• Communications of Mathematical Education
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• v.33 no.3
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• pp.395-423
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• 2019

The purpose of the study is to analyze the levels of cognitive demands and components of the reasoning process presented in the mathematical sequence section of three high school mathematics textbooks in order to provide implications for the development of reasoning tasks in the future mathematics textbooks. The results of the study have revealed that most of the reasoning tasks presented in the mathematical sequence section of the three high school mathematics textbooks seemed to require low-level cognitive demands and that low-level cognitive demands reasoning tasks required only a component of one reasoning process. On the other hand, only a portion of the reasoning tasks appeared to require high-level of cognitive demands, and high-level cognitive demands reasoning tasks required various components of reasoning process. Considering the results of the study, it seems to suggest that we need more high-level cognitive demands reasoning tasks to develop high-level cognitive reasoning that would provide students with learning opportunities for various processes of reasoning, and that would provide a deeper understanding of the nature of reasoning.

• Journal of The Korean Association For Science Education
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• v.38 no.6
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• pp.839-851
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• 2018

The purpose of this study is to analyze the science reasoning differences of elementary school students' science writing. For this purpose, science writing activities and analysis frameworks were developed. Science writing data were collected and analyzed. Third to sixth grade elementary students were selected from a middle high level elementary school in terms of a national achievement test in Seoul. A total of 320 writing materials were analyzed. The results of the analysis were as follows. Science writings show science reasoning at 52 % for $3^{rd}$ grade, 68% for $4^{th}$ grade, 85% for $5^{th}$ grade, and 89% for $6^{th}$ grade. Three types of scientific reasoning such as inductive reasoning, deductive reasoning, and abductive reasoning appeared in science writing of the third to sixth graders. The abductive reasoning appeared very low in comparing with inductive and deductive reasoning. Level three appeared the most frequently in the science writing of the elementary students. The levels of inductive and deductive reasoning in science writing increased according to increasing grade and showed statistical differences between grades. But the levels of abductive reasoning did not show an increasing aspect according to increasing grade and also did not show statistical differences between grades. The levels of inductive reasoning and deductive reasoning of the 3rd grade was very low in comparing with the other grades.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.95-113
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• 2006

The study tries to differentiate the levels of mathematical reasoning from inductive reasoning to formal reasoning for teaching gradually. Because the formal point of view without the relation to objects has limitations in the creation of a new knowledge, our mathematics education needs consider the such characteristics. We propose an intuitive level of proof related in concrete operations and perceptual experiences as an intermediating step between inductive and formal reasoning. The key activity of the intuitive level is having insight on the generality of reasoning. The details of the process should pursuit the direction for going away from objects and near to formal reasoning. We need teach the mathematical reasoning gradually according to the appropriate level of reasoning more differentiated.

• The Mathematical Education
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• v.62 no.4
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• pp.457-471
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• 2023

Measurement is an imperative content area of early elementary mathematics, but it is reported that students' understanding of units in measurement situations is insufficient despite its importance. Therefore, this study examined lower-grade elementary students' quantitative reasoning of units in length measurement by identifying the levels of reasoning of units. For this purpose, we collected and analyzed the responses of second-grade elementary school students who engaged in a set of length measurement tasks using an open number line in terms of unitizing, iterating, and partitioning. As a result of the study, we categorized students' quantitative reasoning of unit levels into four levels: Iterating unit one, Iterating a given unit, Relating units, and Transforming units. The most prevalent level was Relating units, which is the level of recognizing relationships between units to measure length. Each level was illustrated with distinct features and examples of unit reasoning. Based on the results of this study, a personalized plan to the level of unit reasoning of students is required, and the need for additional guidance or the use of customized interventions for students with incomplete unit reasoning skills is necessary.

• 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.

• Proceedings of the Korean Society for Cognitive Science Conference
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• 2002.05a
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• pp.65-71
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• 2002

우리의 기억에 표상되어 있는 개념의 본질과 근원 그리고 이들의 관계에 대한 연구는 연상과 기억구조의 관계에 집중되어 왔다 따라서, 어떤 한 개념과 다른 한 개념이 관계되어 있다는 의미적 혹은 연상적 점화의 양상은 의미기억 구조를 적절히 예시할 수 있을 것이다. 본 연구는 어휘수준에서 보여지는 연상의 양상이 문장수준에서도 유사한 예측을 해낼 수 있는지를 살펴보고자 한다. 즉, 어휘수준에서 연상적 관계에 있는 두 개념이 선행사와 연상 조응사라는 문법성을 띠면서 문장에서 예상되는 역할을 수행할 때는, 의미기억의 또 다른 양상을 보여줄 것이라 예측되며, 이것은 문장의 의미·화용적 추론의 기제로 유인되고 있음을 제안하려고 한다. 또한, 의미·연상적 점화와 추론의 기제간의 적절한 상호작용은 문장의 응집성과 처리속도 간에도 유의미한 예측을 할 수 있음을 제안한다.

• Education of Primary School Mathematics
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• v.21 no.1
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• pp.55-73
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• 2018

The purpose of this study is to investigate the effects of cognitive activity on cognitive activities that students imagine and cope with continuously changing quantitative changes in functional tasks represented by linguistic expressions, table of value, and geometric patterns, We identified covariational reasoning levels and investigated the characteristics of students' reasoning process according to the levels of covariational reasoning in the elementary quantitative problem situations. Participants were seven 4th grade elementary students using the questionnaires. The selected students were given study materials. We observed the students' activity sheets and conducted in-depth interviews. As a result of the study, the students' covariational reasoning level for two quantities that are continuously covaried was found to be five, and different reasoning process was shown in quantitative problem situations according to students' covariational reasoning levels. In particular, students with low covariational level had difficulty in grasping the two variables and solved the problem mainly by using the table of value, while the students with the level of chunky and smooth continuous covariation were different from those who considered the flow of time variables. Based on the results of the study, we suggested that various problems related with continuous covariation should be provided and the meanings of the tasks should be analyzed by the teachers.

• 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 the Korean School Mathematics Society
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• v.23 no.3
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• pp.323-349
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• 2020

In this study, we conducted eight reciprocal peer tutoring classes where each student took either role of a tutor or a tutee to study covariational reasoning in ninth graders. Students were given the opportunity to teach their peers with their covariational reasoning as tutors, and at the same time to learn covariational reasoning as tutees. A heterogeneous group was formed so that scaffolding could be provided in the teaching and learning process. A total of eight reciprocal peer tutoring worksheets were collected: four quantitative graph type questions and four questions of the qualitative graph to the group. The results of the analysis are as follows. In reciprocal peer tutoring, students who experienced a higher level of covariational reasoning than their covariational reasoning level showed an improvement in covariational reasoning levels. In addition, students enhanced the completeness of reasoning by modifying or supplementing their own covariational reasoning. Minimal teacher intervention or high-level peer mediation seems to be needed for providing feedback on problem-solving results.

• School Mathematics
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• v.15 no.4
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• pp.723-742
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• 2013

The purpose of this study was to analyze children's proportional reasoning process on an ill-structured "architectural drawing" problem solving and to investigate their level and characteristics of proportional reasoning. As results, they showed various perspective and several level of proportional reasoning such as illogical, additive, multiplicative, and functional approach. Furthermore, they showed their expanded proportional reasoning from the early stage of perception of various types of quantities and their proportional relation in the problem to application stage of their expanded and generalized relation. Students should be encouraged to develop proportional reasoning by experiencing various quantity in ration and proportion situations.