• Communications of Mathematical Education
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• v.32 no.3
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• pp.297-314
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• 2018

This article aims at providing implication for teacher preparation program through interpreting pre-service teachers' knowledge by using Shulman-Fischbein framework. Shulman-Fischbein framework combines two dimensions (SMK and PCK) from Shulman with three components of mathematical knowledge (algorithmic, formal, and intuitive) from Fischbein, which results in six cells about teachers' knowledge (mathematical algorithmic-, formal-, intuitive- SMK and mathematical algorithmic-, formal-, intuitive- PCK). To accomplish the purpose, five pre-service teachers participated in this research and they performed a series of tasks that were designed to investigate their SMK and PCK with regard to students' misconception in the area of geometry. The analysis revealed that pre-service teachers had fairly strong SMK in that they could solve the problems of tasks and suggest prerequisite knowledge to solve the problems. They tended to emphasize formal aspect of mathematics, especially logic, mathematical rigor, rather than algorithmic and intuitive knowledge. When they analyzed students' misconception, pre-service teachers did not deeply consider the levels of students' thinking in that they asked 4-6 grade students to show abstract and formal thinking. When they suggested instructional strategies to correct students' misconception, pre-service teachers provided superficial answers. In order to enhance their knowledge of students, these findings imply that pre-service teachers need to be provided with opportunity to investigate students' conception and misconception.

• Journal of the Korean School Mathematics Society
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• v.10 no.1
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• pp.1-25
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• 2007

The purpose of this study is to investigate the degree of mathematics teachers' recognition and understanding of mathematics education curriculum at the college of education. The subject of this study is 30 secondary school mathematics teachers who graduated from the department of mathematics education at the college of education. To accomplish this study, loather's knowledge is divided into two groups such as 'subject matter knowledge' (ready-made mathematics) and 'pedagogical content knowledge' (school mathematics and its teaching planning and methods). As a result, this study examines which subjects are required to achieve the pedagogical content knowledge in order to be a professional mathematics teacher.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.461-477
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• 2009

In this study, an operational analysis in the context of linear equations is presented. For the analysis, several second-order models concerning students' whole number knowledge and fraction knowledge based on teaching experiment methodology were employed, in addition to our first-order analysis. This ontogenetic analysis begins with students' Explicitly Nested number Sequence (ENS) and proceeds on through various forms of linear equations. This study shows that even in the same representational forms of linear equations, the mathematical knowledge necessary for solving those equations might be different based on the type of coefficients and constants the equation consists of. Therefore, the pedagogical implications are that teachers should be able to differentiate between different types of linear equation problems and propose them appropriately to students by matching the required mathematical knowledge to the students' potential constructs.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.1
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• pp.23-42
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• 2007

Learners who have taken learner-centered instruction is expected to construct conceptually mathematical knowledge which is. If so, they can have some ability to solve problems they are confronted with in the first time. To know this, First graders who have been in learner-centered instruction during 1 school year was given 7+52+186 which usually appears in the national curriculum for 3rd grade. According to the results, most of them have constructed the logic necessary to solve the given problem to them, and actually solve it. From this, it can be concluded that first, even though learners are 1st graders they can construct mathematical knowledge abstractly, second, they can apply it to the new problem, and third consequently they can got a good score in a achievement test.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.377-394
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• 2019

The purpose of this study is to scrutinize the characteristics of a teacher's discursive competence on the basis of mathematical competencies. For this purpose, we observed all semester-long classes of a middle school teacher, who changed her own teaching methods for the last 20 years, collected video clips on them, and analyzed classroom discourse. Data analysis shows that in problem solving competency, she helped students focus on mathematically important components for problem understanding, and in reasoning competency, there was a discursive competence which articulated thinking processes for understanding the needs of mathematical justification. And in creativity and confluence competency, there was a discursive competence which developed class discussions by sharing peers' problem solving methods and encouraging students to apply alternative problem solving methods, whereas in communication competency, there was a discursive competency which explored mathematical relationships through the need for multiple mathematical representations and discussions about their differences. These results can provide concrete directions to developing curricula for future teacher education by suggesting ideas about how to combine practices with PCK needed for mathematics teaching.

• The Mathematical Education
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• v.60 no.1
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• pp.21-39
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• 2021

The aim of this study was to deduce implications of the growth of mathematics teachers' specialty for effective instruction about the formulae of exponentiation with rational exponents by analyzing teachers' understanding of the definition of rational exponent. In order to accomplish the aim, this study ascertained the nature of the definition of rational exponent through examining previous literature and established specific research questions with reference to the results of the examination. A questionnaire regarding the nature of the definition was developed in order to solve the questions and was taken to 50 in-service high school teachers. By analysing the data from the written responses by the teachers, this study delineated four characteristics of the teachers' understanding with regard to the definition of rational exponent. Firstly, the teachers did not explicitly use the condition of the bases with rational exponents while proving f'(x)=rxr-1. Secondly, few teachers explained the reason why the bases with rational exponents must be positive. Thirdly, there were some teachers who misunderstood the formulae of exponentiation with rational exponents. Lastly, the majority of teachers thought that $(-8)^{\frac{1}{3}}$ equals to -2. Additionally, several issues were discussed related to teacher education for enhancing teachers' knowledge about the definition, features of effective instruction on the formulae of exponentiation and improvement points to explanation methods about the definition and formulae on the current high school textbooks.

• Journal of the Korean School Mathematics Society
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• v.7 no.1
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• pp.37-48
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• 2004

In this article we study on a mathematics(geometry) textbook which is written for the purpose of considering student's individual difference by famous russian author V. A. Gusev. We analyze text and exercise of the experimental textbook, form and extract some didactical ideas that help us to design individualized mathematics classroom activities with students.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.163-178
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• 2012

The efforts to represent the numbers based on the decimal system give us fundamental understanding to construct and teach the concept network on the related knowledge of elementary and secondary school mathematics. In the process to represent natural numbers, integers, rational numbers, real numbers as decimal system, we will classify the extended decimal system. Moreover we will obtain the view to classify real numbers. In this paper, we will study the didactical significance of mathematical knowledge, which arise from process to represent real numbers as decimal system, starting from decimal system representation of natural numbers, and provide the theoretical base about the classification of real numbers. This study help math teachers to understand school mathematics in critical inside-measurement and provide the theore tical background of related knowledge. Furthermore, this study provide a clue to construct coherent curriculum and internal connections of related mathematical knowledge.

• East Asian mathematical journal
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• v.27 no.2
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• pp.181-202
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• 2011

The study was planned to analyze the figure concepts teachers have according to the years of experiences based on the two aspects, the subject matter knowledge and the pedagogical content knowledge. Further, it aims to have the results utilized in teacher education and training, and ultimately to help elementary school students to establish the accurate figure concepts. We administered the test to the random sample of 77 elementary school teachers of the grade 3 to grade 6, from nine schools of the Daegu, Ulsan and Gyeongsangbuk-do districts, and we analyzed the results. Correlational analysis between the years of experience and the knowledge showed that the content understanding and knowledge decreases as the years of experience increases, while the experiential knowledge related to the understanding of the students and the pedagogical methods increases as the years of experience increases.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.411-430
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• 2017

This study examined the understanding of 24 pre-service teachers about the three contexts for constructing the exponential graphs. The three contexts consisted of the infinite points context (2009 revision curriculum textbook method), the infinite straight lines context (French textbook method), and the continuous compounding context (2015 revision curriculum textbook method). As the result of the examination, most of the pre-service teachers selected the infinite points context as easier context for introducing the exponential graph. They noted that it was the appropriate method because they thought their students would easily understand, but they showed the most errors in the graph presentation of this method. These errors are interpreted as a lack of content knowledge. In addition, a number of pre-service teachers noted that the infinite straight lines context and continuous compounding context were not appropriate because these contexts can aggravate students' difficulty in understanding. What they pointed out was interpreted in terms of knowledge of content and students, but at the same time those things revealed a lack of content knowledge for understanding the continuous compounding context. In fact, considering the curriculum they have experienced, they were not familiar with this context, continuous compounding. These results suggest that pre-service teacher education should be improved. Finally, some of the pre-service teachers mentioned that using technology can help the students' difficulties because they considered the design of visual model.