• Communications of Mathematical Education
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• v.24 no.4
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• pp.891-907
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• 2010

This study analyzed the Fundamental Theorem of Calculus from the historical, mathematical, and instructional perspectives. Based on the in-depth analysis, this study suggested an alternative way of teaching the Fundamental Theorem of Calculus.

• Communications of Mathematical Education
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• v.22 no.2
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• pp.165-185
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• 2008

In this paper we analyze various programs of our and other countries related with university-level program in mathematics. We develop two university-level programs 'Calculus I 'and 'Calculus II'. In detail we describe course of study, educational objectives of these programs.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.163-180
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• 2019

This study introduces a development of calculus contents which makes to understand the main concepts of calculus in a short period of time and to enhance problem solving and computational thinking for complex problems encountered in the real world for college freshmen with diverse backgrounds. As a concrete measure, we developed 'Teaching and Learning' contents and Python-based code for Calculus I and II which was used in actual classroom. In other words, the entire process of teaching and learning, action plan, and evaluation method for calculus class with Python based coding are reported and shared. In anytime and anywhere, our students were able to freely practice and effectively exercise calculus problems. By using the given code, students could gain meaningful understanding of calculus contents and were able to expand their computational thinking skills. In addition, we share a way that it motivated student activities, and evaluated students fairly based on data which they generated, but still instructor's work load is less than before. Therefore, it can be a teaching and learning model for college mathematics which shows a possibility to cover calculus concepts and computational thinking at once in a innovative way for the 21st century.

• Communications of Mathematical Education
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• v.31 no.3
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• pp.349-366
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• 2017

The 2015 revised curriculum is an integrated curriculum that reflects national and societal needs to foster creative convergent talent in the school curriculum. Along with these changes, the Ministry of Education introduced a system to change the major from 2017 to the fourth year of university. Therefore, each university should prepare to reflect the curriculum and institutional change before welcoming students who have completed the 2015 revised curriculum. The university needs to study the countermeasures for implementing the 2015 revised curriculum and expanding the period of major change when preparing the curriculum and contents of the calculus courses that freshmen take. Handong University has been studying the operation methods of new students who want to decide their major at the first grade, such as operating calculus courses at various levels and allocating appropriate proportions of calculus for preliminary examinations. This case is similar to the basic purpose of the revised curriculum in 2015, so it can suggest implications for the operation of the university calculus class after the curriculum revision. In this paper, we have analyzed the results of the recent freshman mathematics test for the recent 5 years and the students' calculus grades and compared them with the contents of the calculus curriculum operated by Handong University and the 2015 revised higher mathematics curriculum. As a result, we proposed five classes of calculus suitable for college major and it was found that the calculus curriculum should include the missing quadratic method in the 2015 revised curriculum.

• Journal of the Korean School Mathematics Society
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• v.6 no.2
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• pp.71-85
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• 2003

In this paper we study the usefulness of Maple in school calculus education. The use of computer and calculator is debated in many aspect in mathematics education. By the computer visualization of mathematical image and proper use of computer we can teach inductively and intuitively the mathematical concept and give rise to the students' interest. Maple is very popular in college but is not in middle school because of language. Maple application which is made by Maplet is very useful multimedia teaching-learning tools. We introduce the use of Maplet and some application of the calculus course which we made.

• School Mathematics
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• v.13 no.1
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• pp.65-88
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• 2011

Epistemological development process of the Fundamental Theorem of Calculus is considered in a history of mathematical notions and the genetic process of the Fundamental Theorem is arranged by the order of geometric, algebraic and formalization steps. Based on this, we studied students' episte- mological obstacles and error and analyzed the content of textbooks related the Fundamental Theorem of Calculus. Then, We developed the "Folding Back Model" of the fundamental theorem of calculus for students to lead meaningful faithfully. The Folding Back Model consists of "the Framework of thou- ght"(figure V-1) and "the Model of genetic understanding of concept"(figure V-2). The framework of thought in the Folding Back Model is included steps of pedagogical intervention which is used "the Monitoring working questions"(table V-3) by the mathematics teacher. The Folding Back Model is applied the Pirie-Kieren Theory(1991), history of mathematical notions and students' epistemological obstacles to practical use of instructional design. The Folding Back Model will contribute the professional development of mathematics teachers and improvement of thinking skills of students when they learn the Fundamental Theorem of Calculus.

• Communications of Mathematical Education
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• v.38 no.3
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• pp.443-458
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• 2024

This study analyzed the mathematical academic perspective and the actual status of the school field on the introduction of a definite integral as a 'Fundamental Theorem of Calculus' in the 2015 revised mathematics curriculum. Therefore, in order to investigate the mathematical academic perspective and the actual status of the school field, a study was conducted with 12 professors majoring in mathematical analysis and 36 teachers. From a mathematical academic point of view, professors majoring in mathematical analysis said that introducing a definite integral as a 'Fundamental Theorem of Calculus' in the 2015 revised mathematics curriculum was difficult to significantly represent the essence and meaning of the definite integral. In addition, in the actual status of the school field, teachers recognize the need for a relationship between a definite integral and the area of a figure, but when a definite integral is introduced as a 'Fundamental Theorem of Calculus', students find it difficult to recognize the relationship between the definite integral and the area of a figure. As the 2022 revised curriculum, which will be implemented later, introduces definite integrals as a 'Fundamental Theorem of Calculus' this study can consider implications for the introduction and guidance of static integrals. And, this study proposed a follow-up study on an effective teaching and learning method that can relate the definite integral to the area of the figure when introducing the definite integral as the 'Fundamental Theorem of Calculus' and on various visual tools and media.

• Communications of Mathematical Education
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• v.30 no.1
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• pp.47-65
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• 2016

The purpose of this paper is to compare the effects on the students' academic achievement and satisfaction level in a Calculus course taught by two different teaching modes, blended learning and face-to-face learning. The comparison analysis was made for Calculus 2 course in H university in South Korea offered in the Spring semester of the year 2015. Calculus 2 is a Calculus course designed for the first year students who plan to choose their majors in Engineering. There were two sections of the Calculus course taught in a blended learning mode and one in a conventional face-to-face learning mode. All these three sections including e-learning parts were taught by the author. We discuss some meaningful differences in the effects by the two different teaching modes.

• The Mathematical Education
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• v.59 no.1
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• pp.1-15
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• 2020

In this paper, we analyzed curriculum materials on inequalities as regions. Constructs such as mathematical connections and curriculum articulation were used as a framework. As for articulation, our findings indicate the topic of inequalities as regions addresses meaningful subordinate mathematical thinking and skills that serve prerequisite to calculus. Regarding connections, mathematical concepts involving inequalities extend to multivariate calculus. One implication is, as an unintended consequence of curricular decision of 2015 Revised National Curriculum to teach the topic only in mathematical economics, students who plan to study STEM subjects in college but opt out of mathematics economics in high school may miss the key concept and naturally struggle to understand calculus especially the theory of multivariate function of calculus.

• The Mathematical Education
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• v.42 no.4
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• pp.523-540
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• 2003

The main purpose of this work is to propose programs of calculus for the department of mathematics education of teacher training universities. There is a description of the characteristics, goal and contents of calculus course for pre-service teacher, followed by principles for teaching the subject. We suggest the constituents and something being kept in mind for each part in calculus.