knowledge
1 5 + 2 1 2 3 5 1 5 1 5 1 5 3 5
1 1 5 3 4 2 1 20
2 7 1 3 0.9 5 4 ( 7 1 3 09. ) 7 1 5 4 5 ( 7 2 9 3 = ) 7 1 10 10 4 5 42 = 7 1 5 5 = 8 2 7 1 5 5
= 1 1 5 1 1 5 3 x + 0. 9 = 7 1 4 5 3 x = 7 1 09. 4 5 3 x = 6. 3 4 x = 63. 175. x = 8. 4 8. 4 7 1 = 8 2 7 1 5 5 5 = 1 1 ( ) 5 1 1 5
M.H. 1982 34 1989 320
2 027 27.2 3 7
1 5 1+ 1 x = 18 ax bx = c a b 5 x + 1 5 x = 18
x + 1 5 x = 18 1+ 1 x = 18 5 x = 18 1+ 1 5
2 5 2 5 5 2 2 5 480
1 1 3 3
160 160 1 4 1 4
24 1 3 1 5
3 4 = 75 75 75 100 2 7
3 11 3 11
200 3 5 200 3 5 200 = 120 3 5
3 7
[] 62 63
3 7
1983
1982 31 G.F. 134135 D.C.HeathandCompany1974
85 1947 143 E.De Coneand Lieven VerschaffelBeginning First Graders Initial Representation of Arithmetic World ProblemsThe Journal of Mathematical Behavior41985.
18
1989 3
1 5 1 1 1 5 5
200 4 5 80 300 7 10 4 5 4 5 4 5 7 4 49 9 10 83 1 3 4
3 3 4 1 1 4 3 1 3 1 4 4 4 1 5 4 5 5 4 1 4 1 5 4 13.2 37.1 5 4 5 4 5 10.5 2.9% 5 4 4 5 5 4 5 4 1 2 3
1 _ = 6 1 6 = + 1 = 6 1 + 1 1 6 a c a c a N N + N N b d b d b a c N b d a N( 1 ) b a N( 1 + ) b 4 1 3 2 30 3 4 2 30 3 3 4 2 30 3 3
4 3 5 5 3 28 7 3 7 3 3 12 28 7 7 4 200 5 4 1 200 5
7 6 7 240 6 7 420 6 1-3 7
300 1 4 1 + 1 4 3 5 1 2 30 2 9 3 4 18 3 4 18 6000 1 5 6000 6000 6000 1 1 5 1 5
3 7 4 7
11 5 75 1 1 0.5 3
2 6 1 1 2 3 5 6 1 1 5 3 3 6 1 + 1 4 3 60 5 3 3 5 5
1960 1
5 15 8 x x - 5 8 x = 15 1-5 x = 15x = 15 1-5 x = 40 8 8 1-5 X = 15 1-5 8 8 X = 15 1-5 8
1 2 1 3 1 4
1 2 1 3 1 4
3 10 0 9 14 37% 9 0
3 42
1 1 2 3
3 3 8 3 3 3 3 8 8 3 1 8 3 8 8 8 3 3 3 24 8 3 3 8 = 24 3 24 3 8 8 = 8 83 = 1 = 8 3 8 8 1 8 3 3 3 8 3 = (3 ) ( 3 8 8 = 3 = 8 8 3 8 3 3
2 5 5 2 8 9 9 8 7 5 5 7 8 11 1 9 13 1 7 8 1 = = = 3 3 8
3 3 8 3 3 8 8 1 6 1 5 1 2 3 1 3 8 1 8 3 3 3 8 8 3 3 8 3 3 8 3 3 8 8 3 8 3 3 8 3 5 8 5 8 3 2 2 3 3 2 5 8 3 2 2 3
1 2 1 4
1 3 1 3 1 3 1 3
1 30cm 4 1 1 1 1 1 3 4 8 6 16 3 12 + 1-1 2 3 + 1 4 1 1 2 2
2 1 2
1 1 100 20 4000 5 5 1 4000 = 800 5 2 l 1 1 6
instructionalmaterials
1 2 2 2 3
1 2 1 8 8 10 5 1 2 9 1 8 4 10 10 10 1 1 1 1 4 8 2 4 3 5 4 8 1 1 = 2 = 2 6 12 3 6 = 4 12 1 1 1 1 3 4 6 1 9 9 = 3 12 12 4 11 3 12 4 11 12-3 4 = 1 12 6 3 = 9 4 12 11-3 12 4 = 11 12-9 12 = 2 12 = 1 6
7 7 7 2 1 2 8 8 8 7 1 3 7 2 = 1 3 4 8 4 1 2 1 2 1 2 3 2 3 1 2 2 3 1 1 3 1 1 2 3 1 1 1 2 2 6 2 3 2 3 12 23 1 = 2 6 3 2 4 1 4 4 3 2 2 4 6 3 3 3 5 1 4 6 3 5 4 6
9 10 3 5 4 6 = 9 10 1 4 4 3 3 1 2 4 4 3 4 3 3 4 3 6 = 2 3 4= 6 2 3 5 5 3 4 6 6 4 3 1 4 5 1 5 6 6 5 3 1 3 5 6 4 6 4 3 1 3 = 3 4 5 4 5 20 6 4 2 2 6 = 3 4 = 3
3 2 = 6 4 x = 6 25 15 x10