• School Mathematics
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• v.18 no.1
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• pp.175-191
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• 2016

In the elementary school mathematics textbook that has been revised in 2013, the instructional sequence for teaching addition and subtraction, which had remained unchanged for three decades since 1982, was finally changed in 2013. Particularly, the addition and subtraction of two-digit numbers without regrouping, such as 72+25=97 or 85-24=61, are taught earlier than the composing and decomposing of the number 10 using other numbers. This study examines the appropriacy and validity of these changes. However, the reason for these changes in the national curriculum or teacher's guide could not be determined. Further, several references emphasize the addition of two single-digit numbers, such as 7+8=15, and the subtraction of a single-digit number from a number between 11 and 19, such as 16-9=7, as basic facts. In other countries' textbooks, the teaching of addition and subtraction up to the number 20 is prioritized before teaching the addition and subtraction of two-digit numbers without regrouping. The results of this study indicate that these changes in the instructional sequence in the textbook that was revised in 2013 need to be reconsidered.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.1
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• pp.1-17
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• 2019

In this study, prospective teachers were involved in arranging the teaching sequence of multiplication and division of fractions and decimal numbers based on their experience and knowledge of school mathematics. As a result, these activities provided an opportunity to demonstrate the prospective teachers' perception. Prospective teachers were able to learn the knowledge they needed by identifying the differences between their perceptions and curriculum. In other words, prospective teachers were able to understand the mathematical relationships inherent in the teaching sequence of multiplication and division of fractions and decimal numbers and the importance and difficulty of identifying students' prior knowledge and the effects of productive failures as teaching methods.

• Journal for History of Mathematics
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• v.18 no.4
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• pp.85-100
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• 2005

In recent papers (Pak et al., Pak and Kim), it was suggested to positively use the history of mathematics for the education of mathematics and discussed the determining problem of the order of instruction in mathematics. There are three kinds of order of instruction - historical order, theoretical organization, lecturing organization. Lecturing organization order is a combination of historical order and theoretical organization order. It basically depends on his or her own value of education of each teacher. The present paper considers a concrete problem determining the order of instruction for the concept of angle. Since the concept of angle is defined in relation to figures, we have to solve the determining problem of the order of instruction for the concept of figure. In order to do this, we first investigate a historical order of the concept of figure by reviewing it in the history of mathematics. And then we introduce a theoretical organization order of the concept of figure. From these basic data we establish a lecturing organization order of the concept of figure from the viewpoint of problem-solving. According to this order we finally develop the concept of angle and a related global property which leads to the so-called Gauss-Bonnet theorem.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.59-72
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• 2007

There are three kinds of order of instruction in mathematics, that is, historical order, theoretical organization and lecturing organization-order. Simply speaking, each lecturing organization-order is a combination of two preceding orders. The problem is how to combine between them. In a recent paper, we concretely considered this problem for the case of the concept of angle. The present paper analogously discuss with the concept of vectors. To begin with, we investigate theoretical organization and historical order of the concept of vectors as materials for the construction of its lecturing organization-order. It enables us to establish 4 stages in historical order of the concept of vectors proper to its theoretical organization. As a consequence, we suggest several criteria and forms for constructing its lecturing organization-order.

• The Mathematical Education
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• v.20 no.2
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• pp.7-13
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• 1982

• Journal of KIISE:Software and Applications
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• v.37 no.10
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• pp.723-735
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• 2010

Evaluating the level of achievement and providing the knowledge which is appropriate at the evaluated level have great influence in studying of the human beings. This shows the importance of the order of training and the training order should be considered in machine learning. In this research, to assess the influence of the order of training, we propose a method of controlling the order of training samples utilizing the experience of supervisor in the training of MLP. The supervisor finds out the current state of MLP using teaching experience and student evaluation, and then selects the most instructive sample for MLP in that state. We use CRF to represent and utilize the experience of supervisor. While the proposed method is similar to active learning in selecting samples, it is basically different in that selection is not to reduce the number of samples to be used but to assist the learning progress. The result from classification problem shows that the method is usually effective in terms of time taken in training in contrast to random selection.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.3
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• pp.531-546
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• 2017

This study explores the basis for determining priority among the four arithmetical operations in order to provide useful pedagogical content knowledge for teaching the order of operations. The study also discusses the perspective for viewing the order of operations. It presents the following five suggestions based on the results of the discussion. First, teachers should be made to realize that the same result can be obtained on calculation even when subtraction and division are performed first in mixed operations of addition and subtraction and mixed operations of multiplication and division. Second, teachers should understand why the rule of calculating sequentially from the left side of an equation has become customary. Third, teachers should be offered an explanation for the driver of the rule setting that multiplication takes precedence over addition in mixed operations of multiplication and addition. Fourth, the significance of the quantity within parenthesis must be emphasized to teachers. Fifth, teachers must gain an in-depth understanding about the order of operations by getting a description of all the customary and conceptual perspectives on the order of operations when describing the same in the teacher's guide.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.477-494
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• 2012

This study is to review the content organization and developmental ways of the unit on the mixed calculations and explore the alternatives on the basis of students' responsive examples and error patterns with relation to the mixed calculations, mnemonics of PEMDAS and historical context with relation to the order of operations. Then I analyzed the textbook and manual for teachers of the unit of mixed calculations of fourth grade and improvement about teaching the mixed calculations. First, I pointed out illogical connection between practical problem and rules of order of operations. Second, I suggested constructing a textbook by considering conventional character of order of operations. Third, I pointed out the importance of structural understanding of an expression of mixed calculations and various strategies with relation to teaching and learning. This study is suggestive for textbook development of the mixed calculations.

• Journal of the Korean Institute of Intelligent Systems
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• v.9 no.4
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• pp.451-456
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• 1999

All the teaching items in a textbook are normally arranged in a prescribed teaching order. However, one can easily find that the textbooks of the same kind, even with the same teaching items, show different arrangements. Without learning preceding teaching items, students may have a difficulty in understanding the teaching items. In this sense, it is very important to decide how to arrange teaching items in terms of teaching sequence. As a solution to this problem, lsamu Matsubara presents a method based on the graph theory. The four types defined in his method are the straight type, the group type, the branch type, and the independent type. Among these, the three types except the straight type lack the objectivity. An objective solution to these three types, based on the fuzzy theory. is propopsed in this paper.

• 한국공간정보시스템학회:학술대회논문집
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• 2005.05a
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• pp.327-331
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• 2005

본 연구의 목적은 공간데이터 구축시 아직까지 체계화되어 있지 않은 공간데이터의 품질 평가요소를 정립하는데 있다. 총 17개의 국내 공간데이터 품질관련 법규를 구축 공정, 작업방법, 장비, 정확도 등을 중심으로 분석하였다. 항공사진 촬영이 가능한 대규모 업체를 대상으로 작업순서, 사용장비, 작업순서 전후의 결과물의 정확도를 중심으로 조사하고 팀장급 직원들을 대상으로 현행 관련법규와 실무의 차이에 대하여 조사, 분석하였다. 조사, 분석한 내용을 기반으로 공간데이터의 구축공정을 항공사진을 이용한 수치지도 신규제작, 기존 수치지도 수정제작, 영상지도제작, 수치표고모델 구축 공정으로 구분하고, 각 공정별로 생성되는 공간데이터의 품질을 체크할 수 있는 요소들을 정립하였다.