• Journal for History of Mathematics
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• v.15 no.3
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• pp.49-58
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• 2002

The present paper aims to show basic substitution between metaphysics and mathematical abstraction in the philosophy of mathematics. The general troths of metaphysics and the truths particularly relevant to tile nature of mathematical abstraction serve as speculative guides in ordering the content and discussing the nature of the multiple questions which lie between the disputed frontiers of metaphysics and mathematical abstraction.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.505-514
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• 2008

In this paper we study on derivation of formulas for roots of quadratic equation, cubic equation, and quartic equation through method analogy. Our argument is based on the norm form of polynomial. We also present some mathematical content knowledge related with main discussion of this article.

• East Asian mathematical journal
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• v.37 no.2
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• pp.149-167
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• 2021

The six core competencies included in the mathematics curriculum revised in 2015 are problem solving, reasoning, communication, attitude and practice, creativity and convergence, information processing. In particular, the reasoning is very important for students' enhancing much higher mathematical thinking. Based on this competency, this study selected the four elements of investigation and fact guess, justification, the logical performance of mathematical content and process, reflection of reasoning process, And also this study selected the domain of function which is comprised of the content of the coordinate plane, the graph, proportionality in the seventh grade mathematics textbook. By the subject of the ten kinds of textbook, this study examined how the four elements of the reasoning competency were shown in each textbook.

• Journal of the Korean School Mathematics Society
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• v.16 no.2
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• pp.319-335
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• 2013

Chinese mathematical curriculum is divided 4 areas(number and algebra, space and figure, statistics and probability, practice and synthetic application). The purpose of this paper is to analyze the contents of the practice and synthetic application in yanbian elementary textbook. For this, 12-textbook which was published in yeonbeon a publishing company is analyze by topic, mathematical process, area of content and mathematical activity. mathematical process The following results have been drawn from this study. First, contextual backgrounds of practice are restricted in classroom. The contents of synthetic application are limited in connection of mathematical areas. Mathematical problem solving is a main in mathematical process, whereas reasoning activity is a few. Mathematical experience activity is a main in mathematical process, whereas synthetic activity is a few. We can use the suggestions of this paper for development of textbook and the contents of mathematical process.

• School Mathematics
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• v.17 no.3
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• pp.469-492
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• 2015

This study explored secondary mathematics teachers' mathematical knowledge for teaching [MKT]; in particular, it focused on teachers' knowledge of functions. In order to measure teachers' MKT, we developed items according to Ball, Thames & Phelps (2008)'s domains and conducted to 34 secondary mathematics teachers in 5 high schools in Seoul. The findings from the data analysis suggested as follows: a) overall, the teachers scored average 67.4 out of 100, 87.43 in Common Content Knowledge[CCK], and the average score of Specialized Content Knowledge [SCK] was the lowest; b) correlations among SCK, KCS, and KCT were statistically significant; and c) there was no sign of statistical significance between CCK and the rest.

• Research in Mathematical Education
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• v.14 no.1
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• pp.33-50
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• 2010

The mathematical thinking which transforms important mathematical content and developed into mathematical structure is a vital process in building up mathematical ability as mathematical knowledge based on structure. Such process based on students' recognition of mathematical concept. Developing mathematical thinking into mathematical structure happens when different cognitive units are connected and compressed to form schema of solution, which could happen through some guided problems. The effort of arithmetic approach in problem solving did not necessarily provide students the structure schema of solution. The using of equation to solve the problem is based on the schema of building equation, and is not necessary recognizing the structure of the solution, as the recognition of structure may be lost in the process of simplification of algebraic expressions, leaving only the final numeric answer of the problem.

• 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.

• Communications of Mathematical Education
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• v.35 no.3
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• pp.233-255
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• 2021

The purpose of this study is to develop math anxiety scale for middle school students for planning and implementing math anxiety treatment programs. In this study, we describe the process of developing and validating math anxiety scale for middle school students and detailing exploratory factor analysis and confirmatory factor analysis to verify construct validity. As a result of the study, we developed the Math Anxiety Scale for Middle School Students (MASS-M) of 30 items with four factors: mathematical curriculum content, mathematical attitude, mathematical test, and environment. As a math anxiety factor for middle school students, MASS-M was developed, which includes mathematical anxiety factors such as mathematical test factor and environmental factor, especially mathematical curriculum content factor describing mathematical treatment, and mathematical attitude factor describing psychological treatment. MASS-M, derived from this study, is a standardized scale for measuring math anxiety in middle school students and is expected to serve as the basis for maintaining consistency in research on math anxiety in middle school students and developing programs to treat math anxiety in middle school students.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1403-1418
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• 2019

Let R be a commutative ring with unity. If f(x) is a zero-divisor polynomial such that $f(x)=c_f f_1(x)$ with $c_f{\in}R$ and $f_1(x)$ is not zero-divisor, then $c_f$ is called an annihilating content for f(x). In this case $Ann(f)=Ann(c_f )$. We defined EM-rings to be rings with every zero-divisor polynomial having annihilating content. We showed that the class of EM-rings includes integral domains, principal ideal rings, and PP-rings, while it is included in Armendariz rings, and rings having a.c. condition. Some properties of EM-rings are studied and the zero-divisor graphs ${\Gamma}(R)$ and ${\Gamma}(R[x])$ are related if R was an EM-ring. Some properties of annihilating contents for polynomials are extended to formal power series rings.

• Communications of Mathematical Education
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• v.21 no.4
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• pp.575-596
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• 2007

This study investigates preservice teachers' development of subject-matter knowledge and pedagogical content knowledge in teaching function concept. This development takes place in the pedagogical mathematics courses in which the theory of constructivism and cooperative learning theory are aligned. Pre and post courses test were administered to examine the development and the follow-up interviews were conducted to gain more details. Analysis of the written questionnaire results and interview transcripts reveal that their limited concept image can be extended and developed in depth through pedagogical mathematics courses that apply reformed teaching methods.