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1 ISSN Tottori Journal for Research in Mathematics Education The Rational Number Project RNP Textbook Yoshikazu Tamaki vol.7, no. Mar. 05
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3 F P (& p y t l p k y F =AQ MLA 9RKB O OM CQ =9 o y m y p t p x yoy p a j l p l p o pj p j p t =9 j j p =9 p TQBMM l tp j o j y o y p p ks k p x y p o F87 04B9 4.C 7 7 B =9 ks o j.,. o n =9 j MPQ 7 PF MPQ 7 PF l k y o j y y y TQBMM F cb a t r xt e! & Fcb a =9 j MPQp= P MPQ.,) k y pj Fcb a ( B 07 ( ( 4 L P. & p p k k b c ( l y k j =9 l p s o y k y m p ks o y k ( ju FO Q A.-) k.-) 6 O L., =9 p y k k Fcb a )& 78 7B 4 )& k k d e d e d e y k d
4 e b c k y k m l j d e p l b cpj m & & j d e x b c m pj..( y y k Fe T i 78 7B 4 ) Fcb a 78 7B 4 p k k p d e d e d e d ed epj k..( 6 O L.-& y k d e y ks o y k 6 O L., d e y k p 6 O L.-& d e d e j yoy d e y k y (0) y p d e d e d e p y d e k FO Q A.-) k d e d e y k y o y FO.-& y k l t k k o d e y y m d e x d eo d e k k d e y d e y p k k d e k j m & F e =9 p l y k k 6 O L., y j x FO Q A.-) y y OACQ MLA 8 APRO y ks o kl =AQ M ( k y k m k k k =AQ yk( j m x l pj a RMQ LQ y p y b x k 7 L AO CMMOD LAQ 6 O L k x B Q LL PP l kl kl j 4 C KA kl x y y k :N OAQMO j kl kl j!
5 p k j m p j p j p x & &F N[ l yo =9 k p j p y d e d e y s k y k d e l d e y p t k p d e d e l p j o j.,- d e d e d e d e d e d e x j d ks o y ks o kle kl p j d y e j k a n j.,- d e k l k y s k d e k s k l p k p x j. d e d e y d m w j kk 4 4 w j o yo d e o y pk o l o yoy x y w kkj y k j l d e km e N(&( y k.. d e d e y l k d x k j l d e j kl o d e p d y p k d e pj l y p 4 x m nk l m 5 L 5 x kl k e d p l d t e d t e j ks o x k m k y kl y j e d kl x kl s k m kl ) kl ( kl k l m k y k m d e d e pj e d j j y p l d y e d e k e d( x y pj y j o m j p l A = m n B m n d e k j 0K L j A = m n B m m y k e!
6 j ( y s o k l s o k j y l k e o d ed ed e d e kl k k j y k y k k y k.. k l k dd w & e d w. e dm ( 4 ee kl nk d. ed ( e l 4 d e j y k d e d e y k e dd. e d ( e 4 e y d e j e dd) y ( e o d y ) e kl o d e pj e y k NN,(,) y l t k d t d e kl x k j y kp ke y k N,) d ed ed e kl d y ep k s y j p.. y y k y l k d ks o y ks o kle kl p j N,, dd e p j o l N,, d y 4 5 e kl jm d y e kl d ed ed e d e y!4 j r k p d y e p j l j js kl 4 4 j y k l l kl x k kl j k ny m kl y t y p k kl l d a k b y kle NN,,,- j p k j k e N,- l d ks o y e d a k b a y b e y d e y d e kl js m k j kl p k y d e p x k & F t r xt l yo =9 p d e o p k k s y j m =9 d e d ks o y e y k p d e d e y d e y k d e d e j o j p d ks o e y y k ks kl p d e y d e x y d e y k m yd e y kl
7 o d ed ed ed e j x d e l d e y k y l ks o j j y k y k d e d e p k p d e y kl d e x d e p k o d e d e km yoy d e y k p y k o kpj d e d e d e d e l d o y e l sd e d e k d =AQ yk( j m x l pj e y k d e y!5 k d e t k d e k d e y k y 6 O L.-& j y k m kl x kl x ot y y k d e d =AQ M ( k e y k x k kp d e x k k m d ed ed e y d e y p k s y k y y k j d y e kl j d e d epj y d e y n k j m o p k =9 k p k k d e k y o d e d e d e d e d e d e d
8 e k p j m y k p d e m y k F r xt k =9 TQBMM kp b c k op s s y k.-) d e d e d e j FO Q A.-) d e b cp m j d e x j y k p x y m n p d e x y s l p kl j p kl b c y y k p (& ) k b c 7 pj k kl y j kl nk b Fcb a h c kp d e y y k pj F cb a R m p p l y y y k y y k y y p j k y o k k j Ft jn!6
9 F [ y p h i ( kl o d e d e x y K y m k ) y y o y k k m y y t o j h i k k b c 7 j yk p k k p d e ) p k k h i k k p p k k h i n k k d e m yoy y k p k n d ep k k h i m y k p d e m k k h i d e j s d e mo k yoy d e d ep a j p k & l x k h i y k p k &K7 x y y k =9 TQBMM d e k k m l p p l x x h id e k m p x b c k k e d ep k d e k F 0. 7 B T =9 TQBMM p k k b c x y b c k k k TQBMM (& ) y TQBMM (&&. y y k TQBMM j w t n y t j x j k p o k b c y TQBMM (& ) TQBMM (&&. (& ] ju TQBMM (& ) p k OACQ ML OC k k k d j p e d t k e b c t y k o d e d e m TQBMM (& k ot k d s p s ks p !7 4 B9 9 7 su
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10 F7 B & t jn F7 B t jn o e kl y y k d e kl y k k l ] d e d e!8 km TQBMM (& ) j (&&. y k ( TQBMM p
11 p k y TQBMM l kl y k k w m j k [ b c y k y l k b cp k p j b c k k j p =9 b cp y k p j p =9 j s b c m k k h i u p p o h i p k px k k y =9 TQBMM y x y x kld e k =9 k k y p p y k k kl k p p k k p TQBMM k k =9 p y k o j x =9 y k l m k m 4 p s 4 p xk p 4 4 k l y k k k nk y k o p k p F ]!9 o k =9 y j k k y d e =9 y p nk k k y k y yk p p =9 y TQBMM x p j o p j y o =9 p k ks o o p k o k k p x yoy o y x k k kl TQBMM d e y k k =9 y TQBMM p o k y p s p j ( b c l j ) =9 k b c j p o lm k k b c k m. d e.. d e.,- d e yk NN ( o (& ) d s s e (& dthe Rational Number Project j
12 e d e (& ( Behr, M., Post, T., Silver, E., & Mierkiewicz, D. (980, August). Theoretical Foundations for Instructional Research on Rational Numbers. In R. Karplus (Ed.) Proceedings of Fourth Annual Conference of International Group for Psychology of Mathematics Education (pp ). Berkeley, CA: Lawrence Hall of Science. Behr, M., Lesh, R., Post, T., & Silver E. (98). Rational Number Concepts. In R. Lesh & M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes, (pp. 9-5). New York: Academic Press. Behr, M., Harel, G., Post, T., & Lesh, R. (99). Rational number, ratio and proportion. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 96-). NY: Macmillan Publishing. Cramer, K., Behr, M., Post T., Lesh, R., (009) Rational Number Project: Initial Fraction Ideas Cramer, K., Behr, M., Post T., Lesh, R., (0) RationalNumber Project: Initial Fraction Ideas Abridged edition authors: Kathleen Cramer, Terry Wyberg, Susan Ahrendt, Debbie Monson, Christina Miller Dienes, Z.P. (960),Building Up Mathematics (Fourth Edition),(97),London: Hutchinson Educational, Kieren, T. E. (976),On the mathematical, cognitive, and instructional foundations of rational numbers. In R. Lesh (Ed.), Number and measurement: Papers from a research workshop. Columbus, Ohio: ERIC/ SMEAC, Kieren, T. E.(980),Five faces of mathematical knowledge building. Edmonton: Department of Secondary Education, University of Alberta Post, T., & Reys, R. E. (979). Abstraction Generalization and Design of Mathematical Experiences for Children. In K. Fuson & W. Geeslin (Eds.), Models for mathematics learning. (pp. 7-9). Columbus, OH: ERIC/SMEAC. Reys, R.E. & Post, T. R.(97). The mathematics laboratory theory to practice.boston,prindle, Weber, and Schmidt, Inc., 40 The Rational Number Project!0
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