T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A R T S
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- Mark Fox
- 5 years ago
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Transcription
1 R E L A T I O N S H I P B E T W E E N M A T H E M A T I C S A N X I E T Y A N D A C H I E V E M E N T I N M A T H E M A T I C S : A M E T A - A N A L Y S I S by G A B R I E L E. T A Y L O R B. E d., U n i v e r s i t y o f S a n t i a g o, B. S o c i a l S c., U n i v e r s i t y o f O t t a w a, A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A R T S i n T H E D E P A R T M E N T O F C U R R I C U L U M S T U D I E S F a c u l t y o f E d u c a t i o n W e a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A J a n u a r y G a b r i e l E. T a y l o r,
2 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of (^/^ / Csl(sM S 7~(/ / X~ The University of British Columbia Vancouver, Canada DE-6 (2/88)
3 11 A B S T R A C T T h i s t h e s i s i n v e s t i g a t e d t h e f i n d i n g s o f s t u d i e s o n t h e r e l a t i o n s h i p b e t w e e n m a t h e m a t i c s a n x i e t y a n d m a t h e m a t i c s a c h i e v e m e n t f o r e l e m e n t a r y a n d s e c o n d a r y s c h o o l s t u d e n t s u s i n g m e t a - a n a l y s i s. T w e n t y f i v e s t u d i e s w h i c h m e t a s e l e c t i o n p r o c e s s e s t a b l i s h e d f o r t h i s r e s e a r c h, a n d 4 7 e f f e c t s i z e s r e p r e s e n t i n g s t u d e n t s, w e r e a n a l y z e d. T h e r e s u l t s o f t h e s t u d y i n d i c a t e d t h a t t h e r e i s a n e g a t i v e r e l a t i o n s h i p b e t w e e n m a t h e m a t i c s a n x i e t y a n d m a t h e m a t i c s a c h i e v e m e n t i n t h e e l e m e n t a r y a n d s e c o n d a r y s c h o o l. T h r e e h o m o g e n e o u s g r o u p s w e r e i d e n t i f i e d w i t h c o r r e l a t i o n s , , a n d r e s p e c t i v e l y. H o w e v e r, t h e r e w a s n o e n o u g h i n f o r m a t i o n t o f i n d o u t w h e t h e r e a c h o f t h e g r o u p c o r r e l a t i o n s w e r e i n t h e o p t i m a l a r o u s a l c u r v e. R e s u l t s w e r e f o u n d t o i n d i c a t e t h a t t h i s n e g a t i v e r e l a t i o n s h i p h o l d s a c r o s s g r a d e l e v e l a n d a p p e a r s t o g e t s t r o n g e r f r o m p r i m a r y t o s e c o n d a r y s c h o o l. A n a l y s i s o f t h e s t u d i e s i n d i c a t e d t h a t t h e r e w e r e n o s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s i n t h e m a t h e m a t i c s a n x i e t y - a c h i e v e m e n t r e l a t i o n s h i p a c r o s s g e n d e r. T h e a v e r a g e c o r r e l a t i o n f o r m a l e s w a s a n d f o r f e m a l e s. T h e s t u d y a l s o f o u n d t h a t t h e m a t h e m a t i c s a n x i e t y - m a t h e m a t i c s a c h i e v e m e n t v a r i e s a c r o s s e t h n i c i t y. F o r e x a m p l e t h e a v e r a g e c o r r e l a t i o n f o r A s i a n s t u d e n t s w a s a n d f o r m i x e d ( U S A ) s t u d e n t s.
4 i i i T A B L E O F C O N T E N T S P a g e A b s t r a c t i i T a b l e o f C o n t e n t s i i i L i s t o f T a b l e s v i L i s t o f F i g u r e s v i i A c k n o w l e d g e m e n t s v i i i C h a p t e r I: I n t r o d u c t i o n 1 S t a t e m e n t o f t h e P r o b l e m 4 S i g n i f i c a n c e o f t h e P r o b l e m 5 R e s e a r c h Q u e s t i o n s 6 O p e r a t i o n a l D e f i n i t i o n s 7 L i m i t a t i o n 8 D e l i m i t a t i o n s 8 O r g a n i z a t i o n o f t h e T h e s i s 9 C h a p t e r I I : R e v i e w o f L i t e r a t u r e 1 1 I n t r o d u c t i o n 1 1 N a t u r e o f M a t h e m a t i c s A n x i e t y 1 1 M e a s u r e m e n t o f M a t h e m a t i c s A n x i e t y 1 6 P r e v i o u s R e v i e w s 1 7
5 iv G e n d e r a n d M a t h e m a t i c s A n x i e t y 1 9 E t h n i c i t y a n d M a t h e m a t i c s A n x i e t y 2 1 M a t h e m a t i c s A n x i e t y a n d A c h i e v e m e n t 2 2 S u m m a r y 2 4 C h a p t e r I I I. M e t h o d s a n d P r o c e d u r e s 2 6 I n t r o d u c t i o n 2 6 C r i t e r i a f o r I n c l u d i n g S t u d i e s 2 7 L o c a t i n g S t u d i e s 2 9 D e s c r i b i n g S t u d y C h a r a c t e r i s t i c s 3 3 Q u a n t i f y i n g S t u d y O u t c o m e s 3 4 D a t a A n a l y s i s 3 5 S u m m a r y 3 6 C h a p t e r I V. A n a l y s i s o f D a t a 3 7 I n t r o d u c t i o n 3 7 P r o c e d u r e s 3 8 S a m p l e 3 8 I n s t r u m e n t s 3 8 T h e F i l e D r a w e r P r o b l e m 3 9 A n a l y s i s 4 0 R e s u l t s a n d D i s c u s s i o n 4 2 S u m m a r y 5 5 C h a p t e r V. S u m m a r y, C o n c l u s i o n s, a n d R e c o m m e n d a t i o n s 5 7 I n t r o d u c t i o n 5 7 S u m m a r y 5 7
6 V C o n c l u s i o n s 5 8 S u g g e s t i o n s f o r F u r t h e r R e s e a r c h...: 5 9, R e f e r e n c e s 6 1 A p p e n d i x A : B i b l i o g r a p h y 7 2 A p p e n d i x B : S t u d i e s I d e n t i f i e d b y N u m b e r s 7 6
7 v i L i s t o f T a b l e s P a g e T a b l e 3. 1 S u m m a r y o f t h e s t u d y s e l e c t i o n f r o m t h e p r i m a r y s o u r c e 3 2 T a b l e 3. 2 G u i d e l i n e s f o r c o n v e r t i n g v a r i o u s t e s t s t a t i s t i c s t o r 3 5 T a b l e 4. 1 C o r r e l a t i o n s b e t w e e n m a t h e m a t i c s a n x i e t y a n d m a t h e m a t i c s a c h i e v e m e n t 4 2 T a b l e 4. 2 S t a t i s t i c s o f t h e m a t h e m a t i c s a n x i e t y - m a t h e m a t i c s a c h i e v e m e n t r e l a t i o n s h i p a c r o s s g r a d e 5 0 T a b l e 4. 3 S t a t i s t i c s o f t h e m a t h e m a t i c s a n x i e t y - a c h i e v e m e n t a c h i e v e m e n t r e l a t i o n s h i p b y g e n d e r 5 2 T a b l e 4. 4 S t a t i s t i c s o f t h e m a t h e m a t i c s a n x i e t y - a c h i e v e m e n t a c h i e v e m e n t r e l a t i o n s h i p b y e t h n i c i t y 5 4
8 v i i L i s t o f F i g u r e s P a g e F i g u r e 2. 1 T h e r e l a t i o n s h i p b e t w e e n a r o u s a l a n d h e d o n i c t o n e a c c o r d i n g t o o p t i m a l a r o u s a l t h e o r y 1 2 F i g u r e 4. 1 S t e m - a n d - l e a f d i s p l a y o f t h e 4 7 e f f e c t s i z e s 4 4 F i g u r e 4. 2 S t e m - a n d - l e a f d i s p l a y o f t h e 2 5 c o r r e l a t i o n s u s e d w i t h t h e M a i n R e s e a r c h Q u e s t i o n 4 6 F i g u r e 4. 3 M a t h e m a t i c s a n x i e t y - m a t h e m a t i c s a c h i e v e m e n t c o r r e l a t i o n s a c r o s s g r a d e 5 1
9 Vlll A c k n o w l e d g e m e n t s T h e w r i t e r w o u l d l i k e t o e x p r e s s h i s s i n c e r e t h a n k s t o h i s r e s e a r c h c o m m i t t e e m e m b e r s D r. J a m e s M. S h e r r i l l ; D r. A n n G. A n d e r s o n ; a n d D r. N a n d K i s h o r ; f o r t h e i r g u i d a n c e a n d c o n s t r u c t i v e c r i t i c i s m t h r o u g h o u t t h e d u r a t i o n o f t h i s s t u d y. T h e w r i t e r w o u l d a l s o l i k e t o t h a n k a l l t h e f r i e n d s a n d c o l l e a g u e s w h o p r o v i d e d s u p p o r t a n d e n c o u r a g e m e n t i n v a r i o u s w a y s t o t h e s u c c e s s f u l c o m p l e t i o n o f t h i s s t u d y. A s p e c i a l t h a n k y o u s h o u l d g o t o T o n y C l a r k e, G e o r g e F r e m p o n g, H a r i P. K o i r a l a, a n d J o e l Z a p a t a. F i n a l l y, t h e w r i t e r w o u l d l i k e t o e x t e n d h i s g r a t i t u d e t o t h e p e r s o n n e l i n t h e D e p a r t m e n t o f C u r r i c u l u m S t u d i e s w h o s e c o o p e r a t i o n m a d e i t p o s s i b l e f o r t h e s t u d y t o b e c o m p l e t e d s u c c e s s f u l l y. A m o n g t h e m, s p e c i a l t h a n k s t o S a r o j C h a n d, D i a n a C o l q u h o u n, a n d B o b H a p k e.
10 1 C h a p t e r I: I n t r o d u c t i o n T h e N a t i o n a l C o u n c i l o f T e a c h e r s o f M a t h e m a t i c s ( N C T M ) ( ) s t r e s s e s t h a t l e a r n i n g m a t h e m a t i c s " i n c l u d e s d e v e l o p i n g a d i s p o s i t i o n t o w a r d m a t h e m a t i c s.... D i s p o s i t i o n r e f e r s n o t s i m p l y t o a t t i t u d e s b u t t o a t e n d e n c y t o t h i n k a n d t o a c t i n p o s i t i v e w a y s " ( p ). T h i s e x t r a c t f r o m t h e N C T M ' s C u r r i c u l u m a n d E v a l u a t i o n S t a n d a r d s f o r S c h o o l M a t h e m a t i c s r e f l e c t s t h e w i d e s p r e a d b e l i e f a m o n g m a t h e m a t i c s e d u c a t o r s a n d e d u c a t i o n a l p s y c h o l o g i s t s i n t h e i m p o r t a n c e o f t h e d e v e l o p m e n t o f s t u d e n t s ' p o s i t i v e a t t i t u d e s t o w a r d l e a r n i n g m a t h e m a t i c s. I m p l i c i t i n s u c h s u g g e s t i o n s i s t h e b e l i e f t h a t t h e a f f e c t i v e d o m a i n p l a y s a n i m p o r t a n t r o l e i n l e a r n i n g a n d t e a c h i n g o f m a t h e m a t i c s ( A i k e n, , ; K u l m, ; M c l e o d, , ). A n i m p o r t a n t a f f e c t i v e f a c t o r t h a t e d u c a t o r s g i v e a t t e n t i o n t o, f o r i t s p o t e n t i a l i n f l u e n c e o n l e a r n i n g a n d a c h i e v e m e n t, i s s t u d e n t s ' a n x i e t y t o w a r d m a t h e m a t i c s ( L e d e r, ; M a n d l e r, ; M c l e o d, ; R e y e s, , ). M a t h e m a t i c s a n x i e t y h a s b e e n d e f i n e d a s " t h e g e n e r a l l a c k o f c o m f o r t t h a t s o m e o n e m i g h t e x p e r i e n c e w h e n r e q u i r e d t o p e r f o r m m a t h e m a t i c a l l y " ( W o o d, , p. 1 1 ). W i l l i a m s ( ) r e f e r r e d t o t h e s a m e p r o b l e m a s " b o t h a n e m o t i o n a l a n d a c o g n i t i v e d r e a d o f m a t h e m a t i c s " ( p. 9 6 ). D o n a d y a n d T o b i a s ( ) s u g g e s t e d t h a t m a n y s t u d e n t s d o s u f f e r m a t h e m a t i c s a n x i e t y a n d, a s a r e s u l t, t h e y d o n o t e n g a g e i n m a t h e m a t i c s a c t i v i t i e s a n d t r y t o a v o i d e n c o u n t e r s w i t h m a t h e m a t i c s. R e s e k a n d R u p l e y ( ) r e p o r t e d t h a t m a n y u n i v e r s i t y s t u d e n t s " a r e q u i t e t a l e n t e d i n t h e i r o w n f i e l d s ( e. g., a r e a s o f s o c i a l s c i e n c e s ), b u t d u e t o p o o r e x p e r i e n c e s i n p a s t m a t h e m a t i c s c l a s s e s t h e y h a v e d e v e l o p e d
11 2 m a t h o p h o b i a a n d c o n s e q u e n t l y h a v e p o o r a r i t h m e t i c s k i l l s " ( p ). F u t h e r m o r e, s e v e r a l s t u d i e s s u g g e s t t h a t m a t h e m a t i c s a n x i e t y i s p r e v a l e n t a m o n g s t u d e n t s, a n d i n f l u e n c e s c r i t i c a l a r e a s s u c h a s m a t h e m a t i c s l e a r n i n g, m a t h e m a t i c s a c h i e v e m e n t, e n r o l l m e n t i n m a t h e m a t i c s c o u r s e s a n d s u b s e q u e n t l y, c h o i c e s o f c o l l e g e m a j o r a n d c a r e e r ( B e t z, ; B r u s h, ; H e n d e l, ; P r e s t o n, ; T o b i a s & W e i s s b r o d, ). F o r t h e m a t h e m a t i c a l l y a n x i o u s s t u d e n t, c o n f r o n t a t i o n s w i t h m a t h e m a t i c s a r e r e m e m b e r e d a s a t h r e a t t o t h e e g o a n d a s a n o n c r e a t i v e, r i g i d e x p e r i e n c e ( T o b i a s & K n i g h t, ). A c c o r d i n g t o B u r t o n ( ), m a n y c h i l d r e n a n d a d u l t s a r e v i c t i m s o f t h e s e e x p e r i e n c e s w h i c h s e e m t o b e c o n t a g i o u s a n d f a r - r e a c h i n g i n t h e i r c o n s e q u e n c e s. T h i s p e r c e p t i o n o f h e l p l e s s n e s s, a n d t h e g u i l t a n d s h a m e a s s o c i a t e d w i t h i t, m a y a c c o u n t i n p a r t f o r t h e d e b i l i t a t i n g c o n d i t i o n c a l l e d " m a t h e m a t i c s a n x i e t y " ( B u r t o n, ). M a t h e m a t i c s h a s s e r v e d a s a v o c a t i o n a l f i l t e r ; p e o p l e w h o a v o i d m a t h e m a t i c s e a r l y i n t h e i r c a r e e r s h a v e t h e i r o p t i o n s s e v e r e l y l i m i t e d ( N C T M, ; S e l l s, ; P e r l, ; T o b i a s & K n i g h t, ). C a r e e r s t h a t w e r e c o m f o r t a b l y f r e e o f m a t h e m a t i c s i n t h e s a r e, i n t h e s, m o r e d e p e n d e n t t h a n e v e r u p o n m a t h e m a t i c s k n o w l e d g e ( N C T M, ). A d m i n i s t r a t o r s f r e q u e n t l y d e p e n d t o a g r e a t e x t e n t o n m a t h e m a t i c a l m o d e l s, e l a b o r a t e a c c o u n t i n g s y s t e m s, a n d c o m p u t e r i z e d d a t a a n a l y s i s ( N C T M, , ). T h e p r o f e s s i o n a l a n d e c o n o m i c a d v a n t a g e i n d i v i d u a l s g a i n i n c h a n g i n g t h e i r m a t h e m a t i c s a n x i e t y i n t o m a t h e m a t i c s c o n f i d e n c e i s i m p o r t a n t, b u t t h e p s y c h o l o g i c a l b o o s t t h e y e x p e r i e n c e w h e n t h e y a r e a b l e t o s u c c e e d i s j u s t a s i m p o r t a n t ( N a t i o n a l R e s e a r c h C o u n c i l, ).
12 3 M a t h e m a t i c s a n x i e t y i s b e l i e v e d t o a f f e c t t h e e x t e n t t o w h i c h a s t u d e n t p u r s u e s a n y m o r e t h a n m i n i m a l r e q u i r e m e n t s i n m a t h e m a t i c s, a n d t h e e x t e n t t o w h i c h t h e s t u d e n t i s a b l e t o l e a r n m a t h e m a t i c s, p e r f o r m m a t h e m a t i c s s k i l l s a n d u n d e r s t a n d m a t h e m a t i c s c o n c e p t s ( R i c h a r d s o n & S u i n n, ). B e t z ( ) s t a t e d t h a t m a t h e m a t i c s a n x i e t y i s a n i m p o r t a n t f a c t o r i n a s t u d e n t ' s e d u c a t i o n a l a n d v o c a t i o n a l d e c i s i o n s a n d c o u l d, i n a d d i t i o n, i n f l u e n c e t h e s t u d e n t ' s a c h i e v e m e n t. L a z a r u s ( ) n o t e d t h a t m a t h e m a t i c s a n x i e t y c o u l d a r i s e a t a n y p o i n t d u r i n g a n i n d i v i d u a l ' s s c h o o l e x p e r i e n c e, a n d t h a t t h e p h e n o m e n o n i s u n l i k e l y t o d i s a p p e a r o n i t s o w n w i t h o u t i n t e r v e n t i o n. C h i l d r e n w i t h m a t h e m a t i c s a n x i e t y a r e t r o u b l e d w i t h m a t h e m a t i c s t h r o u g h o u t t h e i r s c h o o l a n d v o c a t i o n a l c a r e e r s ( L a z a r u s, ). T h e s p e c i f i c c a u s e s o f m a t h e m a t i c s a n x i e t y a r e d i f f i c u l t t o r e c o g n i z e a n d t h e i r e f f e c t s m a y n o t b e d e t e c t e d a t t h e b e g i n n i n g ( G o u g h, ). A c c o r d i n g t o B e t z ( ), R i c h a r d s o n a n d W o o l f o l k ( ), a n d S e l l s ( ) l i t t l e i s k n o w n a b o u t t h e p r e v a l e n c e a n d e f f e c t s o f m a t h e m a t i c s a n x i e t y t h a t i s a s s o c i a t e d w i t h a l a c k o f f o r m a l e d u c a t i o n i n t h e s u b j e c t. E d u c a t o r s n e e d t o i d e n t i f y t h e f a c t o r s t h a t a f f e c t t h e f o r m a t i o n o f u n f a v o r a b l e m a t h e m a t i c s a t t i t u d e s. T h e y n e e d t o r e c o g n i z e i m m e d i a t e l y t h o s e s t u d e n t s w h o m e e t f r u s t r a t i o n s w h i c h c a n c a u s e m a t h e m a t i c s a n x i e t y, a n d i n i t i a t e t h e u s e o f c o r r e c t i v e m e t h o d s t o r e m e d i a t e a n d l e s s e n t h e e f f e c t o f t h e s e s c h o o l e x p e r i e n c e s ( M c M i l l a n, ). R e c o g n i t i o n o f m a t h e m a t i c s a n x i e t y d u r i n g i t s d e v e l o p m e n t i n t h e s c h o o l c o u l d h a v e a n i m p a c t o n p r e v e n t i n g l o n g t e r m e f f e c t s. T h i s e a r l y a w a r e n e s s c o u l d l e a d t o t h e d i s c o v e r y o f r e l a t e d f a c t o r s a n d i m p l e m e n t a t i o n o f e f f e c t i v e w a y s o f d e a l i n g w i t h m a t h e m a t i c s a n x i e t y ( B e t z, ; L a z a r u s, ; M c M i l l a n, ). S u c h i n f o r m a t i o n c o u l d o f f e r
13 4 v a l u a b l e g u i d e l i n e s f o r p r o g r a m a n d s t a f f d e v e l o p m e n t e f f o r t s i n t h i s p r o b l e m a t i c a r e a. A g r e a t d e a l o f r e s e a r c h h a s b e e n d i r e c t e d a t t h e i s s u e o f m a t h e m a t i c s a n x i e t y ( M c L e o d, , ), b u t m o s t o f t h e s e s t u d i e s h a v e b e e n c o n c e n t r a t e d o n c o l l e g e s t u d e n t s a n d o t h e r a d u l t s, w i t h n o a t t e n t i o n a t t h e e l e m e n t a r y a n d s e c o n d a r y l e v e l s. E v e n w h e n t h e r e s e a r c h w a s d o n e w i t h a d u l t s t h e r e s u l t s i n d i c a t e d t h a t m a t h e m a t i c s a n x i e t y o f t e n o r i g i n a t e d d u r i n g e a r l y e d u c a t i o n a l e x p e r i e n c e s ( C h i u & H e n r y, ). I n t h e o p i n i o n o f t h i s r e s e a r c h e r m o r e s t u d i e s w i t h y o u n g e r c h i l d r e n a r e n e e d e d a s t e a c h e r s n e e d t o b e c o m e m o r e a w a r e o f s t u d e n t s ' a n x i e t y t o w a r d m a t h e m a t i c s a n d h o w t h e y c a n h e l p s t u d e n t s t o d e a l w i t h i t. F u r t h e r, l i t e r a t u r e r e v i e w s h a v e b e e n d o n e o n m a t h e m a t i c s a t t i t u d e s b u t n o t s p e c i f i c a l l y o n c h i l d r e n ' s m a t h e m a t i c s a n x i e t y. B e c a u s e o f t h e n u m b e r o f s t u d i e s i n t h e b o d y o f l i t e r a t u r e o n m a t h e m a t i c s a n x i e t y, t h e l a c k o f r e v i e w s o n t h e t o p i c o f m a t h e m a t i c s a n x i e t y a n d m a t h e m a t i c s a c h i e v e m e n t, a n d t h e l a c k o f p r i o r i t y g i v e n t o y o u n g e r c h i l d r e n, t h i s s t u d y i s d e s i g n e d t o b r i n g a d e g r e e o f s y n t h e s i s t o t h e p a s t f i n d i n g s i n t h e r e l a t i o n s h i p b e t w e e n m a t h e m a t i c s a n x i e t y a n d m a t h e m a t i c s a c h i e v e m e n t i n e l e m e n t a r y a n d s e c o n d a r y s c h o o l s t u d e n t s. Statement of the problem T h e a i m o f t h i s s t u d y i s t o p r o v i d e a s y n t h e s i s o f r e s e a r c h f i n d i n g s o n m a t h e m a t i c s a n x i e t y i n e l e m e n t a r y a n d s e c o n d a r y s c h o o l s, r e g a r d i n g i t s n a t u r e a n d e f f e c t o n m a t h e m a t i c s a c h i e v e m e n t. T h i s s t u d y w i l l e x p l o r e a n d i n t e g r a t e t h e f i n d i n g s o n t h e r e l a t i o n s h i p b e t w e e n m a t h e m a t i c s a n x i e t y a n d m a t h e m a t i c s a c h i e v e m e n t u s i n g m e t a - a n a l y s i s. F u t h e r, t h e a n a l y s i s o f t h e m a t h e m a t i c s a n x i e t y - m a t h e m a t i c s a c h i e v e m e n t
14 5 r e l a t i o n s h i p w i l l i n c l u d e t h e e x t e n t t o w h i c h i t v a r i e s a c r o s s t h e v a r i a b l e s o f g r a d e l e v e l, g e n d e r, a n d e t h n i c i t y. S i g n i f i c a n c e o f t h e P r o b l e m B a s e d o n t h e l a r g e n u m b e r o f s t u d i e s, d i s s e r t a t i o n s, p u b l i s h e d r e p o r t s o f c o n f e r e n c e p r o c e e d i n g s, a n d p u b l i s h e d d o c u m e n t s d e a l i n g w i t h a n x i e t y t o w a r d s m a t h e m a t i c s, M c L e o d ( ) c o n c l u d e d t h a t t h e t o p i c " h a s p r o b a b l y r e c e i v e d m o r e a t t e n t i o n t h a n a n y o t h e r a r e a t h a t l i e s w i t h i n t h e a f f e c t i v e d o m a i n " ( p ). M c L e o d ( ) w r o t e t h a t " a n a r e a o f m a j o r a n d r e l a t e d i n t e r e s t t o r e s e a r c h o n a t t i t u d e s i s t h e s u b s t a n t i a l a m o u n t o f w o r k t h a t h a s b e e n d o n e o n m a t h e m a t i c s a n x i e t y " ( p ). I n t h e o p i n i o n o f t h i s r e s e a r c h e r, e d u c a t o r s n e e d t o g o b e y o n d t h e a c c u m u l a t i o n o f n e w s t u d i e s w h i c h a t t e m p t t o e x a m i n e s i m i l a r i s s u e s. T h e p o i n t h a s b e e n r e a c h e d w h e r e a s y n t h e s i s o f f i n d i n g s a n d r e s u l t s i s n e e d e d t o d e t e r m i n e c o m m o n t r e n d s a n d p a t t e r n s, a n d t o f i g u r e o u t w h a t s h o u l d b e r e s e a r c h e d i n t h e f u t u r e. G l a s s ( ) p o i n t e d o u t : I n e d u c a t i o n a l r e s e a r c h, w e n e e d m o r e s c h o l a r l y e f f o r t c o n c e n t r a t e d o n t h e p r o b l e m o f f i n d i n g t h e k n o w l e d g e t h a t l i e s u n t a p p e d i n c o m p l e t e d r e s e a r c h s t u d i e s. W e a r e t o o h e a v i l y i n v e s t e d i n p e d e s t r i a n r e v i e w i n g w h e r e v e r b a l s y n o p s e s o f s t u d i e s a r e s t r u n g o u t i n d i z z y i n g l i s t s. T h e b e s t m i n d s a r e n e e d e d t o i n t e g r a t e t h e s t a g g e r i n g n u m b e r o f i n d i v i d u a l s t u d i e s. T h i s e n d e a v o r d e s e r v e s h i g h e r p r i o r i t y n o w t h a n a d d i n g a n e w e x p e r i m e n t o r s u r v e y t o t h e p i l e, ( p. 4 ) S o m e l i t e r a t u r e r e v i e w s h a v e b e e n c o n d u c t e d i n t h e a r e a o f m a t h e m a t i c s a t t i t u d e s w i t h n o a t t e n t i o n t o m a t h e m a t i c s a n x i e t y ( L e d e r, ; M c L e o d, ; R e y e s, , ). F u r t h e r, n o s t a t i s t i c a l a n a l y s e s o f t h e d a t a w e r e p e r f o r m e d i n t h e s e r e v i e w s. S o m e s t a t i s t i c a l a n a l y s i s o f t h e
15 6 d a t a m i g h t r e v e a l r e l a t i o n s h i p s a n d h e l p i d e n t i f y v a r i a b l e s t h a t m a y p r o v i d e i n s i g h t i n d e v e l o p i n g e x p l a n a t i o n s o f t h e r e p o r t e d r e s u l t s. T h i s s t u d y i s b e i n g c a r r i e d o u t b e c a u s e o f i t s p e r c e i v e d s i g n i f i c a n c e a n d i t s p o t e n t i a l c o n t r i b u t i o n t o t h e f i e l d o f m a t h e m a t i c s e d u c a t i o n. I t i s h o p e d t h a t t h e s t u d y w i l l e n h a n c e t h e e x i s t i n g l i t e r a t u r e o n m a t h e m a t i c s a n x i e t y b y i d e n t i f y i n g v a r i a b l e s t h a t c a n s e r v e a s g u i d e l i n e s t o c l a r i f y t h e r e l a t i o n s h i p b e t w e e n m a t h e m a t i c s a n x i e t y a n d a c h i e v e m e n t a t t h e e l e m e n t a r y a n d s e c o n d a r y s c h o o l l e v e l s. T h i s s t u d y w i l l a l s o p r o v i d e a b a s i s f o r r e c o m m e n d a t i o n s c o n c e r n i n g t h e c o n d i t i o n s t h a t s h o u l d b e c o n t r o l l e d a n d s o m e o f t h e v a r i a b l e s t h a t s h o u l d b e m e a s u r e d i n f u t u r e s t u d i e s o f m a t h e m a t i c s a n x i e t y a n d a c h i e v e m e n t. I n t h i s s t u d y, n o t o n l y i s a r e v i e w o f t h e p e r t i n e n t l i t e r a t u r e g i v e n, b u t s e v e r a l s t a t i s t i c a l a n a l y s e s o f t h e d a t a w e r e p e r f o r m e d. T h e s e a n a l y s e s a n d t h e r e v i e w s h o u l d b e h e l p f u l t o m a t h e m a t i c s e d u c a t o r s a n d e d u c a t i o n a l r e s e a r c h e r s w h o a r e a t t e m p t i n g t o m a k e a n a s s e s s m e n t o f t h e i m p a c t o f m a t h e m a t i c s a n x i e t y o n t h e l e a r n i n g a n d t e a c h i n g o f m a t h e m a t i c s. Research Questions T h e p r i m a r y p u r p o s e o f t h i s s t u d y i s t o a n a l y z e t h e a v a i l a b l e r e s e a r c h o n t h e r e l a t i o n s h i p b e t w e e n m a t h e m a t i c s a n x i e t y a n d m a t h e m a t i c s a c h i e v e m e n t f r o m e l e m e n t a r y t h r o u g h s e c o n d a r y s c h o o l, b y m e a n s o f m e t a - a n a l y t i c p r o c e d u r e s ( H e d g e s & O l k i n, ; R o s e n t h a l, ). A s e c o n d a r y p u r p o s e o f t h i s s t u d y i s t o e x a m i n e t h e e x t e n t t o w h i c h t h e m a t h e m a t i c s a n x i e t y - a c h i e v e m e n t r e l a t i o n s h i p v a r i e s a c r o s s g r a d e l e v e l, g e n d e r, a n d e t h n i c i t y. T a k i n g i n t o c o n s i d e r a t i o n t h a t t h e s e s t u d i e s a r e e x p e c t e d t o p r o d u c e v a r i e d r e s u l t s, t h e i n v e s t i g a t i o n w i l l b e g u i d e d b y a
16 7 m a i n r e s e a r c h q u e s t i o n f o l l o w e d b y o t h e r q u e s t i o n s. T h e s t a t i s t i c a l a n a l y s e s f o r t h e s e r e s e a r c h q u e s t i o n s a r e d i s c u s s e d i n C h a p t e r I I I i n t h e s e c t i o n o n d a t a a n a l y s i s. M a i n R e s e a r c h Q u e s t i o n. W h a t i s t h e m a g n i t u d e o f t h e r e l a t i o n s h i p b e t w e e n m a t h e m a t i c s a n x i e t y a n d m a t h e m a t i c s a c h i e v e m e n t f o r e l e m e n t a r y a n d s e c o n d a r y s c h o o l s t u d e n t s, u s i n g t h e c o r r e l a t i o n c o e f f i c i e n t r a s a c o m m o n m e t r i c? F o r p u r p o s e s o f a n a l y s i s, t h e m a i n r e s e a r c h q u e s t i o n w a s b r o k e n d o w n i n t o t h e f o l l o w i n g q u e s t i o n s : Q u e s t i o n 2. T o w h a t e x t e n t d o e s t h e m a t h e m a t i c s a n x i e t y - a c h i e v e m e n t r e l a t i o n s h i p v a r y a c r o s s g r a d e l e v e l? Q u e s t i o n 3. T o w h a t e x t e n t d o e s t h e m a t h e m a t i c s a n x i e t y - a c h i e v e m e n t r e l a t i o n s h i p v a r y a c r o s s g e n d e r? Q u e s t i o n 4. T o w h a t e x t e n t d o e s t h e m a t h e m a t i c s a n x i e t y - a c h i e v e m e n t r e l a t i o n s h i p v a r y a c r o s s e t h n i c i t y? O p e r a t i o n a l D e f i n i t i o n s T h e f o l l o w i n g d e f i n i t i o n s a r e o f f e r e d t o c l a r i f y t h e m e a n i n g o f i m p o r t a n t t e r m s u s e d i n t h e s t u d y : D e p e n d e n t V a r i a b l e s : T h e d e p e n d e n t v a r i a b l e s a r e t h e e f f e c t s i z e s m e a s u r e d b y t h e c o r r e l a t i o n c o e f f i c i e n t s b e t w e e n m a t h e m a t i c s a n x i e t y a n d m a t h e m a t i c s a c h i e v e m e n t o u t c o m e s i n t h e i n d i v i d u a l s t u d i e s. I n d e p e n d e n t V a r i a b l e s : T h e i n d e p e n d e n t v a r i a b l e s a r e t h e s t u d y f e a t u r e s r e l a t e d t o t h e r e s e a r c h q u e s t i o n s a n d e x t r a c t e d f r o m t h e i n d i v i d u a l s t u d i e s.
17 8 M a t h e m a t i c s A c h i e v e m e n t : S c o r e s o n t e s t s i n m a t h e m a t i c s w h e t h e r t e a c h e r m a d e, t e x t b o o k, o r s t a n d a r d i z e d t h a t a r e r e p o r t e d i n t h e s t u d i e s. M a t h e m a t i c s A n x i e t y : S c o r e s o n t e s t s o f a n x i e t y t o w a r d m a t h e m a t i c s m e a s u r e d b y v a l i d a t e d i n s t r u m e n t s t h a t a r e r e p o r t e d i n t h e s t u d i e s. M e t a - A n a l y s i s : T h e s t a t i s t i c a l a n a l y s i s o f a l a r g e c o l l e c t i o n o f r e s u l t s f r o m i n d i v i d u a l s t u d i e s f o r t h e p u r p o s e o f i n t e g r a t i n g t h e f i n d i n g s ( G l a s s, ). U n i t o f A n a l y s i s : T h e c o r r e l a t i o n o u t c o m e s o f t h e i n d i v i d u a l r e s e a r c h s t u d i e s s e l e c t e d f o r t h e m e t a - a n a l y s i s. Limitation T h e r e i s o n e m a i n f a c t o r w h i c h i m p o s e d a l i m i t a t i o n o n t h e p r e s e n t s t u d y. T h e l i m i t i n g f a c t o r c o n c e r n s t h e a v a i l a b i l i t y o f t h e n e c e s s a r y s t a t i s t i c s i n t h e s t u d i e s f o r c o n d u c t i n g a m e t a - a n a l y s i s. S o m e s t u d i e s n e i t h e r p r o v i d e d t h e c o r r e l a t i o n c o e f f i c i e n t s b e t w e e n m a t h e m a t i c s a n x i e t y a n d a c h i e v e m e n t n o r s u f f i c i e n t i n f o r m a t i o n f o r i t s c a l c u l a t i o n. T h i s l e d t o t h e r e j e c t i o n o f t h e s e s t u d i e s i n t h e a n a l y s i s. Delimitations T h e d e l i m i t a t i o n s o f t h e s t u d y a r e r e l a t e d t o d e c i s i o n s t h a t a r e m a d e c o n c e r n i n g t h e f i n a l s e l e c t i o n o f t h e s t u d i e s t o b e i n c l u d e d i n t h e a n a l y s i s o f t h e d a t a. D u r i n g t h e b e g i n n i n g p h a s e s o f t h e s t u d y, p u b l i s h e d a n d u n p u b l i s h e d r e s e a r c h s t u d i e s c o n t a i n i n g t h e d e s i r e d d e s c r i p t o r s - m a t h e m a t i c s a n x i e t y, m a t h e m a t i c s a c h i e v e m e n t a n d m a t h e m a t i c s
18 9 p e r f o r m a n c e - w e r e e x a m i n e d. H o w e v e r, n o t a l l o f t h e s e s t u d i e s c o u l d b e r e t a i n e d f o r t h e a n a l y s i s b e c a u s e t h e y c o u l d n o t m e e t t h e c r i t e r i a l i s t e d b e l o w. T h e s e w e r e : 1. P r o v i d i n g d a t a o n m a t h e m a t i c s a n x i e t y a n d m a t h e m a t i c s a c h i e v e m e n t f r o m e l e m e n t a r y o r s e c o n d a r y s c h o o l c l a s s r o o m s e t t i n g s. 2. U s i n g v a l i d a t e d i n s t r u m e n t t o m e a s u r e m a t h e m a t i c s a n x i e t y. 3. R e p o r t i n g t h e p r o d u c t - m o m e n t c o r r e l a t i o n c o e f f i e n t r, o r s u f f i c i e n t i n f o r m a t i o n f o r i t s c a l c u l a t i o n. T h e s e t h r e e c r i t e r i a a r e d i s c u s s e d i n m o r e d e t a i l i n C h a p t e r I I I. T h e d i s c u s s i o n i n C h a p t e r I I I a l s o d e s c r i b e s c h a r a c t e r i s t i c s o f s o m e o f t h e s t u d i e s w h i c h w e r e e l i m i n a t e d f r o m t h e a n a l y s i s b e c a u s e o f f a i l u r e t o m e e t t h e s e c r i t e r i a. O r g a n i z a t i o n o f t h e T h e s i s T h e s t u d y i s p r e s e n t e d i n a t h e s i s o f f i v e c h a p t e r s. C h a p t e r I p r e s e n t s t h e g e n e r a l r a t i o n a l e o f t h e s t u d y w i t h p e r t i n e n t i n f o r m a t i o n t o s u p p o r t t h e s i g n i f i c a n c e o f t h e s t u d y. T h e c h a p t e r i n c l u d e s a n i n t r o d u c t i o n, s t a t e m e n t o f t h e p r o b l e m, s i g n i f i c a n c e o f t h e p r o b l e m, r e s e a r c h q u e s t i o n s, o p e r a t i o n a l d e f i n i t i o n s, l i m i t a t i o n s, d e l i m i t a t i o n s, a n d o r g a n i z a t i o n o f t h e t h e s i s. C h a p t e r I I s u m m a r i z e s t h e l i t e r a t u r e r e l a t e d t o t h e s t u d y. T h e l i t e r a t u r e r e v i e w i s p r e s e n t e d i n s i x m a i n s e c t i o n s : n a t u r e o f m a t h e m a t i c s a n x i e t y, m e a s u r e m e n t o f m a t h e m a t i c s a n x i e t y, p r e v i o u s r e v i e w s, g e n d e r a n d m a t h e m a t i c s a n x i e t y, e t h n i c i t y a n d m a t h e m a t i c s a n x i e t y, a n d m a t h e m a t i c s a n x i e t y a n d a c h i e v e m e n t.
19 1 0 C h a p t e r I I I i s d e v o t e d t o a d e t a i l e d d e s c r i p t i o n o f t h e p r o c e d u r e s t o b e f o l l o w e d i n a p p l y i n g t h e c r i t e r i a f o r i n c l u d i n g s t u d i e s, l o c a t i n g t h e s t u d i e s, c o d i n g s t u d y f e a t u r e s a n d q u a n t i f y i n g s t u d y o u t c o m e s. T h e p r o c e d u r e s u s e d i n t h e d a t a a n a l y s i s a r e a l s o d e s c r i b e d. C h a p t e r I V p r e s e n t s t h e d a t a. T h e a n a l y s i s o f t h e d a t a a n d i n t e r p r e t a t i o n o f t h e f i n d i n g s a r e a l s o p r e s e n t e d i n t h i s c h a p t e r. C h a p t e r V c o n t a i n s a s u m m a r y o f t h e s t u d y, t h e c o n c l u s i o n s, a n d s u g g e s t i o n s f o r f u r t h e r r e s e a r c h.
20 1 1 C h a p t e r I I. R e v i e w o f L i t e r a t u r e I n t r o d u c t i o n T h e p r i m a r y c o n c e r n o f t h i s s t u d y i s t h e a n a l y s i s o f e x i s t i n g r e s e a r c h o n t h e r e l a t i o n s h i p b e t w e e n m a t h e m a t i c s a n x i e t y a n d m a t h e m a t i c s a c h i e v e m e n t. T h i s c h a p t e r i s a r e v i e w o f t h e l i t e r a t u r e a n d r e s e a r c h f i n d i n g s i n t h e a r e a o f m a t h e m a t i c s a n x i e t y. T h e f i r s t s e c t i o n d e s c r i b e s t h e n a t u r e o f m a t h e m a t i c s a n x i e t y. T h e s e c o n d s e c t i o n r e f e r s t o t h e m e a s u r e m e n t o f m a t h e m a t i c s a n x i e t y. T h e t h i r d s e c t i o n i n t h i s c h a p t e r r e p o r t s o n p r e v i o u s r e v i e w s. T h e f o u r t h s e c t i o n d e a l s w i t h g e n d e r d i f f e r e n c e s i n m a t h e m a t i c s a n x i e t y. T h e f i f t h s e c t i o n r e p o r t e d o n s o m e s t u d i e s t h a t d e a l t w i t h e t h n i c i t y. T h e s i x t h s e c t i o n s u m m a r i z e s f i n d i n g s o n m a t h e m a t i c s a n x i e t y a n d a c h i e v e m e n t i n m a t h e m a t i c s. N a t u r e o f M a t h e m a t i c s A n x i e t y A n x i e t y, i n g e n e r a l, i s a s t a t e o f a p p r e h e n s i o n f e l t b y a p e r s o n. I n W e b s t e r ' s N i n t h N e w C o l l e g i a t e D i c t i o n a r y ( ) a n x i e t y i s d e f i n e d a s a " p a i n f u l o r a p p r e h e n s i v e u n e a s i n e s s o f m i n d u s u a l l y o v e r a n i m p e n d i n g o r a n t i c i p a t e d i l l " ( p. 9 3 ). I t i s n o t u n c o m m o n t o l i k e n t h i s a p p r e h e n s i o n t o f e a r. I n m a n y i n s t a n c e s f e a r a n d a n x i e t y a r e u s e d i n t e r c h a n g e a b l y. H o w e v e r, t h e r e i s a d i s t i n c t i o n t h a t c a n b e m a d e b e t w e e n t h e t w o : f e a r i s o f t e n d e f i n e d a s a r e s p o n s e t o a d e f i n i t e a n d s p e c i f i c t h r e a t o r d a n g e r, w h i l e a n x i e t y i s a f e a r o f s o m e t h i n g u n k n o w n o r i n d e f i n i t e. O n e c a n b e a n x i o u s a n d n o t k n o w w h y b u t o n e c a n n o t b e a f r a i d a n d n o t k n o w t h e c a u s e o f t h e f e a r ( O h m a n, ). A n x i e t y, a s d e f i n e d i n p s y c h o l o g i c a l l i t e r a t u r e, t y p i c a l l y r e f e r s t o a h e i g h t e n e d s t a t e o f a r o u s a l t h a t p r o d u c e s f e e l i n g s o f d i s c o m f o r t, e x c e s s i v e
21 1 2 c o n c e r n o r w o r r y. A r o u s a l i s a c o n d i t i o n, v a r y i n g i n i n t e n s i t y a n d m e d i a t e d b y t h e s y m p a t h e t i c n e r v o u s s y s t e m, i n w h i c h c h a n g e s i n b o d i l y p r o c e s s e s p r e p a r e a n i n d i v i d u a l t o r e s p o n d t o a p e r c e i v e d d e m a n d f o r a c t i o n ( G a t c h e l & B a u m, ; B a n d u r a & A d a m s, ). I n t h e t r a d i t i o n a l a r o u s a l t h e o r y o r i g i n a t e d b y H e b b ( ) t h e f u n d a m e n t a l i d e a i s t h a t t h e r e i s a n o p t i m a l l e v e l o f a r o u s a l a n d t h a t t h i s i s s o m e w h e r e a r o u n d t h e m i d d l e o f t h e a r o u s a l d i m e n s i o n. T h i s i d e a c a n b e r e p r e s e n t e d g r a p h i c a l l y b y a n i n v e r t e d - U c u r v e s h o w n i n F i g u r e " O p t i m a l " m e a n s b o t h o p t i m a l i n t e r m s o f a c h i e v e m e n t a n d o p t i m a l i n t h e s e n s e o f h e d o n i c t o n e ( m o s t p l e a s e n t ). P l e a s a n t R e l a x a t i o n O p t i m a l l e v e l L U n p l e a s a n t B o r e d o m A n x i e t y F i g u r e 2. 1 T h e r e l a t i o n s h i p b e t w e e n a r o u s a l a n d h e d o n i c t o n e a c c o r d i n g t o o p t i m a l a r o u s a l t h e o r y ( H e b b, ). S p i e l b e r g e r ( ) h a s d i s t i n g u i s h e d b e t w e e n t w o a s p e c t s o f a n x i e t y. S t a t e a n x i e t y ( A - S t a t e ) i s " a t r a n s i t o r y e m o t i o n a l s t a t e " ( p. 3 9 ) o f t e n s i o n a n d n e r v o u s r e a c t i o n, w h e r e a s T r a i t a n x i e t y ( A - T r a i t ) i s a c h r o n i c a n x i e t y p r o n e n e s s c h a r a c t e r i z e d b y A - S t a t e r e a c t i o n s i n a w i d e r a n g e o f s t i m u l u s
22 1 3 s i t u a t i o n s. A c c o r d i n g t o S p i e l b e r g e r, A n t o n, a n d B e d e l l ( ) t r a i t - s t a t e t h e o r y, t e s t a n x i e t y i s a f o r m o f t r a i t a n x i e t y. H i g h - a n x i o u s p e o p l e r e s p o n d t o t e s t i n g w i t h e l e v a t i o n s i n A - S t a t e ( o r e m o t i o n a l i t y ) ; w o r r y i s t h e n t r i g g e r e d b y t h e A - S t a t e m a n i f e s t a t i o n s. T h e s e l a t t e r r e a c t i o n s a l s o a c t i v a t e r a n d o m e r r o r t e n d e n c i e s. H e n c e, e m o t i o n a l i t y a n d w o r r y b o t h c o n t r i b u t e t o d e p r e s s e d p e r f o r m a n c e ( S p i e l b e r g e r, A n t o n, & B e d e l l, ). M a t h e m a t i c s a n x i e t y i s d e s c r i b e d b y R i c h a r d s o n a n d W o o l f o l k ( ) a s d i f f e r e n t f r o m t e s t a n x i e t y. M a t h e m a t i c s a n x i e t y i s a r e a c t i o n t o m a t h e m a t i c a l c o n t e n t, t o s o m e o f i t s d i s t i n c t i v e f e a t u r e s a s a n i n t e l l e c t u a l a c t i v i t y a n d i t s c o n n o t a t i v e m e a n i n g s f o r m a n y p e o p l e i n o u r s o c i e t y, a s w e l l a s r e a c t i o n t o e v a l u a t i v e f o r m s o f m a t h e m a t i c a l t e s t s a n d p r o b l e m - s o l v i n g a c t i v i t i e s. I t i s a r e a c t i o n n o t o n l y t o t h e t e s t i n g o f c o n t e n t b u t t o t h e p r e c i s e n a t u r e, t h e l a n g u a g e a n d s y m b o l s a n d t h e a p p a r e n t u s e l e s s n e s s o f s o m e m a t h e m a t i c s t a u g h t i n s c h o o l s ( R i c h a r d s o n & W o o l f o l k, ). R i c h a r d s o n a n d S u i n n ( ) f o u n d t h a t m a t h e m a t i c s a n x i e t y e x i s t s a m o n g p e o p l e w h o d i d n o t o r d i n a r i l y s u f f e r f r o m a n y o t h e r t e n s i o n s. T h e y a l s o s h o w e d t h a t m a t h e m a t i c s a n x i e t y, a l t h o u g h r e l a t e d t o g e n e r a l a n x i e t y, w a s d i f f e r e n t b e c a u s e m a n y p e o p l e w h o w e r e n o t g e n e r a l l y a n x i o u s w e r e a n x i o u s a b o u t m a t h e m a t i c s. W o o d ( ) h a s d e f i n e d m a t h e m a t i c s a n x i e t y a s " t h e g e n e r a l l a c k o f c o m f o r t t h a t s o m e o n e m i g h t e x p e r i e n c e w h e n r e q u i r e d t o p e r f o r m m a t h e m a t i c a l l y " ( p. 1 1 ). W i l l i a m s ( ) r e f e r r e d t o t h e s a m e p r o b l e m a s " b o t h a n e m o t i o n a l a n d a c o g n i t i v e d r e a d o f m a t h e m a t i c s " ( p. 9 6 ). M a t h e m a t i c s a n x i e t y a n d m a t h e m a t i c s a v o i d a n c e w e r e u n n o t i c e d o u t s i d e o f t h e f i e l d o f m a t h e m a t i c s f o r m a n y y e a r s. T r a d i t i o n a l b e l i e f s w e r e t h a t p e o p l e w e r e b o r n w i t h m a t h e m a t i c a l a b i l i t y o r t h e y w e r e n o t.
23 1 4 F r o m t h i s b e l i e f c a m e t h e i d e a t h a t t h e r e w a s n o n e e d t o t r y t o h e l p t h o s e w h o d i d n o t p o s s e s s t h e n e c e s s a r y a b i l i t y ( T o b i a s & K n i g h t, ). B u s h ( ), a n d S e p i e a n d K e e l i n g ( ) s u g g e s t t h a t m a t h e m a t i c s a n x i e t y b e g i n s t o a p p e a r a t a b o u t t h e a g e o f e n t r y t o s e c o n d a r y s c h o o l b u t s o m e t i m e s e v e n i n t h e l o w e r g r a d e s. F u t h e r m o r e, l i m i t e d p a r t i c i p a t i o n i n m a t h e m a t i c s c o u r s e s a t t h e s e c o n d a r y l e v e l h a s b e e n b l a m e d a t l e a s t i n p a r t o n t h e l a c k o f c o n f i d e n c e d u e t o m a t h e m a t i c s a n x i e t y t h a t h a s i t s r o o t s i n t h e e l e m e n t a r y s c h o o l e x p e r i e n c e ( F e n n e m a a n d S h e r m a n, ; F r a r y & L i n g, ; R e y e s, ). B u h l m a n a n d Y o u n g ( ) a f f i r m t h a t m a t h e m a t i c s a n x i e t y i s a s p r e v a l e n t a m o n g e l e m e n t a r y t e a c h e r s a s a m o n g t h e g e n e r a l p u b l i c. A c c o r d i n g t o G i o r d a n o ( ) i f t e a c h e r s h a v e n e g a t i v e f e e l i n g s t o w a r d s a s u b j e c t t h e y a r e t e a c h i n g, s u c h f e e l i n g s " m i g h t b e i n a d v e r t e n t l y p a s s e d t o s t u d e n t s " ( p. 4 3 ). I n t h e l i t e r a t u r e i t i s d i f f i c u l t t o s e p a r a t e r e s e a r c h o n a n x i e t i e s t o w a r d s m a t h e m a t i c s f r o m r e s e a r c h o n b e l i e f s a b o u t m a t h e m a t i c s. F o r e x a m p l e, K l o o s t e r m a n a n d C l a p p - C o u g a n ( ) i n t e r v i e w e d s t u d e n t s f r o m g r a d e o n e t o s i x. T h e s e r e s e a r c h e r s d e s i g n e d a n i n s t r u m e n t w h i c h i n c l u d e d q u e s t i o n s a b o u t s t u d e n t s ' a t t i t u d e s t o w a r d s s c h o o l, t h e i r p e r c e p t i o n s o f m a t h e m a t i c s, a n d t h e i r p e r c e p t i o n s o f t h e m s e l v e s a s m a t h e m a t i c s l e a r n e r s. T h e y s t a t e, " t h e c h i l d r e n w e i n t e r v i e w e d i n d i c a t e d t h a t g r a d e s a n d t e a c h e r f e e d b a c k a b o u t t h e c o r r e c t n e s s o f t h e i r a s s i g n m e n t s r a t h e r t h a n c o n c e p t u a l u n d e r s t a n d i n g w a s t h e b a s i s f o r t h e i r l e v e l o f s e l f - c o n f i d e n c e i n m a t h e m a t i c s. I n a d d i t i o n, b y f o u r t h g r a d e, s t u d e n t s b e g a n t o n o t e t h a t t h e y w e r e b e t t e r a t s o m e t y p e s o f m a t h e m a t i c a l t a s k s t h a n o t h e r s " ( p. 7 ). T h e r e s e a r c h e r c o n c l u d e d : " O v e r a l l, w e f o u n d t h a t a m a j o r i t y b u t c e r t a i n l y n o t a l l s t u d e n t s l i k e d s c h o o l a n d m a t h e m a t i c s. O n l y
24 1 5 a f e w l i k e d s c h o o l m o r e t h a n t h e y l i k e d m a t h e m a t i c s a n d a l m o s t n o n e l i k e d m a t h e m a t i c s s u b s t a n t i a l l y m o r e t h a n t h e y l i k e d s c h o o l i n g e n e r a l " ( p. 7 ). L a z a r u s ( ) a n d T o b i a s ( ) c l a i m t h a t a d i s c o m f o r t w i t h m a t h e m a t i c s i s a c q u i r e d e a r l y i n t h e s c h o o l a n d c a n d e v e l o p i n t o a s y n d r o m e o f a n x i e t y a n d a v o i d a n c e o f m a t h e m a t i c s. M c M i l l a n ( ) c l a i m s t h a t m a t h e m a t i c s a n x i e t y a r i s e s f r o m a n a f f e c t i v e c l i m a t e i n w h i c h n e g a t i v e a t t i t u d e s a n d a n x i e t y a r e t r a n s m i t t e d f r o m a d u l t s t o s t u d e n t s. M c M i l l a n ( ) s u g g e s t s t h a t " t h e f a c t o r s w h i c h h a v e a n i m p a c t o n s t u d e n t a t t i t u d e d e v e l o p m e n t t o w a r d s c h o o l s u b j e c t s r e s i d e w i t h t h e t e a c h e r a n d s t u d e n t a n d n o t w i t h t h e c u r r i c u l u m o r i n s t r u c t i o n a l a p p r o a c h " ( p ). M o r e s p e c i f i c a l l y, B u l m a h n a n d Y o u n g ( ), K e l l y a n d T o w h a v e ( ), a n d L a z a r u s ( ) i n a d d i t i o n t o G i o r d a n o ( ), c i t e d e a r l i e r, s u g g e s t t h a t t e a c h e r s w i t h m a t h e m a t i c s a n x i e t y t r a n s m i t t h e i r a n x i e t y t o t h e i r s t u d e n t s. L a z a r u s ( ) a n d W i l h e l m a n d B r o o k s ( ) a d d e d t h a t n e g a t i v e p a r e n t a l a t t i t u d e s m a y b e t r a n s m i t t e d t o t h e i r c h i l d r e n a n d t h a t p a r e n t s o f t e n r e i n f o r c e t h e i r c h i l d r e n ' s m a t h e m a t i c s a n x i e t y. O n t h e o t h e r h a n d, o t h e r s ( B u s h, , ; B e c k e r, ) a r g u e t h a t n e g a t i v e a t t i t u d e s o f t e a c h e r s d o n o t t e n d t o i n d u c e m a t h e m a t i c s a n x i e t y i n t h e i r s t u d e n t s ; o t h e r s a r g u e t h a t e l e m e n t a r y t e a c h e r s h a v e g e n e r a l l y p o s i t i v e a t t i t u d e s, e v e n t h o u g h t h e y h a d d e v e l o p e d s o m e n e g a t i v e a t t i t u d e s t o w a r d m a t h e m a t i c s w h e n t h e y w e r e s t u d e n t s ( W i d m e r a n d C h a v e z, ). I n s u m m a r y, r e s e a r c h f i n d i n g s i n m a t h e m a t i c s a n x i e t y a r e i n c o n c l u s i v e, b u t s o m e r e s u l t s s e e m t o s u g g e s t t h a t m a t h e m a t i c s a n x i e t y b e g i n s d u r i n g e a r l y e d u c a t i o n a l e x p e r i e n c e s i n t h e s c h o o l o r a t h o m e.
25 1 6 Measurement of Mathematics Anxiety A l i m i t e d n u m b e r o f i n s t r u m e n t s, m a i n l y L i k e r t - t y p e i n v e n t o r i e s, h a v e b e e n d e v e l o p e d f o r t h e m e a s u r e m e n t o f m a t h e m a t i c s a n x i e t y o f s e c o n d a r y s c h o o l s t u d e n t s o r a d u l t s. D r e g e r a n d A i k e n ( ) h a v e d e v e l o p e d a " n u m b e r a n x i e t y " s c a l e f o r u s e w i t h e i g h t h, n i n t h, a n d t e n t h g r a d e s t u d e n t s ( A d w e r e - B o a m a h, M u l l e r, & K a h n, ; D r e g e r & A i k e n, ). R i c h a r d s o n a n d S u i n n ( ) d e v e l o p e d t h e f i r s t c o m p r e h e n s i v e s c a l e d e s i g n e d s p e c i f i c a l l y t o m e a s u r e m a t h e m a t i c s a n x i e t y a n d v a l i d a t e d i t f i r s t w i t h a d u l t s. T h e M a t h e m a t i c s A n x i e t y R a t i n g S c a l e ( M A R S ) c o n s i s t s o f a t o t a l o f 9 8 i t e m s d e s c r i b i n g s i t u a t i o n s t h a t c o u l d a r o u s e m a t h e m a t i c s a n x i e t y. R e s p o n d e n t s i n d i c a t e h o w m u c h t h e y a r e a f f e c t e d b y t h e s i t u a t i o n d e s c r i b e d b y s e l e c t i n g o n e o f t h e f o l l o w i n g o p t i o n s : n o t a t a l l, a l i t t l e, a f a i r a m o u n t, m u c h, a n d v e r y m u c h. S o m e i t e m s a r o u s e v e r y l i t t l e a n x i e t y w h i l e o t h e r s c o u l d a r o u s e a l o t. T h e M A R S w a s c o m p a r e d t o s o m e o t h e r m e a s u r e s o f a n x i e t y f o r v a l i d i t y, t h e r e s u l t i n g P e a r s o n p r o d u c t - m o m e n t c o r r e l a t i o n s w e r e w i t h m e a s u r e s o f s o c i a l a n x i e t y, w i t h t h e T a y l o r M a n i f e s t A n x i e t y S c a l e, a n d w i t h t h e T e s t A n x i e t y S c a l e ( S u i n n, E d i e, N i c o l e t t i & S p i n e l l i, ) S i n c e b o t h t h e s h o r t e n e d ( P l a k e & S p a r k, ) a n d o r i g i n a l v e r s i o n s o f t h e M A R S w e r e d e s i g n e d f o r c o l l e g e s t u d e n t s, t h e M a t h e m a t i c s A n x i e t y S c a l e f o r C h i l d r e n ( M A S C ) w a s d e v e l o p e d b y C h i u a n d H e n r y ( ) " t o b e u s e d i n t h e u p p e r e l e m e n t a r y g r a d e s a n d m i d d l e s c h o o l s " ( p. 2 3 ). T h e t w e l v e i t e m F e n n e m a - S h e r m a n M a t h e m a t i c s A n x i e t y S c a l e ( M A S ), i n i t i a l l y d e s i g n e d f o r u s e w i t h h i g h s c h o o l s t u d e n t s, h a s s u b s e q u e n t l y b e e n e m p l o y e d w i t h a d u l t s ( F e n n e m a & S h e r m a n, ;
26 1 7 L l a b r e & S u a r e z, ; W i k o f f & B u c h a l t e r, ). S a n d m a n ( ) d e v e l o p e d t h e 6 - i t e m M a t h e m a t i c s A t t i t u d e I n v e n t o r y ( M A I ), i n i t i a l l y u s e d w i t h s t u d e n t s i n t h e e i g h t h t o e l e v e n t h g r a d e s, b u t c o n s i d e r e d a p p r o p r i a t e f o r a d u l t s. C o m p a r a t i v e r e l i a b i l i t y, a n d v a l i d i t y d a t a h a v e b e e n r e p o r t e d f o r t h e l a s t t h r e e s c a l e s, f o r e x a m p l e t h e M A S i s c o r r e l a t e d w i t h t h e M A R S ( r = ) a n d w i t h t h e M A I ( r = ) ( D e w, G a l a s s i, & G a l a s s i, , ). A c c o r d i n g t o C o h e n ( ) w h o c o n s i d e r r = l a r g e t h e s e c o r r e l a t i o n s a r e v e r y h i g h. T h e M A R S A d o l e s c e n t F o r m ( M A R S - A ) h a s b e e n u s e d w i t h j u n i o r h i g h a n d s e n i o r h i g h s t u d e n t s ( B a t t i s t a, ; H o l d e n, ; L i n d b e c k & D a m b r o t, ; R o u n d s a n d H e n d e l, ; S a i g h & K h o u r i, ; S u i n n, E d i e, N i c o l e t t i, & S p i n e l l y, ; S u i n n & E d w a r d s, ). S u i n n a l s o d e v e l o p e d a n i n s t r u m e n t f o r a s s e s s i n g m a t h e m a t i c s a n x i e t y a t t h e e l e m e n t a r y l e v e l : t h e S u i n n M a t h e m a t i c s A n x i e t y R a t i n g S c a l e, E l e m e n t a r y F o r m ( M A R S - E ) u s e d w i t h f o u r t h, f i f t h, a n d s i x t h g r a d e s t u d e n t s ( S u i n n, T a y l o r, & E d w a r d s, ). I n s u m m a r y, t h e r e i s a l a c k o f i n s t r u m e n t s t o m e a s u r e m a t h e m a t i c s a n x i e t y i n c h i l d r e n i n t h e l o w e r e l e m e n t a r y g r a d e s, a n d t h e t e s t s o r i g i n a l l y d e v e l o p e d f o r s e c o n d a r y s c h o o l s t u d e n t s h a v e b e e n m a i n l y u s e d w i t h a d u l t s. Previous Reviews S o m e n a r r a t i v e l i t e r a t u r e r e v i e w s h a v e b e e n c o n d u c t e d i n t h e a r e a o f m a t h e m a t i c s a t t i t u d e s w i t h l i t t l e a t t e n t i o n g i v e n t o m a t h e m a t i c s a n x i e t y ( A i k e n, , ; N e a l e, ; M c M i l l a n, ; R o b i n s o n, ). B y r e v i e w i n g d i s s e r t a t i o n s, M c M i l l a n ( ) r e p o r t s t h a t t e a c h e r s ' a t t i t u d e s a n d e n t h u s i a s m t o w a r d a s u b j e c t h a d g r e a t e r i m p a c t o n s t u d e n t
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