• The Mathematical Education
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• v.62 no.4
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• pp.473-490
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• 2023

Previous studies from domestic and abroad are accumulating information on how to reason students' continuous changes through teaching experiments. These studies deal with scenes in which students who make 'smooth reasoning' and 'chunky reasoning' construct mathematical results together in teaching experiments. However, in order to analyze their results in more detail, it is necessary to check what kind of results a student reasoning in a specific way constructs for the tasks of previous studies. According to the need for these studies, the researcher conducted a total of 14 teaching experiments on one first-year high school student who was found to make 'chunky reasoning'. In this study, it was possible to observe a scene in which a student who makes 'chunky reasoning' constructs an output similar to 'a mathematical result constructed by students with various reasoning methods(smooth reasnoning or chunky reasoning) in previous studies.' In particular, the student who participated in this study observed a consistent construction method of constructing the function of 'time-speed' from the function of 'time-distance'. The researcher expected that information on this student's distinctive construction methods would be helpful for subsequent studies.

• Journal of Educational Research in Mathematics
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• v.13 no.2
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• pp.159-178
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• 2003

This study analyzes on the reasoning in the process of justification and mathematical problem solving in our primary mathematics textbooks. In our analyses, we found that the inductive reasoning based on the paradima-tic example whose justification is founnded en a local deductive reasoning is the most important characteristics in our textbooks. We also found that some propositions on the properties of various quadrangles impose a deductive reasoning on primary students, which is very difficult to them. The inductive reasoning based on enumeration is used in a few cases, and analogies based on the similarity between the mathematical structures and the concrete materials are frequntly found. The exposition based en a paradigmatic example, which is the most important characteristics, have a problematic aspect that the level of reasoning is relatively low In Miyazaki's or Semadeni's respects. And some propositions on quadrangles is very difficult in Piagetian respects. As a result of our study, we propose that the level of reasoning in primary mathematics is leveled up by degrees, and the increasing levels are following: empirical justification on a paradigmatic example, construction of conjecture based on the example, examination on the various examples of the conjecture's validity, construction of schema on the generality, basic experiences for the relation of implication.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.655-676
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• 2016

The purpose of this study is to examine the effects of teaching on functional thinking, one of the algebraic thinking in sixth grade students level. For this study, we developed functional thinking based-teaching through analyzing mathematical curriculum and preceding research, which consisted of 12 classes, and we investigated the effects of teaching through quantitative and qualitative analysis. In the results of this study, functional thinking based-teaching was statistically proven to be more effective in improving algebraic reasoning skills and lower elements which is an algebraic reasoning as generalized arithmetic and functional thinking, compared to traditional textbook-centered lessons. In addition, the functional thinking based-teaching gave a positive impact on the functional thinking level. Thus functional thinking based-teaching provides guidance on the implications for teaching and learning methods and study of the functional thinking in the future, because of the significant impact on the mathematics learning in six grade students.

• Journal of Korean Elementary Science Education
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• v.42 no.3
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• pp.421-433
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• 2023

This study examined the reasoning of gifted elementary science students in a socioscientific issues (SSI) classroom discussion on COVID-19-related trash disposal challenges. This study aimed to understand the characteristics of evidence use and decision-making difficulties in each type of SSI-related reasoning. To this end, the transcripts of 17 gifted students of elementary science discussing SSIs in a classroom were analyzed within the framework of informal reasoning. The analysis framework was categorized into three types according to the primary influence involved in reasoning: rational, emotional, and intuitive. The analysis showed that students exhibited four categories of evidence use in SSI reasoning. First, in the rational reasoning category, students deemed and recorded scientific knowledge, numbers, and statistics as objective evidence. However, students who experienced difficulty in investigating such scientific data were less likely to have factored them in subsequent decisions. Second, in the emotional reasoning category, students' solutions varied considerably depending on the perspective they empathized with and reasoned from. Differences in their views led to conflicting perspectives on SSIs and consequent disagreement. Third, in the intuitive reasoning category, students disagreed with the opinions of their peers but did not explain their positions precisely. Intuitive reasoning also created challenges as students avoided problem-solving in the discussion and did not critically examine their opinions. Fourth, a mixed category of reasoning emerged: intuition combined with rationality or emotion. When combined with emotion, intuitive reasoning was characterized by deep empathy arising from personal experience, and when combined with rationality, the result was only an impulsive reaction. These findings indicate that research on student understanding and faculty knowledge of SSIs discussed in classrooms should consider the difficulties in informal reasoning and decision-making.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.1
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• pp.65-80
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• 2010

The aims of our study are to investigate the nature of mathematical reasoning and the teaching of mathematical reasoning in school mathematics. We analysed the process of shaping deduction in ancient Greek based on Netz's study, and discussed on the comparison between his study and Freudenthal's local organization. The result of our analysis shows that mathematical reasoning in elementary school has to be based on children's natural language and their intuitions, and then the mathematical necessity has to be formed. And we discussed on the sequences and implications of teaching of the sum of interior angles of polygon composed the discovery by induction, justification by intuition and logical reasoning, and generalization toward polygons.

• The Mathematical Education
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• v.41 no.3
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• pp.273-289
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• 2002

It tends to be emphasized that mathematics is the important discipline to develop students' mathematical reasoning abilities such as deduction, induction, analogy, and visual reasoning. This study is aimed for investigating the present state about mathematical reasoning in secondary school. We survey teachers' opinions and analyze the results. The results are analyzed by frequency analysis including percentile, t-test, and MANOVA. Results are the following: 1. Teachers recognized mathematics as knowledge constructed by deduction, induction, analogy and visual reasoning, and evaluated their reasoning abilities high. 2. Teachers indicated the importances of reasoning in curriculum, the necessities and the representations, but there are significant difference in practices comparing to the former importances. 3. To evaluate mathematical reasoning, teachers stated that they needed items and rubric for assessment of reasoning. And at present, they are lacked. 4. The hindrances in teaching mathematical reasoning are the lack of method for appliance to mathematics instruction, the unpreparedness of proposals for evaluation method, and the lack of whole teachers' recognition for the importance of mathematical reasoning

• Journal of Science Education
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• v.37 no.2
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• pp.323-337
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• 2013

The purpose of this study was to analyze the scientific reasoning ability during open-inquiry activities of science-gifted 2nd middle school students. Open-inquiry activity is similar to process of scientists' science knowledge generation. Identifying and analyzing the scientific reasoning process and the scientific reasoning ability during open-inquiry activities of science-gifted students, will be able to provide implications for future research. CSRI Matrix(Dolan & Grady, 2010) was used to analyze the complexity of the scientific reasoning ability. The higher degree of complexity of the scientific reasoning is similar to process of scientists' science knowledge generation. The results showed that each process of the open-inquiry activities were distributed by various steps of complexity of the scientific reasoning. Particularly, 'The generating questions' and 'Connecting data to the research question' were 'most complex' step in all teams. On the other side, 'Posing preliminary hypotheses', 'Selecting dependent and independent variables', 'Considering the limitations or flaws of their experiments' were low steps in most teams. And 'Communicating and defending findings' was distributed by most various steps of complexity of the scientific reasoning.

• Education of Primary School Mathematics
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• v.19 no.1
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• pp.79-112
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• 2016

The purpose of this research is to find the effects of learner-centered instruction based on constructivism (LCIC) on their knowledge generation level and reasoning ability. To look for them, after fraction units are re-planed for implementing LCIC, instructions using it provide students in a class. From the data, some conclusions can be drawn as follows: LCIC has more positive influence of students on recall ability, generation ability, and reasoning ability than tractional instruction method. With the data it can be said that the interaction exists between learners' reasoning ability and generation level.

• School Mathematics
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• v.9 no.3
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• pp.427-445
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• 2007

This study presents the results of a case study that investigated a seventh grader's fractional reasoning related to multiplicative reasoning. In addition, by employing domain analysis and taxonomic analysis for analyzing qualitative data, I show how a qualitative methodology was used for the data collected by teaching experiment methodology. The study identifies three distinct issues that emerged as the student engaged in solving fraction problems: a view of fractions as operations vs. results, the issue of units, and mixed numbers vs. improper fractions. These three issues have instructional implications in that each of them is critical in developing multiplicative reasoning and investigating how they relate to each other suggests a way to improve multiplicative reasoning in fractional contexts.

• Journal of The Korean Association For Science Education
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• v.38 no.5
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• pp.635-647
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• 2018

Motivated reasoning refers to biased reasoning that is affected by motivation to achieve a particular result or goal. In this study, we attempted a theoretical study on motivated reasoning that hinders the development of scientific thinking and empirical study on actual context of motivated reasoning in the research experiences of next-generation Korean researchers in the field of science and technology. To be specific, literature reviews were conducted to explore the psychological meaning of motivated reasoning and its negative impact on scientific thinking and science research. To understand the substantial meaning and context of motivated reasoning in the field of real science and technology research, we conducted in-depth interviews with eight graduate students and one young science and technology researcher. As a result of the literature reviews, we found out that motivated reasoning can interfere with the proper theory and data coordination, which is the core process of scientific thinking at the individual level. At the socio-cultural level, it can lead to cessation of constructing scientific knowledge and it can act as a mechanism in the process of using science for specific socio-cultural beliefs or purposes, thereby hindering the development of science and technology based on rationale and objective scientific thinking. Quantitative analysis with in-depth interview data showed that graduate students and the young researcher's experienced motivated reasoning results in trying to protect prior beliefs, make hasty conclusions, protecting socio-cultural belief or rationalizing decisions made by their community. Their motivated reasoning could become an obstacle in constructing valid science and technology knowledge through appropriate theory and evidence coordination. Based on these findings we discussed science education for improving scientific thinking.