12th International Congress on Mathematical Education
Program Name XX-YY-zz (pp. abcde-fghij)
8 July – 15 July, 2012, COEX, Seoul, Korea (This part is for LOC use only. Please do not change this part.)
INTRODUCTION OF FRACTION BY MEASUREMENT
AND THEIR IMPLICATION
Hyo jin Lee, Kwang ho Lee
Guenhwa elementary school, Korea National University of Education
cnuesu@hanmail.net, paransol@knue.ac.kr
INTRODUCTION & STUDY METHOD
Students who have learned without understanding the generative processes and necessity of
the fraction, do not associate their existing mathematical knowledge with fraction. Many
researchers asserted the necessity of teaching introduction of fraction through distribution and
measurement. There are few researches which develop and apply to the program introducing
fraction by distribution and measurement. The purpose of this study is to suggest an implication
about the learning effect of program introducing fraction by measurement to 2nd graders.
The program introducing fraction by measurement developed in this study is composed to
distribution, measurement and comparison situations. We selected five 2nd graders and
gathered video recordings (40 minutes×6 times), sound recordings and worksheets of learning.
STUDY RESULT
Students elaborated fractional expression following the steps such as using of picture or
household word, replacing denominator with number and replacing numerator with number.
They used existing mathematical knowledge beyond the expectations in the process of
expressing unit fraction or proper fraction. Existing mathematical knowledge using students
is symbols such as +, -, × and =, the principle of addition of natural number, the principle of
addition same number repeatedly and characteristics of the figure (○, △ and □). Students
took a pride in their new expressive method to be free from repetition and misunderstanding.
But students had difficulty to distinguish between relative and absolute amount and recognize
relative amount. And they did not understand that size can be same, irrespective of shape.
CONCLUSION
The merit of introducing fraction by measurement is that students can experience the
generative processes of the fraction dynamically through reasoning, justification, proof and
confutation, agreement and reappearance in active communication. Then students can become
mathematician which solve problem in the real world.
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