• Journal for History of Mathematics
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• v.24 no.3
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• pp.77-94
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• 2011

This study aims to provide a teaching strategy accommodating the symbols of the definite integral and guiding students through the meaning of notations in area and volume calculations, based on characterization as to how students comprehend the symbols used in the Riemann sum formula and the definite integral, and their interrelationship. A survey was conducted on 70 high school students regarding the historical background of integral symbols and the textbook contents designated for the definite integral. In the following analysis, the comprehension was qualified by 5 levels; students in higher levels of comprehension demonstrated closer relation to the history of integral notations. A teaching strategy was developed accordingly, which suggested more desirable student understanding on the concept of definite integral symbols in area and volume calculations.

• School Mathematics
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• v.10 no.3
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• pp.375-399
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• 2008

Infinitesimal did not play an explicit role concerning definite integral in the textbook nowadays. But studies which investigate understanding of students on definite integral show that many students comprehend definite integral with infinitesimal. Formally infinitesimal is not taught at mathematics classroom, but many students identify definite integral as infinite sum of infinitesimals. This means that definite integral itself contains some structural elements that allow infinitesimal interpretation. In this study we investigate the role of infinitesimal In the historical development of partition-sum in definite integral, extract didactical issues concerning understanding of definite integral, and analyse Korean mathematics textbooks. Finally we propose some suggestions on the teaching of definite integral which contains the process of refinement intuition.

• School Mathematics
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• v.11 no.1
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• pp.93-110
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• 2009

This paper provides an analysis of a survey on high school students' understanding of definite integral. The purposes of this survey were to identify high school students' private concept definitiones and concept images on definite integral. Definitions and images, as well as the relation between them of the definite integral concept, were examined in 108 high school students. A questionnaire was designed to explore the cognitive schemes for the definite integral concept that evoked by the students. The students' individual answers were collected through written environment. Four types of the private concept definitiones and concept images were identified in the analysis.

• School Mathematics
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• v.11 no.2
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• pp.301-316
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• 2009

There are two distinct processes, definite integral and indefinite integral, in the integral calculus. And the term 'integral' has two meanings. Most students regard indefinite integrals as definite integrals with indefinite interval. One possible reason is that calculus textbooks do not concern the meaning in the relationship between definite integral and indefinite integral. In this paper we investigated the historical development of concepts of definite integral and indefinite integral, and the relationship between the two. We have drawn pedagogical implication from the result of analysis.

• Journal of the Korean School Mathematics Society
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• v.11 no.3
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• pp.421-438
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• 2008

Understanding the concept of definite integral is based on understanding the concept of mensuration by parts. However, several previous studies pointed out the difficulty on teaching the concept of mensuration by parts. The paper provides some didactic strategies which help teaching the concept of mensuration by part. To teach the concept of definite integral, in the high school curriculum, the relation between definite integral and series is dealt with. However, the paper suggests that importing the concept of series is not indispensable to teach the concept of definite integral. It is proper that definite integral is taught as limit of particular sequence not series.

• Communications of Mathematical Education
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• v.26 no.2
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• pp.155-176
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• 2012

In this paper, we present a practical and essential method of using team projects for calculus. We, specifically, take into account the team project that calculate the volume of lung represented on CT scan images. We have demonstrated that the process of analyzing the images in a team project encourage studying numerical methods of integration for calculus. Also, we have used various technological programs(MATLAB, MATHEMATICA, MS Excel) to solve the team project.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.39-57
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• 2022

This study aims to design an integral instruction method that follows the Abstraction in Context (AiC) framework proposed by Hershkowitz, Schwarz, and Dreyfus to help students in acquiring in-depth understanding of the relationship between indefinite integrals and definite integrals and to analyze how the students' understanding improved as a result. To this end, we implemented lessons according to the integral instruction method designed for eight 11th grade students in a science high school. We recorded and analyzed data from graded student worksheets and transcripts of classroom recordings. Results show that students comprehend three knowledge elements regarding relationship between indefinite integral and definite integral: the instantaneous rate of change of accumulation function, the calculation of a definite integral through an indefinite integral, and The determination of indefinite integral by the accumulation function. The findings suggest that the AiC framework is useful for designing didactical activities for conceptual learning, and the accumulation function can serve as a basis for teaching the three knowledge elements regarding relationship between indefinite integral and definite integral.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.5 no.2
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• pp.35-39
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• 1985

The closed form of the stiffness matrix is derived in terms of closed forms of intergrals for analyses of plane frame members containing linerly tapered members with the cross section of thin-walled tube. The series expansion forms of these are also developed to study the errors in the closed form of the stiffness matrix. The useful limits of the closed form of integrals are defined in terms of the relative taper.

• Journal for History of Mathematics
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• v.25 no.1
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• pp.71-88
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• 2012

The purpose of this study is to find the way to build the concept image about natural logarithm and the method is using definite integral in calculus under GeoGebra environment. When the students approach to natural logarithm, need to use dynamic program about the definite integral in calculus. Visible reasoning process through using dynamic program(GeoGebra) is the most important part that make the concept image to students. Also, for understand mathematical concept to students, using GeoGebra environment in dynamic program is not only useful but helpful method of teaching and studying. In this article, about graph of natural logarithm using the definite integral, to explore process of understand and to find special feature under GeoGebra environment. And it was obtained from a survey of undergraduate students of mathmatics. Also, relate to this process, examine an aspect of students, how understand about connection between natural logarithm and the definite integral, definition of natural logarithm and mathematical link of e. As a result, we found that undergraduate students of mathmatics can understand clearly more about the graph of natural logarithm using the definite integral when using GeoGebra environment. Futhermore, in process of handling the dynamic program that provide opportunity that to observe and analysis about process for problem solving and real concept of mathematics.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.8
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• pp.1271-1276
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• 2013

This study selected 22 male subjects to examine the maintenance period of static and ballistic stretching applied to rectus femoris, divided them into 11 static stretching group and 11 ballistic stretching group and analyzed changes in median frequency and in maximal voluntary isometric contraction before stretching and at 30 sec, 1 min, 3 min, 5 min, and 10 min after stretching. Median frequency showed significant differences in changes according to time and groups after the test of main effects. It was reduced after 3 min. in both static stretching and ballistic stretching groups and then increased again. Maximal voluntary isometric contraction showed significant differences in changes according to time and groups from the results of the main effect test. Static stretching group was reduced at 3 min after the experiment and then increased after that and ballistic stretching group was reduced at 5 min after the experiment and then increased again. In conclusion, changes were shown according to time after stretching and the effects of ballistic stretching were maintained a little longer than those of static stretching.