• 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.

• 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.

• School Mathematics
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• v.16 no.3
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• pp.585-611
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• 2014

The purpose of this study is to understand the decision-making behavior of a mathematics teacher in science academy of Korea by applying the framework of class analysis through the theory of goal-oriented decision-making. To this end, we selected as the participant a mathematics teacher in charge of the class of basic calculus of science high school for the gifted in the metropolitan area, and observed the teacher's lesson. Based on a questionnaire derived from previous studies, we analyzed goals, orientations and resources of the teacher. Research results show that there are certain teaching routines by analyzing the behavior patterns that appear repeatedly in the teacher's lesson. Also we understand that it can be used on goals, orientations and resources of the teacher to adequately explain his teaching routine. In the present study, in particular, it was found to have a similar but partially different routines to the teaching routines shown in the study of Schoenfeld. From these findings, We can derive the implications that the theory of goal-oriented decision making can be suitably used as analytical tool for understanding the behavior of the teacher who pursue a productive interaction in mathematics lesson in Korea.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.217-228
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• 1999

The fundamental theorem of calculus is the most 'fundamental' content in teaching calculus. Since the aim of teaching the theorem goes beyond simple application of it, it is difficult to teach it meaningfully. Hence, for the meaningful teaching of the fundamental theorem of calculus, this article seeks to find the educational implication of the fundamental theorem of calculus through reviewing the genetic history of it. A genetic history of the fundamental theorem of calculus can be divided into the following five phases: 1. The deductive discovery of the fundamental theorem of calculus 2. Galileo's Law of falling body and the idea of the fundamental theorem of calculus 3. The discovery of the fundamental theorem of calculus and Barrow's proof 4. Newton's mensuration 5. the development of calculus in 19th century and the fundamental theorem of calculus The developmental phases of the fundamental theorem of calculus discussed above provides the three educational implications. first, we can rediscover this theorem through deductive methods and get the ideas of it in relation to kinetic problems. Second, the developmental phases of the fundamental theorem of calculus shows that the value of this theorem lies in the harmony of its theoretical beauty and practicality. Third, Newton's dynamic image of this theorem can be a typical way of understanding the theorem. We have different aims of teaching the fundamental theorem of calculus, according to which the teaching methods can be adopted. But it is self-evident that the simple application of the theorem is just a part of teaching the fundamental theorem of calculus. Hence we must try to put the educational implications reviewed above into practice.