• 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.

• 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 the Korean School Mathematics Society
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• v.10 no.2
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• pp.149-171
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• 2007

This study is aimed at development of pedagogical content knowledge on fraction in the elementary school mathematics. Elementary students regard fraction as the difficult topic in school mathematics. Furthermore, fraction is the fundamentally important concept in studying mathematics. So it is important to develop the pedagogical content knowledge on fraction. The reason of attention to the pedagogical content knowledge is that improving the quality of teaching is the central focus of a high quality mathematics education. Shulman suggested that various knowledges are required for teacher to improve their classes. Of course, pedagogical content knowledge is the most valuable in teaching mathematics. Pedagogical content knowledge is related to the promotion of students' understanding about the learning. Pedagogical content knowledges are categorized by five factors in this study. These are understanding about curriculum, understanding about students and students' knowledge, understanding about teachers and teachers' knowledge, understanding about the methods, contents, and management of class, and understanding about methods of assessments. I develop the pedagogical content knowledge on fraction according to the these categories. I concentrate on the two types of pedagogical content knowledges in developing. That is, I present knowledges which teachers have to know for teaching fraction effectively and materials which teachers can use during the teaching fraction. Pedagogical content knowledges guarantee teachers as the professionalists. Teachers should not teach only content knowledges but teach various knowledges including the meta-knowledges which have relation to fraction.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.3
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• pp.457-481
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• 2013

Since the importance of teacher knowledge in teaching mathematics has been emphasized, there have been many studies exploring the nature or characteristics of such knowledge. However, there has been lack of research on the tools of investigating teacher knowledge. Given this background, this study explored teachers' knowledge of fraction lessons using classroom video analysis. The analyses of this study showed that knowledge of teaching methods was activated better than that of student thinking or mathematical content. Knowledge of fraction operation was activated better than that of fraction concept. The degree by which teacher knowledge was activated depended on the characteristics of the video clips used in the study. This paper raised some issues about teachers' knowledge of fraction lessons and suggested classroom video analysis as an alternative tool to measure teacher knowledge in the Korean context.

• Journal of Educational Research in Mathematics
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• v.10 no.1
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• pp.103-113
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• 2000

A case study was conducted to investigate the understandings of the subject matter knowledge and pedagogical content knowledge held by 63 elementary preservice teachers in dealing with the division by a fraction. The study results showed that, in terms of the subject matter knowledge, the preservice teachers did not have a conceptual understanding of the division by a fraction and, in terms of the pedagogical content knowledge, they depended heavily on algorithms without a conceptual understanding of the meaning of the division by a fraction.

• The Mathematical Education
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• v.47 no.3
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• pp.291-310
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• 2008

This article is based on an international collaborative study that aimed to investigate mathematical preparation of prospective elementary teachers in several selected education systems in East Asia. This article reports the Korean portion of the study. A survey instrument was developed to explore not only prospective teachers' knowledge of elementary mathematics curriculum and their beliefs in their preparation and mathematics instruction but also their subject matter knowledge and pedagogical content knowledge on the topic of fraction division. A total of 291 seniors in 3 universities participated in the survey. The results reveal these prospective teachers' strengths and weaknesses with regard to their knowledge of fraction division, and suggest that content-specific pedagogical knowledge needs to be emphasized in the teacher preparation program.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.67-85
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• 2005

This study investigated elementary teachers' subject matter knowledge and pedagogical content knowledge of fractions. The subject for data collection were 12 in-service elementary teachers and data were collected through written test problems. The finding imply that most elementary teachers understand fraction construct as part-whole, show low level of understanding of operator, ratio, and measurement constructions and word problem posing, using models, and developing the algorithms to divide fractions. The research results indicates that experienced teachers possess poor knowledge of fractions against novice teachers.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.151-170
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• 2009

The purpose of the study is to analyze the sixth graders' understanding of concepts and operation about fraction. The test was administered and analyzed to 707 sixth graders' performance on fractions after the fraction instructions in elementary schools in Seoul, Korea. The participants are asked to answer two sets of questions for 40 minutes. First, they are asked to answer to 16 problems about the concepts of fraction with respect to part-whole, ratio, operator, measure, quotient, equivalent, and operations. Second, specially, to investigate sixth graders' ability of drawing and describing the situation of division including fraction, the descriptive problem asked students (1) to describe $3\;{\div}\;\frac{1}{2}$ into pictorial representation and (2) to write the solving process. The participants of this study didn't show deep understandings about the concepts and operation of fraction. The degree of understanding of subconstructs of fraction shows that their knowledge of ratio concept with respect to fraction was highest while their understanding of measure with respect to fraction was lowest. Considering their wrong answers, about 59% of participants showed misconception to the question of naming one fraction that appears between $\frac{1}{5}$ and $\frac{1}{6}$. Further, they didn't explain their understanding with drawing about the division of fraction ($3\;{\div}\;\frac{1}{2}$).

• Journal of the Korean School Mathematics Society
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• v.23 no.2
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• pp.203-222
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• 2020

Because the role of the teacher is important for the education to actualize the goals of the curriculum, the interest about the teacher's knowledges has been addressed as an important research topic. Among them, the pedagogical content knowledge is the knowledge that can emphasize the professionalism of the teacher. In this study, I analyzed the elementary pre-service teachers' the problem solving strategies that they imagined the methods that elementary school students can think about fraction division. Pre-service teachers who participated in this study were completed all of the mathematics education courses in the pre-service teachers' education courses. The research was conducted using the four type-problems of fraction division. The results showed that elementary pre-service teachers responded in the order of equal sharing problem-measurement division-partitive division-context of determination of a unit rate problem. They presented significant responses not only with typical algorithms but also with pictures or expressions. On the basis of this research, we have to take an interest in the necessity of sharing and recognizing various methods of fraction division in pre-service teachers education.