• The Mathematical Education
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• v.56 no.4
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• pp.365-385
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• 2017

This study aims to explore mathematics teachers' pedagogical design capacity. For this purpose, we googled and collected 327 lesson plans for middle-school mathematics and investigated how mathematics teachers plan and design their mathematics lessons through the format and structures, objectives and mathematical tasks, anticipation for students' thinking, and assessment and technology use. The findings from the data analysis suggest as follows: a) all the lesson plans are structured in a very similar way; b) the lesson plans seem to be based on the textbooks exclusively, that is, the mathematical tasks and flow is strictly followed and kept in the lesson plans in the way the textbooks suggested; c) the lesson plans do not include any evidence of what teachers anticipate for students' thinking and would do to resolve the students' issues; and d) the lesson plans do not contain any specific plans to assess students' thinking processes and reasoning qualitatively, and not intend to use technology in order to promote effective teaching and meaningful understanding.

• Journal of the Korean Society of Earth Science Education
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• v.15 no.1
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• pp.76-90
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• 2022

In this study, after applying the argument structure class design program for 20 preservice earth science teachers, we conducted individual in-depth interviews, analyzed the data, and derived a scientific argumentation PCK development model. The scientific argumentation PCK development model consists of three dimensions: Scientific argumentation PCK, PCK ecosystem, and reflective practice. Scientific argumentation PCK is demonstrated in the process of designing or executing classes using argumentation structures as an instructional reasoning tool. PCK ecosystem, consisting of the existing conventional PCK components, is a dimension surrounding the scientific argumentation PCK, and these two dimensions develop by interacting with each other. Reflective practice regulates each dimension and develops it in various ways by mediating the two dimensions of the scientific argumentation PCK and the PCK ecosystem. The conclusions drawn based on the results are as follows: First, preservice science teachers can demonstrate scientific argumentation PCK in the process of design and implementation of lessons using argumentation structures as a pedagogical reasoning tool. Second, it is necessary to develop the PCK for pedagogical reasoning tools such as scientific argumentation PCK in advance for the development of science teachers' PCK, since the scientific argumentation PCK can develop various components of the PCK ecosystem. Finally, it is necessary to use scientific argumentation PCK to support the preservice teacher's reflective practice, seeing that the scientific argumentation PCK promotes the development of PCK ecosystem components by inducing reflective practice.

• Journal of the Korean School Mathematics Society
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• v.12 no.1
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• pp.1-25
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• 2009

The purpose of this research is the investigation of mathematics pre service teachers' disposition. Their disposition will be used for preposition of preservice Leacher program for making pre service teachers' participate any program willingly and extend their thinking. For this research, the researcher collected various data from investigation-presentation, report for practice and beauty of mathematics, micro teaching, and peer-evaluation. Preservice teachers had positive attitude for mathematics. They described their feeling, thinking and reflection about various methods of instruction and prefer to have micro teaching. They described that the investigation-presentation was needed to change some. From the results, the teacher preparation program is needed to integrate theory and practice to make preservice teachers gain profound knowledge on pedagogical content knowledge by making them high their interest and sensitivity on mathematics.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.339-356
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• 2010

It is important for children to develop statistical reasoning as they think through data. In particular, it is imperative to provide children instructional situations in which they are encouraged to consider variability in data because the ability to reason about variability is fundamental to the development of statistical reasoning. Many researchers argue that even highperforming mathematics students show low levels of statistical reasoning; interventions attending to pedagogical concerns about child ren's statistical reasoning are, thus, necessary. The purpose of this study was to investigate 15 gifted elementary students' various ways of understanding important statistical concepts, with particular attention given to 3 students' reasoning about data that emerged as they engaged in the process of generating and graphing data. Analysis revealed that in recognizing variability in a context involving data, mathematically gifted students did not show any difference from previous results with general students. The authors suggest that our current statistics education may not help elementary students understand variability in their development of statistical reasoning.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.103-124
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• 2014

The process of analogical reasoning can be conventionally summarized in five steps : Representation, Access, Mapping, Adaptation, Learning. The purpose of this study is to develop more detailed model for reason of analogies considering the distinct characteristics of the mathematical education based on the process of analogical reasoning which is already established. Ultimately, This model is designed to facilitate students to use analogical reasoning more productively. The process of developing model is divided into three steps. The frist step is to draft a hypothetical model by looking into historical example of Leonhard Euler(1707-1783), who was the great mathematician of any age and discovered mathematical knowledge through analogical reasoning. The second step is to modify and complement the model to reflect the characteristics of students' thinking response that proves and links analogically between the law of cosines and the Pythagorean theorem. The third and final step is to draw pedagogical implications from the analysis of the result of an experiment.

• Journal of The Korean Association For Science Education
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• v.37 no.4
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• pp.553-564
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• 2017

This study investigated the change of pre-service elementary teachers' professional visions through video-based reflection on science teaching with focus on their attention and pedagogical reasoning about student learning. Specifically, we compared two reflection cycles before and after pre-service elementary teachers went through the collaborative video-based reflection process in a professional learning community. The primary data were collected from eight pre-service elementary teachers and included their science lesson plans, videotaped lessons, video-reflection papers, and transcripts from the interviews. Pre-service elementary teachers' attention was categorized in five aspects: classroom management & control, teacher's instruction, students' thinking & learning, subject knowledge, and assessment. The level of their pedagogical reasoning about student thinking and learning was determined with six levels based on the number of evidence, evidence area, and evidence type. The findings revealed that 1) individual reflection is not enough - collaborative reflection is essential to change their attention toward students learning and thinking 2) pedagogical reasoning levels increase gradually throughout the individual and collaborative video-based reflection processes. The participants not only attributed student learning solely to the characteristics of students but also connected it with their own instruction or science content knowledge and used different types of evidences as they went through two reflection cycles. Implications for using video in the teacher education program were discussed.

• Journal of The Korean Association For Science Education
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• v.32 no.5
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• pp.805-822
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• 2012

The purpose of this study was to explore the patterns of group model development about blood flow in the heart and reasoning process by small group interaction. The subjects were 14, 8th graders in a Science Gifted Center. The group discussion was made possible by using triggering questions that can be answered based on experiences of hands-on activities such as a siphon pump analogy model activity and a dissection of pigs' hearts. Despite participating in same activities, the groups showed different model development patterns: unchanged, persuasive, and elaborated. Due to the critical revising, the group's explanatory model was elaborated and developed in the added and elaborated pattern. As critical revising is a core element of the developing model, it is important to promote a group interaction so that students become critical and receptive. The pedagogical analogy model and conflict situation enabled students to present elaborated reasoning. The Inquiry activity with the pedagogical analogy model promote students' spontaneous reasoning in relation to direct experience. Therefore offering a pedagogical analogy model will help students evaluate, revise and develop their models of concerned phenomena in science classroom. Conflict situation by rebuttal enable students to justify more solid and elaborate a model close to the target model. Therefore, teachers need to facilitate a group atmosphere for spontaneous conflict situation.

• Journal of The Korean Association For Science Education
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• v.36 no.4
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• pp.551-561
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• 2016

The purpose of this study is to investigate both theoretically and empirically the roles of models in abductive reasoning for scientific problem solving. The context of the study is design-based research the goal of which is to develop inquiry learning programs in the domain of earth science, and the current article dealt with an early process of redesigning an abductive inquiry activity in geology. In the theoretical study, an extensive review was conducted with the literature addressing abduction and modeling together as research methods characterizing earth science. The result led to a tentative scheme for modeling-based abductive inference, which represented relationships among evidence, resource models, and explanatory models. This scheme was improved by the empirical study in which experts' reasoning for solving a geological problem was analyzed. The new scheme included the roles of critical evidence, critical resource models, and a scientifically sound explanatory model. Pedagogical implications for the support of student reasoning in modeling-based abductive inquiry in earth science was discussed.

• Journal of The Korean Association For Science Education
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• v.27 no.9
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• pp.818-831
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• 2007

Recognizing the importance of abductive inquiry in Earth science, some theoretical approaches that deploy abduction have been researched. And, it is necessary that the abductive inquiry in a geological field excursion as a vivid locale of Earth science inquiry should be researched. We developed a geological field trip based on the abductive learning model, and investigated students' abductive inference, thinking strategies used in those inferences, and the impact of a teacher's pedagogical intervention on students' abductive inference. Results showed that students, during the field excursion, could accomplish abductive inference about rock identification, process of different rock generation, joints generation in metamorpa?ic rocks, and terrains at the field trip area. They also used various thinking strategies in finding appropriate rules to construe the facts observed at outcrops. This means that it is significant for the enhancement of abductive reasoning skills that students experience such inquiries as scientists do. In addition, a teacher's pedagogical interventions didn't ensure the content of students' inference while they helped students perform abductive reasoning and guided their use of specific thinking strategies. Students had found reasoning rules to explain the 01: served facts from their wrong prior knowledge. Therefore, during a geological field excursion, teachers need to provide students with proper background knowledge and information in order that students can reason rues for persuasive abductive inference, and construe the geological features of the field trip area by the establishment of appropriate hypotheses.

• Research in Mathematical Education
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• v.24 no.3
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• pp.255-278
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• 2021

Proof serves a critical role in mathematical practices as well as in fostering student's mathematical understanding. However, the research literature accumulates results that there are not many opportunities available for students to engage with proving-related activities and that students' understanding about proof is not promising. This unpromising state of instruction of proof calls for a novel approach to address the aforementioned issues. This study investigated an instruction of proof to explore a pedagogy to teach how to prove. The teacher utilized the way of problem posing to make proving a routine part of everyday lesson and changed the classroom culture to support student proving. The study identified the teacher's support for student proving, the key pedagogical changes that embraced proving as part of everyday lesson, and what changes the teacher made to cultivate the classroom culture to be better suited for establishing a supportive community for student proving. The results indicate that problem posing has a potential to embrace proof into everyday lesson.