• The Mathematical Education
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• v.47 no.4
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• pp.447-465
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• 2008

The purpose of this study is to suggest effective teaching methods on the concept of infinity for students to obtain the right concept in the middle school curriculum. Many people have thought that infinity is something vouge and unapproachable. But, nowadays it is rather something with a precise definition that lies at the core of modern mathematics. To understand mathematics and science very well, it is necessary to comprehend the concept of infinity. But students tend to figure out the properties of infinite objects and limit concepts only through their experience closely related to finite process, and so they are apt to have their spontaneous intuition and misconception about it. Since most of them have cognitive obstacles in studying the infinite concepts and misconception, mathematics teachers need to help them overcome the obstacles and establish the right secondary intuition for the concepts through good examples and appropriate explanation. In this study, we consider the developing process of the concept of infinity in human history and give some comments and suggestions in teaching methods relative to that concept with new suitable examples.

• Journal of Korean Society of Occupational and Environmental Hygiene
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• v.6 no.1
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• pp.77-87
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• 1996

In order to compare the difference of the measurement of delta aminolevulinic acid(${\delta}$-ALA) in urine between HPLC method(HALA) and colorimetric method(CALA), and also to provide useful information for the new diagnostic criteria of ${\delta}$-ALA in urine in lead poisoning, if at all possible in the future, authors studied 234 male lead workers who were selected from 7 storage battery factories, 3 secondary smelting industries, and 2 litharge making industries. Study subjects were selected on the basis of blood Zinc protoporphyrin(ZPP) level from low to high concentration to cover wide range of lead exposure. Study variables for this study were ${\delta}$-ALA measured by two different methods, blood lead(PbB), and blood ZPP. The results were as follows: 1. There was very high correlation between ${\delta}$-ALA measured by two method(r = 0.989 : HALA = -0.8194 + 0.8110 ${\times}$ CALA), but the value of CALA was measured about 2mg/L greater than HALA. 2. While the correlations of ${\delta}$-ALA by two method with blood lead and blood ZPP were 0.46 and 0.37 respectively, they were increased to 0.63 and 0.57 if ${\delta}$-ALA values were log-transformed. 3. Simple linear regression of ${\delta}$-ALA measured by two method on ZPP were as follows: CALA = 2.0421 + 0.0341 ${\times}$ ZPP ($R^2=0.1385$ p = 0.0001) HALA = 0.8006 + 0.0280 ${\times}$ ZPP ($R^2=0.1389$ p = 0.0001) 4. Simple linear regression of ${\delta}$-ALA measured by two method on PbB were as follows: CALA = - 0.4134 + 0.1545 ${\times}$ PbB ($R^2=0.2085$ p = 0.0001) HALA = -1.2893 + 0.1287 PbB ($R^2=0.2154$ p = 0.0001), 5. Simple linear regression of log-transformed ${\delta}$-ALA by two method on ZPP and PbB were as follows: logHALA = 0.3078 + 0.0060 ZPP ($R^2=0.3329$ p = 0.0001) logCALA = 1.0189 + 0.0044 ZPP ($R^2=0.3290$ p = 0.0001) logHALA = -0.0221 + 0.0246 PbB ($R^2=0.4046$ p = 0.0001) logCALA = 0.7662 + 0.0184 PbB ($R^2=0.4108$ p = 0.0001) 6. The cumulative percent of colorimetric method to detect lead workers whose value of PbS and ZPP were over screening level such as $40{\mu}/dl$ and $100{\mu}/dl$ respectively was higher than HPLC method if cut-off level of ${\delta}$-ALA for screening of lead poisoning was 5 mg/L. But if cut-off level of ${\delta}$-ALA measured by HPLC was reduced to 3 mg/L which is compatible to 5 mg/L of ${\delta}$-ALA measured by colorimetric method, there were good agreement between two methods and showed dose-response relationship with other lead exposure indices such as PbB and ZPP.