• Title/Summary/Keyword: intensive quantity

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A Study on Intensive Quantities Handled in Korean Elementary Math Textbooks and Workbooks (우리나라 초등학교 수학 교과서 및 익힘책에서 취급하는 내포량에 관한 연구)

  • Choi, Jong Hyeon;Ko, Jun Seok;Lee, Jeong Eun;Park, Kyo Sik
    • Journal of Elementary Mathematics Education in Korea
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    • v.20 no.1
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    • pp.1-15
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    • 2016
  • In this paper, the following three issues are discussed in connection with intensive quantities. (1) Is there any relationship among intensive quantity, per unit quantity, and ratio? (2) Which intensive quantities obtained by two same extensive quantities are handled? And How are they handled? (3) Which intensive quantities obtained by two different extensive quantities are handled? And How are they handled? Based on the results of this discussions, three implications are suggested as conclusions to explore the direction for the development of handling intensive quantities in elementary math textbooks and workbooks. Firstly, it is necessary to systematize the systemize a series of processes to handle intensive quantities. There is a need to rethink to use terms like speed and velocity before handling the ratio. Secondly, there is a need to rethink the definition of intensive quantities which have the particular names. For example, it is necessary to rethink using average distance in the definition of speed and the average population in the definition of density of population. Thirdly, it is necessary to consider the limiting the kinds of intensive quantities obtained by two same extensive quantities handled in the elementary math. There is a need to set limit to them which are used in daily life, and there is a need to rethink to use them which are used in the specialized area. There is a need to rethink the using hitting ratio in the form of %.

Analysis on High School Students' Recognitions and Expressions of Changes in Concentration as a Rate of Change (변화율 관점에서 농도 변화에 대한 인식과 표현의 변화 과정에 대한 분석)

  • Lee, Dong Gun;Kim, Suk Hui;Ahn, Sang Jin;Shin, Jae Hong
    • Journal of Educational Research in Mathematics
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    • v.26 no.3
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    • pp.333-354
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    • 2016
  • The aim of the present study is twofold. One is to confirm a hypothesis that a student's rate concept influences her conceiving change of a function in the view of rate of change and the other is to build up foundations for understanding the transition process from her rate concept to the concept of rate of change when she investigates the change of concentration as an intensive quantity. We explored how three participating high school students recognized and expressed change of given functions by using their rate concept as a conceptual tool. The result indicates that a change in students' rate concept might have an effect on understanding how function values change in term of rate of change. We also expect that it could be a catalyst for further research for clarifying the relationship between students' rate concept and their development of a concept of rate of change as a foundation for learning calculus.