• Journal of Educational Research in Mathematics
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• v.27 no.2
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• pp.171-189
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• 2017

By designing and applying the lesson helping to discover the power laws, we tried to investigate the characteristics on the class. To do this, we designed a discovery lesson on the power laws and applied to 54 8th grade students. As results, we could observe the overproduction of monotonous laws, tendency to vary the type of development and increase error to students without prior learning experience, and various errors. All participants failed to express the generalization of $a^m{\div}a^n$ and some participants expressed an incomplete generalization using variables partially for the base or power. We could also observe an error of limited generality or a representation error which did not use the equal sign or variables. In the survey of students, there were two contradictory positions to appeal to the enjoyment of the creation and to talk about the difficulty of creation. Based on such results, we discussed the pedagogical implications relating to the discovery of power laws.

• Journal of the Korean earth science society
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• v.25 no.3
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• pp.194-204
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• 2004

The purpose of this literature review is to investigate what kinds of research have been done about scientific inquiry in terms of scientific argumentation in the classroom context from the upper elementary to the high school levels. First, science educators argued that there had not been differentiation between authentic scientific inquiry by scientists and school scientific inquiry by students in the classroom. This uncertainty of goals or definition of scientific inquiry has led to the problem or limitation of implementing scientific inquiry in the classroom. It was also pointed out that students' learning science as inquiry has been done without opportunities of argumentation to understand how scientific knowledge is constructed. Second, what is scientific argumentation, then? Researchers stated that scientific inquiry in the classroom cannot be guaranteed only through hands-on experimentation. Students can understand how scientific knowledge is constructed through their reasoning skills using opportunities of argumentation based on their procedural skills using opportunities of experimentation. Third, many researchers emphasized the social practices of small or whole group work for enhancing students' scientific reasoning skills through argumentations. Different role of leadership in groups and existence of teachers' roles are found to have potential in enhancing students' scientific reasoning skills to understand science as inquiry. Fourth, what is scientific reasoning? Scientific reasoning is defined as an ability to differentiate evidence or data from theory and coordinate them to construct their scientific knowledge based on their collection of data (Kuhn, 1989, 1992; Dunbar & Klahr, 1988, 1989; Reif & Larkin, 1991). Those researchers found that students skills in scientific reasoning are different from scientists. Fifth, for the purpose of enhancing students' scientific reasoning skills to understand how scientific knowledge is constructed, other researchers suggested that teachers' roles in scaffolding could help students develop those skills. Based on this literature review, it is important to find what kinds of generalizable teaching strategies teachers use for students scientific reasoning skills through scientific argumentation and investigate teachers' knowledge of scientific argumentation in the context of scientific inquiry. The relationship between teachers' knowledge and their teaching strategies and between teachers teaching strategies and students scientific reasoning skills can be found out if there is any.

• Journal of Gifted/Talented Education
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• v.7 no.1
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• pp.31-50
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• 1997

'I'his study investigated students' attitude toward mathematics. and how behavior/cognitive training affects level of math anxietv and level of math achievement. Subjects were all the freshmen attending Taejon Science High School, and they were given Mathematics Attitudes Scale and Attributional Style Questionnaire prior to and post training sessions. Twenty out of 84 freshmen voluntarily participated in nine sessions of training program. Participants were asked to do self-evaluation. Math achievement was measured prior to and post training. and was compared between two groups. Training program utilized behavior/cognitive approach. such as understanding one's feeling through muscle relaxation, breathing and meditation; modifying negative attributional style; imitating effective cognitive strategies for math problem solving, and so on. 'I'he result shows that students' math confidence in general was relatively low out of expectation, a nd they perceived teachers not supporting their math abilities :IS much as expected. On the other hand, students in general had strong math achievelment needs, and considered math utility very high. Sex difference was seen in the attitude toward female math abilities, to result that female students had more positive perception than male students. Female students of 'I'aejon Science High School seem free from conventional idea about female abilities including theirs. Participants' ~attitude change was compared with non-participants. and participants showed statistically significant change in their math confidence, and also in their math achievement. Participants had much higher math confidence and ~achievement than non-participants. And, they showed increased level of perceiving teachers' expectation. more realistic in needs, and more involvement in math. Math achievement was found positively related to math confidence, and participants' math achievement change was explained by their belief in math utility. Not only training program effect hut also participants' voluntary involvement and teacher\ulcorner' support of the program and participation seem to increase their math achievement. Based upon the result of study it was suggested that behavior-/cognitive training program be provided along with academic curricula for gifted students of Korea to help their emotional and psychological development enhance the efficacy of their cognitive learning.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.51-69
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• 2012

The cognition of an intrinsic attribute play an important role in the process of theoretical generalization. It is the aim of this paper to study how the theoretical generalization is made. First of all, we suggest the What-if-only-strategy(WIOS) which is the strategy helping the cognition of an intrinsic attribute. And we propose the process of the theoretical generalization that go on the cognitive stage, WIOS stage, conjecture stage, justification stage and insight into an intrinsic attribute in order. We propose the process of generalization adding the concrete process cognizing an intrinsic attribute to the existing process of generalization. And we applied the proposed process of generalization to two mathematical theorem which is being managed in middle school. We got a conclusion that the what-if-only strategy is an useful method of generalization for the proposition. We hope that the what-if-only strategy is helpful for both teaching and learning the mathematical generalization.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.1
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• pp.125-143
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• 2012

This study is designed to see the characteristics of elementary students' arithmetic error patterns and error rates by going up grades and to draw some implications for effective instruction. For this, 580 elementary students of grade 3-6 are tested with the same subtraction, multiplication and division problems. Their errors are analyzed by the frame of arithmetic error types this study sets. As a result of analysis, it turns out that the children's performance in arithmetic get well as their grades go up and the first learning year of any kind of arithmetic procedures has the largest improvement in arithmetic performance. It is concluded that some arithmetic errors need teachers' caution, but we fortunately find that children's errors are not so seriously systematic and sticky that they can be easily corrected by proper intervention. Finally, several instructional strategies for arithmetic procedures are suggested.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.509-525
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• 2016

This study is a follow-up study of the previous research for teacher education(Kim Nam Hee, 2006, 2009, 2013, 2014). This study was conducted with third grade students of the college of education in 2016. In this study, we guided to allow pre-service teachers to develop their teaching research ability and teaching practical skills using the results obtained from the in-service teachers training courses. Processes mainly performed in this study are as follows; learning the theory on Socrates' method, case study for thought experiment activities, instructional simulation using a Socrates' method, class analysis, textbook analysis, peer evaluation, self-assessment. Observing tutorial examples by in-service teachers, pre-service teachers were expanding their limited knowledge and experience. By analyzing the results obtained from this research processes, we checked the points to put more attention in future pre-service teachers education.

• School Mathematics
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• v.16 no.4
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• pp.659-675
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• 2014

The purpose of this study is to investigate the effects of scheme based strategy Instruction on problem solving of word problems of ratio and proportion for students with under achievement or at risk for learning disabilities. Three $7^{th}$ graders of underachieving or at risk LD were participated in this study. Three steps of instructional experiment-testing baseline, intervention with schematic-based strategy, testing for the abilities of problem solving, generalization, & sustainability. The results showed that the schema-based strategy, FOPS was effective method for all three students enhancing problem solving abilities and for generalizing and sustaining the problem solving.

• School Mathematics
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• v.19 no.3
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• pp.571-591
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• 2017

The purpose of this study is to understand the characteristics of mathematical discourse about the length in the class that learns the length of the curve defined by definite integral. For this purpose, this study examined the discourse about length by paying attention to the usage of the word 'length' in the class participants based on the communicative approach. As a result of the research, it was confirmed that the word 'length' is used in three usages - colloquial, operational, and structural usage - in the process of communicating with the discourse participants. Particularly, each participant did not recognize the difference even though they used different usage words, and this resulted in ineffective communication. This study emphasizes the fact that the difference in usage of words used by participants reduces the effectiveness of communication. However, if discourse participants pay attention to the differences of these usages and recognize that there are different discourses, this study suggests that meta - level learning can be possible by overcoming communication discontinuities and resolving conflicts.

• School Mathematics
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• v.19 no.4
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• pp.639-661
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• 2017

The purpose of this study is to investigate the relationship between the distance function average speed and the speed function. Particularly, in this study, we investigate the process of constructing the speed function in the distance function (irrational function, exponential function) which is difficult to weaken the argument in the denominator. In this process, students showed various anxieties and expressions about the procedural knowledge that they constructed first. In particular, if student B can not explain all the knowledge he already knows in this process, he showed his reflection on the process of calculating the differential coefficient. This study adds an understanding of the calculation method of students in differential coefficient learning. In addition, it is meaningful that the students who construct procedural knowledge at the time of calculating the differential coefficient have thought about how to provide opportunities to reflect on the procedure they constructed.

• Education of Primary School Mathematics
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• v.19 no.1
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• pp.19-30
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• 2016

This study examined pre-service teachers' pedagogical content knowledge of fraction division in a context where they were asked to write a story problem for a symbolic expression illustrating a whole number divided by a proper fraction. Problem-posing is an important instructional strategy with the potential to create meaningful contexts for learning mathematical concepts, especially when real-world applications are intended. In this study, story problems written by 135 elementary pre-service teachers were analyzed with respect to mathematical correctness. error types, and division models. Patterns and tendencies in elementary pre-service teachers' knowledge of fraction division were identified. Implicaitons for teaching and teacher education are discussed.