• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.31-61
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• 2013

The purpose of this study is to confirm constructivists' assumption that when a little low level learners are taken in learner-centered instruction based on a constructivism they can also construct knowledge by themselves. To achieve this purpose, the researchers compare the effects of learner-centered instruction based on the constructivism and teacher-centered instruction based on the objective epistemology where second graders learn multiplication facts through the each treatment on learners' reasoning ability and achievement. Some conclusions are drawn from results as follows. First, learner-centered instruction based on a constructivism has significant effect on learners' reasoning ability. Second, learner-centered instruction has slightly positive effect on learners' deductive reasoning ability. Third, learner-centered instruction has more an positive influence on understanding concepts and principles of not-presented mathematical knowledge than teacher-centered instruction when implementing it with a little low level learners.

• Education of Primary School Mathematics
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• v.14 no.2
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• pp.165-185
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• 2011

The purpose of this study is to confirm the effects of the learner-centered instruction based on constructivism on learners' reasoning ability and their achievements which is closely related to reflective abstracting ability. To do it, learner-centered instructions for division was implemented, recall test, generation test, content reasoning test I and II were carried out. The following conclusions were drawn from the data we got. Experimental group(EG) improved their reasoning ability, while comparison group(CG) did not. EG showed statistically significant difference in the achievements of the contents learned in comparing with CG, and the difference in the achievements of the contents unlearned in the treatment in comparing with CG was higher than the one. In addition, the comparisons of the subgroups(high, middle, and low) between EG and CG showed that the treatment had a positive influence on the achievement to all subgroups in EG. That is, the treatment was effective for unable learners. Finally, EG showed statistically significant difference in the sub-domain of simple calculation which might be considered as the benefits of the treatment of the CG as well as in the sub-domain of concept and principle.

• School Mathematics
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• v.18 no.4
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• pp.749-771
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• 2016

The purpose of this study is to analyze mathematical tasks of Korea and the USA textbooks focused on conditions for parallelograms. In this study, structures of task, types of proof and reasoning, and levels of cognitive demand are investigated. The conclusion is as follows: First, with respect to structures of task, structures presented in the USA textbooks are more diverse. Second, with respect to types of proof and reasoning, Korea and the USA prefer IC task and DA task. And task types presented in the USA textbooks are more diverse. Third, with respect to levels of cognitive demand, in both Korea and the USA textbooks, PNC task and PWC task account most. And compared to the USA, Korea prefer algorithms. In addition, we find out implications for reconstruction of Korea textbook. It is as follows: First, with respect to structures of task and types of proof and reasoning, the diversity of composition needs to be raised. Second, with respect to levels of cognitive demand, the concentration in PNC task needs to be declined. And levels of cognitive demand on types of tasks need to be reconsidered. Third, with respect to tasks' topic and material, internal and external connectivities of mathematics need to be strengthened.

• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.189-206
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• 2015

There has been a recurring call for using visual representations in textbooks to improve the teaching and learning of proportional reasoning. However, the quantity as well as quality of visual representations used in textbooks is still very limited. In this article, we analyzed visual representations presented in a Grade 6 textbook from two perspectives of proportional reasoning, multiple-batches perspective and variable-parts perspective, and discussed the potential of the double number line and the double tape diagram to help develop the idea 'things covary while something stays the same', which is critical to reason proportionally. We also classified situations that require proportional reasoning into five categories and provided ways of using the double number line and the double tape diagram for each category.

• School Mathematics
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• v.9 no.4
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• pp.447-466
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• 2007

Math education in schools have to enable students to understand the importance of math and nurture the capacity to resolve various problems in daily life with reasoning, which is therefore, always applicable to the actual world. Proportional reasoning capacity is being often used in daily life, and some kind of unit is not fixed. So students are considering it very difficult. This study looks into the difficulties that students have in proportional reasoning, what kind of problem solving strategy is being used, what the problems are in current textbooks, etc. Based on this, it tried to check the concept changes in students' proportional reasoning by developing the instruction program for 'proportional expression' unit in the 6th grade. Based on the results, this study analyzes the features of proportional reasoning instruction programs and the instruction results. Also it analyzes in-advance & after examination papers of the experimental class and comparison class to contribute to the instruction method and instruction contents improvement of 'proportional expression' unit.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.591-614
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• 2023

For a long time, mathematics education institutions such as NCTM(National Council of Teachers of Mathematics) have emphasized the essential role of writing, and recent surveys by the Ministry of Education report a decline in foundational academic skills in the post-COVID19 period. The purpose of this study is to redefine the significance of mathematics writing in mathematics education, focusing on competencies highlighted in the field, particularly in the areas of problem-solving, communication, and reasoning. The research findings indicate that writing in problem-solving enhances cognitive organization, fostering the ability to grasp concepts and methods. Writing in communication builds confidence through the meta-cognitive process, and writing in inference allows self-awareness of step-by-step identification of areas lacking understanding. Particularly in the future society where artificial intelligence(AI) is utilized, changes in the learning environment necessitate research for the establishment of authenticity judgment through writing and the cultivation of a proper writing culture.

• Communications of Mathematical Education
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• v.8
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• pp.165-177
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• 1999

1989년에 NCTM에서 Curriculum and Evaluation Standards for School Mathematics(이하 Standards)를 발간한 이래로 수학교육은 Standards의 정신에 많은 영향을 받아왔다. 90년대의 수학교육은 학생들의 수학적인 문해능력(literacy)의 중요성을 반영하여 학생들이 수학의 가치를 느끼도록 하며, 자신들의 수학적 능력에 대해서 확신을 가지게 하며, 수학적인 문제해결자가 되도록 하며, 수학적으로 의사소통하는 것을 학습하며, 수학적으로 추론하는 것을 학습함으로서 아동들에게 수학적인 힘을 길러주는데 중점을 두고 있다. 특히 수학적 의사소통능력은 학생들의 수학적인 힘을 기르는데 매우 중요하다. 아동들의 수학적인 의사소통 능력을 향상시키기 위해서 교사는 아동들이 상대방의 아이디어가 받아들일 만한 것인지에 대해서는 비판하고 토론을 하도록 하되 발표한 사람을 비난하는 일이 없도록 각 학급에서는 의사소통과 상호작용에서의 사회적인 규범과 사회-수학적인 규범이 형성되도록 해야 할 것이다. 이런 규범을 바탕으로 교사와 학생이 협력함으로써 서로의 아이디어에 대해 원활한 의사소통을 이룰 수 있다. 그래서 무엇보다 중요한 것은 문화공동체로서의 교실내에 의사소통을 촉진할 수 있는 규범을 형성하는 것이라고 할 수 있다. 이런 규범은 교사 혼자의 노력으로 이루어지는 것이 아니라 교실 구성원 전체의 상호작용에 의해서 장시간에 걸쳐서 형성된다고 할 수 있다.

• 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.19 no.2
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• pp.321-340
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• 2009

The purpose of this study was to analyze how lower graders in elementary school might respond to 4 different problem types in the context of measuring length: unit-length comparison, units and unit counting, unit-length expectation, and length comparison. A total of 375 students(185 second graders and 190 third graders) were surveyed and analyzed. The results showed that students were good at 'unit-length comparison' and 'units and unit counting', whereas they were not as to 'length comparison', This paper includes detailed analysis of students' responses as to both correct answer and incorrect one in conjunction with their typical answers and reasoning behind the answers. This paper suggests that teachers be sensitive to the certain level of reasoning tied to each type of problems and attend to students' difficulties in comparing length.

• School Mathematics
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• v.7 no.1
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• pp.17-32
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• 2005

The purpose of this study is to analyze the effects of calculator use, which is drawing more attention in elementary mathematics, on students' learning of mathematics and to suggest effective ways of using calculators. The present study examined appropriate items commonly used in other papers in the areas of number sense and concepts, problem solving, pattern exploration and reasoning ability. The process of item selection about calculator use were investigated through preservice elementary school teachers' responses to the Questionnaire. The use of calculators In elementary school should be based on teachers' under-standing about why calculators are useful tools for learning mathematics. For more effective use of calculators, more sophisticated experimental studies need to be conducted about selected questions.