• Communications of Mathematical Education
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• v.24 no.2
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• pp.365-384
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• 2010

This paper is an analysis study where we surveyed how well pre-service teachers understand the mathematical concepts taught in elementary school. We analyzed the results focusing on the following: First, what are the pre-service teachers' understandings of the equal sign and variables? Secondly, how exact are their understandings of other elementary school mathematical concepts? The survey was done on the students in Teachers College of Jeju National University. We hope that the results of this study will help the improvement of mathematical education for elementary pre-service teachers.

• The Mathematical Education
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• v.46 no.4
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• pp.423-443
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• 2007

Based on the framework of Huffered-Ackles, Fuson and Sherin(2004), data were analyzed in terms of 3 components: explaining(E), questioning(Q) and justifying(J) of students' mathematical concepts and problem solving in a math classroom. The students used varied presentations to explain and justify their mathematical concepts and ideas. They corrected their mathematical errors or misconceptions through discourses. In addition, they constructed and clarified their concepts and thinking while they were interacted. We were able to recognize there was a special feature in discourses that encouraged the students to construct and develop their mathematical concepts. As they participated in math class and received feedback on their learning, the whole class worked cooperatively in a positive way. Their discourse was improved from the level of the actual development to the level of the potential development and the pattern of interaction moved from ERE(Elicitaion-Response-Elaboration to PD(Proposition Discussion).

• The Mathematical Education
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• v.53 no.1
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• pp.57-73
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• 2014

This study investigated the connections of mathematical thinking of students at the second, fourth, and sixth grades with regard to multiplication, fraction, and proportion, all of which have multiplicative structures. A paper-and-pencil test and subsequent interviews were conducted. The results showed that mathematical thinking including vertical thinking and relational thinking was commonly involved in multiplication, fraction, and proportion. On one hand, the insufficient understanding of preceding concepts had negative impact on learning subsequent concepts. On the other hand, learning the succeeding concepts helped students solve the problems related to the preceding concepts. By analyzing the connections between the preceding concepts and the succeeding concepts, this study provides instructional implications of teaching multiplication, fraction, and proportion.

• Communications of Mathematical Education
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• v.21 no.3
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• pp.499-514
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• 2007

In modern mathematic education, the development of mathematical ability based on the understanding of mathematical concepts has been emphasized in curriculum and teaching methodology. Also, in schools, most math teachers stress the importance of mathematical concepts in doing math well. Thus, in this paper, we outlined the development of mathematical concepts through the literature survey. And then, based on the Sfard's definition of mathematical concepts, which classifies math concepts into the operational approach and structural approach, we analyzed the math concepts of exponential function and logarithmic function units in three highschool math textbooks. As the result, we found that the textbook authors used different approach for the same concepts, and, at the same time, they used both approaches to help develop the students' math concepts.

• Journal of Educational Research in Mathematics
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• v.12 no.2
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• pp.213-228
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• 2002

We know that curriculum is, first of all, related to teaching materials, namely, contents. Therefore, when we think of mathematics curriculum, we must take account of characteristic of mathematics. Vygotsky has studied the development of scientific concepts and everyday concepts. According to Vygotsky, scientific concepts grow down through spontaneous concepts; spontaneous concepts grow upward through scientific concepts. And mathematics is a representative of subjects dealing with scientific or theoretical concept. Therefore, his study provides scientific basis for mathematics curriculum design. In this context, Davydov notes that everyday concepts are developed through empirical abstraction, while scientific concepts require a theoretical abstraction. And Davydov constructed the curriculum materials for the teaching of number concept. Davydov's curriculum is an example of reflecting Vygotsky' theoretical view and his view about the types of abstraction. In particular, it represents mathematical characteristic of a 'science' by introducing number concept through quantitative relationship and use of signs. In conclusion, stance mathematical concepts have scientific characteristic, mathematics curriculum reflects this characteristic.

• Research in Mathematical Education
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• v.13 no.2
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• pp.123-139
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• 2009

In this paper some attempts have been made (a) to identify all the elementary concepts of the major concept "measurement of length" and, (b) to find the sequential order of these elementary concepts. Total 714 elementary concepts have been identified and sequenced.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.831-839
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• 1996

In the last years there has been growing interest in concepts of positive (negative) dependence of stochastic processes such that concepts are considerable us in deriving inequalities in probability and statistics. Lehmann [7] introduced various concepts of positive(negative) dependence in the bivariate case. Stronger notions of bivariate positive(negative) dependence were later developed by Esary and Proschan [6]. Ahmed et al.[2], and Ebrahimi and Ghosh[5] obtained multivariate versions of various positive(negative) dependence as described by Lehmann[7] and Esary and Proschan[6]. Concepts of positive(negative) dependence for random variables have subsequently been extended to stochastic processes in different directions by many authors.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.560-571
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• 2022

In this paper, firstly we introduce the concepts of deferred Cesàro summable and deferred statistically convergent function, and secondly we introduce the concepts of deferred almost summable and deferred almost statistically convergent functions. Furthermore, we investigate the relations between these concepts.

• International Journal of Computer Science & Network Security
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• v.22 no.5
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• pp.149-153
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• 2022

This study examines the effect of using interactive electronic models to teach mathematical concepts on students' achievement in the linear algebra course at university. The field sample consisted of 200 students divided into two equal groups, an experimental group of 100 students and a control group of 100 students. The researcher used an achievement test in some mathematical concepts related to linear algebra. The results of the study showed that there were statistically significant differences (0.05) between the average achievement scores of the experimental and control groups in the post application of the achievement test, in favor of the experimental group. The size of the influence of the independent factor on the results of the study, which is "interactive electronic forms", on the dependent factor, which is the students' academic achievement in the prepared test, had a very large effect. Also, the results of the study showed that there were statistically significant differences (0.05) between the mean scores of the experimental group in the pre and post applications of the achievement test, in favor of the post application. The researcher recommended the use of interactive electronic models in teaching mathematical concepts at the university level and diversifying the strategies of teaching mathematics, using technology to attract learners and raise their academic achievement.

• School Mathematics
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• v.6 no.4
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• pp.325-344
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• 2004

This study was carried out to investigate effects of the mindmap note-taking for the formation of the mathematical concepts structure and the matjematical creativity. Two classes were randomly chosen for this study from the third grade students of a middle school located in a medium size city. Thirty one lecture hours of the mindmap note-taking on the quadratic equation and functions were administered to the experimental class of 41 students, while same lecture hours of the ordinary instruction on the same contents were administered to the control class of 40 students. It was shown from this experiment that there ware significant evidences of improvement both in the formation of students' mathematical concepts structure and mathematical creativity through the mindmap note-taking lecture. Hence, the mindmap note-taking lecture is suggested for the improvement in the formation of student's mathematical concepts structure and mathematical creativity.