• School Mathematics
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• v.7 no.2
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• pp.139-168
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• 2005

The purpose of this study is to investigate children's informal knowledge of the fractional multiplication and to develop a teaching material connecting the informal and the formal knowledge. Six lessons of the pre-teaching material are developed based on literature reviews and administered to the 7 students of the 4th grade in an elementary school. It is shown in these teaching experiments that children's informal knowledge of the fractional multiplication are the direct modeling of using diagram, mathematical thought by informal language, and the representation with operational expression. Further, teaching and learning methods of formalizing children's informal knowledge are obtained as follows. First, the informal knowledge of the repeated sum of the same numbers might be used in (fractional number)$\times$((natural number) and the repeated sum could be expressed simply as in the multiplication of the natural numbers. Second, the semantic meaning of multiplication operator should be understood in (natural number)$\times$((fractional number). Third, the repartitioned units by multiplier have to be recognized as a new units in (unit fractional number)$\times$((unit fractional number). Fourth, the partitioned units should be reconceptualized and the case of disjoint between the denominator in multiplier and the numerator in multiplicand have to be formalized first in (proper fractional number)$\times$(proper fractional number). The above teaching and learning methods are melted in the teaching meterial which is made with corrections and revisions of the pre-teaching meterial.

• Journal of Korean Home Economics Education Association
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• v.12 no.3
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• pp.19-38
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• 2000

This study is about open and secondary level Home Economics Education which is applicable to field and which includes the characteristics, purpose and problems of each open education, secondary education and home economics education. Based on the ideology of open education this study will identify the meaning of openness in terms of Home Economics Education reconstructing meaning purpose, characteristics, curriculum paradigm and curriculum. The instructional model and module which use web, will be presented as the results o the reconstruction works. The open instructional module in Home Economics Education which will be operated on the web is consisted of 1) setting the orientation of curriculum development 2) instructional model development 3) rebuilding the Home Economics Education curriculum 4)development of instructional modules and web-based materials and 5)construction of the web-site. Six instructional module begin with critical/emancipatory curriculum paradigm in open Home Economics Education use module as a unit of class management instead of 1 class, facilitates nest-type integration which is applied from open education keeping the nature of Home Economics Education and focus on practical problem and problem solving through reconceptualization with dialectical perspective on individual, family and society. The practical problem solving model has four steps: Identifying practical problems. Understanding the contexts of problem, Searching for solutions and examining its consequences, Action and evaluation. The web-site has to be developed based on the six instructional module includes those issues : self-identification for reinforcing autonomy and self-esteem, living with family living with friends, autonomous living healthy living and understanding sexuality.