• Journal of Elementary Mathematics Education in Korea
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• v.12 no.1
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• pp.59-78
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• 2008

The purpose of this study was to research and analyze students' informal knowledge before they learned formal knowledge about fraction concepts and to see how to apply this informal knowledge to teach fraction concepts. According to this purpose, research questions were follows. 1) What is the students' informal knowledge about dividing into equal parts, the equivalent fraction, and comparing size of fractions among important and primary concepts of fraction? 2) What are the contents to can lead bad concepts among students' informal knowledge? 3) How will students' informal knowledge be used when teachers give lessons in fraction concepts? To perform this study, I asked interview questions that constructed a form of drawing expression, a form of story telling, and a form of activity with figure. The interview questions included questions related to dividing into equal parts, the equivalent fraction, and comparing size of fractions. The conclusions are as follows: First, when students before they learned formal knowledge about fraction concepts solve the problem, they use the informal knowledge. And a form of informal knowledge is vary various. Second, among students' informal knowledge related to important and primary concepts of fraction, there are contents to lead bad concepts. Third, it is necessary to use students' various informal knowledge to instruct fraction concepts so that students can understand clearly about fraction concepts.

• Education of Primary School Mathematics
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• v.8 no.2 s.16
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• pp.97-113
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• 2004

The purpose of this study is to develop instructional methods for the formalized algorithm through informal knowledge in teaching division of fractions. The following results have been drawn from this study: First, before students learn formal knowledge about division of fractions, they knowledge or strategies to solve problems such as direct modeling strategies, languages to reason mathematically, and using operational expressions. Second, students could solve problems using informal knowledge which is based on partitioning. But they could not solve problems as the numbers involved in problems became complex. In the beginning, they could not reinvent invert-and-multiply rule only by concrete models. However, with the researcher's guidance, they can understand the meaning of a reciprocal number by using concrete models. Moreover, they had an ability to apply the pattern of solving problems when dividend is 1 into division problems of fractions when dividend is fraction. Third, instructional activities were developed by using the results of the teaching experiment performed in the second research step. They consist of student's worksheets and teachers' guides. In conclusion, formalizing students' informal knowledge can make students understand formal knowledge meaningfully and it has a potential that promote mathematical thinking. The teaching-learning activities developed in this study can be an example to help teachers formalize students' informal knowledge.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.145-174
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• 2009

Based on the thinking that people can understand more clearly when the problem is related with their prior knowledge, the Purpose of this study was to analysis students' informal knowledge, which is constructed through their mathematical experience in the context of real-world situations. According to this purpose, the following research questions were. 1) What is the characteristics of students' informal knowledge about fraction before formal fraction instruction in school? 2) What is the difference of informal knowledge of fraction according to reasoning ability and grade. To investigate these questions, 18 children of first, second and third grade(6 children per each grade) in C elementary school were selected. Among the various concept of fraction, part-whole fraction, quotient fraction, ratio fraction and measure fraction were selected for the interview. I recorded the interview on digital camera, drew up a protocol about interview contents, and analyzed and discussed them after numbering and comment. The conclusions are as follows: First, students already constructed informal knowledge before they learned formal knowledge about fraction. Among students' informal knowledge they knew correct concepts based on formal knowledge, but they also have ideas that would lead to misconceptions. Second, the informal knowledge constructed by children were different according to grade. This is because the informal knowledge is influenced by various experience on learning and everyday life. And the students having higher reasoning ability represented higher levels of knowledge. Third, because children are using informal knowledge from everyday life to learn formal knowledge, we should use these informal knowledge to instruct more efficiently.

• Research in Mathematical Education
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• v.22 no.4
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• pp.283-304
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• 2019

This paper investigates what informal knowledge and strategies fifth-grade students brought to a classroom and how much they had potential to solve fraction division story problems. The findings show that most of the participants were engaged to understand the meaning of fraction division prior to their formal instruction at school. In order to solve the story problems, the informal knowledge related to fractions as well as division was actively utilized in student's strategies and justification. Students also used various informal strategies from mental calculation, direct modeling, to relational thinking. Formal instructions about fraction division at schools can be facilitated for sense-making of this complex fraction division conception by unpacking informal knowledge and thinking they might bring to the classrooms.

• Journal of Elementary Mathematics Education in Korea
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• v.10 no.2
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• pp.221-242
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• 2006

For teaching division more effectively, it is necessary to know students' informal knowledge before they learned formal knowledge about division. The purpose of this study is to research students' informal knowledge of division and to analyze meaningful suggestions to link formal knowledge of division in elementary school mathematics. According to this purpose, two research questions were set up as follows: (1) What is the students' informal knowledge before they learned formal knowledge about division in elementary school mathematics? (2) What is the difference of thinking strategies between students who have learned formal knowledge and students who have not learned formal knowledge? The conclusions are as follows: First, informal knowledge of division of natural numbers used by grade 1 and 2 varies from using concrete materials to formal operations. Second, students learning formal knowledge do not use so various strategies because of limited problem solving methods by formal knowledge. Third, acquisition of algorithm is not a prior condition for solving problems. Fourth, it is necessary that formal knowledge is connected to informal knowledge when teaching mathematics. Fifth, it is necessary to teach not only algorithms but also various strategies in the area of number and operation.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.345-363
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• 2010

The purpose of this study is to investigate and analyze informal knowledge of students who do not learn the conception of proportion and to identify how the informal knowledge can be used for teaching the conception of proportion in order to present an effective method of teaching the conception. For doing this, proportion was classified into direct and inverse proportion, and 'What are the informal knowledge of students?' were researched. The subjects of this study were 117 sixth-graders who did not have prior learning on direct and inverse proportion. A total eleven problems including seven for direct proportion and four for inverse proportion, all of them related to daily life. The result are as follows; Even though students didn't learn about proportion, they solve the problems of proportion using informal knowledge such as multiplicative reasoning, proportion reasoning, single-unit strategy etc. This result implies mathematics education emphasizes student's informal knowledge for improving their mathematical ability.

• Journal of the Korean earth science society
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• v.25 no.3
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• pp.185-193
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• 2004

The purpose of this study is to explore high school students' environmental literacy and from its result, to suggest ways to reform environmental education. 1047 students from Seoul and Kyeongki province participated in the survey. The questionnaire consisted of four criteria of environmental literacy including knowledge, skill, attitude and behavior. The result was analyzed and the factors which affect high school students environmental literacy were explored. From this result, we made suggestions to improve environmental education as follows. First, environmental education in school should focus on knowledge criterion. Though school environmental education has been helpful for students to build environmental literacy in attitude and behavior criteria, its effect has not been good enough in knowledge criterion. Second, science education can enhance students' environmental literacy. Students who like science best and students who belong to science major classes were reported to possess better understanding in knowledge criterion. Also, students who like life science appeared to have a more positive attitude in environmental literacy. Third, informal education must be considered to form students' environmental literacy. In particular, the effect of mass media is inarguable. Thus, we should find a way to link formal education and informal education to improve environmental education. Fourth, high school students' interest in the environment must be encouraged since it is evident that higher interest would result in better outcome in environmental education.

• East Asian mathematical journal
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• v.25 no.3
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• pp.247-262
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• 2009

Permutation and combination are the part of mathematics which can be introduced the pliability and diversity of thought. In prior studies of permutation and combination, there treated difficulties of learning, strategy of problem solving, and errors that students might come up with. This paper provides the method so that meaningful teaching and learning might occur through the systematic approach of permutation and combination. But there were little prior studies treated counting numbers that basic of mathematics' action. Therefore this paper tries to help the understanding of permutation and combination with the process of changing from informal knowledge to formal knowledge.

• Hwankyungkyoyuk
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• v.18 no.3 s.28
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• pp.19-32
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• 2005

This paper examines procedure of informal institute-public school collaboration in an elementary school and analysis environmental effects of informal institute-public school collaboration that follows up curriculum based environmental education programs. The purpose of this program is to improve environmental knowledge, attitudes of elementary students. Partnership between informal environmental Institute(NGO's) and public elementary school teachers established through program. Teachers are encouraged to be involved in student's activities and program assesment. The program we discuss here is a community collaboration project that combines environmental and outdoor education based on school curriculum and student's regional properties. The aim of the study was to describe environmental educational-based school-community partnerships and to examine the advantages and limitations for such collaborations. Qualitative and Quantitative Data are collected and analysed. Outcomes of this program are very positive. Students who were participated in this program gained more environmental awareness, attitude, knowledge, skills and affection to their region. More this programs were helpful to teachers who were participated. Further study needs to practice an exemplary collaboration and development of local school-community partnerships, which yields a blueprint for more productive collaboration in other communities.

• Journal of The Korean Association For Science Education
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• v.29 no.2
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• pp.253-266
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• 2009

This study was focused on analyzing students' informal reasoning patterns and their considerations in decision-making on socioscientific issues. This study involved 20 undergraduate students (10 biology majors and 10 non-biology majors) and showed how the two groups responded on socioscientific issues. Semi-structured interviews were conducted twice respectively based on six scenarios of gene therapy and human cloning. The result showed 93% of the total number of participants' decisions were made by rationalistic reasoning, whereas emotional reasoning was 49%, and intuitive reasoning was 27%. Students usually used two or three informal reasoning patterns together. Most of the students took more consideration on social factors. Some perceived ethical and moral implications of the issues, but they did not consider them seriously. They made their decisions depending on their own values, etc. 65% of the participants got their information on socioscientific issues from the mass media. Biology majors hardly used intuitive reasoning compared to non-biology majors. The Biology major group took into deep considerations on socioscientific issues while the non-biology major group seemed to interpret the given scenarios simply. This implied that the content knowledge was a significant factor of their decision-making. Therefore, it is necessary to develop proper science courses for non-major students to improve their decision-making on socioscientific issues. So, when we develop educational materials or programs, we should consider students' reasoning patterns, their considerations in decision-making, and their content knowledge. And because the mass media has the potential to play a key role for an effective education, we need to make a plan to make a practical application.