数学教育における「意味の連鎖」に基づいた「学習軌道仮説」について [in Japanese] A Learning Trajectory with Chain of Signification in Mathematics Education [in Japanese]
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Abstract
The popular teaching pattern of multiplication of division following textbooks in Japan is making an expression at first and solving its answer. For example in division by decimal a problem are shown as follows: <br>"A ribbon is 72 yen for 2.4 m. How much is it per 1 m?" <br>The teaching stages are based on principle of the Permanence of Equivalent Forms and like these: <br>(1) making the expression 72 2.4 by "the word expression" <br>(2) seeking the solution of 72÷2.4 with thinking the price of 24 m ribbon using a line segment figure. <br>(3) calculating 72÷2.4; 72÷2.4=(72×10)÷(2.4×10)=720÷24=30 <br> But this way isn't necessarily natural and understandable to students, as they mistake like this: 72÷2.4=72÷24÷10=0.3 <br> I propose a hypothetical learning trajectory for division by decimal based on the chain of signification as follows: <br>(1) understanding the problem using the picture of a ribbon or a ribbon itself. <br>(2) estimating the price, if it is 72 yen for 2 m or for 3m, using a belt figure. <br>(3) trying how much for □m, based on 72 yen for 2.4 m, using a line segment figure <br>(4) understanding 30 yen per m, on 720 yen for 24 m. <br>(5) expressing the formula of division by decimal based on a expression to figure out the price per m at 2m, 3m. <br> The chain of signification and hypothetical learning trajectory suggest us a mathematics teaching based on constructivism. I would like to investigate a teaching experiment under the learning trajectory.
Journal

 Journal of JASME : research in mathematics education

Journal of JASME : research in mathematics education 10(0), 1319, 2004
Japan Academic Society of Mathematics Education