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Differences between sophomores juniors and seniors in arithmetic abilities

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DIFFERENCES BETWEEN SOPHOMORES, JUNIORS, AND SENIORS
IN ARITHMETIC ABILITIES
A T h esis
P re se n te d to
th e F a c u lty o f th e School o f E d u c a tio n
The U n i v e r s i t y o f S o u th e r n C a l i f o r n i a
In P a r t i a l F u lfillm e n t
o f t h e R e q u ir e m e n ts f o r t h e D eg ree
M a s te r o f S c ie n c e i n E d u c a t i o n
"by
N e e v i l W illia m Helm
F e b r u a r y 1942
UMI Number: EP54224
All rights reserved
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Th is thesis, w rit te n under the direction of the
Cha irm an of the candidate*s Gu id an ce C o m m i t t e e
an d a p p r o v e d by all membe rs of the C om m it te e ,
has been pr es e nt e d to and a c ce p te d by the F acu lty
of the S c h o o l of Ed uc at io n of T h e Unive rsi ty of
Southern California in par ti al fulfillment of the
requirements f o r the degree of M a s t e r of Science
in Education.
_
D a te
January 3 1 , 1942
.......................................................
Guidance C om m ittee
G. G. Crawford
Chairman
D. W elty L efev er
L ou is P . Thorpe
2ABLE O f CONTENTS
CHAPTER
PAGE
I. THE PROBLEM
. . . . . . . . . . . . . . . . . .
Are t h e g r o u p s p r e p a r e d t o work t o g e t h e r ? .
1
. .
1
Are s t u d e n t s i n t h e lo w e r c l a s s e s o versh ad o w ed
by ad v a n c e d s t u d e n t s ?
................................................
2
W i l l t e a c h i n g aims and o b j e c t i v e s f i l l th e
needs o f a l l th r e e groups?
..................................
3
Do t h e lo w e r c l a s s e s r e t a r d t h e ' g ro u p a s a
w h o le?
II.
PROCEDURE
.
........................
5
.
........................................................................
7
The t e s t i n g p ro g ra m
......................................
7
S t a t i s t i c a l te c h n iq u e s used
......................................
12
ANALYSIS Of EXPERIMENTAL RESULTS..................................
17
C om p arison o f t e s t s c o r e s o f t h e t h r e e c l a s s e s
17
S cores i n
a d d itio n
18
S cores i n
s u b t r a c t i o n ....................................
S co res In
m u l t i p l i c a t i o n and s h o r t d i v i s i o n
S cores i n
l o n g d i v i s i o n .......................................
25
S cores i n
a r i t h m e t i c r e a s o n i n g .........................
45
.
...................................................
18
.
III.
. . . . .
.
25
S c o r e s on S t a n f o r d A ch iev em en t T e s t . . . . .
S c o r e s on m id term a c h ie v e m e n t t e s t ...............
In te llig e n c e q u o tie n ts
.
......................................
Summary o f c o m p a ris o n s on a l l t e s t s
. . . . . .
45
55
55
59
iii
CHABBER
BAGS
Summary
17.
............................. . . . . . .
SUMMARY M D C O T C LU SIQ N S ....................................................
O o n o lu s io n s
* ...................................................
64
67
68
£ISQ? O F fABItES
uffiS
C o m p a ra tiv e s c o r e s on an a c h ie v e m e n t t e s t
i n s im p le a d d i t i o n
19
R e l i a b i l i t y o f t h e d i f f e r e n c e s b e tw e e n s c o r e s
on an a c h ie v e m e n t t e s t i n s im p le a d d i t i o n
•
20
C om parison o f num ber o f p ro b le m s a t t e m p t e d on
an a c h ie v e m e n t t e s t i n a d d i t i o n
. . . . . .
22
C o m p a ra tiv e s c o r e s on an a c h ie v e m e n t t e s t i n
s u b tra c tio n
...........................................
. . . . . .
24
R e l i a b i l i t y o f t h e d i f f e r e n c e s b e tw e e n s c o r e s
on an a c h ie v e m e n t t e s t i n s u b t r a c t i o n
. . .
26
C om p ariso n o f num ber o f p ro b le m s a t t e m p t e d on
an a c h ie v e m e n t t e s t i n s u b t r a c t i o n • • • • .
26
C o m p a ra tiv e s c o r e s on an a c h ie v e m e n t t e s t i n
m u l t i p l i c a t i o n ...................
. . . . . . . . . .
30
R e l i a b i l i t y o f t h e d i f f e r e n c e s b e tw e e n s c o r e s
on an a c h ie v e m e n t t e s t i n m u l t i p l i c a t i o n . .
31
C om p ariso n o f number o f p ro b le m s a t t e m p t e d on
an a c h ie v e m e n t t e s t i n m u l t i p l i c a t i o n
. . .
33
C o m p a ra tiv e s c o r e s on an a c h ie v e m e n t t e s t i n
sh o rt d iv is io n
35
R e l i a b i l i t y o f t h e d i f f e r e n c e s b e tw e e n s c o r e s
on an a c h ie v e m e n t t e s t i n s h o r t d i v i s i o n . .
36
V
p ag e
Tm m
X II.
C om p arison o f num ber o f p ro b le m s a t t e m p t e d
on an a c h ie v e m e n t t e s t i n s h o r t d i v i s i o n . .
X III.
C o m p a ra tiv e s c o r e s on an a c h ie v e m e n t t e s t i n
lo n g d i v i s i o n
XIY.
........................
. . . . . . . .
. .
43
C o m p a ra tiv e s c o r e s on an a c h ie v e m e n t t e s t i n
a rith m e tic rea so n in g . . • • • • • • • • • •
X Y II.
41
C om p arison o f number o f p ro b le m s a t t e m p t e d on
an a c h ie v e m e n t t e s t i n lo n g d i v i s i o n . . . .
XVI.
40
R e l i a b i l i t y o f t h e d i f f e r e n c e s b e tw e e n s c o r e s
on an a c h ie v e m e n t t e s t i n lo n g d i v i s i o n
XY*
38
46
R e l i a b i l i t y o f t h e d i f f e r e n c e s b e tw e e n s c o r e s
on an a c h ie v e m e n t t e s t i n a r i t h m e t i c r e a s o n ­
in g
X Y II I.
..........................................................................................
C o m p a ra tiv e s c o r e s on a s t a n d a r d i z e d a c h i e v e ­
ment t e s t i n a r i t h m e t i c
XIX.
47
c o m p u ta t io n
. . . .
49
R e l i a b i l i t y o f t h e d i f f e r e n c e s b e tw e e n s c o r e s
on a s t a n d a r d i z e d a c h ie v e m e n t t e s t i n a r i t h ­
.................................
m e t i c c o m p u ta tio n
XX.
C o m p a ra tiv e s c o r e s on a s t a n d a r d i z e d a c h i e v e ­
ment t e s t i n a r i t h m e t i c
XXI.
60
re a so n in g
. . . . .
52
R e l i a b i l i t y o f t h e d i f f e r e n c e s b e tw e e n s c o r e s
on a s t a n d a r d i z e d a c h ie v e m e n t t e s t i n a r i t h ­
m e tic re a s o n in g
. . . . . . .
.............................
53
vi
page
TAQJjE
X X II•
C o m p a ra tiv e s c o r e s on a m id te rm t e s t i n
"bu siness a r i t h m e t i c . .
X X III•
......................................
R e l i a b i l i t y o f t h e d i f f e r e n c e s "between s c o r e s
on a m id term t e s t i n b u s i n e s s
XXIY*
XXYI.
............................
57
60
61
R e l i a b i l i t y o f t h e d i f f e r e n c e s b e tw e e n s c o r e s
te s ts
.
63
R e l i a b i l i t y o f t h e d i f f e r e n c e s b e tw e e n s c o r e s
o f s e n i o r s and sophom ores on a l l t e s t s
X X VIII.
.
R e l i a b i l i t y o f t h e d i f f e r e n c e s b e tw e e n I . Q’ s .
o f s e n i o r s and j u n i o r s on a l l
XXYII,
a rith m e tic
C om parison o f c l a s s e s a c c o r d i n g t o i n t e l l i ­
gence q u o tie n t
XXY.
56
. .
65
R e l i a b i l i t y o f t h e d i f f e r e n c e s b e tw e e n s c o r e s
o f j u n i o r s and sophom ores on a l l t e s t s
. .
66
LIST OF FIGURES
FIGURE
1.
BAGS
C om p arison o f mean s c o r e s on an a c h ie v e m e n t
te s t
2.
t e s t i n s im p le a d d i t i o n .....................................
.............................
.
...........................................
42
C om parison o f p ro b le m s a t t e m p t e d on an a c h i e v e ­
ment t e s t i n lo n g d i v i s i o n ...........................................
11.
39
C om parison o f mean s c o r e s on an a c h ie v e m e n t
t e s t i n lo n g d i v i s i o n .........................................................
10,
37
C om parison o f p ro b le m s a t t e m p t e d on an a c h i e v e ­
ment t e s t i n s h o r t d i v i s i o n ...........................................
9.
34
C om p ariso n o f mean s c o r e s on an a c h ie v e m e n t
t e s t in sh o rt d iv is io n
8.
32
C o m p arison o f p ro b le m s a t t e m p t e d on an a c h i e v e ­
ment t e s t i n m u l t i p l i c a t i o n ...........................................
7.
29
C om parison o f mean s c o r e s on an a c h ie v e m e n t
t e s t i n m u l t i p l i c a t i o n ‘ ....................................................
6.
.2 7
C om p arison o f p ro b le m s a t t e m p t e d on an a c h i e v e ­
m ent t e s t i n s u b t r a c t i o n
5.
25
C om parison o f mean s c o r e s on an a c h ie v e m e n t
t e s t i n s u b t r a c t i o n ..............................................................
4.
SI
C om p ariso n o f p ro b le m s a t t e m p t e d on an a c h i e v e ­
ment
3.
i n s im p le a d d i t i o n . . . . . . . . . . . .
-44
C om p arison o f mean s c o r e s on an a c h ie v e m e n t
t e s t in a r ith m e tic re a so n in g
• • • • • • • • •
48
viii
PIGUR33
IE .
PAGB
O om parison o f mean s c o r e s on a s t a n d a r d i z e d
a c h ie v e m e n t t e s t i n a r i t h m e t i c c o m p u ta tio n
13.
51
. . .
54
C om parison o f mean s c o r e s on a m id term t e s t
in b u sin e ss a r ith m e tic
15.
.
O om parison of. mean s c o r e s - o n a s t a n d a r d i z e d
a c h ie v e m e n t t e s t i n a r i t h m e t i c r e a s o n i n g
14.
.
..........................
C o m parison o f means o f i n t e l l i g e n c e q u o t i e n t s
•
58
.
6E
CHAPTER I
THE PROBLEM
The g e n e r a l o b j e c t i v e o f t h i s s t u d y i s t o i n v e s t i ­
g a t e t h e r e l a t i v e p r o g r e s s made by so p h o m o re s, j u n i o r s , and
s e n i o r s i n b u s i n e s s a r i t h m e t i c and t o d e t e r m i n e , i f p o s s i ­
b l e , t h e a b i l i t y o f t h e t h r e e c l a s s e s t o w ork t o g e t h e r a s a
u n if o r m g r o u p .
In o rd e r t h a t a v a l i d e v a lu a tio n o f th e
g e n e r a l p ro b le m m ig h t be made t h e c o n s i d e r a t i o n o f s e v e r a l
s p e c i f i c f a c t o r s seem t o be i n d i c a t e d *
Are t h e g r o u p s p r e p a r e d t o w ork t o g e t h e r ?
S tu d e n ts
e n t e r i n g t h e h i g h s c h o o l i n m ost c a s e s h ave had r e c e n t
t r a i n i n g i n t h e s im p le f u n d a m e n ta ls o f a r i t h m e t i c .
They
a c h ie v e a s k i l l w h ich e n a b l e s them t o com pete f a v o r a b l y
w i t h t h e u p p e r c l a s s e s and t h e r e i s no p ro b le m o f j u n i o r s
and s e n i o r s h a v in g an a d v a n ta g e o f m a t u r i t y o r e x p e r i e n c e .
H ow ever, up on t r a n s i t i o n from sim p le f u n d a m e n ta ls t o t h e
p r a c t i c a l a p p l i c a t i o n o f t h o s e f u n d a m e n ta ls i n p ro b le m
s o l v i n g d i f f i c u l t i e s i n co m p re h e n sio n become a p p a r e n t .
It
i s b e l i e v e d t h a t t h e s e d i f f i c u l t i e s , on t h e p a r t o f t h e
lo w e r c l a s s e s , a r e e n h a n c e d by l a c k o f e x p e r i e n c e .
Some o f t h e g e n e r a l l y a c c e p t e d r e a s o n s f o r t h e i n a ­
b ility
o f s t u d e n t s t o g r a s p r e a s o n i n g p ro b le m s a r e :
a.
L ack o f v o c a b u l a r y .
2
b,
F a ilu r e to see a l l th e e le m e n ts ,
o.
I n a b i l i t y t o r e a d b e tw e e n t h e l i n e s ,
d.
F a ilu r e to i n t e r p r e t cues c o r r e c t l y ,
ev
F a i l u r e t o u n d e r s t a n d f u n d a m e n ta l r e l a t i o n s ,
p a r t i c u l a r l y t h o s e o f t h e i n v e r s e .ty p e .
I t i s r e a s o n a b l e t o assume t h a t t h e s t u d e n t makes
p r o g r e s s a s he a d v a n c e s from one g r a d e t o a n o t h e r ,
T hrou gh
e x p e r i e n c e and t r a i n i n g h i s v o c a b u l a r y s h o u ld become more
e f f e c t i v e , he s h o u ld be a b l e t o s e e r e l a t i o n s h i p s more
c l e a r l y , and he s h o u ld be more a n a l y t i c a l and d i s c e r n i n g i n
h i s c o n s i d e r a t i o n and i n t e r p r e t a t i o n o f r e a s o n i n g p r o b le m s .
I f n o rm a l p r o g r e s s i s made t h e n , i n g e n e r a l , s t u d e n t s s h o u ld
do b e t t e r w ork i n p ro b lem s o l v i n g i n e a c h s u c c e e d i n g g r a d e .
H owever, we have no d e f i n i t e a s s u r a n c e t h a t s u c h i s a c t u a l l y
th e c a s e .
One o f th e o b j e c t i v e s o f t h i s s t u d y w i l l be t o
d e t e r m in e how much c r e d e n c e may be p l a c e d i n t h e a s s u m p tio n
t h a t t h e g r o u p s a r e u n f i t t e d t o w ork t o g e t h e r .
Are s t u d e n t s i n t h e lo w e r c l a s s e s o vershad ow ed b y
advanced s t u d e n t s ?
T h ere i s some j u s t i f i c a t i o n f o r th e
b e l i e f t h a t sophomore and j u n i o r s t u d e n t s do n o t work up t o
t h e i r c a p a c i t y i n a m ixed c l a s s o f s o p h o m o re s , j u n i o r s , and
se n io rs .
The lo w e r c l a s s e s m ig h t w e l l be f r u s t r a t e d and
d e f e a t e d from t h e v e r y b e g i n n i n g , b e c a u s e o f r e a l o r
i m a g in a r y d i f f e r e n c e s , u n l e s s p r e c a u t i o n a r y m e a s u re s a r e
ta k e n a t th e o u t s e t .
The sophom ores a r e "burdened w i t h t h e
p ro b le m o f o r i e n t i n g th e m s e l v e s i n t h e i r new s u r r o u n d i n g s .
T h is p ro b lem i n i t s e l f i s eno ug h t o d i s r u p t n o rm a l p r o g r e s s
i n some o a s e s .
Then i t seems t h a t we a r e o n l y a d d in g f u e l
to th e f i r e i f
we b u r d e n them f u r t h e r w i t h t h e h a n d i c a p o f
c o m p etin g w i t h more m a tu re s t u d e n t s .
T h is p ro b le m a lo n e
seems to be ample j u s t i f i c a t i o n f o r t h e a d m i n i s t r a t i v e
r e g u l a t i o n , b a s e d on t r a d i t i o n , e x p e d ie n c y , and good common
s e n s e , t h a t p u p i l s s h o u ld advance, i n r a t h e r a r e g u l a r
fa s h io n th ro u g h th e g ra d e s .
W i l l t e a c h i n g aim s and o b j e c t i v e s f i l l t h e n e e d s o f
a l l th re e groups?
P re s u m a b ly we t e a c h c h i l d r e n t o p r e p a r e
them t o do b e t t e r t h e t h i n g s t h a t t h e y do i n * l i f e .
S tu d e n ts
t a k i n g b u s i n e s s a r i t h m e t i c , i n m ost c a s e s , a r e t a k i n g t e r ­
m in a l w ork p r e p a r a t o r y t o m aking a l i v i n g and i t i s incum ­
b e n t upon t e a c h e r s t o p r o v i d e
is fu n c tio n a l,
liv in g .
t h e ty p e o f i n s t r u c t i o n t h a t
t h a t w i l l m eet t h e i r n e e d s i n e v e r y d a y
I n o r d e r to p r o v i d e t h i s ty p e o f i n s t r u c t i o n , i t i s
n e c e ss a ry to c o n s id e r th e stu d e n t* s e x p e rie n c e .
We c a n n o t
hope f o r t h e a c c o m p lish m e n t o f o b j e c t i v e s i f we em ploy
te a c h in g m a t e r i a l s t h a t a re n o t w ith in th e range o f e x p e r i ­
en c e o f t h e s t u d e n t .
The sophomore s t u d e n t m ust lo o k f o r w a r d t o two more
y e a rs o f h ig h sc h o o l.
He i s n o t y e t s e r i o u s l y c o n c e r n e d
w i t h t h e p ro b le m o f making a l i v i n g .
H is im m e d ia te o b j e c ­
t i v e s a r e more ac ad e m ic i n n a t u r e and M s m ost d i r e c t
i n t e r e s t i s t h a t o f c o m p le tin g t h e h u r d l e s n e c e s s a r y f o r
p r o m o tio n t o t h e n e x t g r a d e l e v e l .
'T he j u n i o r i s em erg in g from t h e more j u v e n i l e c o n ­
c e p t s o f t h e so p h o m o re.
He s t i l l h a s a n o t h e r y e a r o f h i g h
s c h o o l , b u t h i s g r a d u a t i o n i s n o t q u i t e so r e m o te as i t was
th e p re v io u s y e a r.
He i s b e g i n n i n g t o be c o n c e r n e d a b o u t
m aking money and a c q u i r i n g t h e t o o l s o f l e a r n i n g t h a t w i l l
a s s i s t him i n t h e m aking o f money.
The s e n i o r may lo o k f o rw a r d t o c o m p le t io n o f com­
p u l s o r y f o rm a l e d u c a t i o n w i t h t h e c u r r e n t y e a r .
E d u c a tio n a l
v a l u e s t o him h av e ch an g ed c o n s i d e r a b l y b e c a u s e o f t h e
n earn ess o f h is g ra d u a tio n .
G e t t i n g a jo b i s o f p aram o u n t
im p o r ta n c e and th e v a l u e o f h i s s t u d i e s i s i n d i r e c t p r o p o r ­
t i o n t o t h e e x t e n t t h e y w i l l h e l p him i n g e t t i n g o r k e e p in g
a jo b .
The aim o f m odern e d u c a t i o n a l p r a c t i c e i s t o g i v e
e a c h s t u d e n t t h e o p p o r t u n i t y to ad v an ce i n a c c o r d a n c e w i t h
h i s o r h e r c a p a c i t y t o do s o .
D u rin g t h e t h r e e y e a r s o f
s e n i o r h i g h s c h o o l s t u d e n t s m a tu re r a p i d l y and w i t h e a c h
su c c e e d in g y e a r th e r e i s a g r e a t e r rang e o f p o s s i b i l i t y
f o r t h e s t u d e n t t o do academ ic w o rk .
in a b i liti e s
T h is i n c r e a s e d r a n g e
o f a m ixed g ro u p o f so p h o m o re s, j u n i o r s , and
s e n i o r s i n t r o d u c e s a c ad e m ic and s o c i a l p ro b le m s w hich
demand a d j u s t m e n t .
I t seems u n l i k e l y t h a t any one s e t o f o b j e c t i v e s w i l l
m eet t h e n e e d s o f t h e s e t h r e e d i v e r s e g r o u p s .
Do t h e lo w e r c l a s s e s r e t a r d t h e g ro u p a s a w h o le ?
The t r a d i t i o n a l g r a d e c o n c e p t i s p r e d i c a t e d upon t h e assu m p ­
t i o n t h a t t h e s t u d e n t w i l l make n o rm a l p r o g r e s s w i t h e a c h
su c c e e d in g y e a r.
A c c o r d in g l y t h e w ork i n c r e a s e s i n d i f f i ­
c u l t y a s t h e s t u d e n t p a s s e s from one g r a d e t o a n o t h e r .
The
more p r o g r e s s a s t u d e n t makes a t e a c h g r a d e l e v e l t h e b e t t e r
he s h o u ld be e q u ip p e d w i t h t h e t o o l s o f l e a r n i n g and t h e
b e t t e r he s h o u ld be f i t t e d f o r e a c h s u c c e e d i n g g r a d e .
If,
b e c a u s e o f t h e w ide r a n g e o f a b i l i t i e s o f a g ro u p o f m ixed
c l a s s e s , i t i s n e c e s s a r y t o p r o g r e s s more s l o w l y t h e n t h e
b e t t e r s t u d e n t i s w o rk in g u n d e r a d i s t i n c t h a n d i c a p .
He
h a s no i n c e n t i v e o r m o t i v a t i o n t o work up t o h i s c a p a c i t y *
I t seems r e a s o n a b l e t o b e l i e v e t h a t t h e lo w e r g r a d e s ,
b e c a u s e o f l a c k o f e x p e r i e n c e and s k i l l i n c a l c u l a t i o n ,
m ig h t r e t a r d t h e g r o u p a s a w h o le .
H ow ever, i t i s e n t i r e l y
p o s s i b l e t h a t t h e w ide d i f f e r e n c e b etw e en t h e b e s t and t h e
p o o r e s t s tu d e n ts i n each g ra d e w i l l be g r e a t e r th a n th e
mean d i f f e r e n c e b e tw e e n t h e t h r e e c l a s s e s .
The f o r e g o i n g q u e s t i o n s seem t o h ave a d e f i n i t e
b e a r i n g on t h e e x p e d ie n c y o f t e a c h i n g b u s i n e s s a r i t h m e t i c
t o so p h m o re s , j u n i o r s , and s e n i o r s a l i k e i n a m ixed g r o u p .
A lth o u g h su c h g r o u p i n g may o f t e n s e r v e an a d m i n i s t r a t i v e end
i t may w e l l he t h a t s u c h a p o l i c y w i l l d e f e a t i t s own
p u rp o s e #
f h e f o l l o w i n g c h a p t e r s a r e d e s ig n e d t o p r e s e n t
ev id en ce s u p p o rtin g th e b e l i e f t h a t c l a s s , o r sc h o o l g ra d e ,
se g re g a tio n i s d e s ir a h le •
CHAPTER I I
PROCEDURE
T h is i n v e s t i g a t i o n was c a r r i e d on i n two b u s i n e s s
a r i t h m e t i c c l a s s e s i n t h e S a n t a Ana S e n i o r H ig h S c h o o l t h e
f i r s t s e m e s t e r o f 1941-1942*
B o th c l a s s e s w ere composed
o f m ixed g r o u p s r e p r e s e n t i n g a l l t h r e e g r a d e l e v e l s i n t h e
s e n io r h ig h s c h o o l.
The p l a n o f d e v e lo p m e n t o f t h i s
c h a p t e r i s t w o f o ld and w i l l c o m p ris e c o n s i d e r a t i o n o f t h e
t e s t i n g p ro g ra m and s t a t i s t i c a l t e c h n i q u e s u s e d i n t h e
h a n d lin g o f t e s t s c o re s .
The t e s t i n g p r o g r a m .
At t h e b e g i n n i n g o f t h e sem­
e s t e r a s e r i e s o f t e s t s on s im p le a d d i t i o n , s u b t r a c t i o n ,
m u l t i p l i c a t i o n , s h o r t d i v i s i o n , and lo n g d i v i s i o n was g i v e n
t o t h e two c l a s s e s a t t h r e e - d a y i n t e r v a l s .
The s t u d e n t s
w ere i n s t r u c t e d i n e a c h i n s t a n c e t o w ork as a c c u r a t e l y and
a s r a p i d l y as p o s s i b l e .
However t h e im p o r ta n c e o f a c c u r a c y
was s t r e s s e d a s t h e p r e d o m in a n t f a c t o r .
Mo e x p l a n a t i o n was
o f f e r e d t h e s t u d e n t s as t o t h e r e a s o n f o r g i v i n g t h e t e s t s ,
t h e i m p l i c a t i o n b e i n g t h a t t h e y w ould be g r a d e d on t h e
b a s i s o f t h e i r a c h ie v e m e n t .
I t was b e l i e v e d t h a t u n d e r
s u c h c i r c u m s t a n c e s t h e y w ould w ork w i t h more s e r i o u s n e s s o f
purpo se.
The t e s t p ro b le m s w ere s e l e c t e d a t random from
B u s i n e s s A r i t h m e t i c , by G u rry and R i c e , t h i r d e d i t i o n , and
8
o n l y s u f f i c i e n t tim e was a llo w e d f o r a r e p r e s e n t a t i v e
s a m p lin g o f e a c h g r o u p .
f h e t e s t s v a r i e d i n l e n g t h from
te n to f i f t e e n m in u te s.
An a c c u r a t e r e c o r d was made o f t h e
num ber o f p ro b le m s a t t e m p t e d as w e l l as a c t u a l s c o r e s made
on t h e s e t e s t s i n
o r d e r t o d e t e r m in e t h e d i f f e r e n c e , i f
a n y , b e tw e e n t h e g r o u p s i n
c a lc u la tio n .
a c c u r a c y a s w e l l as s p e e d i n
In o rd e r to f a c i l i t a t e th e s e g re g a tio n o f
t e s t p a p e r s an d t h e r e c o r d i n g o f r e s u l t s a d i f f e r e n t c o l o r
o f p a p e r was u s e d
fh e s e r i e s
fo r each g rade l e v e l ,
o f t e s t s i n f u n d a m e n ta ls was
f o llo w e d by
a te a c h e r - m a d e a c h ie v e m e n t t e s t i n a r i t h m e t i c r e a s o n i n g .
I t was composed o f t e n p ro b le m s w h ic h i n c r e a s e d p r o g r e s ­
s iv e ly in d if f ic u lty ,
f h e f o l l o w i n g a r e sam ple p ro b le m s
t a k e n from t h e r e a s o n i n g t e s t .
1.
S a l e s i n t h e s t u d e n t c a f e t e r i a f o r t h e week o f O c to b e r
1 4 t h w ere a s f o l l o w s :
W ednesday # 7 9 .2 5 ;
Monday $ 7 5 .4 6 ;
f h u r s d a y # 7 3 .9 2 ;
f u e s d a y $ 7 7 .3 1 ;
F rid a y $ 7 2 ,3 0 .
What w ere t h e a v e r a g e s a l e s f o r t h e f i v e d a y s ?
2.
A t r u c k l o a d e d ? / i t h g r a i n w eig h e d 1 3 ,9 8 5 p o u n d s ,
t r u c k w eig h e d 4 ,8 7 5 pounds when i t was em p ty .
fh e
At 60
p ounds t o t h e b u s h e l , how many b u s h e l s o f g r a i n d i d i t
c o n ta in ?
3.
A s t u d e n t p u r c h a s e d a s e c o n d h and a u to m o b ile on w h ich
t h e s p e e d o m e te r r e a d 7 ,5 9 1 m i l e s .
At t h e tim e o f t h e
9
p u r c h a s e t h e c a r was e q u i p e d w i t h f o u r new t i r e s w o r t h
$50.
When t h e t i r e s w ere r e p l a c e d w i t h new ones t h e
s p e e d o m e te r r e a d i n g was 2 2 ,7 4 5 m i l e s .
What was t h e t i r e
c o s t f o r e a c h h u n d re d m i l e s ?
4*
J . B. Brown r e p o r t e d t h e f o l l o w i n g f a c t s r e g a r d i n g an
a u to m o b ile t r i p :
t o t a l m i l e s on t h e s p e e d o m e te r a t t h e
b e g i n n i n g o f t h e t r i p , 2 2 ,1 2 3 ; m i l e s on t h e s p e e d o m e te r
a t t h e en d o f t h e t r i p , 5 2 ,5 0 9 ; num ber o f g a l l o n s o f
g a s o lin e i n th e ta n k a t th e b e g in n in g o f th e t r i p , 18;
num ber o f g a l l o n s o f g a s o l i n e p u r c h a s e d , 59 7; number o f
g a llo n s o f g a s o lin e i n th e ta n k a t th e c o n c lu sio n o f
th e t r i p , 11.
fin d :
( a ) t h e t o t a l number o f m i l e s
t r a v e l e d , i b ) t h e number o f g a l l o n s o f g a s o l i n e u s e d ,
and ( c ) t h e a v e ra g e num ber o f m i l e s p e r g a l l o n *
5.
C h a r l e s May h a s a l o t 250 f e e t l o n g and 140 f e e t w id e .
W illia m J e n n i n g s c o n t r a c t e d t o d i g a d i t c h 2 f e e t w ide
and 3 f e e t deep a ro u n d t h e l o t , t h e o u t e r edge o f t h e
d i t c h b e in g 1 fo o t in s i d e th e d i v i s i o n l i n e o f th e l o t .
f h e c o n t r a c t p r i c e i s z i t f a c u b ic f o o t .
How much w i l l
Mr. J e n n i n g s r e c e i v e f o r h i s w ork?
f h e tim e l i m i t f o r t h i s t e s t was d e t e r m in e d by t h e
l e n g t h o f tim e t h a t i t t o o k f o r t h e f i r s t s t u d e n t t o
c o m p le te a l l p r o b le m s .
As a f u r t h e r c h e c k on th e a c h ie v e m e n t o f t h e t h r e e
10
g r o u p s a S t a n f o r d A ch iev em en t T e s t , form D, u n i t s 4 and 5 ,
was 'g i v e n , t h e week f o l l o w i n g t h e te a c h e r - m a d e a c h ie v e m e n t
t e s t and r a t i n g s w ere c a l c u l a t e d b y means o f t h e e d u c a t i o n a l
p r o f i l e c h a r t acco m pan yin g t h e t e s t .
T h is s t a n d a r d i z e d t e s t
was s e l e c t e d b e c a u s e o f t h e h i g h r e l i a b i l i t y c o e f f i c i e n t s o f
e a c h u n i t and b e c a u s e t h e c o n s t r u c t i o n o f t h e . u n i t s seem ed
i d e a l f o r t h e ty p e o f m e asu rem e n t i n d i c a t e d #
In b o th u n i t s ,
c o m p u ta tio n and r e a s o n i n g , t h e i n i t i a l p ro b le m s a r e v e r y
sim p le , b u t th e y in c re a s e p r o g r e s s iv e ly i n d i f f i c u l t y th u s
a l l o w i n g f o r f u l l e x p r e s s i o n o f th e s t u d e n t s a c h ie v e m e n t .
The n a t u r e o f t h e e x p e r i m e n t i n d i c a t e d t h e d e s i r a ­
b i l i t y o f o b t a i n i n g i n t e l l i g e n c e q u o t i e n t s o f t h e two
c l a s s e s so t h a t t h e r e p r e s e n t a t i v e n e s s o f t h e t h r e e g r o u p s
m ig h t be d e t e r m i n e d .
The S a n t a Ana S e n i o r H igh S c h o o l g i v e s
e a c h in c o m in g sophmore t h e C a l i f o r n i a T e s t o f M e n ta l
M a t u r i t y and th e g r a d e o r r a t i n g made by e a c h s t u d e n t i s
made a p a r t o f h i s p e rm a n e n t r e c o r d .
T h is b e i n g t h e c a s e
i t was p o s s i b l e t o o b t a i n t h e i n t e l l i g e n c e q u o t i e n t o f e a c h
s t u d e n t by r e c o u r s e t o s c h o o l r e c o r d s .
The d a t a t a k e n from
th e s e re c o rd s are in a c c u r a te to th e e x te n t t h a t fiv e
s tu d e n ts t r a n s f e r r e d to o th e r sc h o o ls b e fo re th e re c o rd s
w ere s e a r c h e d and o f c o u r s e t h e i r p e rm a n e n t r e c o r d c a r d s
w ere n o t t h e n a v a i l a b l e .
I’o u r o t h e r s t u d e n t s t r a n s f e r r e d
t o S a n t a Ana from o t h e r d i s t r i c t s and t h e i r r e c o r d s a l s o
w ere n o t a v a i l a b l e .
In s p i t e o f th e ap p aren t la rg e
11
p e r c e n t a g e o f s c o r e s l a c k i n g t h e number o b t a i n e d i n e a c h
g ro u p was a b o u t a s r e p r e s e n t a t i v e o f t h e g ro u p a s were t h e
r e s u l t s o b t a i n e d on p r e v i o u s t e s t s b e c a u s e o f t h e number
o f s tu d e n ts a b sen t in each c a se .
As a c o n c l u s i o n t o t h e t e s t i n g program t h e r e s u l t s
o f a te a c h e r - m a d e a c h ie v e m e n t t e s t w h ich was u s e d as a
m id te rm e x a m i n a t i o n was t a b u l a t e d as an i n d i c a t i o n o f
s t u d e n t p r o g r e s s d u r i n g t h e n i n e w eeks o f t h e f i r s t q u a r t e r
o f th e sc h o o l y e a r .
T h is t e s t was composed o f s i x p r o b le m s ,
f o u r o f w hich w ere s im p le a r i t h m e t i c f u n d a m e n ta ls i n v o l v i n g
c a l c u l a t i o n o n l y , an d two s im p le r e a s o n i n g p r o b le m s .
The
f o l l o w i n g i s a copy o f th e t e s t i n i t s e n t i r e t y .
1 s t Q u a r t e r E x a m in a tio n
B u s in e s s A r i t h m e t i c
1.
F in d t h e sum s.
a)
c)
2.
52196
45574
80539 t )
61428
27854
Check by a d d in g i n r e v e r s e .
l / l 3 + 3 / l l + 9 /2 2 + 5 / 6 :
84 3 / 7 + 579 2 / 3 + 63 5 /9 + 123 1 3 /2 1 + 347 2 3 /2 7 =
S u b tra c t.
a)
24639
15974
t)
57346 .
28457
o)
1 3 /l6 - l l / 2 4 =
a)
1 5 /2 7 - 1 7 /3 8 =
12
3.
M u ltip ly ,
a)
364 x 527 r
c)
B)
4.
5.
7 /9 x 2 7 /2 8 =
16 3 / 8 x 36. 2 / 3 =
D iv id e .
a)
43662 * 264 =
B)
3 /2 2 * 3 / l l =
e)
7962 7 /8 * 4 =
d)
176 3 / 5 + 7 1 /2 =
1/4 o f H en ry Brow n’s p r o p e r t y i s
B o n d s.
i n l a n d and l / 3 i s i n
T h e r e m a in d e r ( $ 1 5 6 0 .9 5 ) i s
cash.
'What i s t h e
v alu e o f h is e s t a t e ?
6.
How much coke w i l l t h r e e f i r e s B urn i n 27 d a y s , a l l o w ­
in g 7 l / 2
h o u r s p e r d a y and 8 l / 4 p o un ds o f coke p e r
hour f o r each f ir e ?
E ac h s t u d e n t s t a r t e d t h e e x a m i n a t i o n a t t h e same
tim e and was a llo w e d f i f t y m in u t e s t o c o m p le te t h e t e s t .
S t a t i s t i c a l te c h n iq u e s u s e d ,
f h e t e s t i n g p ro gram
s u p p l i e d a m ass o f s c o r e s w h ich s e r v e d as t h e raw m a t e r i a l
f o r t h e d e v e lo p m e n t o f v a r i o u s s t a t i s t i c a l d a t a ,
fh ese
d a t a w ere d e s i g n e d t o r e v e a l r e l a t i o n s h i p s and i n d i c a t e
t r e n d s u po n w h ic h a v a l i d c o m p a ris o n o f t h e t h r e e g r o u p s
13
m ig h t be mad©.
P r o c e d u r e s w ere a l s o d e v i s e d t o i n d i c a t e
t h e p r o b a b i l i t y and e x t e n t o f e r r o r i n t h e r e s u l t s o b t a i n e d .
E a c h g ro u p o f t e s t s c o r e s was t a b u l a t e d i n t o a
f r e q u e n c y d i s t r i b u t i o n w i t h th e c l a s s i n t e r v a l s v a r y i n g i n
e a c h c a s e a c c o r d i n g t o t h e ra n g e o f s c o r e s #
Prom t h e s e
r e c o r d s , w i t h t h e u s e o f m a t h e m a t i c a l f o r m u l a s , t h e m ean,
t h e s t a n d a r d d e v i a t i o n , and th e s t a n d a r d e r r o r w ere f o u n d .
B e f o r e a v a l i d a p p r a i s a l o f a g ro u p may be made i t
i s n e c e s s a ry to d is c o v e r th e g e n e ra l tr e n d , or c e n tr a l
te n d en cy o f t h a t g ro u p .
th a t purpose.
The mean s c o r e s w ere u s e d t o s e r v e
B u t , as t h e mean i n i t s e l f i s s u b j e c t t o
e r r o r and a s t h e r e m ust n e c e s s a r i l y be c o n s i d e r a b l e v a r i a ­
b i l i t y i n t h e s c o r e s o f e a c h g ro u p we c o u ld a t b e s t make
o n ly v ag u e g e n e r a l i z a t i o n s from e a c h o f t h e mean s c o r e s .
Such v ag u e g e n e r a l i z a t i o n s w ere n o t s u f f i c i e n t e v i d e n c e f o r
t h e d e v e lo p m e n t o f any d e f i n i t e c o n c l u s i o n s w it h o u t d e t e r ­
m in in g t h e r e l i a b i l i t y o f t h e m e a s u re m e n t.
I n o t h e r w ords
i t was n e c e s s a r y t o d e t e r m in e t o w hat e x t e n t t h e means
c o u ld be a c c e p t e d as b e i n g t r u l y r e p r e s e n t a t i v e o f t h e
d iffe re n t c lasse s.
The s t a n d a r d d e v i a t i o n i n e a c h i n s t a n c e i n d i c a t e d
t h e s p r e a d o r v a r i a b i l i t y i n s c o r e s by m e a s u r in g t h e m id d le
tw o - th ir d s o f th e s c o re s .
T h is d e v i c e h e l p s i n d e t e r m i n i n g
how much c r e d e n c e may be p l a c e d i n t h e mean s c o r e s .
The s t a n d a r d e r r o r i s e s s e n t i a l l y t h e same
14
n u m e ric a lly as sta n d a rd d e v ia tio n b u t g iv e s a d i f f e r e n t
in te rp re ta tio n .
W hereas s t a n d a r d d e v i a t i o n s t a n d s f o r f a c t ,
i n d i c a t i n g th e a c tu a l sp re a d o f s c o r e s , th e s ta n d a rd e r r o r
i s p r e d i c t i v e a n d a l lo w s f o r a g e n e r a l i z a t i o n , o f o b s e rv e d
sco res.
f h e t o t a l number o f s t u d e n t s i n t h e t h r e e c l a s s e s was
n i n e t y - o n e , w i t h f i f t y - e i g h t so p h o m o re s, tw e lv e j u n i o r s , and
tw e n ty - o n e s e n i o r s ,
f h e s e num bers v a r i e d s l i g h t l y on th e
d i f f e r e n t t e s t s b e c a u s e o f a b s e n c e s and p ro g ra m c h a n g e s made
by s t u d e n t s a f t e r th e b e g i n n i n g o f t h e e x p e r i m e n t .
I t w ill
be n o t e d t h a t t h e j u n i o r and s e n i o r g ro u p s a r e n o t g r e a t
en ou gh n u m e r i c a l l y t o p r e s e n t s u f f i c i e n t c a s e s t o be r e p r e ­
s e n t a t i v e o f t h e g ro u p a s a w hole*
I n o r d e r to make p r o p e r
a l lo w a n c e s f o r t h e s m a l l number o f c a s e s i n some o f th e
c o m p u t a t i o n s , t h e f o l l o w i n g c o r r e c t i o n f o r m u la s w ere u s e d .
When H - 2 0 -2 9 (
=
/S" - T
When 1$ = 1 0 -19 k =
M
/IT - 2
When I : 9 o r l e s s
= *.
<r
■- M /r - sr
W ith t h e f o r e g o i n g d a t a i t was p o s s i b l e t o n o t e t h e
o b s e r v e d d i f f e r e n c e i n t h e means o f th e t h r e e c l a s s e s and
t o d e t e r m in e t h e l i m i t s w i t h i n w h ich two t h i r d s ( 6 8 , 2 6 p e r
15
c e n t) o f th e sc o re s a c tu a l ly f e l l , i n each c a se , o r to p r e ­
d i c t - w i t h i n w hat l i m i t s t w o - t h i r d s o f a l l m eans so fo u nd
w ould f a l l *
H ow ever, i t was d e s i r e d t o go a s t e p f u r t h e r
i n t h e c o m p a ris o n o f t h e t h r e e g r o u p s an d t o d e t e r m in e t h e
r e l i a b i l i t y o f t h e d i f f e r e n c e b e tw e e n t h e mean s c o r e s o f
s e n i o r s and j u n i o r s , s e n i o r s and s o p h o m o re s , and j u n i o r s
and sophom ores*
T h is was a c c o m p lis h e d b y d e t e r m i n i n g t h e
s t a n d a r d e r r o r a t t h e d i f f e r e n c e i n t h e mean s c o r e s f r o
w h ich t h e f o l l o w i n g f o r m u la was u s e d .
A f te r f in d in g th e s ta n d a rd e r r o r o f th e d i f f e r e n c e i t
was t h e n p o s s i b l e t o s t a t e t h a t t h e c h a n c e s w ere two t o one
t h a t t h e t r u e d i f f e r e n c e i n e a c h c a s e w ould l i e w i t h i n
c e rta in d e fin ite lim its .
A l l o f t h i s s t i l l l e f t a d e g r e e o f u n c e r t a i n t y and
i t was d e s i r a b l e t o know w hat t h e c h a n c e s w ere t h a t t h e
c l a s s w i t h t h e b e s t s c o r e w ould alw a y s have a d i f f e r e n c e i n
its
fav or.
T h is i n f o r m a t i o n was o b t a i n e d by f i r s t f i n d i n g
t h e r a t i o b e tw e e n t h e d i f f e r e n c e and i t s s t a n d a r d e r r o r f o r
w h ic h t h e f o r m u la i s :
RATIO = D / ^
The r a t i o i n d i c a t e s how many
( e r r o r o f th e
16
d i f f e r e n c e ) u n i t s t h e o b s e r v e d d i f f e r e n c e i s above z e ro *
A f t e r f i n d i n g t h e r a t i o r e c o u r s e was made t o S t a t i s t i c s f o r
T e a c h e r s , b y T ie g s and C raw ford*
The d e s i r e d d a t a was
o b t a i n e d from f a b l e XIX, p ag e 1 3 7 , e n t i t l e d C hances t h a t
m e a s u r e s w ill* n o t f a l l b e lo w v a r i o u s s t a n d a r d e r r o r u n i t
v a lu e s*
A ll o f th e d a t a o b ta in e d by th e a p p l i c a t i o n o f th e
f o r e g o i n g s t a t i s t i c a l t e c h n i q u e w ere r e c o r d e d i n t a b u l a r
form and form s t h e b a s i s f o r t h e a n a l y s i s o f r e s u l t s
o u t l i n e d i n C h a p te r I I I *
CHAPTER I I I
ANALYSIS OF EXPERIMENTAL RESULTS
I n o r d e r - t o d e t e r m in e t h e a b i l i t y o f so p h o m o re s ,
J u n i o r s , and s e n i o r s t o work t o g e t h e r a s a u n if o r m g r o u p ,
a s e r i e s o f te a c h e r - m a d e t e s t s on a r i t h m e t i c f u n d a m e n t a l s ,
a te a c h e r - m a d e t e s t on a r i t h m e t i c r e a s o n i n g , and a S t a n f o r d
A chievem en t T e s t , Form D, were g i v e n a t th e b e g i n n i n g o f
t h e s e m e s t e r i n S e p te m b e r .
T hese t e s t s w ere g i v e n a t i n t e r ­
v a l s o f a b o u t t h r e e d ay s and th e r e s u l t s a r e i n d i c a t i v e o f
t h e l e v e l s o f m a s t e r y i n t h e v a r i o u s f u n d a m e n ta l p r o c e s s e s
o f a r ith m e ti c a t th e b e g in n in g o f th e c o u rs e .
At t h e end o f
t h e f i r s t . q u a r t e r , i n November, a te a c h e r - m a d e a c h ie v e m e n t
t e s t was g i v e n as a m id term e x a m i n a t i o n .
The r e s u l t s o f
t h i s t e s t a r e an i n d i c a t i o n o f th e p r o g r e s s and l e a r n i n g
a b i l i t y o f th e th r e e c l a s s e s .
C om parison o f t e s t s c o r e s o f t h e t h r e e c l a s s e s .
co m p arin g t h e s c o r e s o f t h e t h r e e c l a s s e s , i t
In
s h o u ld be
t a k e n i n t o c o n s i d e r a t i o n t h a t t h e sophom ore c l a s s h a s had
much more r e c e n t d r i l l i n t h e f u n d a m e n t a l s - o f a r i t h m e t i c .
The j u n i o r s and s e n i o r s i n a l l c a s e s had had no r e c e n t d r i l l
i n t h e v a r i o u s f u n d a m e n ta ls e x c e p t a s t h e y come i n t o c o n t a c t
w ith a r ith m e ti c c a l c u l a t i o n i n t h e i r every d ay l i v i n g o r in
o t h e r h ig h s c h o o l s u b j e c t s .
For th e p u rp o ses o f t h i s s tu d y ,
18
th e com p arison s o f t e s t r e s u l t s w i l l he made on th e h a s is o f
m a tu r ity or G la ss g r o u p in g s .
S cores in a d d i tio n .
On e x a m i n a t i o n o f f a b l e I , i t
w i l l be n o t e d t h a t t h e mean o f t h e j u n i o r s 1 s c o r e s was
s l i g h t l y g r e a t e r t h a n t h a t o f t h e sophom ores o r s e n i o r s .
H ow ever, a f t e r 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 e s t a n d a r d
e r r o r o f t h e means o f e a c h c l a s s , i t w i l l be r e a d i l y s e e n
t h a t t h e d i f f e r e n c e i n e a c h c a s e i s n o t g r e a t enough t o
be o f any g r e a t s i g n i f i c a n c e .
The r e l i a b i l i t y o f th e
d i f f e r e n c e s i s i n d i c a t e d i n T a b le I I .
The ch an ce t h a t
t h e t r u e d i f f e r e n c e i n e a c h c a s e w i l l be above o r b elow
z e r o , a s th e c a s e may b e , i s so s m a l l t h a t t h e d i f f e r e n c e
i n s c o r e s m ig h t w e l l be a t t r i b u t e d t o a c c i d e n t .
A fu rth e r
a i d t o t h e c o m p a ris o n o f mean s c o r e s i s p r e s e n t e d g r a p h i ­
c a l l y i n F ig u re 1 .
I t i s i n t e r e s t i n g t o n o t e t h a t ev e n
th o u g h t h e j u n i o r s w ere h i g h e r i n t h e a c t u a l s c o r i n g , t h e
s e n i o r s l e d i n t h e num ber o f p ro b le m s a t t e m p t e d .
B ut a g a i n ,
a s shown by T a b le I I I , t h i s d i f f e r e n c e i s so s m a ll t h a t i t
may a l s o be a t t r i b u t e d to c h a n c e .
The s l i g h t d i f f e r e n c e
i n mean s c o r e s i s shown i n t h e g r a p h i c p r e s e n t a t i o n i n
F ig u re 2 .
S cores in s u b t r a c t i o n .
The v a r i a t i o n o f s c o r e s on
t h e t e s t i n s u b t r a c t i o n i s shown by T a b le I T .
The d i f f e r ­
e n c e b e tw e e n t h e c l a s s e s i n t h e o r d e r o f t h e i r m a t u r i t y i s
19
Tmm
i
COMPARATIVE SCORES OB' M
ACHIEVEMENT
TBST IE SIMHE ADDITION
S cores
Sopiiomores
fre q u e n c ie s
Ju n io rs
o
1
1
H
CO
H
1
S e n io rs
1
1 6 — 17
2
1
1 2 — 13
8
1
3
3
10
2
3
8— 9
9
1
4
6— 7
10
4— 5
10
2— 3
3
0
1
1
H
H
1 4 — 15
T o ta l
2
4
1
4
10
52
21
Mean
8 .8 1
1 0 .0 0
9 .6 7
S t a n d a r d Dev.
3 .4 2
4 .7 6
4 .5 4
.4 8
1 .6 8
1 .0 3
S ta n d a rd E r.
20
TABLE I I
ESLIABILITY OP THE D II’EEBENCES BETWEEN SCORES ON AN
ACHIEVEMENT TEST IN SIMPLE ADDITION
com pared
^
R a tio
C hances
-* 3 3
1 .9 7
.17
1 .3 to 1
— Sophs.
.86
1 .1 3
.7 6
3 .4 to 1
— S o p h s,
1 .1 9
1 .7 5
.68
3 .0 to 1
St s .
-- Jrs.
S rs.
Jrs.
21
C lass
Mean s c o r e
S e n io rs
9 .6 7
Ju n io rs
1 0 .0 0
Sophomores
G ra p h ic p r e s e n t a t i o n
8 .8 1
FIGURE 1
COMPARISOH OF ISAM SCORES OH AH ACHIEVEMENT
TEST IH SIMPLE ADDITION
22
pabxiB
in
COMPARISON OF NUMBER OF PROBLEMS' AI1TEMP'EEB ON AN
ACHIETOMEOT PBST Ilf ADDITION
Sophomores
F re q u en cies
Ju n io rs
S e n io rs
1
1
1
1
1
1
1 6 — 17
6
0
5
1 4 — 15
10
1
2
1 2 — 13
20
3
7
1 0 — 11
6
2
2
8— 9
5
2
3
to
3
£1
1
2 0 —21
H*
CD
1
1
H
P ro b le m s
c o m p le te d
lo ta l
52
10
21
Mean
1 3 .1 6
1 3 .4 0
1 4 .0 4
2 .9 2
3 .7 8
3 .2 4
.4 0
1 .3 3
.7 3
S t a n d a r d B ev.
S ta n d a rd S r .
23
G la s s
Mean s c o r e s
S e n io rs
14* 04:
Ju n io rs
13*40
Sophomores
1 3 .1 6
G ra p h ic p r e s e n t a t i o n .
FIGURE 2
COMPARISON OF PROBLEMS AO?TEMPTED OR AN ACHIEVEMENT
TEST IN SIMPLE ADDITION
24
EABEE IV
COMPARATIVE SCOH1S OH AH ACHIEVBMSM
m ST
Scores
IH SUBEBAOIIOH
Sophomores
5 0 — 54
1
1
1
3
4
3 5 — 39
4
3 0 — 54
8
2 5 — 29
15
1
2
2 0 —24
5
1
2
15 — 19
2
3
2
9
5— 9
2
it*
d*
0
1
1
2
B eni o r s
H
0
1
1
H
d^
4 5 — 49
F re au en o les
Ju n io rs
3
2
1
4
1
9
19
3?otal
51
Mean
26*72
3 0 .8 5
33*55
S ta n d a r d J)ev*
11 #50
12*65
1 1 .9 0
1*60
4 .8 0
2 .8 0
S ta n d a rd E r .
25
n o t g r e a t enough t o he s i g n i f i c a n t , h u t t h e d i f f e r e n c e
b e tw e e n t h e s e n i o r s and sophom ores i s o f some c o n s e q u e n c e .
The s t a t i s t i c a l r e l i a b i l i t y o f t h i s d i f f e r e n c e r e v e a l e d i n
f a b l e Y i n d i c a t e s t h a t w h ile th e c h a n c e s a r e good t h a t t h e
d i f f e r e n c e b e tw e e n t h e s e n i o r s and t h e sophom ores s c o r e s
w i l l be above z e r o , t h e e v id e n c e s t i l l i s n o t c o n c l u s i v e #
Ihe r e l a t i v e speed o f c a lc u l a ti o n in s u b tr a c tio n i s r e ­
v e a l e d i n f a b l e YI#
f h e h i g h e r c l a s s e s showed a s l i g h t
s u p e r i o r i t y b u t n o t enough t o be s i g n i f i c a n t ,
fig u re s 3
and 4 e x h i b i t a v i s u a l c o m p a ris o n o f t h e above s c o r e s #
S c o r e s i n m u l t i p l i c a t i o n and s h o r t d i v i s i o n ,
fa b le s
Y I I , Y I I I , IX, and X, X I, X I I , r e v e a l r e s u l t s much t h e same
as t h o s e o u t l i n e d above#
f h e h i g h e r s c o r e s w ere made i n
each in s t a n c e by th e c l a s s e s i n th e o r d e r o f t h e i r m a t u r i t y ,
b u t i n no i n s t a n c e was t h e d i f f e r e n c e l a r g e enough t h a t i t
c o u ld n o t be a t t r i b u t e d t o c h a n c e ,
f i g u r e s 5 , 6 , 7 , and 8
e x h i b i t th e graphiG com parison i n each i n s t a n c e .
S c o r e s i n lo n g d i v i s i o n #
f h e d i s p a r i t y i n mean
s c o r e s o f t h e t h r e e c l a s s e s i n lo n g d i v i s i o n i s a g a i n i n
fa v o r o f each c l a s s i n th e o rd e r o f i t s m a tu r i ty w ith a
m arked d i f f e r e n c e b etw e en s e n i o r s and so p h o m o re s,
fh is is
m a n i f e s t i n f a b l e X I I I ; and f a b l e XIY r e v e a l s t h a t w h ile
t h e d i f f e r e n c e b e tw e e n s e n i o r s and sophom ores i s s i g n i f i c a n t ' ,
i t i s by no means c o n c l u s i v e ,
f a b l e XY s e t s f o r t h t h e
26
‘ TABLE 7
RELIABILITY OF THE DIEIEREHCES BETWEEN SCORES OH AH
ACHIEVEMENT TEST IN SUBTHACTIOH
C roups
com pared
3
Sd
R a tio
C h ances
S rs.
-- Jrs.
2 .7 0
5 .5 5
.4 9
2 .2 to 1
S rs.
— S ophs.
6 .8 3
3 .2 2
2 .1 2
5 7 .8 t o 1
Jrs.
- - Sophs.
4 .1 3
5 .0 6
.8 2
3 .9 to 1
27
C lass
Mean s c o r e s
S e n io rs
3 5 .5 5
Ju n io rs
3 0 .8 5
Sophomores
2 6 .7 2
G-raphic p r e s e n t a t i o n
EIGURE 3
COMPARISON O f MEAN SCORES ON AN ACHIEVEMENT
TEST IN SUBTRACTION
28
TABL3 VI
COMPARISON OP NUMBER OP PROBLEMS ATTEMPTED ON AN
ACHIEVEMENT TEST IN SUBTRACTION
P ro b lem s
c o m p le te d
&op&omores
F re q u en cies
Ju n i or s
S e n io rs
1
55— 59
1
5 0 — 54
3
4 5 — 49
5
4 0 — 44
3
1
2
5 5 — 39
9
1
5
3 0 — 34
8
1
2
2 5 — 29
8
2 0 — 24
9
3
2
1 5 — 19
5
H
0
1
1
H
60—?64
1
T o ta l
51
3
1
3
2
9
19
Mean
3 2 .2 0
3 7 .5 0
3 6 .7 1
S t a n d a r d D ev.
1 0 .4 0
1 2 .5 0
1 2 .2 5
1 .4 6
4 .7 2
2 .8 8
S ta n d a rd E r.
29
Mean s c o r e s
C lass
S e n io rs
3 6 .7 1
Ju n io rs
3 7 .5 0
Sophomores
3 S .S 0
C r a p h ie p r e s e n t a t i o n
1
FICUHE 4
COMPARISON OF PROBLEMS ATTEMPTED ON AN ACHIEVEMENT
TEST IN SUBTRACTION
30
TABES T i l
COMPARATIVE SCORES OH AN ACHIEVEMENT
TEST IN MULTIPLICATION
S cores
Sophomores
12
1
11
1
P re eru en o ie s
Ju n io rs
S e n io rs
1
2
1
10
3
9
6
8
4
2
7
5
2
6
16
2
2
5
6
2
1
4
4
3
6
2
3
1
2
3
3
54
1
3
10
20
Mean
6*28
7 .1 0
7 .7 0
S t a n d a r d Dev.
2 .3 0
2 .3 0
2 .9 6
.3 1
.8 1
*
cr>
CD
T o ta l
2
S ta n d a rd E r.
31
TABLE V IIX
RELIABILITY 01 THE BIMBRE1CES B1T?/1BR SCORES OR AIT
ACHIEYEMEET TEST IR MULTIPLICATION
C roups
com pared
13
S r s . ■— J r s .
.6 0
S r s , — Sophs.
J r s . — S o p h s.
R a tio
C hances
1 .0 6
.6 7
2 .4 to 1
1 ,4S
.75
1 .8 9
3 3 .8 t o 1
• SB
.87
.9 4
4 .8 to 1
£d
SB
G la s s
Mean s c o r e s
S e n io rs
7 .7 0
J Ulli 0 r S
7 .1 0
Sophomores
6 .£ 8
G ra p h ic p r e s e n t a t i o n
ksuamuamicalamisiihbuaiawlawa
fIGUBE 5
OOMPABISOB Of MEAN SCOBES OB AN ACHIEYEMBM?
TEST IN MULTIPLICATION
33
TABLE I Z
COMPARISON Of NUMBER Of PROBLEMS ATTEMPTED ON AN
ACHIEVEMENT TEST IN'MULTIPLICATION
P ro b le m s
c o m p le te d
Sophomores
fre q u e n c ie s
Ju n io rs
16
S e n io rs
2
15
14
1
1
13
6
1
1
IS
S
1
2
11
7
10
8
1
3
9
10
4
3.
8
10
2
2
7
7
1
6
2
1
5
1
T o ta l
54
5
11
20
Mean
9 .9 3
1 0 .6 0
1 1 .0 0
S t a n d a r d L ev .
2 .0 9
2 .2 0
2 .4 8
.21
.7 8
.5 7
S ta n d a rd E r.
34
C la ss
Mean s c o r e s
S e n io rs
1 1 .0 0
Ju n io rs
1 0 .6 0
Sophomores
G ra p h ic p r e s e n t a t i o n
t
Ilf* IWtwi® irsig' i^il®
9 .9 3
FIGURE) 6
COMPARISON OF PROBLEMS ATTEMPTED ON AN ACHIEVEMENT
TEST IN MULTIPLICATION
35
TABES Z
COMPARATIVE SCORES OH Alf ACHIEVEMENT
TEST IN SHORT DIVISION
S cores
2 2 —23
Sophomores
fre q u e n c ie s
Ju n io rs
S e n io rs
1
2 0 —21
3 .
18— 19
4
3
1
1 6 — 17
11
1
5
14— 15
7
1
3
1 2 — 13
6
1
2
10— 11
5
2
1
8— 9
5
6— 7
4
1
4— 5
3
1
2— 3
5
0— 1
1
3
1
1
T ot a l
52
10
20
Mean
1 2 .0 8
1 3 .6 0
1 4 .1 0
5 .3 6
4 .8 4
5 .2 8
.7 5
1 .7 1
1 .2 1
S t a n d a r d Dev.
S ta n d a rd E r .
56
TABLE XI
RELIABILITY OR THE DIEEEREM5ES BBTWE1E SCORES OH AH
ACHIEVEMENT TEST IE SHORT DIVISION
Groups a
com pared
S r s . —• J r s .
D
£L
W
D
R a tio
C hances
*50
2*09
*24
1*5
to 1
S r s . — Sophs.
2*02
1 .4 2
1*42
1 1 .9
to 1
J r s . — S o p h s.
1 .5 2
1 .8 7
.8 1
3 .8
to 1
37
G la s s
Mean s c o r e s
S e n io rs
1 4 .1 0
Ju n io rs
1 3 .6 0
Sophomores
I S .0 8
G ra p h ic p r e s e n t a t i o n
f iw
i w w1!i\riwlirsi®ftfli®*\w
ttf itfi iwic^is* iff *«f
FIGURE 7
COMPARISON OF MEAN SCORES ON M
TEST IN SHORT D IV ISIO N
ACHIEVEMENT
i wi
58
IABEB X I I
COMPARISON OF NUMBER OF PHOBDEMS ATTEMPTED ON AN
ACHIEVEMENT TEST IN SHOE! DIVISION
P ro b le m s
c o m p le te d
Sophom ores
F req u en cies
Ju n io rs
S e n io rs
2 4 — 25
2
1
2
2 2 —25
2
1
2
2 0 —21
4
1 8 — 19
7
1 6 — 17
11
3
4
1 4 — 15
7
2
3
1 2 — 13
6
1
3
1 0 — 11
4
i
2
8— 9
3
i
1
6— 7
6
4
P o ta l
52
10
20
Mean
1 5 .3 2
1 6 .2 0
1 6 .6 0
4 .8 0
4 .6 8
4 .3 2
.6 7
1 .6 7
.99
S ta n d a r d D ev,
S ta n d a rd B r.
59
[ean s c o r e s
C la ss
S e n io rs
16*60
Ju n io rs
1 6 .2 0
Sophom ores
1 5 .5 2
G ra p h ic p r e s e n t a t i o n
"imimiw is?
twnstw
FIGURES 8
COMPARISOF OF PROBLEMS APPBMPPRL OF AS ACHIEVEMENT
PESP I S SHOM L I T I S I OF
if »■
40
fABBE X I I I
COMBAHAflVE SCORES OH AH ACHIEVEMENT
TEST IH DOHG BIVISIOH
S cores
15
Sophomores
fre q u e n c ie s
J u n io rs
Seni o rs
1
12
11
3
10
1
1
0
2
9
6
8
1
7
5
1
3
6
2
1
1
5
8
1
3
4
6
4
1
5
4
2
1
2
10
2
1
8
1
0
5
1
1
54
11
19
T o ta l
Mean
4 .6 9
5 .0 5
6 .5 5
S ta n d a r d Dev*
2*95
2 .4 2
3 .4 0
.40
.81
.8 0
S ta n d a r d E r .
41
table
xiv
RELIABILITY OF THE DIFFERENCES BETWEEN SCORES ON AN
ACHIEVEMENT TEST IN LONG DIVISION
G roups
com pared
^
v
fD
.
R a tio
C hances
S rs.
— Jrs.
1 .5 0
1 .1 4
1 .3 2
9 .7 to 1
S rs.
- - S o p h s.
1 .8 6
.89
2 .0 9
5 3 .5 t o 1
Jrs.
- - S o p h s.
.3 6
.9 0
.4 0
1 .9 to 1
42
Mean s c o r e s
G la s s
S e n io rs
6 .5 5
J u n io rs
5*05
Sophomores
4 .6 9
G ra p h ic p r e s e n t a t i o n
FIGHEE 9
COMPARISON OF MEAN SCORES ON AN ACHIEVEMENT
TEST IN hONG D IV ISIO N
43
TABUS XV
COMPARISON Of NUMBER Of PROBLEMS ATTEMPTED ON AN
ACHIEVEMENT TEST IN LONG- DIVISION
P ro b le m s
c o m p le te d
fre q u en cies
Ju n io rs
S e n io rs
13
1
1
IS
1
3
1
1
14
Sophomores
1
11
2
10
7
9
6
2
8
4
2
7
5
6
10
3
2
5
9
1
2
4
9
3
1
T o ta l
54
4
4
1
1
19
11
Mean
7 .3 7
8*96
9 .1 9
S ta n d a r d Dev*
2*42
2 .5 4
2*64
.3 3
.8 4
.62
S ta n d a r d E r .
44
G la s s
Mean s c o r e s
G ra p h ic p r e s e n t a t i o n
Seni or s
9 .1 9
m n m m w m m m m m m vsicmwmmmwu m
J u n io rs
8 .9 6
n<jh* i r
Sophomores
7 .3 7
wifis^
ip is?
ito i® iwitf iw
if»©t®if iwiy
if iof is^if in' r t
isiiwirp»:
FIGURE 10
COMPARISON OF PROBLEMS ATTEMPTED ON AN ACHIEVEMENT
m $T
IN LONG DIVISION
45
d i f f e r e n c e i n mean s c o r e s com puted on s p e e d i n c a l c u l a t i o n .
H ere a g a i n t h e d i f f e r e n c e i s n o t s i g n i f i c a n t , h u t i n e a c h
c a s e th e h i g h e r s c o r e i s i n f a v o r o f t h e more a d v a n c e d c l a s s .
F i g u r e s 9 and 1 0 , p a g e s 4E and 4 4 , a r e p r e s e n t e d a s a v i s u a l
a i d i n t h e f o r e g o i n g c o m p a r is o n s .
S cores in a r ith m e ti c r e a s o n in g .
The t e s t , i n a r i t h ­
m e t i c r e a s o n i n g , in a sm u c h a s more e m p h a sis i s p l a c e d up o n
r e a s o n i n g a b i l i t y t h a n upon s p e e d o f c a l c u l a t i o n i n f u n d a ­
m e n t a l s , m ig h t w e l l he e x p e c t e d t o r e v e a l a d e f i n i t e
s u p e r i o r i t y on th e p a r t o f t h e more m a tu re s t u d e n t s , h u t
s u c h was n o t th e c a s e .
'T a b le XVI r e v e a l s t h a t th e s e n i o r s
as i n o t h e r i n s t a n c e s , had t h e h i g h e s t mean s c o r e , t h e
so p ho m ores n e x t , and j u n i o r s l a s t .
H ow ever, a f t e r 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 e s t a n d a r d e r r o r o f t h e mean, t h e
a c t u a l p la c e m e n t o f t h e j u n i o r and sophom ore s c o r e i s
r e l a t i v e l y u n im p o rta n t.
A s u p e r i o r i t y o f s e n i o r s was
i n d i c a t e d , h u t t h e r e l i a b i l i t y as p o i n t e d o u t i n T a b le XVII
shows t h a t s u c h s u p e r i o r i t y i s by no means c o n c l u s i v e and
m ig h t a g a i n be a t t r i b u t e d t o c h a n c e .
F ig u r e 11 p r e s e n t s
an a d d i t i o n a l c o m p a r is o n o f t h e mean s c o r e s o f t h e t h r e e
.c la s s e s .
S c o r e s on S t a n f o r d A ch iev em en t T e s t .
The d a t a s e t
f o r t h i n T a b le s X V III, XIX, XX, and XXI i n d i c a t e much t h e
same r e s u l t s a s t h o s e o u t l i n e d i n p r e v i o u s t e s t s .
In ev ery
46
TABLE! XVI
COMPARATIVE! SCORES ON AN ACHIEVEMENT
TEST IN ARITHMETIC REASONING
<
S cores
Sophomores
F re a u e n c ie s
Ju n io rs
S e n io rs
7
1
6
1
5
4
4
10
3
10
3
1
2
18
1
2
1
11
4
2
0
2
T o ta l
57
3
2
3
5
2
10
18
Mean
3*13
2 .8 0
3 .9 5
S ta n d a rd L ev.
1 .4 7
1 .2 7
1 .9 5
.2 0
.45
.4 7
S ta n d a rd B r.
47
IABES XVII
RELIABILITY Of THE DIFFERENCES BETWEEN SCORES ON AN
ACHIEVEMENT TEST IN ARITHMETIC REASONING
G roups
com pared
®
S rs. — J r s .
1 .1 5
.6 5
1 .7 7
2 5 .0 to 1
.82
.5 1
1 .6 0
1 7 .2 t o 1
-.3 3
.4 9
.6 7
2 .9 to 1
S r s . — Sophs.
Jrs. —
Sophs.
R a tio
Chance s
48
Mean s c o r e s
G la s s
S en ! o r s
3 .9 5
Ju n io rs
2 *80
Sophomores
3 .1 3
G ra p h ic p r e s e n t a t i o n
M w w w w i1
FIGURE 11
COMPARISON OF MEAN SCORES OH M
ACHIETEMEOT
TEST IN AREEHMBTIC SEASONING .
49
TABIE XVIII
COMPARATIVE SCOHES Oil A BTATOAEDI2BB ACHIEVEMENT
TEST IB ARITHMETIC COMPUTATION
s c o r e s
Sophom ores
F re q u en cies
Ju n io rs
120— 124
S e n io rs
1
H O — 114
3
105— 109
4
100 — 104
6
1
4
95 — 99
16
1
4
90 — 94
9
1
4
85 — 89
3
4
84
9
1
79
3
1
70—• 74
3
1
1
1
0
1 1 5 - 119
CD
1
1
1
IQ
Z>
6 5 - 69
4
3
1
1
1
T o ta l
57
12
21
Mean
9 3 .8 2
9 6 .6 6
9 7 .0 3
S t a n d a r d Dev.
1 0 .6 0
1 3 .6 5
1 3 .5 0
1 .4 1
4 .3 5
3 .0 2
S ta n d a rd E r.
TABLE XIX
RELIABILITY Of THE DIFFERENCES BETWEEN SCORES ON A
STANDARDIZED ACHIEVEMENT TEST IN ARITHMETIC COMPUTATION
G roups
com pared
D
S rs, — J r s ,
.3 ?
S r s , — S o p h s.
J r s . — S o p h s.
R a tio
C hances
5 .3 0
.0 7
1 .1 to I
3 .SI
3 .3 8
.9 5
4 .8 to 1
S . 84
4 .5 6
,6S
£ .6 t o 1
51
G la s s
Mean s c o r e s
S e n io rs
97 *03
J u n i o rs
96*66
Sophomores
93*82
G ra p h ic p r e s e n t a t i o n
FIGURE 12
COMPARISON OF MEAN SCORES ON A STANDARDIZED
ACHIEVEMENT TEST IN ARITHMETIC COMPUTATION
52
TAB£G XX
COMPARATIVE SCORES 01 A STAHMBDIZB3) ACHIEVEME1T
test
S co res
i i a r it h m e t ic r b a s o e ih c
Sophomores
F re a g e n c i e s
Ju n io rs
1 2 0 — 124
S e n io rs
1
115 — 119
1
2
2
H O - 114
4
2
3
1 0 5 —109
6
2
2
1 0 0 — 104
9
95 — 99
13
1
6
90 — 94
5
3
2
8 5 — 89
5
2
1
8 0 — 84
10
75— 79
4
1
2
7 0 — 74
T o ta l
57
12
Mean
95*40
99*60
1 0 0 .3 6
S t a n d a r d B ev.
10*60
6 .2 0
1 2 .7 0
1 .4 0
1 .9 6
ro
•
CD
1
S ta n d a rd S r .
21
53
T& Bm XXI
BS&IABILITY OE TEE DIEEBBEHCBS BETWBBN SCOEES OH A
SEAJTOARDIZED AOHIBVMSHT TtEST IH ABiaZHMETIC SEASONING
Groups
com pared
33
S rs. — J r s .
*76
S r s . — S o p h s.
Jrs.
— S o p h s.
E a tio
Ohances
3 .4 4
,2 2
1*4 t o 1
4 ,9 6
3 .2 6
1 .5 4
1 5 .5 t o 1
4 .2 0
2 .4 0
1 .7 5
2 4 .0 to 1
54
G la s s
. Mean s c o r e s
S e n io rs
100.556
Ju n io rs
99*60
S ophomo r e s
9 5 .4 0
G ra p h ic p r e s e n t a t i o n
I
1IGURE 13
COMPARISON 01 MEAN SCORES ON A STANDARDIZE!)
achievement t e s t
i n a r it h m e t ic r ea so n in g
55
i n s t a n c e t h e s c o r e s w ere i n t h e o r d e r o f c l a s s m a t u r i t y .
Mean s c o r e s may he more r e a d i l y com pared by . r e f e r r i n g t o
F i g u r e s 12 and 1 3 , p a g e s 51 and 54 r e s p e c t i v e l y .
S c o r e s on m id te rm a c h ie v e m e n t t e s t .
The s c o r e s on
t h e m id te rm t e s t a r e more s i g n i f i c a n t t h a n m ig h t he e x p e c t e d
i n v ie w o f r e s u l t s o b t a i n e d i n o t h e r t e s t s .
B u t, i t w i l l
he rem em b ered , a l l o f t h e o t h e r t e s t s w ere g i v e n a t t h e
b e g i n n i n g o f t h e c o u r s e , and t h e m id te rm t e s t was d e s i g n e d
t o r e f l e c t t h e p r o g r e s s o f a l l s t u d e n t s a t t h e m id te r m .
T a b le XXII shows o n ly a s l i g h t d i f f e r e n c e i n t h e mean
s c o r e s o f t h e j u n i o r and sophomore g r o u p s , b u t i n t h e c a s e
o f t h e s e n i o r s , t h e r e i s a momentous d i f f e r e n c e .
T a k in g
i n t o c o n s i d e r a t i o n t h e s t a n d a r d e r r o r o f t h e m e an s, t h e one
s i g n i f i c a n t f e a tu r e i s t h a t th e s e n io r s have, as a gro u p ,
w ith o u t doubt in d ic a te d a d e f i n i t e s u p e r i o r i t y i n p r o g re s s
o v e r t h e so p h o m o re s, and a s l i g h t s u p e r i o r i t y o v e r t h e
ju n io rs.
F u r t h e r e v i d e n c e i s p r e s e n t e d i n T a b le X X III
w hich i n d i c a t e s t h a t t h e c h a n c e s t h a t t h e s e n i o r c l a s s i s
s u p e r i o r t o t h e j u n i o r s a r e good b u t n o t c o n c l u s i v e .
On
t h e o t h e r hand t h e c h a n c e s t h a t th e s e n i o r s a c h ie v e m e n t
i s g r e a t e r t h a n t h a t o f th e sophom ores a r e c o n c l u s i v e .
d i f f e r e n c e i n mean s c o r e s w i l l be r e a d i l y o b s e r v e d i n
F ig u r e 1 4 .
In te llig e n c e q u o tie n ts .
As f u r t h e r means o f
The
56
TABES. X X II
COMPARATIVE SCORES ON A MIDTERM TEST
IN BUSINESS ARITHMETIC
-
S cores
Sophomores
70— 74
fre q u e n c ie s
Ju n io rs
S e n io rs
1
65— 69
60— 64
5 5 ,- 5 9
1
5 0 — 54
1
4 5 — 49
1
4 0 — 44
6
3 5 — 59
10
2
3 0 — 34
9
1
2 5 —29
9
2 0 —24
10
4
1 5 — 19
4
1
1 0 — 14
8
3
1
2
5
2
5— 9
5
2
1
O?otal
58
12
19
Mean
2 8 .7 1
2 9 .6 0
44*86
S t a n d a r d Bey.
1 0 .1 5
1 9 .4 0
1 2 .5 0
1 .3 4
6 .0 8
2 .9 4
S tan d a rd E r.
57
IABLE X X III
RELIABILITY GE THE DIMEHENCES BETWE1H SO CESS OH A
MIDTERM TEST IE BUSINESS ARITHMETIC
Groups
com pared
D
€D
R a tio
G hances
8 5 .5 t o 1
S rs,
— Jrs.
1 5 .2 6
6 .7 5
2 .2 6
S rs.
—• S o p h s.
1 6 .1 5
5 .2 4
5 .0 0 *
Jrs.
— Sophs.
.8 9
6 .2 0
.1 4
m illio n s to 1
1 .3 to 1
58
Mean s c o r e s
C lass
S e n io rs
44*86
Ju n io rs
29*60
G ra p h ic p r e s e n t a t i o n
Sophomores
FIGURE 14
C0MBARI30R OF MEA S SCORES OR A MIDTERM TEST
Iff BUSIEESS ARITHMETIC
59
c o m p a r is o n , t h e means o f i n t e l l i g e n c e q u o t i e n t s o f t h e t h r e e
g r o u p s a r e p r e s e n t e d i n T a b le X K JY •
The i n t e l l i g e n c e
q u o t i e n t s f o l l o w t h e same p a t t e r n as t h o s e o f m ost o f t h e
t e s t s g iv e n w ith th e h ig h e r sc o re s i n fa v o r o f c l a s s e s i n
th e o rd e r o f t h e i r m a tu r i ty .
T a b le ZXT r e v e a l s t h a t some
c r e d e n c e s h o u ld be g i v e n t o t h e f a c t t h a t t h e s e n i o r s mean
i n t e l l i g e n c e q u o t i e n t i s h i g h e r t h a n t h a t o f t h e so p h o m o res;
h o w e v e r, t h e f a c t t h a t p r a c t i c a l l y a l l o f t h e s e n i o r s and.
j u n i o r s h av e t a k e n two i n t e l l i g e n c e t e s t s w h i l e t h e s o p h o ­
m ores h av e t a k e n o n ly o n e , w ould p e r h a p s e x p l a i n p a r t o f
th e d is c re p a n c y i n s c o r e s .
A g r a p h i c c o m p a r is o n o f t h e mean
s c o r e s i n F ig u r e 15 r e v e a l s t h e c o m p a r a tiv e d i f f e r e n c e
b e tw e e n t h e t h r e e c l a s s e s .
Summary o f c o m p a ris o n s on a l l t e s t s .
I n T a b le 1X 7 1
i t may be o b s e r v e d t h a t t h e s e n i o r s had h i g h e r s c o r e s t h a n
j u n i o r s on a l l o f t h e n i n e t e s t s g i v e n w i t h one e x c e p t i o n
w h ic h was t h e f i r s t t e s t i n s im p le a d d i t i o n , t h e d i f f e r e n c e
i n t h a t c a s e b e i n g so s l i g h t a s t o be o f no c o n s e q u e n c e .
The c o n s i s t e n c y o f t h e more m a tu r e g r o u p ’s h i g h e r s c o r e s
w ould t e n d t o i n d i c a t e t h a t t h e g ro u p a s a w hole was s u p e r i ­
o r t o t h e j u n i o r s i n th e m a s t e r y o f t h e f u n d a m e n ta ls o f
a rith m e tic .
T e s t .number n i n e , t h e m id term e x a m i n a t i o n ,
m a n ife s ts a ls o a s u p e r i o r i t y i n p ro g re s s o f th e s e n io r s , b u t
i t may r e a d i l y be s e e n t h a t t h i s i n d i c a t i o n i s n o t by any
60
TABLE XXIY
COMPARISON Of CLASSES ACCORDING TO
INTELLIGENCE QUOTIENT
I . Q 'a .
Sophomores
fre q u e n c ie s
Ju n io rs
1 35 — 139
S e n io rs
1
1 30 — 134
1 25 — 129
1 20 — 124
1 15 — 119
1
1 1 0 — 114
2
1 0 5 — 109
8
3
7
1 00 — 104
4
1
1
9 5 — 99
10
2
2
90— 94
6
1
2
85— 89
10
1
1
00
t
1
o
00
7
7 5— . 79
1
7 0— 74
1
3
2
1
1
20
T o ta l
49
10
Mean
94 . 44
9 9 .5 0
1 0 2 .0 0
S t a n d a r d Dev.
9 .7 5
1 1 .0 0
1 4 .3 5
S ta n d a r d E r .
1 .3 9
3 .9 0
3 .3 0
61
Q?ABIiE XX?
HUIiIABIlXfY OF m 1 DIFFERENCES BETWEEN I* Q ' s .
com pared
®
fjj
R a tio
C hances
S rs.
— Jrs.
2 .5 0
5 .1 0
.49
2 .2 to 1
S rs.
— Sophs.
7 .5 6
3 .5 8
2 .1 1
5 6 .3 t o 1
Jrs.
— Sophs.
5 ,0 6
4 .1 7
1 .2 1
7 .9 t o 1
62
C la s p
Mean s c o r e s
S e n io rs
1 0 2 ♦GO
Ju n io rs
9 9 ,5 0
Sophomores
9 4 .4 4
G ra p h ic p r e s e n t a t i o n
PIGURE 15
COMPARISON OP MEANS OP IOTB11IGSNCE QUOTIENTS
63
TABLE XXVI
RELIABILITY OF THE DIFFERENCES BETWEEN SCORES
OF SENIORS AND JUNIORS ON ALL TESTS
T e sts
D
^D
R a tio
C hances
A d d itio n
-.3 3
1 .9 7
.1 7
1 .3 to 1
S u b tra c tio n
£ .7 0
5 .5 5
.4 9
£ .£ to 1
M u l t i p l i c a t i on
.6 0
1 .0 6
.57
£ .4 to 1
S h o rt d iv i s i o n
.5 0
£ .0 9
.£ 4
1 .5 t o 1
Long d i v i s i o n
1 .5 0
1 .1 4
1 .3 2
9 .7 t o 1
R e a s o n in g
1 .1 5
.65
1 .7 7
£ 5 .1 t o 1
C o m p u ta tio n ( s t a n . )
.37
5 .3 0
.07
1 .1 t o 1
R e a s o n in g ( s t a n . )
.7 6
3 .4 4
.£ £
1 .4 to 1
M idterm
1 5 .£ 6
6 .7 5
£ .£ 6
8 3 .3 t o 1
I . Q * s.
£ .5 0
5 .1 0
.49
£ .£ t o 1
means c o n c l u s i v e *
T a b le XXVII r e v e a l s t h a t t h e s e n i o r s , i n e v e r y t e s t ,
r a n k e d h i g h e r t h a n t h e so p h o m o re s.
T h ere i s no s i g n i f i c a n t
d i f f e r e n c e i n any o f t h e t e s t s g i v e n a t t h e “b e g i n n in g o f
th e te rm , h u t t h e i r c o n s is te n c y th ro u g h o u t th e s e r i e s o f
t e s t s seems t o make i t v e r y a p p a r e n t t h a t as a gro up * t h e y
a r e s u p e r i o r ; t o t h e sophom ores i n m a s t e r y o f t h e f u n d a ­
m e n ta ls.
T e s t num ber n i n e , t h e m id te rm e x a m i n a t i o n , l e a v e s
no d o u b t a s t o a s u p e r i o r i t y i n l e a r n i n g a b i l i t y and p r o ­
g r e s s o f t h e s e n i o r c l a s s o v e r th e so p h o m o re s.
T a b le XXVIII sh o w s t h a t t h e j u n i o r s and sophom ores
a r e much n e a r e r t h e same l e v e l o f a c h ie v e m e n t and p r o g r e s s
t h a n t h e j u n i o r s and s e n i o r s , o r t h e s e n i o r s and so p h o m o re s .
The sophom ores had a h i g h e r mean s c o r e on one t e s t , w h ile
t h e j u n i o r s had a h i g h e r mean s c o r e on e i g h t t e s t s .
T h is
m ig h t seem t o i n d i c a t e a s l i g h t m e a su re o f s u p e r i o r i t y on
t h e p a r t o f t h e j u n i o r s , b u t - i n no i n s t a n c e was t h e d i f f e r ­
e n c e i n s c o r e s g r e a t enough t h a t i t c o u ld n o t be a t t r i b u t e d
to a c c id e n t or chance.
Summary.
On summing up t h e e v id e n c e p r e s e n t e d i n
th e fo re g o in g t a b l e s , i t i s p l a i n l y ap p a re n t t h a t th e
s e n i o r s i n th e e x p e r i m e n t w ere d e f i n i t e l y s u p e r i o r , a s a
g r o u p , t o th e so p h o m o re s .
T here was no c o n c l u s i v e e v i d e n c e
t h a t s u c h s u p e r i o r i t y e x i s t e d i n t h e o t h e r g r o u p co m b in a­
tio n s .
tabes xxvti
RELIABILITY OF THE DIFFERENCES BETWEEN SCORBS.
OF SENIORS AND SOPHOMORES ON ALL TESTS
T ests
D
R a tio
C hances
A d d itio n
.8 6
1 .1 3
.7 6
3 .4 to 1
S u b tra c tio n
6 .8 3
3 .2 2
2 .1 2
5 7 .8 t o 1
M u ltip lic a tio n
1 .4 2
.7 5
1 .8 9
3 3 .8 t o 1
S h o rt d i v is i o n
2 .0 2
1 .4 2
1 .4 2
1 1 .9 t o 1
Long d i v i s i o n
1 .8 6
.89
2 .0 9
5 3 .5 t o 1
.82
.51
1 .6 0
1 7 .2 t o 1
C o m p u ta tio n ( s t a n . )
3 .2 1
3 .3 8
.9 5
4 .8 to 1
R e a s o n in g ( s t a n . )
4 .9 6
3 .2 6
1 .5 4
1 5 .5 t o 1
1 6 .1 5
3 .2 4
5 .0 0 m i l l i o n s t o 1
R e a s o n in g
M idterm
66
TABLE XXVIII
RELIABILITY OF TEE, DIFFERENCES BETWEEN SCORES ’*
OF JUNIORS AND SOPHOMORES OH ALL TESTS
T ests
D
^D
R a tio
C hances
A d d itio n
1 .1 9
1*75
.6 8
3 .0 to 1
S u b t r a c t i on
4 .1 3
5 .0 6
.82
3 .9 to 1
M u ltip lic a tio n
*82
.87
.9 4
4 .8 to 1
S h o rt d iv is io n
1*52
1 .8 7
.81
3 .8 to 1
.3 6
.9 0
.40
1 .9 to 1
R e a s o n in g
-.3 3
.4 9
.67
2 .9 to 1
C o m p u ta tio n ( s t a n . )
2 *84
4 .5 6
.62
2 .6 t o 1
R e a s o n in g ( s t a n . )
4*20
2 .4 0
1 .7 5
2 4 .0 to 1
M idterm
• 89
6 .2 0
.1 4
1 .3 to 1
I . Q, *a •
5 .0 6
4 .1 7
1 .2 1
7 .9 t o 1
Long d i v i s i o n
CHAPTER IV
SUMMARY ■AMD CGITCLUSIOHS
T h is c h a p t e r w i l l g i v e a b r i e f summary o f t h e p r o b ­
le m , t h e e x p e r i m e n t a l p r o c e d u r e f o l l o w e d , and t h e r e s u l t s
o b ta in e d .
I t w i l l a ls o o u t l i n e th e c o n c lu s io n s fo rm u la te d
on t h e b a s i s o f t h e e x p e r i m e n t a l f i n d i n g s .
The o b j e c t i v e o f t h i s s t u d y was t o i n v e s t i g a t e t h e
r e l a t i v e p r o g r e s s made by s o p h o m o re s , j u n i o r s , and s e n i o r s
i n b u s i n e s s a r i t h m e t i c , and t o d e t e r m in e t h e i r a b i l i t y t o
work t o g e t h e r a s a u n if o r m g r o u p .
As a b a s i s f o r th e s t u d y , a s e r i e s of. t e s t s i n
a r i t h m e t i c f u n d a m e n ta ls was g i v e n a t f r e q u e n t i n t e r v a l s
f o llo w e d b y a t e a c h e r - m a d e a c h ie v e m e n t t e s t and a s t a n d a r d ­
i z e d t e s t i n b o t h r e a s o n i n g and c o m p u ta t io n .
At t h e end o f
t h e q u a r t e r , a te a c h e r - m a d e m id te rm e x a m i n a t i o n was g i v e n
as a c o n c l u s i o n t o t h e t e s t i n g p ro g ram t o m e a su re t h e p r o ­
g r e s s made b y e a c h g r o u p .
I n t e l l i g e n c e q u o t i e n t s w ere
o b t a i n e d by r e c o u r s e t o s c h o o l r e c o r d s .
A ll t e s t sc o re s
w ere r e c o r d e d i n t a b u l a r form and i n e a c h i n s t a n c e t h e m ean,
s t a n d a r d d e v i a t i o n , and s t a n d a r d e r r o r ?/ere com puted a s a
means o f c o m p a r is o n .
F u r t h e r d a t a i n th e form o f e r r o r o f
t h e d i f f e r e n c e , r a t i o , and c h a n c e s w ere com puted t o g i v e a
m e a su re o f r e l i a b i l i t y t o t h e co m p a riso n s, m a d e.
The d a t a o b t a i n e d by t h e e x p e r im e n t f u r n i s h e d t h e
68
f o l l o w i n g c o m p a ris c o s :
The c l a s s e s w ere n o t o f e q u a l a b i l i t y .
A lth o u g h i n
no one i n s t a n c e was t h e d i f f e r e n c e i n t e s t s c o r e s c o n c l u s i v e ,
th e c o n s is te n c y o f h ig h e r sc o re s in d ic a te s a s l i g h t s u p e r i­
o r i t y o f c l a s s e s i n th e o r d e r o f t h e i r m a t u r i t y .
The d i f f e r e n c e i n s c o r e s o f t h e g r o u p s i n c h r o n o l o g i ­
c a l o r d e r d i d n o t i n d i c a t e a m ark ed s u p e r i o r i t y o f one o v e r
th e o th e r.
H ow ever, th e d i f f e r e n c e b e tw e e n s e n i o r s and
so p h o m o re s , and t h e c o n s i s t e n c y o f t h a t d i f f e r e n c e , was
g r e a t enough t o show t h a t t h e s e n i o r s w ere b e t t e r p r e p a r e d .
P r o g r e s s was g r e a t e r i n e a c h i n s t a n c e i n f a v o r o f
t h e more m a tu re g r o u p s .
B ut t h i s d i f f e r e n c e b e tw e e n c l a s s e s
i n th e o r d e r o f t h e i r s e n i o r i t y was n o t s t a t i s t i c a l l y g r e a t
enough i n r e l a t i o n t o i t s
sta n d a rd e r r o r t h a t i t
c o u ld n o t
be a t t r i b u t e d t o c h a n c e .
The d i f f e r e n c e i n p r o g r e s s b e tw e e n s e n i o r s and s o p h o ­
m o r e s , h o w e v e r, was g r e a t en o ug h t o show c o n c l u s i v e l y t h a t
t h e s e n i o r s w ere a much s u p e r i o r g r o u p .
C o n c lu sio n s.
I n v ie w o f t h e f i n d i n g s r e l a t e d i t may
be s t a t e d t h a t s o p h o m o re s , j u n i o r s , and s e n i o r s a r e n o t
s u i t e d t o work t o g e t h e r a s a u n if o r m g r o u p .
C o n tra ry to e x p e c t a t i o n s , th e ev id en ce d id n o t i n d i ­
c a t e t h a t sop ho m o res and j u n i o r s , o r j u n i o r s and s e n i o r s
c o u ld n o t be com bined i n t o one hom ogenious g r o u p .
H ow ever,
69
t h e s p r e a d b e tw e e n t h e sophom ores and s e n i o r s was g r e a t
en o ug h to i n d i c a t e t h e u n s u i t a b i l i t y o f t h e s e two g r o u p s
t o w ork t o g e t h e r .
The c o m p a ris o n s w ould seem t o i n d i c a t e f u r t h e r t h a t
a s t h e s e n i o r s made more p r o g r e s s t h e y , as a g r o u p , w ould
r e c e i v e m ost o f t h e h i g h g r a d e s *
I f t h i s f a c t w ere known
t o t h e so p h o m o res, i t m ig h t w e l l s e r v e t o f r u s t r a t e
or
d i s c o u r a g e them as a group*
f h e r a n g e i n a b i l i t i e s o f t h e t h r e e g ro u p s w ould
seem t o p r e c l u d e any p o s s i b i l i t y o f a r r i v i n g a t any one s e t
o f t e a c h i n g o b j e c t i v e s t h a t w ould f i t t h e n e e d s o f a l l o f
them*
The s u p e r i o r i t y o f s e n i o r s o v e r sophom ores i n d i c a t e s ,
t o o , t h a t t h e s e n i o r s a r e c a p a b le o f d o in g work more r a p i d l y
as w e l l a s a s s i m i l a t i n g more i n s t r u c t i o n ,
fhus i t i s
a p p a r e n t t h a t t h e s l o w e r c l a s s r e t a r d s t h e g r o u p as a w h o le .
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