• 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 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.

• Research in Mathematical Education
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• v.17 no.1
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• pp.15-27
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• 2013

Division of fractions is always a difficult topic for primary school students. Most of the presentations in teaching the topic in textbooks are procedural, asking students to invert the second fraction and multiply it with the first one, that is, $$\frac{a}{b}{\div}\frac{c}{d}=\frac{a}{b}{\times}\frac{d}{c}$$. Such procedural approach in teaching diminishes both the understanding of structure in mathematics and the interest in learning the subject. This paper discussed the formulation of teaching the division of fractions, which based on research lessons in some primary five classrooms. The formulated lessons started with an analogy to division of integers and working with division of fractions with equal denominators and then extended to division of fractions in general. It is found that the using of analogy helps students to invent their procedure in working the division problem. Some procedures found by students are discussed, with the focus on the development of their invention and mathematical thinking.

• The Mathematical Education
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• v.56 no.2
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• pp.193-212
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• 2017

This study focuses on cuisenaire rods that can be used when teaching fractions to elementary school students. First of all, this study critically examines the use of cuisenaire rods in learning of fraction proposed by various researches. Then, based on this review, this study explores in detail the use of cuisenaire rods in teachers' manuals developed from the revised curriculum by 2009 and in lessons related to fraction. The results of this study show that there are subtle differences in how to use cuisenaire rods in learning fractions and these subtle differences have a significant impact on students' understanding of the fractions. Therefore, the teachers should be able to accurately grasp the differences and utilize appropriate methods for teaching purpose. The followings are some of the implications for teachers or textbook developers when using cuisenaire rods in fraction learning: First, we should use cuisenaire rods in ways that can fully exploit the interpretations of the fraction as a part-whole and the fraction as a ratio. Second, we should focus on quantitative reasoning with unit to determine what each cuisenaire rod refers to. Third, it is necessary to take a more careful and sensitive approach to the use of cuisenaire rods. Teachers and textbook developers should constantly explore ways to make good use of mathematical manipulatives to help students understand conceptually in fractional learning. Furthermore, when teaching various mathematical topics using different manipulatives, I expect that there will be sufficient discussions and specific studies on how to use each of these manipulatives.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.1-18
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• 2024

Teachers' ability to notice is a crucial indicator of their instructional expertise. Despite the significance of this ability, research in mathematics teacher education has predominantly focused on the noticing of preservice teachers, with limited exploration into the noticing abilities of experienced in-service teachers. This study addresses this gap by examining the noticing characteristics of in-service elementary teachers actively developing their competency in elementary mathematics education. For this purpose, 23 elementary school teachers were asked to complete an analysis sheet while viewing the mathematics lesson video depicting on the concept of (fraction)÷(natural number), allowing us to scrutinize their attending, interpreting, and responding skills in detail. The study's results revealed that teachers demonstrated a tendency to attend mathematically significant aspects related to the teaching of fraction division. They interpreted the observed phenomena through the lens of fraction division's instructional principles, proposing specific pedagogical alternatives. These findings offer valuable insights for mathematics teacher education research.

• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.189-203
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• 2006

Teaching of fractions is very challengeable for elementary and middle school teachers. Many teachers feel uncomfortable teaching the subject. How shall we introduce the concept of fractions? Shall we focus more on concept development or computational procedures and skills? What methodology can be used in teaching those important topics? These are the kind of questions many teachers and researchers try to answer. In this article, the authors are to look at this issue from a cross nation perspective, by examining how the Chinese mathematics curriculum and the Chinese teachers deal with this subject.

• Education of Primary School Mathematics
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• v.25 no.2
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• pp.179-195
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• 2022

Mathematical communication competency, one of the six mathematical competencies emphasized in the latest mathematics curriculum, plays an important role both as a means and as a goal for students to learn mathematics. Therefore, it is meaningful to find instructional methods to improve students' mathematical communication competency and analyze their communication competency in detail. Given this background, this study analyzed 64 sixth graders' mathematical communication competency after they participated in the lessons of fraction division emphasizing mathematical communication. A written assessment for this study was developed with a focus on the four sub-elements of mathematical communication (i.e., understanding mathematical representations, developing and transforming mathematical representations, representing one's ideas, and understanding others' ideas). The results of this study showed that students could understand and represent the principle of fraction division in various mathematical representations. The students were more proficient in representing their ideas with mathematical expressions and solving them than doing with visual models. They could use appropriate mathematical terms and symbols in representing their ideas and understanding others' ideas. This paper closes with some implications on how to foster students' mathematical communication competency while teaching elementary mathematics.

• Education of Primary School Mathematics
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• v.13 no.2
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• pp.67-84
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• 2010

The purpose of the research is to assure the effect of learner-centered instruction driven from the constructivism. The school in participation of the research is one of them called "achievement increase intensive school". Quasi-experimental design is applied for the research. Some conclusions were drawn from the research. Experimental group' achievements of both "learned contents" and "none learned contents" were more superior than ones gained from comparative group with statistically significant difference. The results implied that learner-centered instruction is effective for students who have low achievements from standards tests.