collected for statistical analyses. The protocals written by all subjects on the paper sheets to investigate the misconceptions were analyzed. The statistical analysis has been tabulated on the scale of 100. On the analysis of written protocals, misconception patterns has been identified. The conclusions drawn from the results obtained in the present study are as follows; First, the belief systems in solving problems is splited almost equally, 52.95% students with the belief vs 47.05% students with lack of the belief in their efforts to tackle the problems. Almost half of them lose their belief in solving the problems as soon as they given. Therefore, it is suggested that they should be motivated with the mathematical problems derived from the daily life which drew their interests, and the individual difference should be taken into account in teaching mathematical problem solving. Second. the students who readily approach the problems are full of confidence. About 56% students of all subjects told that they enjoyed them and studied hard, while about 26% students answered that they studied bard because of the importance of the mathematics. In total, 81.5% students built their confidence by studying hard. Meanwhile, the students who are poor in mathematics are lack of belief. Among are the students accounting for 59.4% who didn't remember how to solve the problems and 21.4% lost their interest in mathematics because of lack of belief. Consequently, the internal factor accounts for 80.8%. Thus, this suggests both of the cognitive and the affective objectives should be emphasized to help them build the belief on mathematical problem solving. Third, the effects of the belief systems in problem solving ability show that the students with high belief demonstrate higher ability despite the lack of the memory of the problem solving than the students who depend upon their memory. This suggests that we develop the mathematical problems which require the diverse problem solving strategies rather than depend upon the simple memory. Fourth, the analysis of the misconceptions shows that the students tend to depend upon the formula or technical computation rather than to approach the problems with efforts to fully understand them This tendency was generally observed in the processes of the problem solving. In conclusion, the students should be taught to clearly understand the mathematical concepts and the problems requiring the diverse strategies should be developed to improve the mathematical abilities.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.315-335
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• 2010

The goal of this research was to study the effects of the Mathematical Problem Generating Program on problem solving ability and learning attitude. The experiment was carried out between two classes. One class was applied with the experimental program (treatment group), and the other continued with normal teaching and learning methods (comparative group). In this study, two 5th grade elementary classes participated in Seoul city. In this study, the students were tested their problem solving abilities by the IPSP test and learning attitude by the Korean Education Development Institute (KEDI) before and after use of the program. The collected results were t-tested to find any meaningful changes. The results showed the followings. First, use of the mathematical generating program showed meaningful progressive results in problem solving ability. Second, the students that used the program showed positive results in learning attitude. In conclusion, learning mathematics using the problem generating method helps students deeper understand and solve complex problems. In addition, problem solving abilities can be improved and the attitude towards mathematics can be changed while students are using an active and positive approach in problem solving processes.

• The Mathematical Education
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• v.60 no.2
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• pp.133-157
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• 2021

Ill-structured problems have drawn attention in that they can enhance problem-solving skills, which are essential in future societies. The purpose of this study is to analyze and evaluate students' spatial reasoning(Intrinsic-Static, Intrinsic-Dynamic, Extrinsic-Static, and Extrinsic-Dynamic reasoning) and problem solving abilities(understanding problems and exploring strategies, executing plans and reflecting, collaborative problem-solving, mathematical modeling) that appear in ill-structured problem-solving. To solve the research questions, two ill-structured problems based on the geometry domain were created and 11 lessons were given. The results are as follows. First, spatial reasoning ability of sixth-graders was mainly distributed at the mid-upper level. Students solved the extrinsic reasoning activities more easily than the intrinsic reasoning activities. Also, more analytical and higher level of spatial reasoning are shown when students applied functions of other mathematical domains, such as computation and measurement. This shows that geometric learning with high connectivity is valuable. Second, the 'problem-solving ability' was mainly distributed at the median level. A number of errors were found in the strategy exploration and the reflection processes. Also, students exchanged there opinion well, but the decision making was not. There were differences in participation and quality of interaction depending on the face-to-face and web-based environment. Furthermore, mathematical modeling element was generally performed successfully.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.545-562
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• 2009

This study is trying to analyze characteristics of mathematical thinking processes of the mathematical gifted students in an objective and a systematic way, by using "Protocol Analysis Method"and "Problem Behavior Graph" which is suggested by Newell and Simon as a qualitative analysis. In this study, four middle school students with high achievement in math were selected as subjects-two students for mathematical gifted group and the other two for control group also with high scores in math. The thinking characteristics of the four subjects, shown in the course of solving problems, were elicited, analyzed and compared, through the use of the creative test questionnaires which were supposed to clearly reveal the characteristics of mathematical gifted students' thinking processes. The results showed that there were several differences between the two groups-the mathematical gifted student group and their control group in their mathematical talents. From these case studies, we could say that it is significant to find out the characteristics of mathematical thinking processes of the mathematical gifted students in a more scientific way, in the sense that this result can be very useful to provide them with the chances to get more proper education by making clear the nature of thinking processes of the mathematical gifted students.

• Journal of The Korean Association For Science Education
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• v.25 no.4
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• pp.526-532
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• 2005

The purpose of this study was to analyze physics problem solving processes to qualitative and quantitative problems in the area of 'Force and Motion' in high school science. The students who have already learned the area of 'Force and Motion' during the first semester of 10th grade have taken physics test to choose students who have basic knowledge of physics. Eight students were selected. After explaining the purpose and the procedure of this study, think-aloud method was instructed to the students, and the students practiced it. After that, the students solved three problems in each quantitative and qualitative type. Then, the questionnaire of belief system on physics and physics problem solving and the prerequisite knowledge test were administered. By recording the students' solving processes, protocol was made and analyzed. After solving problems, the students expressed their confidence, intimacy, and preference. Quantitative problems needed much time at planning step than qualitative problems did. Moreover, solving time was longer and repeating frequency was more than those of qualitative problems. It seemed because even though the students qualitatively knew the answer, they should determine the given quantitative conditions, consider formulae, and recall the specific numbers. Since the students usually got access to many quantitative items in their physics study, they were accustomed to solve problems by using formulae. In addition, they put confidence in formulae, so they tended to solve problems quantitatively. As the result, they preferred quantitative problems to qualitative problems.

• The Mathematical Education
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• v.44 no.4 s.111
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• pp.627-651
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• 2005

This study was conducted to attain an in-depth understanding of students' mathematical representations and to present the educational implications for teaching them. Twelve mathematical tasks were developed according to the six types of problems. A task performance was executed to 151 third graders from four classes in DaeJeon and GyeongGi. We analyzed the types and forms of representations generated by them. Then, qualitative case studies were conducted on two small-groups of five from two classes in GyeongGi. We analyzed how individuals' representations became elaborated into group representation and what patterns emerged during the collaborative small-group learning. From the results, most students used more than one representation in solving a problem, but they were not fluent enough to link them to successful problem solving or to transfer correctly among them. Students refined their representations into more meaningful group representation through peer interaction, self-reflection, etc.. Teachers need to give students opportunities to think through, and choose from, various representations in problem solving. We also need the in-depth understanding and great insights into students' representations for teaching.

• The Journal of Korean Academic Society of Nursing Education
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• v.20 no.4
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• pp.482-490
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• 2014

Purpose: This research compares self-leadership, team efficacy, problem solving processes and task satisfaction in response to teaching methods applied to nursing students, and determines whether variations exist. Method: This research experiments before and after the training of a nonequivalent group. The subjects were 36 learners of action learning methods and 39 learners of nursing course methods, and the research took place from October through December 2012. Results: Prior to the training, the general features and measurable variables of the two groups of subjects were similar, and self-leadership, team efficacy, problem solving process and task satisfaction in both groups were elevated compared to pre-training. In particular, in comparison with the nursing course, there was a notable difference in scores, the action learning method receiving high scores in the problem solving process (t=2.92, p=.005) and task satisfaction (t=2.54, p=.013) Conclusion: It is recommended that educators not only conduct the practice training course for teaching methods, but also incorporate action learning.