University of Kentucky. Lexington, Kentucky
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1 U Kk Lx, Kk A COMPARISON OF TWO METHODS OF ADDITION INSTRUCTION, TOUCHPOINTS AND MANIPULATIVES, WITH FIRST GRADE STUDENTS WITH LEARNING DISABILITIES IN A RESOURCE CLASSROOM TO DETERMINE EFFICIENCY AND EFFECTIVENESS P LA L U Kk
2 ABSTRACT OF THESIS A COMPARISON OF TWO METHODS OF ADDITION INSTRUCTION, TOUCHPOINTS AND MANIPULATIVES, FOR FIRST GRADE STUDENTS WITH LEARNING DISABILITIES IN A RESOURCE CLASSROOM SETTING T, q k T : R T T A, x KEYWORDS: M, A, E I, E I, T, TM, M
3 A COMPARISON OF TWO METHODS OF ADDITION INSTRUCTION, TOUCHPOINTS AND MANIPULATIVES, WITH FIRST GRADE STUDENTS WITH LEARNING DISABILITIES IN A RESOURCE CLASSROOM TO DETERMINE EFFICIENCY AND EFFECTIVENESS B LA L D T D G S D
4 RULES FOR THE USE OF THESES U M U Kk L, B, q, k Ex q D G S U Kk A x N D
5 THESIS LA L T G S U Kk 2003
6 A COMPARISON OF TWO METHODS OF ADDITION INSTRUCTION, TOUCHPOINTS AND MANIPULATIVES, WITH FIRST GRADE STUDENTS WITH LEARNING DISABILITIES IN A RESOURCE CLASSROOM TO DETERMINE EFFICIENCY AND EFFECTIVENESS THESIS A q M S C E U Kk B LA L D, Kk D: C M N, P S E Lx, Kk 2003
7
8 MASTER S THESIS RELEASE I z U Kk L S: D:
9
10 ACKNOWLEDGEMENTS M D Mk N x Y q I, I k j I, x I k M U Kk C S E I k I I x k E x x I M M k, I Y I Y I M Y I I Y z I I T I I M k Y Tk I k k Tk W I, I Y!
11 TABLE OF CONTENTS Ak L T L F C O: I 1 C T: R L 3 M A A S L D 3 N R S M A 4 R L F 5 B F 5 L I 5 I S T M 6 I I S B P 9 P R 10 C T: M 11 P 12 S 15 M 15 D C 17 P 18 G P 18 B 18 I 19
12 P S 19 G P T 20 T Aq 20 I: TM S 1 21 S 2 22 G P M 22 I: M S 1 22 S 2 23 G P C S 24 D P 24 T S C 24 Ex D 24 R 25 S V 26 D A 27 E T M 27 D 27 K 30 R 33 M 35 R 37 T 39 E T M 41
13 S P T M 43 C F: D 45 L 47 I F R 48 A A T C P 50 B A S 53 C S A P Wk S 55 D S B P Wk S 58 E S C P Wk S 61 F C D P 64 G R S R B P S 66 H S R T Aq 71 I S 73 J S L P T 78 K P R P 81 L S S 86 R 88 V 95
14 LIST OF TABLES T 1 D 14 T 2 I 42 T 3 I TM 42 T 4 I 43 T 5 S 44
15 LIST OF FIGURES F 1 D P D 29 F 2 K P D 32 F 3 R P D 34 F 4 M P D 36 F 5 R P D 38 F 6 T P D 40
16 C O: I S 1900, U S z (J, 1995; M & M, 1997) T N C T M (NCTM) (F & K, 1996) A, x S (M & M, 1997) T A C M (1989), A x T N C I T E 956 C S B E (Dx, C, L, W, & C, 1998) S A x, A M M (1997) x, R k ( 54) W, k 1
17 T k, k,,, TM T NTCM x A I, q,, T ERIC O, Kk V L, j, M I R, I, TM, TM 2
18 C T: R L M A A S L D R (F, G, & S, 1982; F, & M, 1997; C & M, 1989; M, 1997; G & F, 1983) T (C & M, 1989; G, & F, 1983) (F, 1982; ML & A, 1982), (W, A, Sk, D, & Ck, 1980; C, BkKzk, & U, 1992; C & M, 1989; G & S, 1977) I ML A (1982), k q k M k F (1982) k q G F (1983) k, 8 13, T z T O T, (F, 1982; E, 1995; G, P, & Mz, 1988) C, Fz, S, K B (1979) 3
19 , I, C M (1989),, q 2 1 k N R S M A A US D E O E R I (C, 2000), T, A N A Rk, A 1983 T N C Ex E A US D E (C, 2000) 1982,, x (Gz, 2000) A, T NCTM, z, (M, 1997; F & K, 1996) T NCTM : S S S S S (F & K, 1996, 4) 4
20 F K (1996) x, M, x, z z ( 5) O (M, 1997) Dx C (1990) NCTM z,, M M (1997) k ( 33) I, R L F B A NCTM, k M (1997) x x k I, M M (1987) k k z M M (1997) x k x k k Dx (1994) (,,, ) B k k L M (1997) U:,, M 5
21 M j (Y, 1991, 7) 1930 (S, 1989) M (M & Ck, 1996), (J, T, & T, 1985), k x (B, 1992), j (TS & J, 1980), k (S & H, 1977) S (B, 1989, 4) M (1997),,, A M (1997), I S T M M, J, M (1994) z R TS J (1980), j ( 363) B (1989), j H (j, j, j) x k E C (1990) 6
22 k E C S (1993) S (1993) TM, I L C, I, :,, G I TM, k Ax A T k,,,, A k T,,, T j A, 100% T T T 20 A O 100% 3 6k z T j O 100%, 89% T 0% T 7
23 , 0% 40%, 100% k Kkk (1975) T T ( 9, 12, 12, 13) k T q T O z,, K K k TM, (,,,, ) k T : ; ; ; E / K K (1973),, E C (1990) T 8
24 x: Ex AW,, C M C, T E E C (68% 60% ), A I k I I S B P L ; k (K, 1997, 247) K K P O k (A & R, 1974; K & N, 2002) G k T,, (K, 1997, 91) W, N M (1994) k 9
25 W, P R T T TM, T P M S T S B G T P M S (F, 1998) T q: 1 W, TM,? 2 W, TM,? 3 W TM? E q k T q 10
26 C T: M A T T, D F, I (S 1), T q ( ) T (S 2), qk, ( ) x W S 1, O W S 1, W S 2,, S, S 2, x,, W,, I, 11
27 ,, P Sx, I D E A, A, A, k S q k 18, 18, k, 18, S, W x, q W I S C, (WISCIII) T x (M) 4 B D I, F Iz E P (IEP) F,, k j S (SE L) IEP E P, E x T 1 12
28 z 13
29 T 1 D N G A E K M 6 A D M 6 A R M 6 A R M 6 A M M 6 B T M 6 A E IQ / 69 SE L S A A M / G L L S E P R R R R R R D T S E P B G IEP 14
30 T x S x T M T q M E B D T,, z T O 9 x k T S q T S A S 27,612 T 620 I S k I x M I 3, T A 15
31 A W, k T T k T E 1520 D, k Ax B N Ax C, D, E k T, T z z F, k I 2 11 x E T P O z 36 D TM, M ( ) S B A / :,,, z E T z k, k, G B G (K & N, 2002) 16
32 T O D, D, D H W, N P D C T k z E k A, B, C T k A B C k k, x 9 T k 40 T k T z k E k O, x,, T q N E N S C H () () q T q 17
33 E 20 A 10 T S C T, P W, T T (M, 1997) D T, T P G T,, S : TM B B 1 Wk S k P, k 18
34 S z T I D, T W, W, W, k T,,, k, T q E W, q T J F (1995) I, ( Ax F ) T H W (W & W, 1998) F D S T P (1995) 123 M: E D C 212 N A O D, P P (S A) (S B) ( Ax G 19
35 ) P T k T k z I, G P T T q T // (W, 1992) I Bk (1998) TM F G C K G T T,,,, ( Ax A ) T T Nx C E 100% 5 x A, q S A x A 20
36 K x H q 1 W, 1 W, ( Ax H ) I: TM 1 Bk (1998) TM q T, q T TM k (Bk, 1998),, ( Ax I ) I 100% ( 3 ) T, k M A, x A x I 60%, I K q 4 2+5, 4 5+2, H x x K ( q k ) 21
37 T A, S 2 T TM T S F x, 8+5, : S 8, 9,10,11, 12, 13 G P M I: 1 A,, T q k S,, (), F x, 3+6,, x (F, FM, G, G, M, & T, 1998) A Ax J M A, x A x W, F T P M S, () (F, 1998) T 22
38 , k k, q A k, W, K q 4 3+6, x T K x A, S 2 T T T P M S F x, 6+3, T x T, S A A, S B T k z A, k,, N k 23
39 G P C S D P T, k, N T O, D, H ;, T S C D S A S B T C S C T z T k Ex D A (S, R, & W, 1985) C ( ) A x S,,, z k 24
40 R R P, k I, T T ( 100) k ( Ax G) (T & G, 1984) I, T k k T k 20% P,, ( Ax K) T 100 (B, W, & M, 1980) O q, 100% P T S 1, S 2, 25
41 O, 100% P S 1 2 P 100% S 97% S V W (1978) T S T, k, Kk L G A Ex 1519 (://kk///p/t/ x) W (1978) S k A, Kk C C M A (MAE122) (://kk//// 30) T k (W, 1978) A, k,, 26
42 C F: D A E T M D W D (S 1; F 1), I 5, A S 2, D, H 10 S 1 19 D S 2 U S 2, A F 1,,, S 2 A 35 32, D W D, ( ) H 9 20 D S 2, D 15 E, D T, 27
43 k T 1 A D k D (C B), D k O k, D D S 1 14 D S 2, D 31 33, D D k,, L, D C C, k A F 1, S 1, D,, H, S 2, D A S 2, I C C, 1,4,5, 9 (S C ) A T D 28
44 F 1 D P D 29
45 K S D, K ( F 2) T T 25 K M,, K K (S 2) I S A ( ), k H : 4; S 1 967; 298;, 3267 T H, K (S 2) T K D, K k k I, K, H k D C C K, A k K z 30
46 H, I, k T K O, K T k T W K, (C C) T K H, S 2 31
47 F 2 K P D 32
48 R T F 3 k R D,, (S C) H S 1; R H ;, S 2, R T D S 2, R T R C C H W R, A (S 2), R R k 33
49 F 3 R P D 34
50 M D, M T H M 4 12 (S 1) ( ) W, M (S 2) H 28 H 106 S 1 30 S 2 S, M, W M, B (13 ) S 1 (10 ) H 13 (S 2) W C C, M 35
51 F 4 M P D 36
52 R A F 5,, R W R, S 1 H 6 15 T S 2 H R 25 H S S 2 W, R S 1 T S 2 H 3 18 T R S 1 S 2 T 4 8 H C C, H
53 F 5 R P D 38
54 T D S 1, T 4 14 T 15 13, 2 15 T T T A F 6, S 1 A, T S 2 M, T (16, 3 ) S 1 2 O, T C C T 1 5 W, 4 20 T N 39
55 F 6 T P D 40
56 E T M T 2 K q 2 z H I q, T 3 T 4, K q H q 10 7 D, q 4 2+5, 3 5+2, W, K 4 3+6, K q 3 2 T q (52 ) (58 ) O, q A, H, q W ( 194),
57 T 2 I N T K D R R M T A T 3 I TM N T K D R R M T A :
58 T 4 I N T K D R R M T A S P T M T 5,, A k ( Ax L) E,, A k, k x K, I R D, I k R x M k T, W k x, T k W T, k T k 43
59 T L, k T I T T T 5 T T 5 S W,,? N T M K D R R M T T:
60 C F: D T q, TM E C, (R: 24 ; 19 ) x (M: 30 ; 13 ) W, T, C C T x C R H, R F x I E P T K,,, K q,, A k q A T q k 45
61 T q S A 731 T S B 592 L 139 H, j, qk (537 ) (592) T q F, H, T q W k,,, 5 6 T A T, T T 5 A S A, k W, A, k A O q, q 46
62 TM U TM A T, q L S F, q T ;, A q q k I k A, 2+5 T x : 5+2, 2+8, 5+8 T : 8+2, 8+5, 2+2, 5+5, 8+8 O T k k T q A, z A F x, A 7, 10, 13, 4, 16 A,,, z A S 2 x T I 47
63 S 2, D M (1997) A W q q, q T F, TM H, z I F R T x (B, 1981) TM W, z k T P, (,, k, ) I, TM, S z TM A, 48
64 F O I L C, I,, R z I z I z I q z, I z z k Ex A x, (, ), k, F M M (1997) k ( 54), TM N, 49
65 Ax A T C P 50
66 Ax A T C P 50
67 T T : O T : O, T,, O,, T k : O,,, T q : O,,,, T T, 51
68 6 T x T, Sx : O,, x T : O,, x, T T 7 T, 8 T : O,, x, T k k C, T : O,, x,, : T 9 T A, T 52
69 APPENDIX B A S 53
70 A S SET A U TOUCH MATH q N 2,5,8 SET B U N 3,6,7 SET C C S N 1,4,
71 APPENDIX C S A P Wk S (S k k ) 55
72 S A P Wk N: # :
73
74 APPENDIX D S B P Wk S (S k k ) 58
75 S B P Wk N: T :
76
77 APPENDIX E S C P Wk S (S k k ) 61
78 S C P Wk N: # :
79
80 APPENDIX F C D P 64
81 C D P CONSEQUENCES L q I (W, 1998) A T q 1, 2, 3 M: E D C 212 (1995) S 1: T 1 S 2: T 2 S 3: T 3 T 2 T S 4: W, I, 2 TIME OUT RULES T T 65
82 APPENDIX G R S R B P S S S A Wk # 1 S S B Wk # 1 66
83 S S R P S S A Wk # 1 I: LA L D: S: R : Mk + T P A k # 1 T T R N R R R R R T TOTAL ( k) CORRECT: TOTAL INCORRECT: 67
84 Bk S A k # 1 R N R R R R R T N : D N + : x 100 R : 68
85 S S R P S S B Wk # 1 I: LA L D: S: R : Mk + T P B k # 1 T T R N R R R R R T TOTAL ( k) CORRECT: TOTAL INCORRECT: 69
86 Bk S B Wk # 1 R N R R R R R T N : D N + : x 100 R : 70
87 APPENDIX H S R T Aq 71
88 S R T Aq I: LA L D: NOTES: C = 100% 5 Mx 2 / A A Mk + N N: N N: T : S : 72
89 APPENDIX I S 73
90 74 S T : I A S B T R S ( ) : T : L A L D : F _ S k : M : T M S x ; k T T E I : O, S j T ( H x ) B C k ( M / ) W k, A T ( )? S S S A / C T T I S B T S ( k ) T ( S k ( k ) T (
91 75 S T : I A S B T R S ( ) : T : L A L D : F _ S k : M : T M S x ; k T T E I : O, S j T ( H x ) B C k ( M / ) W k, A T ( )? S S S A / C T T I S B T S ( k ) T ( S k ( k ) T (
92 76 S T : I A A / C S B T R I S B T ( C ) N ( P ) L S T O N x, K? S k ( k ) T (, ), S T ( C ) N ( H x ) L 5 ( M ) Y C I S S S T S k ( k, T (, ),
93 77 S T : I A A / C S B T R I S B T ( C ) N ( P ) L S S k ( k ) T,, S T ( C )
94 APPENDIX J S 78
95 79 S T : I A S B T R S ( ) : T : L A L D : F S k : M : A S x ; k T T E I : O, S j T T ( ) T I T I k x 6 I 6 N I W k, A S A / C T T I S B T S ( k ) T ( S k ( k ) T (
96 80 S T : I A A / C S B T R I S B T D H I? ( P 3 ) N? ( P 6 ) H? ( C ) N ( P ) U S k ( k ) T (, ), k S T ( C ) S P k S k ( k ) T (, ), k
97 APPENDIX K P R P S P S S T Aq S A M S A T 81
98 P R P O: D: P: Mk I S : OK D D k I k, k x k P P P G M k, P D C N : D : 13 X 100 P : 82
99 P R T Aq O: D: T Aq Mk A T S T T S T S T N : D : 9 X 100 P : 83
100 A M Mk P A P R A M T T S T T S T S T T T S T S T O: D: N : D : 17 X 100 P : 84
101 P R A T O: D: T A Mk A T T S T T S T S T T S T T S T S T N : D : 18 X 100 P : 85
102 APPENDIX L S S 86
103 N: C k I k 5 +3 I k
104 R A, T & R, M D (1974) E J A B A, 7, 7176 B, A J (1989) M A T, 37, 45 B, F F, W, O R, & M, R (1980) P : A x B A, 2, B, J S (1981) Ex x A I D D, 1, B, V A (1992) I k 46 E L, MI: N C R T L (ERIC D R S N ED ) Bk, J K (1998) TM F G A K G C S, CO: I L C C, J R, H, C M, & Mzz, J (2000) NAEP 1999 T : T US D E O E R I N C E S (O) A: ://///1999/ C, J F, BkKzk, S, & U, A (1992) Sk x T Ex C, 24,
105 C, J F, Fz, A M, S, R, K, H, & B, H, III (1979) LD : A L D Q, 2, 2944 C, J F, & M, J H (1989) C : A k? J L D, 23, , 259 Dx, B (1994) R E S P, 13, 4755 Dx, R C, & C, D W (1990) I M I T A D I N, 10, 14 Dx, R C, C, D W, L, D, W, J, & C, D (1998) R C R q x (O) A: :///~/// E, S R (1995) A q L D: A M J, 6, 912 E, D, & C, D (1990) M T A D I N, 10, 4855 F, J (1995) T T B, MD: G H, I 89
106 F, F, FM, J, G, H P, G, C, M, S J, T, W (1998) T! C S, CO: I L C, I F, J E, G, K, & S, M (1982) P F L P M, 4, 4755 F, J E, & M, M A (1997) M : M S P R, 26, F, J E, Nz, M B, & Mz, E S (1987) D k J L D, 20, F, A S, & K, M R (1996) M S A W, CA: T C M, I G, K, & F, J E (1983) Az L D Q, 6, G, S R, P, J W, & Mz, D L (1988) Ex : S C I, 5, Gz, P, C, C, J, L, Mk, K K, D, A, S, W, T, & T, W (2000) P x: C US,
107 N C E S, US D E (O) A: ://// G, J, & S, P S (1977) T K D A T P S, 14, J, R N, (1995) W E, 116, 6571 J, G A, T, C A, & T, M A (1985) A : x J L D, 18, K, J M (1997) C (6 ) U S R, NJ: M/P H Kk D E C C M A (O) A: ://kk//// 30 Kk D E L G A Ex (O) A: ://kk///p/ T/x K, M M, & N, C M (2002) S (4 ) C, OH: C E M Kkk, S (1975) A k E T M R, 10,
108 K, T, & K, D A (1973) A E T M R, 8, M, L G, & Ck, N L (1996) T L D R & P, 11, 5865 ML, T M, & A, S W (1982) L Sk L D Q, 5, M, C D (1997) S (5 ) U S R, NJ: MP H M, C D, J, L, & M, S P (1994) I T J S E, 28, M, S P & M, C D (1997) E J L D, 30, 4756 M, S P & M, C D (1997) T : k I S & C, 32, M, J H & M, C P (1987) M L D R, 2, N C Ex E A k: T (O) A: :////NARk/ 92
109 P, T W (1995) 123 M: E D C 212 (2 ) G E, IL: C M, I S, K (1993) M Ex, 4, S, E J (1989) E J R M E, 20, S, P T, R, M S, & W, R J (1985) A E T C, 8, 6776 S, M N, & H, J L (1977) A : E L, MI: N C R T L (ERIC D R S N ED ) T, J W & G, D L (1984) S j C, OH: C E M TS, J A & J, P A (1980) M j : x J R M E, 11, U, R G, U, A E, & H, J W (1980) D C, OH: M 93
110 W, M M, A, GR, Sk, JB, D, DD, & Ck, FL (1980) A : A, x (R N 13) L: U K C R L W, M, A, M J, & D, P M (1992) T S M S D: U W P, NY: L P G W, M M (1978) S : T j J A B A, 11, W, H K, & W, R T (1998) T F D S M V, CA: H K W P, I Y, K (1991) M: M E L, MI: N C R T L (ERIC D R S N ED ) 94
111 61 R A, T & R, M D (1974) E J A B A, 7, 7176 B, A J (1989) M A T, 37, 45 B, F F, W, O R, & M, R (1980) P : A x B A, 2, B, J S (1981) Ex x A I D D, 1, B, V A (1992) I k 46 E L, MI: N C R T L (ERIC D R S N ED ) Bk, J K (1998) TM F G A K G C S, CO: I L C C, J R, H, C M, & Mzz, J (2000) NAEP 1999 T : T US D E O E R I N C E S (O) A: ://///1999/
112 62 C, J F, BkKzk, S, & U, A (1992) Sk x T Ex C, 24, 4043 C, J F, Fz, A M, S, R, K, H, & B, H, III (1979) LD : A L D Q, 2, 2944 C, J F, & M, J H (1989) C : A k? J L D, 23, , 259 Dx, B (1994) R E S P, 13, 4755 Dx, R C, & C, D W (1990) I M I T A D I N, 10, 14 Dx, R C, C, D W, L, D, W, J, & C, D (1998) R C R q x (O) A: :///~/// E, S R (1995) A q L D: A M J, 6, 912
113 63 E, D, & C, D (1990) M T A D I N, 10, 4855 F, J (1995) T T B, MD: G H, I F, F, FM, J, G, H P, G, C, M, S J, T, W (1998) T! C S, CO: I L C, I F, J E, G, K, & S, M (1982) P F L P M, 4, 4755 F, J E, & M, M A (1997) M : M S P R, 26, F, J E, Nz, M B, & Mz, E S (1987) D k J L D, 20, F, A S, & K, M R (1996) M S A W, CA: T C M, I G, K, & F, J E (1983) Az L D Q, 6, G, S R, P, J W, & Mz, D L (1988) Ex : S C I, 5,
114 64 Gz, P, C, C, J, L, Mk, K K, D, A, S, W, T, & T, W (2000) P x: C US, N C E S, US D E (O) A: ://// G, J, & S, P S (1977) T K D A T P S, 14, J, R N, (1995) W E, 116, 6571 J, G A, T, C A, & T, M A (1985) A : x J L D, 18, K, J M (1997) C (6 ) U S R, NJ: M/P H Kk D E C C M A (O) A: ://kk//// 30 Kk D E L G A Ex (O) A: ://kk///p/ T/x K, M M, & N, C M (1998) S (3 ) C, OH: C E M
115 65 Kkk, S (1975) A k E T M R, 10, K, T, & K, D A (1973) A E T M R, 8, M, L G, & Ck, N L (1996) T L D R & P, 11, 5865 ML, T M, & A, S W (1982) L Sk L D Q, 5, M, C D (1997) S (5 ) U S R, NJ: MP H M, C D, J, L, & M, S P (1994) I T J S E, 28, M, S P & M, C D (1997) E J L D, 30, 4756 M, S P & M, C D (1997) T : k I S & C, 32, M, J H & M, C P (1987) M L D R, 2,
116 66 N C Ex E A k: T (O) A: :////NARk/ P, T W (1995) 123 M: E D C 212 (2 ) G E, IL: C M, I S, K (1993) M Ex, 4, S, E J (1989) E J R M E, 20, S, P T, R, M S, & W, R J (1985) A E T C, 8, 6776 S, M N, & H, J L (1977) A : E L, MI: N C R T L (ERIC D R S N ED ) T, J W & G, D L (1984) S j C, OH: C E M TS, J A & J, P A (1980) M j : x J R M E, 11,
117 67 U, R G, U, A E, & H, J W (1980) D C, OH: M W, M M, A, GR, Sk, JB, D, DD, & Ck, FL (1980) A : A, x (R N 13) L: U K C R L W, M, A, M J, & D, P M (1992) T S M S D: U W P, NY: L P G W, M M (1978) S : T j J A B A, 11, W, H K, & W, R T (1998) T F D S M V, CA: H K W P, I Y, K (1991) M: M E L, MI: N C R T L (ERIC D R S N ED )
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