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Prognosis in intermediate algebra

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PROGNOSIS IN INTERMEDIATE ALGEBRA
A T hesis
P re se n ted to
th e F a c u lty of the School of E d u catio n
The U n i v e r s i t y o f S o u t h e r n C a l i f o r n i a
In P a r tia l F u lfillm en 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 ee
M aster of Science i n E ducation
M a r t i n B. F a r r e l l
A u g u s t 1941
UMI Number: EP64952
All rights reserved
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T h i s thesis, w r i t t e n u n d e r the direc tion of the
C h a ir m a n o f the ca nd id a te’s G u id a n c e C o m m i t t e e
a n d a p p r o v e d by all m e m b e r s of the C o m m i t t e e ,
has been p r e s e n t e d to a n d a c c e p t e d b y the F a c u l t y
of the S c h o o l of E d u c a t i o n of T h e U n iv e r s i t y of
S ou th e r n Ca l i fo r n i a in p a r t i a l f u lfi llm e nt of the
r eq ui re m en ts f o r the d e g r e e of M a s t e r of S c ie n ce
in Ed u ca ti on .
DateAanU8-r 7. 21 ? 1942
Guidance C om m ittee
D. W elty L efev er
Chairman
L ouis P . Thorpe
Paul F ish e r
TABLE OF CONTENTS
CHAPTER
I.
PAGE
‘THE PROBLEM*
ITS IMPORTANCE AND
ORGANIZATION....................................................................
1
The p r o b l e m ...........................................
1
The p r o b l e m ...............................................
1
Sub p r o b l e m
.......................
1
............................................
2
M a j o r i s s u e s ...............................................................
2
I n t r o d u c t io n to study
.......................................
2
................................................
3
O rg a n iz a tio n of study
Im portance of stu d y
E d u c a ti o n a l 'guidance • • • . . . . . • •
Im p o rta n t i s s u e s in v o lv e d i n guidance
II.
RELATED STUDIES
3
.
3
...............................................................
5
D iversified se ttin g s
............................... . . .
D iscrepancies in c o rr e la tio n s
....................
Consensus of o p in io n . . . . . . . . . .
5
5
7
F a c t o r s which i n f l u e n c e s u c c e s s
i n c o l l e g e a l g e b r a ............................................
7
P r e d ic tio n equ ation s fo r success
i n c o l l e g e m a t h e m a t i c s ..................................
A study of a lg e b r a p ro g n o sis
........................
9
10
An e v a l u a t i o n o f m e th o d s o f
p r e d ic tin g school success in ■
m athem atics
. . . . . . . .
13
ill
CHAPTER
III.
PAGE
15
PROCEDURE............................
C o l l e c t i n g and r e c o r d in g of d a ta
• .
15
K in d a n d s o u r c e o f d a t a .........................
-15
R ecording of d a ta
16
Measurement . • • • • • . . • • • •
16
M e a s u r e s e m p lo y e d ............................................
17
The a c h i e v e m e n t t e s t i n e l e m e n ­
ta ry alg eb ra
. . . . . . . . . .
17
The a c h i e v e m e n t t e s t i n i n t e r ­
m e d i a t e a l g e b r a .................................
Classroom t e s t s
• • • • • • • • • •
18
18
Homework...............................................................
19
P s y c h o lo g ic a l exam ination * • . . .
19
P r e v i o u s g r a d e s . . ..................................
20
Summary a n d c l a s s i f i c a t i o n o f
m easures
C lassificatio n
...........................................
20
.......................................
20
The c r i t e r i o n ............................
IV.
22
C o r r e l a t i o n o f m e a s u r e s ..............................
22
C o e ffic ie n ts of c o rre la tio n . . . .
22
P r e d i c t i v e power
.......................................
22
CONTRIBUTING- FACTORS............................................
24
iv
CHAPTER
PAGE
W ithdraw al
f r o m s c h o o l ...................................
Is s u e s involved.
. . . . . . . . . .
25
R e s u l t s ..................... . . . ............................
25
S e x .................................... ..............................................
27
Data a v a i l a b l e
• • • • • • • • • • •
R esult . . . . . .
S ch o lastic
27
.......................................
background
Data a v a i l a b l e
...........................
27
29
• • • • • • • • • • •
R e s u l t s .........................................................
29
•
29
A g e ..................................................................................
31
Data a v a i l a b l e
........................
R e s u l t s .........................................................
THE CRITERION
. . .
O bjective
31
♦
31
........................................
34
............................................
34
Comparison of s u c c e s s m ea su res . . .
33
A n a ly s is of su c c e ss m easures . . . .
39
W eighted s c o r e s .
. • • • • • • • . •
42
C onverted s c o re s
.
.................................
44
.
45
G r a d e s ....................................................................
45
The c r i t e r i o n
V I.
24
..............................
Data a v a i l a b l e
V;
24
THE PSYCHOLOGICAL EXAMINATION AS
A PREDICTIVE AGENT .............................................
49
V
CHAPTER
PAGE
P r e d i c t iv e v alue of se p a ra te
scores
........................
. . . .
49
E x am p le s o f r e l a t i v e p r e d i c t i v e
p ower
.
............................. ..........................
51
L im its of p r e d i c t i o n from g r o s s
p s y c h o l o g i c a l s c o r e s .......................
. .
I n term s of th e grade p o i n t . . . . .
V II.
52
53
E x a m p l e ......................................................
55
R e s u l t s ......................................................
56
THE VALUE OF THE PREVIOUS SCHOLASTIC
RECORD IN PREDICTING SUCCESS IN
INTERMEDIATE ALGEBRA ............................................
R e la tio n s h ip to o th e r m easures
. . . .
57
........................
57
P r e d i c t i v e powe r ................................................
59
R e la tiv e p r e d i c ti v e valu e
R e s u l t s ......................................................
V III.
57
61
THE ACHIEVEMENT TEST IN ELEMENTARY
ALGEBRA AS A PROGNOSTIC MEASURE
. . . .
63
C o r r e l a t i o n s .................................
P r e d ic t iv e value
63
.................................. ....
I n t e r p r e t a t i o n of r e s u l t s
.
63
........................
67
R e s u l t s ......................................................
67
vi
CHAPTER
IX.
PAGE
THE COMBINED PREDICTIVE MEASURES............
69
R e la tiv e s ig n if ic a n c e of the
p r e d ic tiv e m easures.
.........................
S ig n ific a n c e of in d iv id u a l m easures.
69
•
69
Combined s i g n i f i c a n c e ...............................
71
R e s u l t s ......................................................................
74
I n g e n e r a l ............................................................ .
I n t e r m s o f t h e g r a d e p o i n t ............
X.
74
75
SUMMARY AND CONCLUSION....................................... . .
79
M i n o r i s s u e s ....................* ......................................
79
C o n t r i b u t i n g f a c t o r s .......................................
79
S u p e rflu o u s p r e d i c t i v e m easures
80
. . .
R e s u l ts i n term s of the grade p o i n t s
. .
The p s y c h o l o g i c a l e x a m i n a t i o n . . . .
81
81
Averages of p re v io u s g rad es
i n m athem atics .
......................................
82
The a c h i e v e m e n t t e s t i n e l e m e n t a r y
alg eb ra.
82
The co m b in ed p r e d i c t i v e i n d e x
. . . .
C o m p a r a t i v e r e s u l t s ............................
83
84
Com parative s i g n i f i c a n c e of
p r o g n o s tic m easures
.................................
84
v il
CHAPTER
PAGE
........................
87
C o n c l u s i o n ....................................................................
87
I n t e r p r e t a t i o n of r e s u l t s
C o n c l u s i o n s ...........................................
BIBLIOGRAPHY. .
89
...............................................................
91
APPENDIX.......................................................................................
94
LIST OF TABLES
TABLE
I.
PAGE
Table X II, P e r r y Study:
Showing I n t e r -
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 tw ee n
T e a c h e r s ’ M ark s on M a t h , 1 , M a t h ,
2 , Ma th 3 , M a t h . 4 , an d O r i e n t a t i o n
S c o r e s o n Iowa M a t h e m a t i c s T e s t ,
P u r d u e E n g l i s h T e s t , Iowa C h e m i s t r y
T e s t , I n t e l l i g e n c e T e s t ( A m e r ic a n
C o u n c i l ) , an d P u r d u e P e r s o n a l i t y
R a t i n g s . . . ......................................
II.
11
C o m p a r i s o n o f t h e A v e r a g e s Made by
S t u d e n t s who W it h d r e w from S c h o o l
W it h Those Made b y S t u d e n t s Who
C o m p le t e d t h e E n t i r e C o u r s e o f
S t u d y .........................................................
III.
C o m p a r i s o n o f t h e A v e r a g e s Made
by 14 G i r l s a n d 50 Boys . . . . . . .
IV .
26
28
C o m p a r i s o n o f A v e r a g e s Made by
S t u d e n t s w i t h Minimum M a t h e m a t i c a l
R e q u i r e m e n t s w i t h T hose Made by
S t u d e n t s w i t h More Than Minimum
R equirem ents
.....................................................
30
TABLE
V.
C o r re la tio n of S tu d en ts C hronological
Age W i t h t h e V a r i o u s P r o g n o s t i c
a n d S u c c e s s M e a s u r e s Employed
i n t h e S t u d y . . . . . .............................
VI.
The I n t e r c o r r e l a t i o n s o f t h e F i v e
Success M easures:
Score D if f e r e n c e s
(T 2-T 1), Second A chievem ent T e s t i n
E le m e n ta ry A lg e b ra (T 2 ), Achievement
T e s t i n I n t e r m e d i a t e A lg e b ra (T3),
A v e r a g e s o f G r a d e s on C l a s s r o o m
T e s t s ( T 4 ) , A v e r a g e s o f G-rades i n
Homework ( H ) ............................. ....
V II.
C o r r e l a t i o n s B e tw ee n F i v e S u c c e s s
Measures:
Score D if f e r e n c e s
( T 2 - T 1 ) J S e c o nd A c h i e v e m e n t T e s t
i n E lem entary A lg eb ra (T2), A chieve­
m ent T e s t i n I n t e r m e d i a t e A l g e b r a
( T 3 ) , A v e r a g e s o f G-rades on C l a s s ­
room T e s t s ( T 4 ) , A v e r a g e s o f G-rades
i n Homework ( H ) , a n d S e v e n P r o g n o s t i c
M e a s u r e s ................................................
V III.
The M eans, S t a n d a r d D e v i a t i o n s , and
C o e ffic ie n ts of M ultiple C o rre la tio n
o f t h e F i v e S u c c e s s M e a s u r e s ....................
X
TABLE
PAGE
IX .
W e i g h t s o f S u c c e s s M e a s u r e s ............................ ..... . A3
X.
C o r r e l a t i o n of S u c c ess Measures
w i t h t h e C r i t e r i o n ............................................... . .
XI.
46
The D i s t r i b u t i o n o f G r a d e s on t h e
S u c c e s s S c a l e ............................ ........................ ......... . 48
X II.
C o r r e l a t i o n s B e tw ee n Q u a n t i t a t i v e
P sy ch o lo g ica l Scores (Q ), L in g u is tic
P s y c h o lo g ic a l S co res ( L ) , Gross
P s y c h o l o g i c a l S c o r e s ( G ) , a nd
V a r i o u s P r o g n o s t i c a nd S u c c e s s
Measures
X III.
...................................................................
50
G r a d e s and S u c c e s s S c o r e s (K) P r e ­
d i c t e d by G r o s s P s y c h o l o g i c a l
S c o r e s ( G ) .................................
XIV.
54
C o r r e l a t i o n s o f P r e v i o u s G ra d e A v e r a g e s
i n M a t h e m a t i c s (PM), a nd S u b j e c t s
O ther than M athem atics (P ), w ith
V a r i o u s P r o g n o s t i c and S u c c e s s
M e a s u r e s ........................
XV.
58
G r a d e s and S u c c e s s S c o r e s (K) P r e ­
d i c t e d by P r e v i o u s Gra de A v e r a g e s
i n M a t h e m a t i c s ( P M ) ............................
60
xi
PAGE
TABLE
XVI.
C o r r e l a t i o n s B e tw ee n A c h i e v e m e n t
T e s t i n E lem en tary A lg e b ra (T l)
and th e V a rio u s P r o g n o s t i c and
S u c c e s s M e a s u r e s ............................................
XVII.
64
G r a d e s a n d S u c c e s s S c o r e s ( K) P r e ­
d i c t e d by S c o r e s on An A c h i e v e ­
ment T e s t i n E l e m e n t a r y A l g e b r a ( T l )
XV III.
66
C o r r e l a t i o n s o f th e Four M ajor
P ro g n o s tic M easures, the Gross
P s y c h o l o g i c a l S c o r e ( G ) , The
P r e v i o u s Gra de A v e r a g e i n M a t h e ­
m a t i c s (PM), t h e A c h i e v e m e n t T e s t
i n E lem entary A lg eb ra ( T l ) ,
the
Combined I n d e x (G 4* PM + T l ) ,
w ith V a rio u s P r o g n o s tic and
S u c c e s s M e a s u r e s ........................................
XIX.
•
70
The A v e r a g e s , S t a n d a r d D e v i a t i o n s ,
S tan d ard Probable E rro rs of
E s t i m a t e , f o r t h e M a jo r P r o g ­
n o s t i c M easures:
And t h e Mean
and S ta n d a rd D e v ia tio n o f th e
. C riterio n .
. . . . . .
72
x ii
PAGE
TABLE
XX.
P r e d i c t i o n o f G r a d e s a nd S u c c e s s
S c o r e s by a Combined I n d e x o f
th e G ross P s y c h o l o g i c a l Score
( G ) , t h e P r e v i o u s Grade A v e r a g e
i n M a t h e m a t i c s (PM), a nd t h e
E le m e n ta ry A lg e b ra Achievement
T e s t (Tx ) ..................................................
XXI.
76
The R e l a t i v e S i g n i f i c a n c e o f
Four P r o g n o s t i c Measures
I n d i c a t e d i n Terms o f t h e
G rad e P o i n t
XX II.
...........................................
.
77
C o r r e l a t i o n s of th e Four Major
P r o g n o s t i c M e a s u r e s , The G r o s s
P s y c h o lo g ic a l Score (G ), the
P r e v i o u s G ra d e A v e r a g e i n M a t h e ­
m a t i c s (PM), t h e A c h i e v e m e n t T e s t
i n E lem entary A lg e b ra (T ^), the
Combined I n d e x (G * PM * T]_), w i t h
V a rio u s P r o g n o s t i c and S u c c ess
M e a s u r e s ........................................................................
85
x iii
TABLE
X X III.
PAGE
The A v e r a g e s , S t a n d a r d D e v i a t i o n s ,
S ta n d a r d and P ro b a b le E r r o r s of
E s t i m a t e , f o r t h e M ajor P ro g n o s­
t i c M e a s u r e s ; And t h e Mean a n d
S tan d ard D e v ia tio n of the
C r i t e r i o n ..................................
XXIV.
. . . . . .
86
The R e l a t i v e S i g n i f i c a n c e o f
Four P r o g n o s ti c M easures
I n d i c a t e d i n Terms o f t h e
Grade P o i n t
.......................
88
CHAPTER I
THE PROBLEMS
ITS IMPORTANCE AND ORGANIZATION
T h is stu d y in v o lv e d an a n a l y s i s o f th e p r e d i c ­
t i v e c a p a c i t y o f s e v e r a l e d u c a t i o n a l m e a s u r e s when
used as in d ic e s to su ccess in in te rm e d ia te a lg e b r a .
The o b j e c t was t o e s t a b l i s h a more e x a c t b a s i s f o r
s t u d e n t c o u n s e l l i n g i n f r e s h m a n m a t h e m a t i c s a t a tw oyear ju n io r college.
I.
The p r o b l e m .
THE PROBLEM
The p r o b l e m was t o d e t e r m i n e t h e
b e s t p r e d ic tio n p o s s ib le of a s tu d e n t ’ s grade i n i n t e r ­
m e d i a t e a l g e b r a when g i v e n ( 1 ) h i s s c o r e on a p s y c h o l o g i
c a l exam ination,
( 2 ) h i s s c o r e on an a c h i e v e m e n t t e s t
i n e l e m e n t a r y a l g e b r a a n d ( 3 ) an a v e r a g e o f h i s p r e v i o u s
grade s .
Sub p r o b l e m .
As c o r o l l a r i e s o r su b p r o b l e m s ,
t h e f o l l o w i n g q u e s t i o n s were i n v e s t i g a t e d .
What k i n d
o f a p r e d i c t i o n may be made o f a s t u d e n t ' s p r o b a b l e
s u c c e s s i n i n t e r m e d i a t e a l g e b r a fro m (1). h i s s c o r e on
an achievem ent t e s t in elem en tary a lg e b r a alone?
h i s s c o r e on a p s y c h o l o g i c a l e x a m i n a t i o n a l o n e ?
average of h is p revious grades?
(2)
(3) a n
2
II,
ORGANIZATION OF STUDY
Ma.1 o r I s s u e s ,
I n any problem o f p r o g n o s i s i t
i s i m p e r a t i v e t h a t a v a l i d and r e l i a b l e c r i t e r i o n o f
s u c c e s s o r s t a n d a r d o f c o m p a r i s o n be e s t a b l i s h e d *
One
o f th e most im p o r t a n t i s s u e s i n t h i s stu d y in v o lv e d
the e s ta b lis h m e n t of a c r i t e r i o n of su ccess in i n t e r ­
m ediate alg eb ra*
The way i n w h i c h t h e s c a l e o f s c o r e s
w h i c h m e a s u r e d s u c c e s s was d e t e r m i n e d i s d e s c r i b e d i n
C hapter I I I .
A f t e r t h e c r i t e r i o n was e s t a b l i s h e d , t h e n e x t s t e p
was t o compare i t w i t h m e a s u r e s o f i n t e l l e c t u a l c a p a ­
c i t y , m a th e m a tic a l a b i l i t y and s c h o l a r s h i p *
The
r e s u l t i n g r e l a t i o n s h i p s have been c o m p le te ly r e p o r t e d
under a p p ro p ria te c h ap ter headings, i . e . ,
In tellig en ce,
C h a p te r VI; S c h o l a r s h i p , C h a p te r V II; M a th em atica l
A b i l i t y , C hapter V I I I .
I n o r d e r to so lv e th e problem a s s t a t e d , i t
was n e c e s s a r y t o e s t a b l i s h t h e r e l a t i o n s h i p b e t w e e n
th e c r i t e r i o n and the p r e d i c t i v e m easu res u se d a s a
team o r b a t t e r y .
i n C hapter IX.
T his r e l a t i o n s h i p h as been r e p o r t e d
A d i s c u s s i o n a n d summary o f t h e f i n d ­
in g s of the e n t i r e
s t u d y i s c o n t a i n e d i n C h a p t e r X.
In tr o d u c tio n to stu d y .
The r e m a i n d e r o f t h i s
c h a p te r has been devoted to a c o n s i d e r a ti o n of the
im p o rtan c e of th e study*
The f o l l o w i n g c h a p t e r
c o n t a i n s a resume o f s e v e r a l r e l a t e d i n v e s t i g a t i o n s .
The p r o c e d u r e f o l l o w e d ,
t h e m in o r i s s u e s i n v o l v e d ,
and t h e c r i t e r i o n o f s u c c e s s i n t h i s s t u d y h a v e b e e n
c o n sid ere d i n C hapters I I I ,
III.
IV, a n d V, r e s p e c t i v e l y .
IMPORTANCE OF STUDY
E du cation al gu id an ce.
T h i s s t u d y m i g h t be
c o n s i d e r e d w o r t h w h i l e f o r a number o f s p e c i f i c r e a ­
sons.
A l l o f th e s e r e a s o n s , however, a re i n c l u d e d
by t h e b r o a d t e r m o f e d u c a t i o n a l g u i d a n c e .
There i s
no l e v e l a t w h i c h g u i d a n c e i s o f more i m p o r t a n c e
th an the j u n i o r c o l l e g e .
F urther,
the f a c t o r s i n ­
volved in g iv in g s tu d e n t counsel i n re g a rd to f r e s h ­
man m a t h e m a t i c s a n d t o t h e s p e c i f i c s u b j e c t i n t e r ­
m ediate a lg e b ra a re e s p e c i a l l y p e r t i n e n t .
Im portant i s s u e s Involved in g u id an c e .
The
i s s u e s in v o lv e d in ' the stu d y of freshm an m athem atics,
p a r t i c u l a r l y a l g e b r a , h a v e b e e n c o n t r o v e r s i a l am ongst
e d u c a t o r s f o r a g r e a t number o f y e a r s .
These i ssu e s*
may be sum m arize d b r i e f l y a s f o l l o w s :
1.
What i s t h e r e a s o n f o r t h e r e l a t i v e l y
h i g h m o r t a l i t y r a t e i n some f r e s h m a n m a t h e m a t i c s
4
classes?
2.
What i s t h e b a s i s f o r s t u d e n t c o u n s e l l i n g
i n r e g a r d to the study of a lg e b ra?
3.
What a r e t h e f a c t o r s w h i c h i n f l u e n c e
su c c e ss o r f a i l u r e i n the s u b je c t?
4.
Does t h e s t u d y o f a l g e b r a r e q u i r e s p e c i a l
ab ilities?
5.
I s i t p o s s ib le to p r e d i c t success or
f a i l u r e i n the su b je c t?
I n t h i s s t u d y i t was n o t d e s i r e d t o e n t e r i n t o
a prolonged d is c u s s io n of r e l a t i v e e d u c a tio n a l m e rits
of in term ed iate a lg e b ra.
I t was, h o w e v e r , h o p e d
t h a t d a t a s i g n i f i c a n t t o t h e i s s u e s i n v o l v e d w o u ld
be r e v e a l e d .
CHAPTER I I
RELATED STUDIES
O nly a few o f t h e n um erous r e l a t e d s t u d i e s h a v e
been re p o rte d in t h i s c h a p te r.
An a t t e m p t h a s b e e n
made t o i n d i c a t e t h e g e n e r a l t r e n d o f o p i n i o n .
D iv ersified s e ttin g s .
A num ber o f s t u d i e s
s i m i l a r t o t h i s one h a v e b e e n m ade.
The g r e a t m a j o r -
i t y considered the f a c t o r s in flu e n c in g success in
m ath em atics o n ly as they r e l a t e d to su c c e s s i n o th e r
subjects.
Of t h e s t u d i e s w h i c h c o n s i d e r e d o n l y t h e
s p e c i f i c s u b j e c t , a l g e b r a , t h e g r e a t e r num ber were
made a t t h e h i g h s c h o o l o r j u n i o r h i g h s c h o o l l e v e l .
A few h a v e b e e n made a t t h e c o l l e g e l e v e l .
The i n ­
v e s t i g a t o r was u n a b l e t o d i s c o v e r a s i m i l a r s t u d y
a t the j u n i o r c o lle g e l e v e l .
D iscrepancies in c o r r e la tio n s .
R esu lts in d i ­
c a t e d by t h e s e s t u d i e s v a r i e d c o n s i d e r a b l y .
A corre­
l a t i o n o f . 4 2 was r e p o r t e d by 0 . C. R o s s '1' b e t w e e n
m a r k s i n m a t h e m a t i c s a n d t h e Terman i n t e l l i g e n c e
0.
C. R o s s , The R e l a t i o n B e tw ee n G-rade S c h o o l
R ecord and High S ch o o l A ch iev em en t: A S tudy o f th e
D i a g n o s t ic Value of I n d i v i d u a l Record C a r d s , t e a c h e r s
C o l l e g e C o n t r i b u t i o n s t o E d u c a t i o n , Ho. 16 6 , Hew Y o r k ,
1925.
6
e x a m in a tio n , w h ile a c o r r e l a t i o n o f ,80 h a s b een
r e p o r t e d by F e i n g o l d
a lg e b r a marks.
2
betw een i n t e l l i g e n c e and
I n t h e l a t t e r s t u d y , h o w e v e r , m ark s
on c l a s s r o o m r e c i t a t i o n s a n d t e s t s were c o n s i d e r e d
r a t h e r than the a c t u a l te a c h e r g ra d e s .
C orrelations
r e p o r t e d i n o t h e r s t u d i e s ra n g e d betw een t h e s e e x trem es.
►
In a study of a lg e b r a p ro g n o s is , P a u lin e
P a r k e r i n d i c a t e s a c o r r e l a t i o n o f .46 b e t w e e n i n 3
t e l l i g e n c e a n d B9 a l g e b r a t e s t s c o r e s .
H a r r y E.
E l d e r , i n a s t u d y o f t h e same k i n d , r e p o r t s a c o r r e l a ­
t i o n o f .60'. b e t w e e n m a r k s i n a l g e b r a a n d i n t e l l i 4
g e n c e a s m e a s u r e d by t h e O t i s i n t e l l i g e n c e t e s t .
S i m i l a r d i s c r e p a n c i e s were n o t e d b e t w e e n m a r k s i n
a l g e b r a and a v e r a g e s o f p r e v i o u s g r a d e s i n a r i t h m e tic .
The c o r r e l a t i o n
. 5 8 r e p o r t e d by T. L. K e l l y
5
G u s t a v e A. F e i n g o l d , " C o r r e l a t i o n b e t w e e n
I n t e l l i g e n c e and S c h o l a r s h i p , " S c h o o l R e v i e w , V o l . 32;
4 5 5 -4 6 9 , J u n e , 1924.
^ P a u l i n e P a r k e r , "A S t u d y o f A l g e b r a
( u n p u b l i s h e d M a s t e r ' s t h e s i s , The U n i v e r s i t y
C a l i f o r n i a , Los A n g e l e s , 1 9 3 1 ) , p . 6 1 .
4
H a r r y E. E l d e r ,
P e r c e n t i l e Rank i n
gence as a P ro g n o sis of Success i n A lg e b ra ,"
R e v i e w , V o l . 3 4, 5 4 3 - 5 4 6 , S e p t e m b e r , 1926.
P ro g n o sis,"
of Southern
In te lli­
School
^ T. L* K e l l y , S t a t l s t i c a l Method (New Y o r k :
The M a c M i ll a n Company, 1923)*
7
s t a n d s a b o u t mid-way b e t w e e n t h e e x t r e m e s o f t h e s e
relatio n sh ip s.
Consensus of o p i n i o n .
were d u e , f o r t h e m o s t p a r t ,
These d i s c r e p a n c i e s
to f a c t o r s of which the
i n v e s t i g a t o r s were u s u a l l y q u i t e a w a r e .
The c o n c l u ­
s i o n s d raw n f r o m a l l s t u d i e s would f o r e xam ple i n c l u d e
the fo llo w in g p o i n t s :
1.
T h e r e was a m ark e d t e n d e n c y t o w a r d h i g h e r
c o r r e l a t i o n s w i t h s u c c e s s i n a l g e b r a and most of th e
o t h e r f a c t o r s e m p lo y ed when t h i s s u c c e s s was i n d i c a t e d
by m e a s u r e s o t h e r t h a n t e a c h e r s ' g r a d e s .
2.
I t was m o st g e n e r a l l y c o n c l u d e d t h a t t h e
b e s t i n d i c a t i o n o f s u c c e s s i n any s u b j e c t c o u l d be
s e c u r e d from a m e a s u r e o f a b i l i t y o r p r e v i o u s e x ­
p e rie n c e i n the s p e c i f i c s u b je c t i t s e l f .
3*
H i g h e s t c o r r e l a t i o n s were g e n e r a l l y s e c u r e d
betw een s u c c e s s i n a l g e b r a and a c o m b in a tio n of
m easures.
S i n c e t h e t r e n d o f o p i n i o n seemed t o be i n one
d i r e c t i o n , a d e t a i l e d a n a l y s i s o f o n l y a few o f t h e
more i m p o r t a n t a n d more c l o s e l y r e l a t e d s t u d i e s h a s
been r e p o r t e d h e r e .
8
F a c t o r s which t n f l u e n c e su c c e s s i n c o l l e g e a l g e b r a .
A s t u d y u n d e r t h i s t i t l e by M*. V. M a r s h a l l ^ was r e p o r t e d
i n a 1939 i s s u e o f ‘'The M a t h e m a t i c s T e a c h e r " .
study has been r e p o r te d here because i t
approxim ates the study a t hand.
The
so c l o s e l y
In d e te rm in in g the
f a c t o r s which i n f l u e n c e d s u c c e s s o r f a i l u r e i n c o l l e g e
a l g e b r a , M a r s h a l l was c o n c e r n e d w i t h t h e r e l a t i o n s h i p s
betw een f o u r f a c t o r s .
T hese f a c t o r s were g r a d e s i n
c o lle g e a lg e b r a , p re v io u s achievem ent i n a lg e b r a , i n ­
t e l l i g e n c e and m a th e m a tic a l a p t i t u d e .
Measurement of
t h e c a p a c i t i e s and a b i l i t i e s o f 44 f r e s h m e n e n r o l l e d i n
t h r e e c o l l e g e a l g e b r a c l a s s e s was made i n t h e f o l l o w i n g
manner:
1.
Knowledge o f h i g h s c h o o l a l g e b r a was mea­
s u r e d by t h e C o lu m b ia R e s e a r c h B u r e a u A l g e b r a T e s t .
( M a r s h a l l s t a t e d t h a t he c o n s i d e r e d t h i s a more
r e l i a b l e m e a s u r e t h a n c o u l d be o b t a i n e d by a v e r a g i n g
the s tu d e n ts p re v io u s g rad e s i n a lg e b r a ) .
2 . A cad em ic i n t e l l i g e n c e was m e a s u r e d by t h e
A m erican C o u n c il P s y c h o l o g i c a l E x am in a tio n .
3. M athem atical a p t i t u d e ( s p e c i f i c m athem ati­
c a l i n t e l l i g e n c e ) was m e a s u r e d by t h e Iowa A l g e b r a
A ptitude t e s t .
4.
The t h r e e p r e c e d i n g m e a s u r e s we re made a t
M. V. M a r s h a l l , "Some F a c t o r s ? /hich I n f l u e n c e
S u c c e s s i n C o l l e g e A l g e b r a , " The M a t h e m a t i c s T e a c h e r ,
XXXII, 1 7 2 - 7 4 , A p r i l , 1 9 3 9 .
9
the b e g in n in g of the c o u rse .
The f o u r t h f a c t o r ,
s t u d e n t a c c o m p l i s h m e n t i n c o l l e g e a l g e b r a , was
i n d i c a t e d by t h e p r o f e s s o r ’ s te r m g r a d e . M a r s h a l l
a r r a n g e d t o have g r a d e s d i s t r i b u t e d i n a c c o r d a n c e
w i t h a s y s t e m o f m a r k i n g w h ic h r e d u c e d i n d i v i d u a l
i d i o s y n c r a c i e s i n j u d g m e n t t o a minimum. M arks
o b t a i n e d by t o t a l l i n g s t u d e n t s c o r e s on t e s t s and
e x a m in a tio n s , a c c o rd in g to t h i s system , ranged
fro m 52 t o 6 0 0 .
C o e f f i c i e n t s o b t a i n e d by c o r r e l a t i n g t h e f i r s t
t h r e e m e a s u r e s w i t h t h e f o u r t h we re a s f o l l o w s :
1.
Grade w i t h a p t i t u d e . 5 5 7 .
2.
Gra d e w i t h a c h i e v e m e n t . 7 8 8 .
3.
G rad e w i t h p s y c h o l o g i c a l e x a m i n a t i o n . 4 9 2 .
4.
G ra d e w i t h ( a c h i e v e m e n t , a p t i t u d e , and
p sy c h o lo g ic a l e x am in a tio n ,) .84.
From t h e s e r e l a t i o n s h i p s , M a r s h a l l c o n c l u d e s t h a t
" th e b e s t s i n g l e in d ex of a s t u d e n t ' s grade i s the
r e s u l t o f an a c h i e v e m e n t t e s t c o v e r i n g h i s p r e v i o u s
high school a lg e b r a .
(.
. . ) and f u r t h e r t h a t a
co m bin ed i n d e x o f h i g h s c h o o l a c h i e v e m e n t , a l g e b r a i c
a p t i t u d e , and g e n e r a l i n t e l l i g e n c e y i e l d s a v e ry
h ig h c o r r e l a t i o n w ith achievem ent i n c o lle g e a l g e b r a . ”
P re d ic tio n eq uations fo r success in college
m athem atics.
T h i s s t u d y was made by R o b e r t D. P e r r y
7
i n f u l f i l l i n g the re q u ir e m e n ts f o r the deg ree of
7
R o b e r t D. P e r r y , " P r e d i c t i o n E q u a t i o n s f o r
S u c c e s s i n C o l l e g e M a t h e m a t i c s , " (George P e a b o d y
C ollege f o r T eachers, N a s h v ille :
Collom a n d G h e r t n e r
Company, 1 9 3 4 ) .
10
d o c to r o f p h ilo so p h y i n the g ra d u a te school of edu­
c a t i o n o f George Peabody C o lle g e f o r T e a c h e r s .
For
w e l l s t a t e d re a s o n s P e r r y w ished to p re d e te rm in e
s tu d e n t su ccess in m athem atics.
The s t u d y was made
a t P u r d u e U n i v e r s i t y a n d 400 s t u d e n t s were s e l e c t e d
a t random fro m t h e c l a s s o f 1929* - F r e s h m e n a t t h e
u n i v e r s i t y w e re r e q u i r e d t o t a k e a b a t t e r y o f s t a n d ­
a r d i z e d t e s t s d u r i n g o r i e n t a t i o n w e ek .
H a vin g r e ­
c o r d e d d a t a fro m t h e s e t e s t s P e r r y p r o c e d e d t o t r a c e
the s tu d e n ts through f o u r sem esters of m ath em atics.
A few o f t h e r e s u l t s may be i n f e r r e d fro m t h e
r e p r o d u c t i o n o f Table I ,
s t u d y ) , page 11.
( T a b l e XII o f t h e P e r r y
F r o m ‘t h e s e r e l a t i o n s h i p s , P e r r y
draws th e f o l l o w i n g c o n c l u s i o n s :
1 . The o r d e r o f t h e p r e d i c t i v e v a l u e o f t h e
t e s t f o r t e a c h e r s * m ark s i n M a t h . 1 i s :
Iowa
M a t h e m a t i c s T e s t , Iowa Chemis-try T e s t , P e r s o n a l ­
i t y r a t i n g , I n te llig e n c e T est, E nglish T e st.
2 . The c o r r e l a t i o n o f M a t h . 1 w i t h t h e
b a t t e r y o f t e s t s I s so s t r o n g t h a t t h e r e g r e s s i o n
e q u a tio n technique should ren d e r q u ite a c c u ra te
p red ictio n s.
' 3* The t e s t s l o s e much o f t h e i r p r e d i c t i v e
v a lu e s t a r t i n g p r o g r e s s i v e l y w ith Math. 2 . W ith
Math. 4 a s a c r i t e r i o n , how ever, Math. 1, M ath. 2,
a n d M a t h . 3 , b e g i n t o show p r e d i c t i v e v a l u e .
A study of a lg e b ra p r o g n o s is .
T h i s s t u d y was
made by P a u l i n e P a r k e r 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
11
TABLE I
(TABLE X I I PERRY STUDY)
Showing I n t e r - C o r r e l a t i o n C o e f f i c i e n t s Be tw ee n
T e a c h e r s * M arks on M a t h . 1 , M a th . 2 , Math 3, Math* 4 ,
a n d O r i e n t a t i o n S c o r e s on Iowa M a t h e m a t i c s T e s t ,
P u r d u e E n g l i s h T e s t , Iowa C h e m i s t r y T e s t , I n t e l ­
l i g e n c e T e s t (American C o u n c i l ) , and Purdue P e r s o n a l i t y
R atin g s.
N
Math. 3
Math. 2
M ath. 1
Iowa M a t h .
In tellig en ce
Iow a Chem.
P u r d u e Eng.
P erso n ality
M a t h . Math,.M a th . M a t h .
4
2
1
3
1?1
5oo
235 369
.26
.39
• 25
.24
.08
.16
.0 6
.19
♦21
.18
♦13
.13
.10
.13
.1 6
.3 2
.42
.41
.35
.32
.42
.74
.51
.6 6
.23
.52
Iowa I n t e l ­
M a th . l i g e n c e
4oo
400
. 52
.55
.46
.34
.68
.65
.27
Iowa
Chem.
400
.55
.30
Purdue
Eng.
400
.30
re q u irem e n ts f o r the degree of m aster of a r t s a t
the U n iv e rs ity of Southern C a lif o r n ia .
8
The p r o b l e m
was t o d e t e r m i n e t h e p r o g n o s t i c v a l u e o f a number o f
m easures i n o rd e r to give p u p ils adequate co u n sel
i n re g a rd to h ig h school a lg e b ra .
M iss P a r k e r
c o l l e c t e d d a t a r e g a r d i n g p u p i l s o f two j u n i o r h i g h
s c h o o l s a s t h e y p r o g r e s s e d t h r o u g h t h e B8, A8, and
B9 g r a d e s .
posal:
The f o l l o w i n g m e a s u r e s w e r e a t h e r d i s ­
I n te llig e n c e q u o tie n t, chro n o lo g ical age,
m ental age, a r it h m e t ic re a so n in g , a r i th m e t ic funda­
m e n t a l s , a r i t h m e t i c r e a d i n g , B8 a n d A8 m a t h e m a t i c s
t e s t a v e r a g e s , B9 a l g e b r a t e s t a v e r a g e .
By c o m p a r in g
t h e s e m e a s u r e s w i t h t h e B9 a l g e b r a t e s t a v e r a g e she
concludes:
1 . T h a t a much g r e a t e r r e l a t i o n s h i p e x i s t s
b e t w e e n B8 a n d A8 m a t h e m a t i c s a n d B9 a l g e b r a
t h a n b e t w e e n an y o f t h e o t h e r f a c t o r s .
(T his
c o e f f i c i e n t was r e p o r t e d a s . 7 4 3 ) .
2 . T h i s c o r r e l a t i o n .7 4 3 i s r a i s e d t o o n l y
. 7 5 2 by c o m b i n i n g i t w i t h I . Q . a n d a r i t h m e t i c
fundame n t a 1 s .
3* I n t e l l i g e n c e q u o t i e n t , m e n t a l a g e , a r i t h ­
m e tic r e a s o n i n g , a r i t h m e t i c fu n d a m e n ta ls and
a r i t h m e t i c r e a d i n g have v ery n e a r l y e q u a l c o r r e ­
l a t i o n s w i t h B9 a l g e b r a .
(T h ese a v e r a g e d a r o u n d
.4 1 ).
Q
P a r k e r , opt, c i t .
13
An e v a l u a t i o n o f m e t h o d s o f p r e d i c t ! n g s c h o o l
success In m athem atics»
T h i s study was made by Ge o rg e
Raymond Z i e g e n f u s s ^ i n f u l f i l l i n g t h e r e q u i r e m e n t s
f o r the degree of m a ste r of a r t s i n e d u c a tio n a t th e
U n iv e rs ity of Southern C a l i f o r n ia ,
Z ie g e n fu s s wished
t o e v a l u a t e d i f f e r e n t methods u s e d i n a d v i s i n g c e r t a i n
s tu d e n ts concerning t h e i r study of m athem atics.
As
a p a r t o f t h e s t u d y i t was d e s i r e d t o d e t e r m i n e t h e
e v id e n c e which e x i s t e d to J u s t i f y th e use o f th e
f o l l o w i n g b a s i s a s s t a n d a r d s f o r p r e d i c t i n g mathema­
t i c a l success.
a.
The p u p i l ’ s i n t e l l i g e n c e q u o t i e n t ?
b . A p u p i l ’s success in o th er school su b je c ts
b a s e d e i t h e r upon t e a c h e r ' s e s t i m a t e s , g r a d e s o r
tests?
c . Would a c o m b i n a t i o n o f a l l t h e f a c t o r s
used in our school fu rn is h a s c i e n t i f i c b a s is
f o r p r e d i c t i n g s u c c e s s i n m athem atics?
As a r e s u l t o f a r a t h e r e x t e n s i v e i n v e s t i g a t i o n
o f n u m ero u s s t u d i e s p e r t a i n i n g t o t h e s e q u e s t i o n s ,
Z i e g e n f u s s came t o t h e f o l l o w i n g c o n c l u s i o n s :
a.
The c o r r e l a t i o n b e t w e e n s u c c e s s i n m a t h e ­
m a t i c s and i n t e l l i g e n c e a s d e t e r m i n e d by s u c h *
^ G e org e Raymond Z i e g e n f u s s , ”An E v a l u a t i o n o f
M e th o d s o f P r e d i c t i n g S c h o o l S u c c e s s i n M a t h e m a t i c s , ”
(u npublished M a s te r 's t h e s i s , th e U n iv e rs ity of Southern
C a l i f o r n i a , L os A n g e l e s , 1929 )* .*
14
t e s t s a s t h e C h i c a g o , Teraian a n d O t i s r a n g e s
from a low o f . 1 9 t o a h i g h o f .51* T h e r e f o r e ,
a p u p i l 1s i n t e l l i g e n c e q u o t i e n t c a n n o t he r e ­
l i e d upon a s a s o l e b a s i s f o r th e c l a s s i f i c a t i o n
of p u p i ls i n m athem atics.
b . E l e m e n t a r y s c h o o l m ark s c o r r e l a t e h i g h e r
w i t h s u c c e s s i n h i g h s c h o o l m a t h e m a t i c s t h a n do
t e s t s i n elem entary school s u b j e c t s .
C o rrelatio n s
r a n g i n g f r o m . 0 2 t o . 7 0 we re f o u n d b e t w e e n s u c c e s s
i n v a r i o u s sch o o l s u b j e c t s and m ath em a tics.
c . F i n d i n g s seem t o i n d i c a t e t h a t p r o b a b l y
n o t much more may be e x p e c t e d o f t e s t s u s i n g a
c o m b i n a t i o n o f f a c t o r s t h a n may be e x p e c t e d
from g e n e r a l i n t e l l i g e n c e t e s t s .
(Z ieg en fu ss,
however, r e p o r t e d t h a t K e lly , Flem ing and o t h e r s
g o t c o r r e l a t i o n s r a n g i n g fro m . 8 4 t o .8 9 by
u s i n g a com posite of f a c t o r s to p r e d i c t su c ce ss
in m athem atics).
CHAPTER I I I
PROCEDURE
I n C h a p t e r I i t was i n d i c a t e d t h a t t h i s s t u d y
in v o lv e d th e measurement of c e r t a i n s t u d e n t c a p a c i t i e s .
T h es e m e a s u r e s were t h e n com pa red w i t h a c r i t e r i o n
of su ccess in in te r m e d i a t e a lg e b r a in o r d e r to
d e term in e t h e i r p r e d i c t i v e powers.
The f o l l o w i n g
c h a p t e r d e s c r i b e s how t h e s e m e a s u r e s w ere made an d
t h e way i n w h i c h t h e y were compare d w i t h t h e c r i ­
terio n .
I.
COLLECTING AND RECORDING OF DATA
Kind a n d s o u r c e o f d a t a .
Data f o r t h i s stu d y
c o n s i s t e d f o r t h e m o st p a r t i n s c o r e s , r a t i n g s and
g r a d e s made by s t u d e n t s e n r o l l e d i n t h r e e j u n i o r
college c la ss e s in in te rm e d iate a lg e b ra.
The i n i t i a l
e n r o l l m e n t o f t h e t h r e e c l a s s e s was e i g h t y - f o u r
stu d en ts.
D uring th e c o u rse o f th e s e m e s te r , twenty
s t u d e n t s w i t h d r e w fro m s c h o o l .
six ty -fo u r students,
T his l e f t a t o t a l of
t h i r t e e n were g i r l s a n d f i f t y -
one b o y s .
T h e r e were n i n e so p ho m o re s a n d f i f t y - f i v e
freshm en.
The a v e r a g e a g e was e i g h t e e n y e a r s e l e v e n
m onths.
The a g e s r a n g e d fr om s e v e n t e e n y e a r s t h r e e
16
m o n th s t o t w e n t y - f o u r y e a r s .
The t h r e e c l a s s e s
w e re t a u g h t by t h e same I n s t r u c t o r a n d e a c h c l a s s
m et f o r one h o u r t h r e e t i m e s a w e ek.
The t e x t b o o k
u s e d t h r o u g h o u t t h e s e m e s t e r was W e l l ’ s a n d H a r t
In term ed iate A lgebra.
R ecording of d a ta .
G r a d e s on home work and
a t t e n d a n c e r e c o r d s w e re k e p t i n t h e u s u a l c l a s s
r o l l book.
During the course of the se m e s te r,
n um ero us m e a s u r e s o f v a r i o u s t y p e s were m ade.
Data
r e g a r d i n g t h e s e m e a s u r e s were k e p t on i n d i v i d u a l
student record cards.
The s t u d e n t ’ s name, c l a s s ,
and age a p p e a re d a t th e top of th e c a r d .
S p a c e was
a l l o t t e d f o r s t u d e n t ’ s r a t i n g on t e s t s i n t h e form
o f raw s c o r e , p e r c e n t i l e
converted sc o re .
score,
s c a l e d s c o r e , and
R e c o r d was a l s o k e p t o f t h e r a n g e ,
mean, a n d s t a n d a r d d e v i a t i o n o f a l l t e s t s .
M easurem ent.
A s ta n d a rd iz e d achievem ent t e s t
i n e l e m e n t a r y a l g e b r a was g i v e n a p p r o x i m a t e l y one
week a f t e r t h e b e g i n n i n g o f t h e s e m e s t e r .
was r e p e a t e d a t t h e c l o s e o f t h e s e m e s t e r .
T his t e s t
The p s y ­
c h o l o g i c a l e x a m i n a t i o n was a l s o g i v e n a t t h e f i r s t
o f the s e m e s te r.
11T e a c h e r - m a d e ” t e s t s c o v e r i n g v a r i o u s
p h a s e s o f t h e work w e r e g i v e n a t t h r e e t o f o u r week
17
i n t e r v a l s th ro u g h o u t th e sem ester*
A ” teacher-m ade”
t e s t c o v e r i n g t h e e n t i r e , s u b j e c t was a l s o g i v e n a t
t h e end o f t h e s e m e s t e r .
A s ta n d a rd iz e d achievem ent
t e s t i n i n t e r m e d i a t e a l g e b r a was g i v e n a t t h e c l o s e
of the se m este r.
To u n d e r s t a n d e a c h o f t h e m e a s u r e s
t a k e n , i t i s b e s t t o c o n s i d e r them s e p a r a t e l y .
II.
MEASURES EMPLOYED
The a c h i e v e m e n t t e s t i n e l e m e n t a r y a l g e b r a .
T h i s was a s t a n d a r d i z e d t e s t p u b l i s h e d by t h e Co­
op erative Test S ervice.
I t was p r e p a r e d by J o h n A.
Long o f t h e U n i v e r s i t y o f T o r o n t o a n d T. P . S i c e l o f f
o f C o lu m b ia U n i v e r s i t y .
w as:
The f u l l t i t l e
of the t e s t
A m erican C o u n c il on E d u c a tio n C o o p e ra tiv e
A lg eb ra T e s t, E lem entary A lgebra through Q u a d r a tic s ,
R e v i s e d S e r i e s , Form P , 19 3 9* 1
The r e l i a b i l i t y i n ­
d i c a t e d by t h e p u b l i s h e r s f o r a Hs t a n d a r d g r o u p ’1
was . 9 2 4 .
The t e s t was g i v e n a t b o t h t h e b e g i n n i n g
and c l o s e o f th e s e m e s t e r .
The c o r r e l a t i o n b e t w e e n
t h e two a p p l i c a t i o n s o f t h i s t e s t was . 9 0 .
The p u r ­
p o s e h e r e was n o t t o c h e c k t h e r e l i a b i l i t y o f t h e
t e s t b u t to determ ine th e d i f f e r e n c e i n sc o re s f o r
each stu d e n t.
The s c o r e d i f f e r e n c e s t h e n c o m p r i s e d
a s e p a r a te m easure.
See A p p e n d i x A
18
The a c h i e v e m e n t t e s t i n i n t e r m e d i a t e a l g e b r a .
T h i s t e s t was a l s o p u b l i s h e d by t h e C o o p e r a t i v e T e s t
S e r v i c e a n d was a l s o p r e p a r e d by Long a n d S i c e l o f f .
The f u l l t i t l e
was:
A m e r i c a n C o u n c il^ on E d u c a t i o n
C o o p e rativ e I n t e r m e d i a t e Algebra. T e s t , Q u a d r a tic s and
B eyond, R e v i s e d S e r i e s , Form P , 1939*2
The r e l i a b i l i t y
i n d i c a t e d by th e p u b l i s h e r s f o r a ” s t a n d a r d g ro u p ”
was *931*
ester,
The t e s t was g i v e n a t t h e e n d o f t h e sem­
By c o r r e l a t i n g two p a r t s o f t h e t e s t a c o e f ­
f i c i e n t o f . 8 4 was o b t a i n e d .
A r e l i a b i l i t y o f ,91.
was t h e n i n d i c a t e d f o r t h e whole t e s t (S p e arm a n
fo rm u la).
Classroom t e s t s .
tests.
T h e r e w ere f i v e o f them g i v e n d u r i n g t h e
sem ester.
work.
Thes e we re 11t e a c h e r - m a d e ”
The l a s t t e s t c o v e r e d t h e e n t i r e s e m e s t e r ' s
A t t h e end o f t h e s e m e s t e r t h e p e r c e n t i l e
s c o r e s on t h e s e t e s t s were a v e r a g e d .
The c o r r e l a ­
t i o n s b e t w e e n t h e f i v e t e s t s r a n g e d fro m . 8 0 t o .91*
The c o r r e l a t i o n o f t h e f i n a l o r f i f t h
o t h e r f o u r was a p p r o x i m a t e l y .91*
t e s t w i t h the
The f i n a l t e s t
s c o r e was w e i g h t e d t w i c e a s much a s t h e o t h e r s when
2
Ibid .
19
t h e s c o r e s were a v e r a g e d .
The a v e r a g e d s c o r e s w ere
t h e n th o u g h t o f as a measure of accom plishm ent i n
interm ed iate alg eb ra.
Home-work.
G r a d e s i n home-work w ere g i v e n on
a b a s i s of. a p o s s i b l e one h u n d r e d p o i n t s f o r e a c h
assignm ent.
Thes e s c o r e s w ere numerous and c o n s i d e r ­
a b l e v a r i a b i l i t y was e n c o u n t e r e d .
a g e d a t t h e en d o f e a c h week.
G r a d e s w ere a v e r ­
C o r r e l a t i o n s betw een
some o f t h e w e e k l y a v e r a g e s r a n g e d fr om .2 0 t o . 9 3 .
The c o r r e l a t i o n b e t w e e n a v e r a g e s f o r t h e f i r s t and
l a s t h a l f o f t h e s e m e s t e r was a p p r o x i m a t e l y
.88.
The
s e m e s t e r ’ s a v e r a g e s w e re u n d o u b t e d l y f a i r l y r e l i a b l e ,
b u t w e re n o t c o n s i d e r e d t o be a s v a l u a b l e e s t i m a t e s
o f s t u d e n t a c h i e v e m e n t o r a c c o m p l i s h m e n t a s were some
of the o t h e r m easures.
P sychological exam ination.
T his e x a m in a tio n
was p r e p a r e d by L. L. T h u r s t o n e a n d Thelma G-winn
T hurstone.
Its fu ll title
was:
American C o u n c il
on E d u c a t i o n P s y c h o l o g i c a l E x a m i n a t i o n f o r C o l l e g e
3
4F r e s h m e n , 1939 E d i t i o n .
Thurstone r e p o r t s the
r e l i a b i l i t y of t h i s t e s t as a .9 5 .
No a t t e m p t was
3I b i d .
4
L. L. T h u r s t o n e , Thelma G-winn T h u r s t o n e , a n d
D o r o t h y C. A d k i n s , ’’The 1938 P s y c h o l o g i c a l E x a m i n a t i o n
by L. L. T h u r s t o n e a n d Thelma Gwinn T h u r s t o n e , ” The
E d u c a t i o n a l R e c o r d . XX, ( A p r i l , 1 9 3 9 ) , p . 2 9 8 .
20'
made t o e s t a b l i s h t h e r e l i a b i l i t y o f t h e m e a s u r e i n
t h i s study.
The e x a m i n a t i o n c o n s i s t e d o f s i x s e p a r a t e
t e s t s w h i c h w ere c l a s s i f i e d i n t o two m a j o r d i v i s i o n s ;
q u a n t i t a t i v e and l i n g u i s t i c .
The q u a n t i t a t i v e ,
l i n g u i s t i c , a n d g r o s s s c o r e s on t h i s e x a m i n a t i o n were
considered s e p a ra te ly in p a r ts of t h i s stu d y .
The
g r o s s s c o r e was c o n s i d e r e d t o m e a s u r e g e n e r a l a c a d e m i c
in te llig en c e .
Previous g ra d e s .
Records of s t u d e n ts p re v io u s
g r a d e s were o b t a i n e d f r o m t h e f i l e s o f t h e s c h o o l
reg istrar.
P re v io u s g ra d e s i n m ath em atics and i n
a l l s u b j e c t s o t h e r t h a n m a t h e m a t i c s w e re a v e r a g e d
s e p a r a t e l y and r e c o r d e d i n term s o f g ra d e p o i n t s .
They were l o o k e d u p o n a s m e a s u r e s o f a c a d e m i c u n d e r ­
standing or a p titu d e .
III.
SUMMARY AND CLASSIFICATION OF MEASURES
C lassific atio n .
A t t h e end o f t h e s e m e s t e r ,
s c o r e s fro m t w e l v e © p a r a t e m e a s u r e s were a v a i l a b l e .
M e a s u r e s t a k e n on o r b e f o r e t h e o p e n i n g o f t h e se m es­
t e r were c l a s s i f i e d a s p r e d i c t i v e m e a s u r e s .
Those
made a t t h e c l o s e o f t h e s e m e s t e r were c o n s i d e r e d t o
be m e a s u r e s o f s u c c e s s .
S i n c e t h e h a n d l i n g o f so
21
many m e a s u r e s p r o v e d awkward e a c h was s y m b o l i z e d .
The c l a s s i f i c a t i o n a n d s y s t e m o f sy m bols u s e d was a s
follow s:
A.
M e a s u r e s w h i c h m i g h t be u s e d t o p r e d i c t
success in in te rm e d iate a lg e b ra.
(1 )
T^_; S c o r e s made on t h e f i r s t a p p l i c a ­
t i o n of the achievem ent t e s t i n elem entary
alg eb ra.
(2) Q,: Q u a n t i t a t i v e s c o r e s on t h e p s y c h o l o ­
g i c a l exam ination.
(3) L: L i n g u i s t i c s c o r e s on t h e p s y c h o l o g i ­
c a l exam ination.
(4) G: G r o s s s c o r e s on t h e p s y c h o l o g i c a l
exam ination.
(5) P : ' A v e r a g e s o f s t u d e n t s * p r e v i o u s g r a d e s
i n a l l s u b je c ts o t h e r than m athem atics.
(6) P . M.: A v e r a g e s o f s t u d e n t s * p r e v i o u s
g rad es i n m athem atics.
(7) A:
B.
Students*
chronological ages.
Those m e a s u r e s w h i c h i n d i c a t e d s u c c e s s i n
interm ediate a lg e b ra.
(1) T2 : S c o r e s r e c e i v e d fro m t h e s e c o n d
a p p l i c a t i o n o f th e a ch iev em en t t e s t i n elem en­
ta ry a lg eb ra.
(2)
a n d Tr
T0 - T t :
. d
1
S c o r e d i f f e r e n c e s b e t w e e n To
d
(3) T.,: S c o r e s made on a n a c h i e v e m e n t t e s t
in interm ediate a lg e b ra.
(4) T^: A v e r a g e s o f g r a d e s made o n f i v e
classroom t e s t s .
22
(5)
H:
A v e r a g e s o f g r a d e s i n hom e-w ork .
The c r i t e r i o n .
The s c o r e s d e r i v e d f ro m t h e
f i v e s u c c e s s m e a s u r e s e a c h i n d i c a t e d some fo rm o f
achievem ent o r accom plishm ent i n i n te r m e d i a t e a lg e b r a .
I t was t h o u g h t t h a t i f
the.se s c o r e s c o u l d be 'combined,
t h e r e s u l t i n g s c o r e s w o u ld be b e t t e r and more a c c u ­
r a t e in d ic a tio n s of success than u su a l te a c h e r g rad es.
The f a c t o r s t o b e c o n s i d e r e d i n t h e s e co m bined s c o r e s
w e re so n um ero u s t h a t a s e p a r a t e c h a p t e r , C h a p t e r V,
has been devoted to a d e s c r i p t i o n of t h i s p ro c e s s .
However, t h e s e s c o r e s , when co mbined f o r m e d a n a d d i ­
t i o n a l m easure, th e c r i t e r i o n .
IV.
CORRELATION OF MEASURES
C o e ffic ie n ts of c o r r e l a t i o n .
in c lu d e d t h e r e , were, i n a l l ,
m easures.
The c r i t e r i o n
th ir te e n separate
C o r r e l a t i o n c h a r t s were made a n d c o e f f i ­
c i e n t s b e t w e e n a l l o f t h e m e a s u r e s were co mputed by
t h e u s u a l p r o d u c t moment m e t h o d .
T h es e r e s u l t s have
b e e n r e p o r t e d i n A p p e n d i x D*
P r e d i c t iv e power.
A f te r e s t a b l i s h i n g the
r e l a t i o n s h i p s betw een th e p r o g n o s t i c m easu res and
s u c c e s s i n i n t e r m e d i a t e a l g e b r a , i t was p o s s i b l e t o .
23
illu stra te
t h e p r e d i c t i v e power o f t h e f o r m e r by
re g re ssio n equ ations.
I t was a l s o p o s s i b l e t o i n d i ­
c a t e t h e com b ined s i g n i f i c a n c e o f t h e s e m e a s u r e s a n d
th u s so lv e the problem a s s t a t e d i n C h a p te r I .
CHAPTER IV
CONTRIBUTING FACTORS
B efore th e r e l a t i o n s h i p s betw een th e v a r i o u s
p r e d i c t i v e m easures and s u c c e s s i n i n t e r m e d i a t e
a l g e b r a c o u l d b e d e t e r m i n e d , i t was n e c e s s a r y t h a t
the in f lu e n c e o f c e r t a i n f a c t o r s such as ag e, sex,
s c h o l a s t i c b a c k g r o u n d , e t c * be i n v e s t i g a t e d .
A re­
p o r t on t h e i n f l u e n c e o f t h e s e f a c t o r s h a s b een g iv e n •
in th is chapter.
I.
WITHDRAWAL FROM SCHOOL
I s s u e s i n v o l v e d . , The i n i t i a l e n r o l l m e n t o f
t h e t h r e e c l a s s e s was e i g h t y - f o u r s t u d e n t s .
Only
s i x t y - f o u r of th e s e s tu d e n ts com pleted th e c o u rs e .
i
T h u s , t h e t w e n t y s t u d e n t s who w i t h d r e w c o m p r i s e d a p ­
p r o x i m a t e l y 24 p e r c e n t o f t h e o r i g i n a l e n r o l l m e n t .
Of t h e t w e n t y s t u d e n t s , n i n e t e e n were b o y s , one a
g irl.
T h i s d e c r e a s e was c o n s i s t e n t " w i t h t h e d e c r e a s e
i n p o p u l a t i o n o f t h e whole s c h o o l a t t h e t i m e .
This
drop i n e n r o llm e n t i s , however, a c h a r a c t e r i s t i c
p r o b l e m o f t h e two y e a r j u n i o r c o l l e g e .
I t is a
t o p i c w o r t h y o f s e r i o u s i n v e s t i g a t i o n , b u t due t o
c h a n g i n g c o n d i t i o n s a d i f f i c u l t one t o a t t a c k .
The
25
m a t t e r was c o n s i d e r e d h e r e o n l y a s i t a f f e c t e d t h e
r e l i a b i l i t y of t h i s p a r t i c u l a r stu d y .
Data a v a i l a b l e ♦
Many o f t h e s t u d e n t s w i t h d r e w
w i t h i n t h e f i r s t two o r t h r e e weeks o f s c h o o l .
T h us,
i t was d i f f i c u l t t o o b t a i n s i g n i f i c a n t d a t a on t h e
group a s a w hole.
Only n i n e s c o r e s were a v a i l a b l e ,
f o r e x a m p l e , on t h e p s y c h o l o g i c a l e x a m i n a t i o n .
The
r e a s o n f o r w i t h d r a w a l c o u l d be t r a c e d t o i n a b i l i t y
t o cope w i t h s c h o o l s u b j e c t s i n o n l y t h r e e c a s e s .
I n none o f t h e s e c a s e s c o u l d d i f f i c u l t y w i t h t h e s p e ­
c ific
s u b j e c t i n v o l v e d be g i v e n a s t h e s o l e r e a s o n
f o r w ithdraw al.
The s e v e n t e e n o t h e r c a s e s p r e s e n t e d
a v a r i e t y of p o s s ib l e re a so n s f o r d is c o n tin u in g school;
jo b s,
s i c k n e s s , c hang e o f r e s i d e n c e , e t c .
Since only
a few o r no s c o r e s were a v a i l a b l e f o r e a c h m e a s u r e ,
no r e l i a b l e
c o m p a r i s o n c o u l d be made b e t w e e n t h i s
g r o u p a nd t h o s e who h a d c o m p l e t e d t h e w ho le s e m e s t e r ’ s
work.
A v e r a g e s b a s e d on a v a r y i n g number o f c a s e s
were co m pa red a n d h ave b e e n r e p o r t e d i n T a b l e I I ,
page 26.
H esuits.
I t would seem fro m t h e s c a n t y e v i ­
d e n c e a v a i l a b l e t h a t t h e s t u d e n t s who w i t h d r e w b e f o r e
26
TABLE I I
COMPARISON OF THE AVERAGES MADE BY STUDENTS WHO
WITHDREW FROM SCHOOL WITH THOSE MADE BY STUDENTS WHO
COMPLETED THE ENTIRE COURSE OF STUDY
S t u d e n t s who
com pleted
64 c o u r s e
S t u d e n t s who
withdrew
fr o m s c h o o l
1s t achievem ent t e s t in
elem entary a lg e b ra
G r a d e s on c l a s s ­
room t e s t s
Number
of
cases
Mean
Mean
18
21
24
9
25
47
10
24
31
10
51
6r
Q uan titativ e
p sy ch o lo g ical
L in g u istic
psychological
Gross
p sy ch o lo g ical
Previous grades
i n m athem atics
10
75
92
18
1.70
2.15
P revious grades o th er
th a n m athem aties
18
2*10
2.44
27
t h e e n d o f t h e s e m e s t e r were o f a somewhat l o w e r
c a l i b r e t h a n t h o s e who c o m p l e t e d t h e s e m e s t e r * s
work.
C o n d i t i o n s , h o w e v e r , c h an g e f r o m y e a r t o
y e a r a n d t h e r e was i n s u f f i c i e n t e v i d e n c e h e r e t o
come t o any d e f i n i t e c o n c l u s i o n .
th erefore,
The s t u d y was,
conducted on a b a s i s of ev id en ce f u r n i s h e d
o n l y by t h e s i x t y - f o u r s t u d e n t s who c o m p l e t e d t h e i r
w h o le s e m e s t e r ' s w o rk.
II.
Data a v a l l a b l e .
SEX
The r e l a t i o n s h i p b e t w e e n s e x
and s c h o l a s t i c c a p a c i ty h as been th o ro u g h ly i n v e s t i ­
gated elsew here.
The p r e p o n d e r a n c e o f o p i n i o n i n d i ­
c a t e s t h a t t h e r e i s no d i f f e r e n c e b e t w e e n t h e s e x e s
i n r e g a r d t o a b i l i t y t o l e a r n a n d t o p r o f i t by e d u ­
c a tio n a l experience.
T h e r e was n o t h i n g I n t h i s
s t u d y t o i n d i c a t e any o p i n i o n t o t h e c o n t r a r y .
Of t h e s i x t y - f o u r s t u d e n t s c o m p l e t i n g t h e
c o u r s e , f o u r t e e n w ere g i r l s a nd f i f t y b o y s .
I t was
c o n s i d e r e d s u f f i c i e n t t o compare o n l y t h e a v e r a g e s .
T h es e h a v e b e e n p r e s e n t e d i n T a b l e I I I ,
R esu lt.
p ag e 2 8 .
Se x d i f f e r e n c e s h a d no e f f e c t u p o n
the r e l i a b i l i t y o f t h i s stu d y .
TABLE I I I
COMPARISON OF THE AVERAGES MADE
BY 14 GIRLS AMD 5 0 "BOYS
5 0 'Boys
M
1s t achievem ent t e s t
i n elem entary a lg e b ra
2n d a c h i e v e m e n t t e s t i n
e l e m e n t a r y a l g e b r a T2
Score d i f f e r e n c e s
T2-T1
T2-- T i
Achievement t e s t i n
i n t e r m e d i a t e a l g e b r a T33
A v e r a g e s o f g r a d e s on
T4
c l a s s r o o m t e s t s T4
Average of g ra d e s
i n homework H
H
Q u a n t it a t i v e psychologic a l l scores
Q,
L in g u is tic psychological
scores
L
Gross p s y c h o lo g ic a l
G
scores
P revious grades o th e r
th a n m athem atics
P
Previous grades
i n m athem atics
PM'
C h r o n o l o g i c a l a ge
a^e
A
C r ite r io n of success
in te rm e d iate algebra K
i4 G irls
M
25.68
20.79
31.92
28.93
6
8
17.60
17.43
47.35
47.71
54.58
6 5 .2 8
31.12
29.00
6 0 .6 0
63.50'
91.72
92.50
2.37
2.53
2 .0 2
2 .1 6
18/10
19/1
5 0 .0 0
50.00
29
III.
SCHOLASTIC BACKGROUND
D ata a v a i l a b l e .
Of t h e s i x t y - f o u r s t u d e n t s
c o m p le tin g th e s e m e s te r * s work, f o r t y - s i x had p r e ­
v i o u s l y c o m p l e t e d j u s t t h e minimum r e q u i r e m e n t s i n
h ig h school m athem atics, i . e . ,
a nd p l a n e g e o m e t r y .
elem entary a lg e b ra
E ig h te e n of th e s t u d e n ts had ta k e n
one o r more c o u r s e s b e yo n d t h i s minimum.
Three of
t h i s l a t t e r group had ta k e n e l e v e n t h y e a r a l g e b r a
i n h i g h s c h o o l , two h a d t a k e n t r i g o n o m e t r y , f i v e h a d
t a k e n e l e v e n t h y e a r a l g e b r a a n d s o l i d g e o m e t r y , two
had tak e n e l e v e n t h y e a r a l g e b r a and t r ig o n o m e tr y ,
and s i x had t a k e n e l e v e n t h y e a r a l g e b r a , s o l i d
geom etry, and trig o n o m e tr y .
The g r o u p was t o o s m a l l
and too d i v e r s i f i e d w i t h in i t s e l f
to a tte m p t to e s ­
t a b l i s h any r e l i a b l e r e l a t i o n s h i p s w i t h th e v a r i o u s
m easu res employed.
G e n e ra l a v e ra g e s of t h i s group
w e r e , h o w e v e r , compa red w i t h t h o s e o f s t u d e n t s who
h a d p r e v i o u s l y t a k e n j u s t t h e minimum m a t h e m a t i c a l
requirem ents.
T hes e a v e r a g e s h ave b e e n r e p o r t e d i n
T a b l e IV, p a ge 3 0 .
R esu lts.
The c o m p a r i s o n o f t h e s e two g r o u p s
p r e s e n t s many i n t e r e s t i n g p r o b l e m s w h i c h w ou ld
30
TABLE IV
COMPARISON OF AVERAGES MADE BY STUDENTS WITH
MINIMUM MATHEMATICAL REQUIREMENTS WITH THOSE MADE BY
STUDENTS WITH MORE THAN MINIMUM REQUIREMENTS
2^
stu d en ts
w i t h minimum
requirem ents
M
1s t achievem ent t e s t i n
e l e m e n t a r y a l g e b r a T1
2nd a c h i e v e m e n t t e s t i n
e l e m e n t a r y a l g e b r a T2
Score
differences
T2- T1
Achievement t e s t i n
i n t e r m e d i a t e a l g e b r a T3
A v e r a g e s o f g r a d e s on
T4
classroom t e s t s
Averages of g rad es
i n homework
H
Q u a n tita tiv e psycholo­
g i c a l score
Q
L in g u istic psychologi­
c a l score
L
Gross p sy c h o lo g ic a l
score
G
Previous grades o th er
P '
th an m athem atics
Previous grades
PM
i n m athem atics
C hronological
A
age
C r i te r i o n of success
- in te r m e d ia te algebra K
18
stu d en ts
w ith over
minimum
requirem ents
M
22.13
29.33
29.76
35.11
7i63
5 .7 8 '
16.74
2 0 .6 1
44.87
52.06
57.63
54.89
30.02
32.28
61.91
6 1 .6 6
91.15
9 2 .1 6
2.47
2 .2 0
2.14
1.82
18.99
18.70
48.30
53.72
31
r e q u ir e a s e p a ra te study i n them selv es.
T h e r e i s no
doubt b u t what th e added y e a r s o f s tu d y o f th e s m a ll ­
e r group has g r e a t l y i n c r e a s e d t h e i r c a p a c i ty to
cope w i t h i n t e r m e d i a t e a l g e b r a .
T h i s g r o u p seems
t o s c o r e e q u a l l y w i t h t h e l a r g e r g r o u p on t h e m a j o r
p r e d i c t i v e m e a s u r e s s u c h a s i n t e l l i g e n c e , an d
s c h o l a r s h i p , b u t g r e a t l y e x c e ls th e l a r g e r group
on t h e m a j o r s u c c e s s m e a s u r e s .
However, s i n c e i n
a l l p r o b a b i l i t y t h i s w o u ld t e n d t o l o w e r t h e c o r ­
r e l a t i o n betw een the p r e d i c t i v e m easures and th e
su ccess m easures i t
should n o t a f f e c t the r e l i ­
a b i l i t y o f t h i s s t u d y t o an y g r e a t d e g r e e .
I t is,
however, u n f o r t u n a t e t h a t s u f f i c i e n t d a t a to th o ro u g h ­
ly in v e s tig a te
t h i s m a t t e r was n o t a v a i l a b l e .
IV . AGE
Data a v a l l a b l e .
been recorded,
S in c e each s t u d e n t * s age had
t h e e f f e c t o f age on s u c c e s s i n a l g e ­
b r a c o u l d be q u i t e a c c u r a t e l y d e t e r m i n e d .
C orrelation
c o e f f i c i e n t s were c a l c u l a t e d b e t w e e n t h e age s c a l e
and a l l o f th e m e a su re s.
T h ese h a v e b e e n r e p o r t e d
i n T a b l e V, p a ge 3 2 .
R esu lts.
I t i s i n t e r e s t i n g to note th a t a l l
32
TABLE V
CORRELATION OF STUDENTS CHRONOLOGICAL AGE
WITH THE VARIOUS PROGNOSTIC AND SUCCESS
MEASURES EMPLOYED IN THE STUDY
C hronological
ag e A
-.1 9
-.25
-.1 4
-.1 7
.«
00
-.0 5
-.1 2
00
.
rH
.04
.
H
1
■ -.0 6
1
.
O
1s t achievem ent t e s t i n
elem entary a lg e b ra
T1
2n d a c h i e v e m e n t t e s t i n
elem entary a lg e b r a
T2
Score
d ifferen ces
T2 -T1
Achievem ent t e s t i n
in term ed iate alg eb ra
T3
A v e r a g e s o f g r a d e s on
T4
classroom t e s t s
A verages of g rad es
H
i n homework
Q u a n tita tiv e psycho­
lo g ic a l scores
....Q.
L in g u is tic psycho­
lo g ic a l scores
L
G ross psycho­
lo g ic a l scores
G
Previous grades o th e r
th an m athem atics
P?
Previous grades
PM
i n m athem atics
C r ite r io n of success
in term e d iate alg eb ra
K
33
of th e c o r r e l a t i o n s e x c e p t t h a t w ith the l i n g u i s t i c
s c o r e s o f t h e p s y c h o l o g i c a l e x a m i n a t i o n were n e g a t i v e .
A more e x t e n s i v e s t u d y b a s e d on a g r e a t e r number o f
c a s e s m ight produce ev id en ce t h a t younger p u p i l s i n
t h e j u n i o r c o l l e g e h a v e a t e n d e n c y t o do b e t t e r
work.
H ow ever, i t was s u f f i c i e n t t o s t a t e h e r e
t h a t age w i t h i n th e ra n g e u s u a l l y found i n the
j u n i o r c o l l e g e h a d no e f f e c t u p o n s u c c e s s i n i n t e r ­
m ediate a lg e b r a .
S i n c e t h e c o r r e l a t i o n o f age w i t h
t h e c r i t e r i o n was - . 0 3 i t was c o n s i d e r e d s u p e r f l u o u s
to w rite a re g r e s s io n e q u a tio n .
CHAPTER V
THE CRITERION
I n C h a p t e r I I i t was e x p l a i n e d t h a t t h e s c o r e s
f r o m f i v e s u c c e s s m e a s u r e s were t o be co m bined t o
form t h e c r i t e r i o n o f s u c c e s s f o r t h e c o u r s e i n
interm ediate alg eb ra.
The way i n w h i c h t h e s e s c o r e s
were co m bined h a s b e e n i n d i c a t e d i n t h i s c h a p t e r .
O b jectiv e.
The t a s k h e r e was much t h e same
as th a t of a ssig n in g student g rad es.
The o b j e c t i v e ,
h o w e v e r , was n o t o n l y t o a s s i g n g r a d e s o f A, B, C,
D, an d F , b u t a l s o t o c o n s t r u c t a f i n e l y a n d a c c u ­
r a t e l y d iv id e d grade s c a l e .
I t was e s s e n t i a l t h a t
e ach s t u d e n t ’ s s c o r e be th e b e s t p o s s i b l e e s t i m a t e
of h i s a c t u a l su c ce ss o r achievem ent i n in te r m e d ia te
alg eb ra.
The s c o r e s o b t a i n e d f r o m t h e f i v e
success
m easures r e p r e s e n te d th e b e s t a v a i l a b l e evidence of
t h e s t u d e n t s ’ !a c c o m p l i s h m e n t s .
fore,
The p r o b l e m was, t h e r e ­
t o combine t h e f i v e s e p a r a t e s c o r e s f o r e a c h
s t u d e n t i n s u c h a way t h a t t h e r e s u l t i n g s i n g l e s c o r e
w o u ld be t h e b e s t p o s s i b l e m e a s u r e o f h i s s u c c e s s .
S i n c e t h e f i v e s u c c e s s m e a s u r e s w ere n o t o f
e q u a l v a l u e i t was a p p a r e n t t h a t e a c h w o u ld n e c e s s a r i l y
b ear a d i f f e r e n t w eight.
There was, to th e i n v e s t i ­
g a t o r ’ s k n o w l e d g e , no e x a c t s t a t i s t i c a l p r o c e e d u r e
35
f o r c o m b i n i n g t h e s c o r e s so a s t o t a k e i n t o a c c o u n t
the e x a c t n a tu re of each of the f iv e m easures.
m e a s u r e s w e r e co m p ared a s t o v a r i a b i l i t y ,
The
s i z e a nd
num ber o f s c o r e s , r e l i a b i l i t y and v a l u e .
The w e i g h t s
a s s i g n e d t o e a c h m e a s u r e we re b a s e d u p on t h e s e com­
p a r i s o n s , b u t i n the f i n a l a n a l y s i s were,
extent a t le a s t,
t o some
em p irical.
Comparison o f s u c c e s s m e a s u r e s .
The r e l a t i o n ­
s h i p s b e t w e e n e a c h o f t h e f i v e s u c c e s s m e a s u r e s them­
s e l v e s have been p r e s e n t e d i n Table V I, page 36, i n
th e form of c o e f f i c i e n t s o f c o r r e l a t i o n .
The c o r ­
r e l a t i o n s betw een t h e s e m easures and th e p r e d i c t i v e
m easu res have been r e p o r t e d i n Table V I I , page 37t
D ata c o n c e rn in g the r e l a t i o n s h i p and d i s t r i b u t i o n o f
s c o r e s h a s b e en g iv e n i n Table V I I I , page 38.
The w e i g h t e a c h t e s t w ould b e a r a c c o r d i n g t o
t h e s i z e a nd v a r i a b i l i t y o f s c o r e s was d e t e r m i n e d by
a com parison of th e s ta n d a r d d e v i a t i o n s o f the f i v e
d istrib u tio n s,
i.e .,
c o e f f i c i e n t s were d e t e r m i n e d so
a s to weigh a l l s c o r e s e q u a l l y .
I t was, however,
n o t d e s i r e d to weigh a l l s c o r e s e q u a l l y .
c ie n ts of m u ltip le c o r r e la tio n , i . e . ,
The c o e f f i ­
the c o r r e l a t i o n s
b e t w e e n e a c h s u c c e s s m e a s u r e and t h e o t h e r f o u r
36
TABLE VI
THE INTERCORRELATIONS OF THE FIVE SUCCESS
MEASURES: SCORE DIFFERENCES'(T2-T1), SECOND ACHIEVE­
MENT TEST IN ELEMENTARY ALGEBRA ( T 2 ) , ACHIEVEMENT TEST
IN INTERMEDIATE ALSEBRA ( T 3 ) , AVERAGES OF GRADES ON
CLASSROOM TESTS ( T 4 ) , AVERAGES OF GRADES IN HOMEWORK ( H) .
S u e
T2-T1
Averages of grad es
i n homework
HA v e r a g e s o f g r a d e s on
classroom t e s t s
T4
Achievement t e s t i n
i n t e r m e d i a t e a l g e b r a T3
2 nd a c h i e v e m e n t t e s t i n
e l e m e n t a r y a l g e b r a T2
Score
d ifferen ces
T2-T1
c e s s
T2
m e a s u r e s
T4
H
T3
•
.3 3
.45
.4 5
.2 0
.81
.78
.37
.8 5
• 28
.2 8
.6 4
.64
. 7 8 ..
.4 5
.85
.8 1
. .4 5
.37
.2 0
.33
37
TABLE V I I
CORRELATIONS BETWEEN FIVE SUCCESS MEASURES:
SCORE- DIFFERENCES ( T 2 - T 1 ) , SECOND ACHIEVEMENT TEST IN
ELEMENTARY ALGEBRA ( T 2 ) , ACHIEVEMENT TEST IN
INTERMEDIATE ALGEBRA ( T 3 ) , AVERAGES OF GRADES ON CLASS­
ROOM TESTS ( T 4 ) , AVERAGES OF GRADES IN HOMEWORK ( H ) ,
AND SEVEN PROGNOSTIC MEASURES
§
•08
.5 5
.48
.46
00
■.
L
.1 2
.4 6
.48
.50
.32
G
•05
• 57
.5 2
.54' _ .39
P
.2 2
.44
.36
.4 9
• 33
PM
.2 1
.6 0
.50~
.8 6
.5 0
T1
.9 0
.7 7
.7 6
.34
A
■3«H
1
*•25
-.1 7
-.0 5
00
•
It
Q u a n tita tiv e psycho­
lo g ic a l scores
L in g u is tic psycho­
lo g ic a l scores
G ross p s y c h o lo g ic a l
scores
Previous grades o th e r
th an m athem atics
Previous grades in
m athem atics
1s t achievem ent t e s t i n
elem entary a lg e b ra
C h ronological
a ge
m e a s u r e s
T4
T3
H
i
.
o
VO
S u c c e s s
T2-T1
T2
38
TABLE V I I I
THE MEANS, STANDARD DEVIATIONS, AND COEFFICIENTS
OF MULTIPLE CORRELATION OF THE FIVE SUCCESS MEASURES
Score
differences
T2 -T1
2nd a c h i e v e m e n t t e s t
i n e l e m e n t a r y a l g e b r a T1
Achievement t e s t i n
in term ed iate alg eb ra
T2
A v e r a g e s o f g r a d e s on
classroom t e s t s
T4
Averages of g rad es
i n homework
h;
M u l t i p l e
R
M
SD
7.12
4.14
(T 2-T l)(T 2.T 3.T 4.H )
.64
31-34
1 0 .0 0
(T2)(T2-T1.T3.T4.H )
.8 8
17.50
9.79
(T3)(T2-T1.T2.T4.H )
.98
47.42
24.21
(T4)(T2-T1.T2.T4.H )
.91
59.69
22.77
(H )(T2-T1,T2,T3,T4)
.64
39
m e a s u r e s r e p r e s e n t e d t o some e x t e n t t h e d e g r e e t o
w h i c h l i k e q u a l i t i e s were m e a s u r e d .
T his a b i l i t y
t o m e a s u r e l i k e q u a l i t i e s c o u l d a l s o be i n f e r r e d
f ro m t h e c o e f f i c i e n t s i n T a b l e s VI a n d V I I I .
Before
t h e w e i g h t s w ere f i n a l l y f i x e d , a c r i t i c a l a n a l y s i s
was made o f e a c h i n d i v i d u a l m e a s u r e .
A nalysis of success m easures.
1.
(T2 ~ T^) l, o f a l l t h e s u c c e s s m e a s u r e s ,
t h a t i n d i c a t i n g th e d i f f e r e n c e betw een e le m e n ta ry
a c h i e v e m e n t t e s t s one a n d two v/as t h e m o s t d i f f i c u l t
to i n t e r p r e t .
From t h e r e l a t i o n s h i p s e x p r e s s e d i n
T a b l e s VI a n d V I I i t was d i f f i c u l t t o d e t e r m i n e j u s t
what, i f a n y th i n g , th e s e s c o re s m easured.
F o u r m onth s
e l a p s e d b e t w e e n t h e f i r s t an d s e c o n d a d m i n i s t r a t i o n s
of th is t e s t .
I t was t h o u g h t t h a t t h e s c o r e d i f f e r ­
e n c e s m i g h t i n d i c a t e i n c r e a s e d k n o w le d g e o f t h e f u n d a ­
m e n ta l c o n c e p ts o f a l g e b r a b u t t h i s d id n o t prove to
be t h e c a s e .
The c o r r e l a t i o n s b e t w e e n t h e t e s t d i f ­
f e r e n c e s c o r e s , T a b l e V I I , an d t h e o t h e r m e a s u r e s
e m p lo y ed w ere l o w .
The c o e f f i c i e n t o f - . 0 9 w i t h t h e
s c o r e s r e c e i v e d from th e f i r s t a d m i n i s t r a t i o n o f the
a c h i e v e m e n t t e s t , T^» i n d i c a t e d a r e g r e s s i v e e f f e c t ,
i.e .,
i f t h e m e a s u r e m e n t made b y t h e f i r s t a p p l i c a t i o n
o f t h e e l e m e n t a r y a c h i e v e m e n t t e s t was i n e r r o r ,
th is
40
e r r o r was a p t t o be p o s i t i v e f o r h i g h s c o r e s a n d
n e g a t i v e f o r low s c o r e s .
The t e n d e n c y was t h e n ,
f o r th e s e s c o r e s to r e v e r t to norm al upon th e s e ­
cond a p p l i c a t i o n o f t h e t e s t .
T h i s e r r o r would
e f f e c t th e s c o re d i f f e r e n c e s c o n s i d e r a b l y and te n d
t o p r o d u c e a n e g a t i v e c o r r e l a t i o n w i t h t h e T^ s c o r e s .
T hen t o o , t h e t e s t was o f s u c h a n a t u r e t h a t a f t e r
a c h i e v i n g a c e r t a i n minimum s c o r e i t became i n c r e a s ­
i n g l y more d i f f i c u l t t o i n c r e a s e t h e s c o r e .
I t w a s,
no d o u b t , a s d i f f i c u l t f o r a s t u d e n t who h a d a t t a i n e d
a h i g h s c o r e t o i n c r e a s e t h i s s c o r e by one p o i n t , a s
i t was f o r a s t u d e n t who h a d o b t a i n e d a low s c o r e t o
i n c r e a s e h i s s c o r e by s i x o r s e v e n p o i n t s .
This b eing
t h e c a s e , i t was d e c i d e d t o w e i g h t t h e t e s t d i f f e r ­
ence s c o r e s v e ry l i t t l e
2.
T2 :
if at a ll.
I n s p i t e o f the low r e l a t i o n s h i p s o b ­
t a i n e d from t h e t e s t d i f f e r e n c e s c o r e s , t h e s c o r e s
r e c e i v e d from t h e s e c o n d a p p l i c a t i o n o f t h e e l e m e n t a r y
a lg e b ra achievem ent t e s t c o r r e l a t e d very w e ll w ith the
o th e r m easures.
The d i f f i c u l t y i n u s i n g t h e s e s c o r e s
a s a p a r t o f t h e t o t a l s u c c e s s s c o r e was t h a t t h e y
m i g h t l e a d t o a s p u r i o u s c o r r e l a t i o n w i t h t h e T^
scores.
I t was h o w e v e r f o u n d t h a t t h e same d e g r e e o f
r e l a t i o n s h i p c o u l d be m a i n t a i n e d b e t w e e n t h e c r i t e r i o n
41
s c o r e s a n d t h e T^ s c o r e s when t h e c r i t e r i o n e x c l u d e d
t h e T2 s c o r e s .
The c o r r e s p o n d i n g i n c r e a s e o f w e i g h t s
on T^ a n d T^ were s u c h t h a t none o f t h e r e l a t i o n s h i p s
c h a n g e d t o an y s i g n i f i c a n t d e g r e e .
T his b e in g the
c a s e an d s i n c e a s u c c e s s s c a l e w h i c h i n c l u d e d t h e T2
s c o r e s was i n k e e p i n g w i t h i n s t r u c t o r s ’ o p i n i o n o f
w h a t t h e s c o r e s s h o u l d b e , t h e s e s c o r e s w e re w e i g h t e d
e q u a l l y w i t h t h e T^ s c o r e s *
3,
T^;
The a c h i e v e m e n t t e s t i n i n t e r m e d i a t e
a l g e b r a was s t a n d a r d i z e d .
Norms we re a v a i l a b l e w h i c h
h a d b e e n d e r i v e d f r o m a wide v a r i e t y o f s a m p l e s .
The
a v e ra g e , ra n g e , and sta n d ard d e v ia tio n of the sc o res
r e c e i v e d from t h i s t e s t i n t h i s s t u d y were a l m o s t
i d e n t i c a l w i t h t h o s e i n d i c a t e d f o r much l a r g e r g r o u p s .
S in c e t h i s t e s t had b een e s p e c i a l l y d e s ig n e d t o measure
a chievem ent i n the s p e c i f i c s u b j e c t , i n t e r m e d i a t e
a l g e b r a , and s i n c e th e c o r r e l a t i o n w i t h th e o t h e r
s u c c e s s m e a s u r e s was e x t r e m e l y h i g h , t h e s e s c o r e s
c o u l d b e a r c o n s i d e r a b l e w e i g h t i n mak ing up t h e c r i ­
terio n .
4.
T^:
I t w i l l be r e c a l l e d t h a t t h i s m e a s u r e
was i t s e l f d e t e r m i n e d by a v e r a g i n g s c o r e s r e c e i v e d
u p o n a l l t h e c l a s s r o o m t e s t s t h a t were g i v e n d u r i n g t h e
sem ester.
The a v e r a g e c o r r e l a t i o n b e t w e e n t h e s e
42
i n d i v i d u a l c l a s s r o o m t e s t s was a b o u t . 9 0 .
From t h e
s t a n d p o i n t o f t h e number o f s c o r e s a n d t h e r e l i a b i l i t y
o f t h i s m e a s u r e i t was d e c i d e d t h a t i t s h o u l d i n f l u ­
ence the c r i t e r i o n c o n s id e ra b ly *
cated,
As h a s b e e n i n d i ­
the c o r r e l a t i o n w ith th e o th e r su c c e ss m easures
co m bined was . 9 1 .
5.
Hi
The a v e r a g e s o f g r a d e s i n homework
h a d a l s o b e e n d e r i v e d fr o m .a g r e a t number o f s a m p l e s
of stu d en t a b i l i t y .
The s c o r e s , h o w e v e r , were n o t
a s v a l u a b l e a s t h o s e r e c e i v e d on c l a s s r o o m t e s t s .
StiAdents o f t e n became q u i t e a d e p t a t g e t t i n g homework
done w i t h o u t n e c e s s a r i l y a c q u a i n t i n g t h e m s e l v e s w i t h
the p r i n c i p l e s in v o lv e d .
The homework s c o r e s r e l a t e d
t o t h e o t h e r s u c c e s s m e a s u r e s i n o n l y a m e d i o c r e way.
I t was d e c i d e d t o w e i g h t th em , i f p o s s i b l e , i n k e e p i n g
w ith t h e i r r e l a t i o n s h i p w ith the o th e r success m easures.
W eighted s c o r e s .
S u c c e s s s c a l e s d e r i v e d by
c o m b i n i n g s c o r e s b e a r i n g d i f f e r e n t w e i g h t s we re d e v e l ­
oped.
By t r i a l a nd e r r o r ,
then, but w ith w eights
b a s e d p r i m a r i l y u p o n k n o w le d g e a s t o t h e n a t u r e ,
v a r i a b i l i t y a nd r e l i a b i l i t y o f t h e m e a s u r e s t h e
w e i g h t s were f i x e d a s i n T a b l e I X , p a g e 43*
Thus t h e
r e s u l t i n g s u c c e s s s c a l e was made up o f s u c c e s s
43
TABLE I X
WEIGHTS OF SUCCESS MEASURES
S .D .
Score
differences
T£2-T1
2 nd a c h i e v e m e n t t e s t i n
T2
elem entary a lg e b ra
Achievement t e s t i n
in te rm ed iate algebra
T3
A v e r a g e s o f g r a d e s on
classroom t e s t s
T4
A verages o f grade s
i n homework
H
W e i g h t*
4.14
1'
1 0 .0 0
6
9.79
6
24.21
3 __
22.77
1
NOTE: ^ W e ig h t h e r e i n d i c a t e s t h e number by
w h i c h s c o r e s o f e a c h o f t h e s u c c e s s m e a s u r e s was
m u l t i p l i e d i n m akin g u p t h e c r i t e r i o n s c a l e .
The
r e l a t i v e s i g n i f i c a n c e o f e a c h o f t h e m e a s u r e s may
b e i n f e r r e d by c o m p a r i n g t h e w e i g h t w i t h t h e s i z e
o f the s ta n d a r d d e v i a t i o n (S*D .).
44
m e a s u r e s com bined i n a p p r o x i m a t e l y t h e f o l l o w i n g
p ro p o rtio n s ;
(l)
te s t d iffe re n c e s,
two p e r c e n t ;
( 2 ) a v e r a g e s o f g r a d e s i n homework, t e n p e r c e n t ;
( 3 ) se c o n d a c h i e v e m e n t t e s t i n e l e m e n t a r y a l g e b r a ,
tw e n ty -e ig h t p e r c e n t;
(4 ) s c o r e s on a n a c h i e v e m e n t
t e s t in in te rm e d ia te a lg e b r a , tw e n ty -e ig h t p e r c e n t;
a n d ( 3 ) s c o r e s on c l a s s r o o m t e s t s , 32 p e r c e n t .
C o n v e r te d s c o r e s .
S c o r e s , when t o t a l e d ,
r a n g e d fro m 106 t o 914 w i t h a mean a t 496 a n d a
s ta n d a rd d e v ia tio n of 198.
d ix D ).
(See d a t a s h e e t , A ppen­
T h ese t o t a l e d s c o r e s f o rm e d a f a i r l y n o rm a l
d i s t r i b u t i o n , b u t w ere awkward t o h a n d l e .
They w e r e ,
t h e r e f o r e , c o n v e r t e d i n t o a c o m p a ra b le a n d more c o n ­
v e n ie n t s e r ie s .
T h i s c o n v e r s i o n was i n a c c o r d w i t h
m e th o d s c i t e d by H enry E. G arrett.**"
S co res th u s
c o n v e r t e d r a n g e d from 0 t o 100 w i t h a mean a t f i f t y
and a sta n d a rd d e v ia tio n of f o u r te e n .
As a n exam ple o f t h e way i n w h ic h s c o r e s w ere
com b in ed a n d c o n v e r t e d , t a k e t h e f i v e s u c c e s s s c o r e s
H enry E . G a r r e t t , S t a t i s t i c s i n P s y c h o lo g y
a n d E d u c a t i o n . (New Y o rk ;
Logmans, G re e n a n d Company,
L t d . ) , p . 2 8 3 , c i t i n g P s y c h o l o g i c a l R e v ie w . V o l . XIX,
p p . 9 7-123.
45
o f s t u d e n t n o . 17 ( d a t a s h e e t , A p p e n d ix D ) .
s c o r e s i n d i c a t e d by m e a s u r e s
^ 1 * ^ 2 * an<i T3
w ere 1 0 , 9 0 , 3 2 , 2 2 , a n d 6 4 r e s p e c t i v e l y .
e a c h s c o r e by t h e num ber i n colum n
The
M u ltip ly
(w e ig h t)•
t o t a l o f t h e s u c c e s s s c o r e s so w e i g h t e d i s 6 l 6 .
The
Sub-
s t i t u t e 616 f o r X^, i n t h e e q u a t io n " Xg = 15 ♦ ”X^.
The
c o n v e r t e d s c o r e X^ was t h e n 5 8 .
The c r i t e r i o n .
The c o n v e r t e d s e r i e s o f s u c c e s s
s c o r e s was t h e n c o n s i d e r e d t o be t h e b e s t p o s s i b l e
m e a s u re o f s u c c e s s i n i n t e r m e d i a t e a l g e b r a .
T h is
m e a s u re was r e f e r r e d t o a s t h e c r i t e r i o n o f s u c c e s s
f o r t h i s s t u d y a n d was d e s i g n a t e d by t h e sym bol K.
The way i n w h ic h t h e s e f i n a l s u c c e s s s c o r e s c o r r e l a ­
te d w ith th e f i v e su c c e ss m easures h as b een i n d ic a t e d
i n T a b le X, p a g e 4 6 .
G rades.
S u c c e s s s c o r e s w ere v e r y e v e n l y d i s ­
t r i b u t e d on t h e c r i t e r i o n . s c a l e .
The p ro b le m was t o
a s s i g n e a c h s t u d e n t a g r a d e w h ic h w ould be i n a c c o r d
w ith h is su ccess sc o re .
S i n c e t h e g r o u p a s a w hole
seem ed t o be q u i t e n o r m a l , t h e s t a n d a r d d e v i a t i o n s
o f t h e s u c c e s s s c o r e s was u s e d a s th e b a s i s f o r th e
grad e d i s t r i b u t i o n s .
T h is d e v ia ti o n r e p r e s e n te d
46
TABLE X
CORRELATION OF SUCCESS MEASURES WITH THE CRITERION
C rite rio n
K
S core
d iffe re n c e
2 nd a c h i e v e m e n t t e s t
i n e le m e n ta ry a lg e b r a
A c h ie v e m e n t t e s t i n
in te rm e d ia te a lg e b ra
A verages of g ra d e s
on c l a s s r o o m t e s t s
A verages of g ra d e s
i n homework
T2-T1
• 34
T2
.9 2
T3
.9 3
T4
.9 2
H
.6 4
47
f o u r t e e n p o i n t s on t h e s u c c e s s s c a l e .
As h a s b e e n
i n d i c a t e d on p a g e 9 8 ^ g r a d e s o f C w ere a s s i g n e d t o
p u p i l s h a v i n g s c o r e s l y i n g w i t h i n t h e l i m i t s o f th e
mean s u c c e s s s c o r e p l u s o r m inus one h a l f , th e s t a n d ­
a r d d e v i a t i o n ; o r b e tw e e n t h e l i m i t s 43 t o 5 7 ; g r a d e s
o f D w ere a s s i g n e d w i t h s c o r e s b e tw e e n t h e l i m i t s
o f 29 t o 4 3; g r a d e s o f B b e tw e e n l i m i t s o f 57 t o
71; g r a d e s o f F w ere b elow 29 and A abov e 71*
G ra d e s
t h u s d i s t r i b u t e d w e re i n a p p r o x i m a t e l y t h e f o l l o w i n g
p ro p o rtio n s:
F , t h r e e p e r c e n t ; D, t h i r t y p e r c e n t ;
C, f o r t y - o n e p e r c e n t ; B, s e v e n t e e n p e r c e n t ; A,
n in q p e r c e n t .
The d i s t r i b u t i o n o f g r a d e s on t h e
s u c c e s s s c a l e h a s b e e n i n d i c a t e d i n T a b le X I, page
48.
T h i s was a s n o rm a l a d i s t r i b u t i o n o f g r a d e s
a s w o u ld be e x p e e t e d when d e a l i n g w i t h s i x t y - f o u r
cases.
F u r t h e r , i t was q u i t e i n k e e p i n g w i t h t h e
i n s t r u c t o r s 1 o p in io n o f what i t sh o u ld b e , and i n
a c c o rd w ith d ep artm en t s ta n d a r d s .
See a l s o d a t a s h e e t , A p p e n d ix D.
48
TABLE XI
THE DISTRIBUTION OF GRADES ON THE
SUCCESS SCALE
SD = 14
Low s c o r e
36
22
29
H ig h s c o r e
64
50
57
43
71
3
100
-A-
-FPer cent
78
30
41
17
CHAPTER VI
THE PSYCHOLOGICAL EXAMINATION
AS A PREDICTIVE AGENT
The p u r p o s e o f t h i s c h a p t e r was t o r e p o r t
upon th e v a lu e o f th e i n t e l l i g e n c e t e s t i n p r e d i c t ­
in g su c c e ss in in te rm e d ia te a lg e b ra .
i n C h a p te r I ,
As e x p l a i n e d
th e p s y c h o lo g ic a l e x a m in a tio n u se d i n
t h i s s t u d y was d i v i d e d i n t o two p a r t s ;
t i v e and th e l i n g u i s t i c .
th e q u a n t i t a ­
The s i g n i f i c a n c e o f e a c h
p a r t h a s been c o n s id e r e d and an a n a l y s i s o f th e
p r e d i c t i v e p o w e rs o f t h e e x a m i n a t i o n a s a w hole h a s
b e e n g iv e n *
P r e d i c t i v e v a lu e o f s e p a r a te s c o r e s .
In
T a b l e X II, p a g e 5 0 , t h e c o r r e l a t i o n s o f t h e q u a n t i t a ­
tiv e ,
l l n q u i s t l c , a n d g r o s s s c o r e s on t h e p s y c h o l o ­
g i c a l e x a m in a tio n s w ith th e o t h e r m easu res have
been in d ic a te d .
From t h e s e c o r r e l a t i o n s i t
c o u ld
have been i n f e r r e d t h a t th e q u a n t i t a t i v e and th e
lin g u is tic
s c o r e s on t h e e x a m i n a t i o n w o u ld be o f
a p p ro x im a te ly e q u a l v a lu e i n p r e d i c ti n g su c ce ss s c o re s ,
K, a n d t h a t t h e g r o s s s c o r e w o u ld be o f s l i g h t l y
g r e a t e r v a lu e th an e i t h e r .
R e g re ssio n e q u a tio n s f o r p r e d ic tin g su ccess o r
K s c o r e s fro m q u a n t i t a t i v e ,
l i n g u i s t i c , and g r o s s
50
TABLE X II
CORRELATIONS BETWEEN QUANTITATIVE PSYCHOLOGICAL
SCORES ( Q ) , LINGUISTIC PSYCHOLOGICAL SCORES ( L ) ,
GROSS PSYCHOLOGICAL SCORES ( G ) , AND VARIOUS
PROGNOSTIC AND SUCCESS MEASURES
-
L
G
•6 1
.4 8
.5 8
• 55
.4 6
.5 7
.0 8
.1 2
.0 5
.4 8
.4 8
.5 2
.4 6
.5 0
.5 4
.3 8
• 32
.5 9
.6 1
04
.
.6 1
CO
Q
.9 5
CO
•
1 s t ach iev em en t t e s t i n
e le m e n ta ry a lg e b r a
T1
2 nd a c h i e v e m e n t t e s t i n
e le m e n ta ry a lg e b r a
T2
S core
d iffe re n c e s
T2 -T1
A c h ie v e m e n t t e s t i n
in te rm e d ia te a lg e b ra
■TJ
A v e r a g e s o f g r a d e s on
c la ss ro o m t e s t s
T4
A verages of g ra d e s
H
i n homework
Q u a n tita tiv e p sy c h o lo ­
g ic a l sco res
Q
L in g u is tic psycho­
lo g ic a l scores
L
G ross p sy ch o ­
lo g ic a l scores
G
P re v i ous g rad e s ot h e r
P
t h a n m a t h e m a ti c s
P re v io u s g rad es
PM
i n m a t h e m a ti c s
C h ro n o lo g ic a l
.a g e
A
C rite rio n of success
in te rm e d ia te a lg e b ra
K
P s y c h o lo g ic a l sco res
.9 5
.6 3
.4 9
.4 7
.36
.5 1
.4 8
-* 1 2
.1 8
.0 4
• 55
.5 6
.6 1
51
p s y c h o l o g i c a l s c o r e s w ere s e t up i n s c o r e form a s
fo llo w s;
(1 )
K = .8 2 Q ♦ 25
S (e s t.k )
P -E - ( e s t . k )
(2 )
K = .4 4 L + 24
(ll)
13- 32
=
S ( e s t> lc ) = 1 1 .2 3 ( 1 1 )
(3 ) K = . 35 S ♦ 18
E x am p le s o f r e l a t i v e p r e d i c t i v e p o w e r .
The
v a l u e o f e a c h p r e d i c t i v e m e a s u re was i n d i c a t e d by t h e
s ta n d a rd e r r o r in p r e d i c ti n g K scores*
I t w as, s t a t i s ­
t i c a l l y , a l m o s t c e r t a i n t h a t a t r u e s c o r e w o uld l i e
w i t h i n t h e l i m i t s e x p r e s s e d by t h e s c o r e p r e d i c t e d a s
m o st p r o b a b l e , p l u s o r m in u s t h r e e t i m e s t h e s t a n d a r d
e r r o r f o r e s t im a t i n g th e K o r s u c c e ss s c o r e s .
A rough
i d e a o f r e l a t i v e p r o g n o s t i c p o w ers o f t h e t h r e e mea­
s u r e s Q, L , a n d G, may q u i c k l y b e g a i n e d by t a k i n g
e a c h e q u a l t o z e r o i n t h e above e q u a t i o n s .
If
th e
s ta n d a rd e r r o r of e s tim a te i s ta k e n a s a p p ro x im a te ly
11 i n e a c h c a s e ,
s c o r e s o f 25 t 3 3 , 2 4 + 3 3 , a n d
18 + 33 w o u ld .b e o b t a i n e d fro m z e r o p r e d i c t i v e
The h i g h e s t p o s s i b l e
scores.
s u c c e s s s c o r e s w h ic h c o u l d be
52
o b t a i n e d fro m q u a n t i t a t i v e ,
l i n g u i s t i c , and g ro s s
p s y c h o l o g i c a l s c o r e s o f z e r o w ould be 5 8 , 5 7 , and
51 r e s p e c t i v e l y *
From t h e g r a d e d i s t r i b u t i o n o f
s u c c e s s s c o r e s ( c r i t e r i o n s c a l e ) i t may t h e n be
i n f e r r e d t h a t i t w o uld be p o s s i b l e f o r a s t u d e n t
m ak in g a s c o r e o f z e r o on e i t h e r p a r t o r a l l o f t h e
p s y c h o lo g ic a l e x a m in a tio n to o b t a i n a g ra d e of F,
D, o r C, i n i n t e r m e d i a t e a l g e b r a .
Thus, i t
seem ed t h a t th e p r e d i c t i v e p o w e rs
o f t h e s e t h r e e m e a s u r e s w ere a p p r o x i m a t e l y t h e same*
From a c o m p a r is o n o f t h e c o r r e l a t i o n s w i t h t h e c r i ­
t e r i o n , fro m t h e r e g r e s s i o n e q u a t i o n s , a n d fro m t h e
co m p a rativ e s i z e o f th e s ta n d a r d e r r o r s of e s t im a t e ,
i t w as, how ever, a p p a r e n t t h a t o f th e t h r e e m easu res
t h e g r o s s s c o r e on t h e p s y c h o l o g i c a l e x a m i n a t i o n was
t h e m o st v a l u a b l e .
T h is b e in g th e c a s e , and s in c e
t h e s e m e a s u r e s a r e se ld o m c o n s i d e r e d s e p a r a t e l y ,
r e s u l t s w ere r e p o r t e d on t h e b a s i s o f t h e g r o s s
s c o r e s on t h e p s y c h o l o g i c a l e x a m i n a t i o n o n l y .
L i m i t s o f p r e d i c t i o n fro m g r o s s p s y c h o l o g i c a l
sco res*
E q u a t i o n 3 , p a g e 5 1 , was u s e d f o r p r e d i c t i n g
K o r s u c c e s s s c o r e s fro m g r o s s p s y c h o l o g i c a l s c o r e s G-.
53
I n T a b le X I I I , p a g e 5 4 , g r o s s p s y c h o l o g i c a l s c o r e s
h a v e b e e n s e l e c t e d w h ic h p r e d i c t K o r s u c c e s s s c o r e s
w h ic h l i e
a t t h e m i d - p o i n t s o f t h e g r a d e s A, B, G,
D, a n d F on t h e s u c c e s s s c a l e ,
T a b le ).
(S ee K s c a l e below
The g r o s s s c o r e , t h e m o st p r o b a b l y s u c c e s s
s c o r e and t h e p r o b a b l y l i m i t s o f t h e d e v i a t i o n o f
t h e t r u e o r a c t u a l K s c o r e s have b e e n i n d i c a t e d ,
A f a i r l y a c c u ra te e s tim a te of th e s i g n i f i ­
cance of th e p s y c h o lo g ic a l e x a m in a tio n i n p r e d i c t i n g
s u c c e s s i n i n t e r m e d i a t e a l g e b r a may be g a i n e d from
T ab le X I I I .
I t i s , h o w e v e r, u n l i k e l y t h a t a p r e ­
d i c t e d s c o r e w o u ld l i e a t e x a c t l y t h e m i d - p o i n t o f
any s p e c i f i e d g r a d e .
I t w o u ld , f o r e x a m p le , be
p o s s i b l e f o r th e t r u e g rad e o f a s tu d e n t w ith a p r e ­
d i c t e d sc o re l y in g a t th e v e ry to p o f th e F s c o re s
t o v a r y n o t fro m F t o C, a s i n d i c a t e d i n t h e T a b l e ,
b u t fro m F t o B, o r from 29 t o 6 2 ,
I n term s of th e g ra d e p o i n t .
T h is b e in g th e
c a s e , i t was d e c i d e d t o I n t e r p r e t t h e g e n e r a l e f f e c ­
t i v e n e s s o f t h e g r o s s p s y c h o l o g i c a l s c o r e i n te r m s o f
g rad e p o in ts , i . e . ,
A = 4, B = 3 ,
a s c a l e b a s e d on u n i t y , s u c h a s
C = 2 , D = 1, and F = 0 .
One g r a d e
p o i n t was t a k e n e q u a l t o 14 p o i n t s on t h e K o r
54
TABLE X III
GRADES AND SUCCESS SCORES (K) PREDICTED
BY GROSS PSYCHOLOGICAL SCORES (G)
Gi­
ll
35
91
131
171
P ro b a b le d e v ia ti o n o f a c t u a l sc o re
o r &rade
C e rta in *
50 i n 100
6 8 i n 100
K
22
F
36
D
50
C
64
B
78
A
15 t o
F
29 t o
D
43 t o
C
57 t o
B
71 t o
A
29
11
F
25
F
39
D
53
B
67
B
43
57
71
85
to
to
to
to
to
to
to
to
to
to
33
D
47
C
6l
B
75
A
89
A
0
F
3
F
17
E
31
D
45
C
to
to
to
to
to
to
to
to
to
to
55
C
69
B
83
A
97
A
100
A
* 3 X 8 . D . ( „ tJC)>
K S c a le
22
36
I 29
I
0 — --------- !--------------D
43
50
64
78
I
57
I 71
I
-i-------r------ 1--------------B
A
G- S c a l e
40
lo
69
92
115
157
100
55
c rite rio n sc a le .
I n t h i s way i t was p o s s i b l e t o
e s t i m a t e th e p r o b a b l e c h a n c e s o f a t r u e
success
s c o r e d e v i a t i n g fro m a p r e d i c t e d s c o r e by any num ber
o f g r a d e p o i n t s o r by a n y f r a c t i o n a l p a r t o f a g r a d e
p o in t.
The c h a n c e s o f a t r u e s c o r e v a r y i n g fro m a
p r e d i c t e d s c o r e by o n e - h a l f a g r a d e p o i n t a n d by
one g r a d e p o i n t h a v e b e e n i n d i c a t e d u n d e r r e s u l t s .
The g r e a t e s t p o s s i b l e g r a d e p o i n t d e v i a t i o n h a s
a ls o been r e p o rte d .
E x a m p le .
As a n e x am p le o f t h e way i n w h ic h
t h e s e r e s u l t s w ere o b t a i n e d ,
th e c a l c u l a t i o n o f t h e
c h a n c e s o f a d e v i a t i o n o f one g r a d e p o i n t w i l l be
illu s tra te d .
The s t a n d a r d e r r o r when p r e d i c t i n g
K o r s u c c e s s s c o r e s , from Or o r g r o s s p s y c h o l o g i c a l
s c o r e s was ( e q u a t i o n 3 , p a g e 51) 1 0 . 7 4 .
One g r a d e
p o i n t r e p r e s e n t e d 14 p o i n t s on t h e s u c c e s s s c a l e .
(K s c a l e , T a b le X I I I ) .
One g r a d e p o i n t i n t e r m s o f
th e s ta n d a rd e r r o r o f e s tim a te
(sta n d a rd d e v ia tio n
o f p r e d i c t e d s c o r e s ) was e q u a l t o 14 d i v i d e d by
1 0 .7 4 o r 1 .3 0 t i m e s t h e s t a n d a r d e r r o r .
The p r o b a b l e
c h a n c e s o f a s c o r e v a r y i n g by n o t more t h a n + 1 .3 0
t i m e s t h e s t a n d a r d d e v i a t i o n w ere a p p r o x i m a t e l y
81 o u t o f 1 0 0 .
T h i s may b e v e r i f i e d by r e f e r r i n g
56
t o a n y s t a t i s t i c a l t a b l e w h ic h g i v e s t h e f r a c t i o n a l
p a r t s o f t h e t o t a l a r e a u n d e r t h e n o rm a l p r o b a b i l i t y
c u rv e *
R e su lts*
As a r e s u l t o f t h i s s t u d y i t was
d e te rm in e d t h a t th e q u a n t i t a t i v e and l i n g u i s t i c
s c o r e s on t h e p s y c h o l o g i c a l e x a m i n a t i o n w ere o f
a p p ro x im a te ly e q u a l v a lu e i n p r e d i c ti n g su c c e ss in
V.
i n t e r m e d i a t e a l g e b r a a n d t h a t t h e g r o s s s c o r e was
o f s l i g h t l y g r e a t e r v a lu e th a n e i t h e r .
The p r o b a b l e
o r c h a n c e d e v i a t i o n s o f a t r u e s c o r e o r g r a d e fro m
s c o r e s o r g ra d e s p r e d i c t e d by th e g r o s s p s y c h o lo g i­
c a l s c o r e , i n te r m s o f g r a d e p o i n t s w ere a s f o l l o w s :
(1 )
The c h a n c e s w ere a p p r o x i m a t e l y 48 o u t
o f 100 t h a t t h e t r u e g r a d e w ould n o t d e v i a t e fro m
t h e p r e d i c t e d g r a d e by m ore t h a n o n e - h a l f a g r a d e
p o in t.
(2 )
The c h a n c e s w ere 81 o u t o f 100 t h a t t h e
t r u e g r a d e w ould n o t d i f f e r fro m t h e p r e d i c t e d g r a d e
by more t h a n one g r a d e p o i n t .
(3 )
I t was o n l y s t a t i s t i c a l l y
c e rta in th a t
t h e t r u e g r a d e w ould n o t d e v i a t e fro m t h e p r e d i c t e d
g r a d e by m ore t h a n two a n d o n e - t h i r d g r a d e p o i n t s .
CHAPTER V II
THE VALUE OF THE PREVIOUS SCHOLASTIC RECORD IN
PREDICTING SUCCESS IN INTERMEDIATE ALGEBRA
The p u r p o s e o f t h i s c h a p t e r was t o d e t e r m i n e
w h e t h e r o r n o t k n ow ledg e o f a s t u d e n t * s p r e v i o u s
s c h o l a s t i c r e c o r d w o u ld b e o f any s i g n i f i c a n t v a l u e
i n p r e d ic tin g su ccess o r f a i l u r e in in te rm e d ia te
a lg e b ra *
As h a s b e e n p r e v i o u s l y s u g g e s t e d , g r a d e
r e c o r d s i n m a th e m a tic s and i n s u b j e c t s o t h e r th a n
m a t h e m a t i c s w ere c o n s i d e r e d s e p a r a t e l y *
R e la tio n s h ip to o t h e r m e a su re s*
The s t u d e n t ’ s
p r e v io u s g r a d e s i n m ath e m a tics and i n s u b j e c t s o t h e r
t h a n m a t h e m a t i c s w e re a v e r a g e d and r e c o r d e d s e p a r a t e l y
i n term s o f g ra d e p o i n t s .
T h ese a v e r a g e s w ere sy m b ol­
i z e d a s PM a n d P r e s p e c t i v e l y .
The c o r r e l a t i o n s
b e tw e e n t h e s e tw o m e a s u r e s and a l l o f t h e o t h e r
m e a s u r e s em p lo y ed i n t h i s s t u d y h a v e b e e n r e p o r t e d
i n T a b le XIV, p a g e 5 8 .
As was t o be e x p e c t e d ,
th ese
c o e f f i c i e n t s i n d ic a te d t h a t th e p re v io u s g ra d e s in
m ath em a tics f u r n i s h th e b e t t e r b a s i s f o r p r e d i c t i n g
success in in te rm e d ia te a lg e b ra .
R e la tiv e p re d ic tiv e v a lu e ♦
The two e q u a t i o n s
58
TABLE XIV
COHRELLATIONS OF PREVIOUS GRADE AVERAGES IN
MATHEMATICS (PM), AND SUBJECTS OTHER
THAN MATHEMATICS ( P ) } WITH VARIOUS
PROGNOSTIC AND SUCCESS MEASURES
P re v io u s g rade
av erag es
PM'
P
T1
♦56
.3 8 •
T2
♦60
.4 4
T 2 -T 1
.2 1
.2 2
T3
.5 0
.3 6
T4
.8 6
.4 9
H
.5 0
• 33
Q
•63
.3 6
L
.4 9
_____ .5 1
G
.4 7
.4 8
P’
.8 0
.
00
0>
1 s t ach iev e m e n t t e s t i n
e le m e n tary a lg e b ra
2 nd a c h i e v e m e n t t e s t i n
e le m e n ta ry a lg e b r a
S core
d iffe re n c e s
A c h ie v e m e n t t e s t i n
in te rm e d ia te a lg e b ra
A v e r a g e s o f g r a d e s on
c la ssro o m t e s t s
A verages o f g ra d e s
i n homework
Q u a n tita tiv e
p sy c h o lo g ic a l sco res
L in g u istic
p sy c h o lo g ic a l sc o res
G ross
p sy c h o lo g ic a l sc o res
P re v io u s g rad es o th e r
th a n m a th e m a tic s
P re v io u s g rad e s
i n m ath em a tics
C h ro n o lo g ic a l
age
C r ite r io n of success
in te rm e d ia te a lg e b ra
PM
A
-.1 4
- .0 6
K
•63
.4 4
59
u s e d t o p r e d i c t K o r s u c c e s s s c o r e s fro m t h e p r e v i o u s
a v e r a g e s w ere a s f o l l o w s : :
(1 ) K = 1 1 .4 7 P * 2 1 . 9
p -E * (e s t . K ) = 8 , 1 3
S (e s t.K )
(2 ) 1 = 11.86PM ♦ 2 4 . 7
" 1 2 *°6 ( 1 2 >
P .E .,
^
= 7 .1
(7 )
ve S t *K;
S.
z 10*53 (11)
(e s t.K )
S i n c e i t was a p p a r e n t fro m t h e c o m p a r a t i v e s i z e s o f
t h e s t a n d a r d e r r o r s o f e s t i m a t e t h a t t h e m a t h e m a ti c s
g r a d e was much t h e b e t t e r p r e d i c t i v e a g e n t , i t was
c o n s id e re d s u p e r f lo u s to f u r t h e r a n a ly z e th e p r e ­
d i c t i v e p o w e rs o f t h e o t h e r g r a d e a v e r a g e s *
R e su lts
h av e, t h e r e f o r e , been in d ic a te d f o r th e p re v io u s
g r a d e a v e r a g e s i n m a t h e m a t i c s o n ly *
P r e d i c t i v e p ow er.
I n T a b le XV, p a g e 6 0 ,
p r e v i o u s g r a d e a v e r a g e s i n m a t h e m a t i c s , PM, ha v e
b e e n s e l e c t e d so a s t o p r e d i G t m o st p r o b a b l e s u c c e s s
o r K s c o r e s w h ic h l i e a t t h e m id p o i n t s o f t h e g r a d e s
A, B, C, D, a n d F on t h e K s c a l e .
A c o m p a r is o n o f
t h i s t a b l e w ith T ab le X III r e v e a l s th e p r e v io u s g rad e
a v e r a g e i n m a t h e m a t i c s to be o f a p p r o x i m a t e l y t h e
same p r e d i c t i v e v a l u e a s t h e p s y c h o l o g i c a l s c o r e s *
H ow ever, a c o m p a r is o n t h e a c t u a l s t a n d a r d e r r o r s
60
TABLE XV
GRADES AND SUCCESS SCORES (K) PREDICTED
BY PREVIOUS GRADE AVERAGES IN MATHEMATICS (PM)
PM
CM
♦
1
.9 5
■2.13
3 .3 1
■4.49
K
22
F
36
D
50
C
6k
B
78
A
P ro b a b le deviation
50 i n 100
15 t o 29
F
29 t o 43
D
43 t o 577
C
57 t o 71
B
71 t o 85
A
a t a c tu a l score o r g r a d e
C e rta in *
6 8 i n 100
0 t o 55
11 t o 33
F to C
F to D
25 t o 47
3 t o 69
F to C
F to B
39 t o 61
17 t o 83
F to A
D to B
31 t o 9 V
53 t o 75
B to A
D to A
67 t o 89
45 t o 100
B to A
C to A
K S c a le
22
29
F
50
36
43
D
64
j 57
C
j
78
_ 71
B
100
A
1
PM S c a l e
A = 4 , B = 3, C = 2 , D * 1, F = 0
61
( c l o s e s t a p p r o x i m a t i o n was u s e d i n t a b l e s ) r e v e a l s
t h e m a t h e m a ti c s g r a d e t o be s l i g h t l y t h e more
s ig n ific a n t.
As i n t h e c a s e o f th e p s y c h o l o g i c a l s c o r e ,
i t i s v ery u n l ik e l y t h a t th e average of p re v io u s
g r a d e s i n ' m a t h e m a t i c s w ould be s u c h a s t o p r e d i c t
a s u c c e s s sc o re l y in g a t e x a c tl y th e m id -p o in t o f
any s p e c i f i e d g r a d e .
T h e r e fo r e , a s i n th e case of
th e p s y c h o lo g ic a l e x a m in a tio n , page 5 4 , th e p r e d i c ­
t i v e pow er o f t h e p r e v i o u s m a t h e m a ti c s a v e r a g e was
i n d i c a t e d i n term s o f th e g rad e p o i n t .
And a s
b e f o r e , p ag e 5 4 , one g r a d e p o i n t was t a k e n a s e q u a l
t o 14 p o i n t s on t h e s u c c e s s s c a l e , a n d t h e p r o b a b l e
d e v ia tio n s of a tru e score e stim a te d a c c o rd in g ly .
R e su lts.
I t was d e t e r m i n e d t h a t t h e p r e v i o u s
g r a d e a v e r a g e s i n m a t h e m a t i c s w ere o f more v a l u e i n
p r e d i c t i n g s u c c e s s i n m a t h e m a t i c s t h a n w e re t h e
av erag es of g rad es in o th e r s u b je c ts .
I t was a l s o
I n d i c a t e d t h a t t h e m a t h e m a ti c s a v e r a g e s w e re o f o n ly
s l i g h t l y g r e a t e r s i g n i f i c a n c e i n t h i s r e s p e c t th an
w ere g r o s s s c o r e s o n t h e p s y c h o l o g i c a l e x a m i n a t i o n .
The s i g n i f i c a n c e o f t h e p r e v i o u s g r a d e a v e r a g e i n
m ath em a tics i n p r e d i c t i n g s u c c e ss i n i n te r m e d i a t e
62
a l g e b r a may be i n t e r p r e t e d i n t e r m s o f th e g r a d e
p o in t a s fo llo w s:
1.
The c h a n c e s w ere a p p r o x i m a t e l y 49 to 100
t h a t t h e t r u e g r a d e w ou ld n o t d e v i a t e from t h e p r e ­
d i c t e d g r a d e by more t h a n h a l f a g r a d e p o i n t .
2.
The c h a n c e s w e re 82 o u t o f 100 t h a t t h e
t r u e g r a d e w o u ld n o t d i f f e r from t h e p r e d i c t e d g r a d e
by more t h a n one g r a d e p o i n t .
3.
I t was s t a t i s t i c a l l y
c e r t a i n t h a t th e tr u e
g r a d e w o u ld n o t v a r y fro m t h e p r e d i c t e d g r a d e by more
t h a n two a n d o n e - t h i r d g r a d e p o i n t s .
CHAPTER V I II
THE ACHIEVEMENT TEST IN ELEMENTARY
ALGEBRA AS A PROGNOSTIC MEASURE
The p u r p o s e o f t h i s c h a p t e r was t o r e p o r t
u p o n t h e p o s s i b l e v a l u e o f a s t u d e n t * s s c o r e on a n
ac h iev e m e n t t e s t i n e le m e n ta ry a lg e b r a i n p r e d i c t i n g
h i s p ro b a b le su c c e ss o r f a i l u r e in h i s stu d y of
in te rm e d ia te a lg e b ra .
C o rre la tio n s.
The c o e f f i c i e n t s o f c o r r e l a ­
t i o n b e tw e e n t h e a c h i e v e m e n t t e s t i n e l e m e n t a r y
a l g e b r a a n d a l l o f t h e o t h e r m e a s u r e s e m p lo y ed i n
t h i s s t u d y h a v e b e e n p r e s e n t e d i n T a b le XVI, pa g e
64.
C o r r e l a t i o n s w i t h t h e s e T^ s c o r e s , w ere i n
g e n e ra l,
c o n s id e r a b ly h ig h e r th a n th o s e w ith th e
o t h e r p r e d i c t i v e m e a s u r e s , T a b l e s X II a n d XIV.
It
was i n f e r r e d fro m t h e c o r r e l a t i o n o f .8 4 w i t h t h e
c r i t e r i o n t h a t ' th e e le m e n ta ry a lg e b r a a ch iev em en t
t e s t w ould p r o b a b l y p r o v e o f g r e a t e r v a l u e i n p r e ­
d i c t i n g s u c c e s s i n i n t e r m e d i a t e a l g e b r a t h a n h a d th e
p s y c h o lo g ic a l e x a m in a tio n o r th e p re v io u s g ra d e a v e r ­
age.
( C h a p t e r s VI and V I I ) .
64
TABLE XVI
CORRELATIONS BETWEEN ACHIEVEMENT TEST
IN ELEMENTARY ALGEBRA ( T l ) AND THE
VARIOUS PROGNOSTIC AND SUCCESS
MEASURES
E le m e n t a r y
a ch iev e m e n t
te s t
Tl
i
.
o
VO
.9 0
.7 7
.7 6
.3 4
.6 1
.
VJ1
00
.4 8
.3 8
.5 6
-.1 9
CO
.
2 nd a c h i e v e m e n t t e s t i n
e le m e n ta ry a lg e b r a
Tl
Score
T2 -T 1
d iffe re n c e s
A c h ie v e m e n t t e s t i n
in te rm e d ia te a lg e b ra
T3
A v e r a g e s o f g r a d e s on
c la ss ro o m t e s t s
T4
A verages o f g ra d e s
i n homework:
H
Q u a n tita tiv e
p sy c h o lo g ic a l sco res
_Q
L in g u i s t l c
p s y c h o lo g ic a l sco res
L
G ross
p sy c h o lo g ic a l sco res
G
P re v io u s g rad es
o t h e r th a n m ath em a tics
P
P re v io u s g rad es
PM
i n m ath em a tics
C h ro n o lo g ic a l
. age
A
C rite rio n of success
K
in te rm e d ia te a lg e b ra
65
P r e d i c t i v e v a lu e >
The r e g r e s s i o n e q u a t i o n
e m p lo y ed t o p r e d i c t K o r s u c c e s s s c o r e s from e le m e n ­
t a r y a c h i e v e m e n t t e s t o r T^ s c o r e s was a s f o l l o w s :
K = 1 .4 2 T1 + 1 5 .8 8
^ (e s t.k )
“ 7 .7 2
( e s t . k ) = 5 *21
The p r e d i c t i v e v a l u e o f t h e T-^ s c o r e s a s i n d i c a t e d
by t h e s t a n d a r d e r r o r , 7 . 7 2 , f o r p r e d i c t e d s u c c e s s
o r K s c o r e s was c o n s i d e r a b l y g r e a t e r t h a n t h a t o f
t h e p s y c h o l o g i c a l s c o r e s , page 5 1 , and t h e p r e v i o u s
g ra d e a v e r a g e s , page 6 5 .
As i n C h a p t e r s VI a n d V I I ,
s c o r e s w ere s e l e c t e d so a s to p r e d i c t s u c c e s s
s c o r e s l y i n g a t t h e m i d - p o i n t s o f g r a d e s A, B, C, D,
a n d F , on t h e K o r s u c c e s s s c a l e .
The e l e m e n t a r y
a l g e b r a a c h i e v e m e n t s c o r e s , T ^, t h e m o st p r o b a b l e
s u c c e s s o r K s c o r e s , and t h e p r o b a b l e l i m i t s o f t h e
d e v ia ti o n of th e tru e
s u c c e s s s c o r e s a n d g r a d e s have,
b e e n p r e s e n t e d i n T a b le X V II, pag e 6 6 .
As i n
T a b l e s X I I I a n d XV, t h e c h a n c e v a r i a t i o n s o f t h e t r u e
s c o r e i n t h i s T a b le was i n d i c a t e d i n te rm s o f t h e
sta n d a rd e r r o r f o r p r e d ic tin g K s c o re s .
The r e s p e c ­
t i v e v a lu e s of th e t h r e e p r e d i c t i v e m e a su re s, con­
s i d e r e d so f a r , may be i n f e r r e d fro m a c o m p a r is o n o f
66
TABLE XVII
GRADES AND SUCCESS SCORES (K) PREDICTED BY SCORES
ON AN ACHIEVEMENT TEST IN ELEMENTARY ALGEBRA ( T l)
Tl
4*31
1 4 .1 6
2 4 .0 2
3 3 .8 8
4 3 .7 5
P ro b a b le d e v ia tio n
of a c t u a l sc o re o r grade
C e rta in *
68 i n 100
50 i n 100
14 t o 30
0 " t o 45
17 t o 27
F
F to C
F to D
28 t o 44
13 t o 59
31 t o 4 l
F to C
F + - t o CD 42 t o 58
45 t o 55
27 t o 73
C
Df t o C- F t t o A- 5 9 t o 69
56 t o '(%
41 t o 87 ""
B+ t o A
B ;
C+ t o A 70 t o 86
55 t o 1 0 0 '
72 t o 63
C+ t o A
B* t o A
A
K
22
F
36
D
50
C
.. 64"
B
78 .
A
* 3 X SD
(e s t.K )
K S c a le
22
36
29
57
43
D
C
s
71
34
a
M
78
.100
B
T l S c a le
“"24
14
|
low
64
50
44
1
h ig h
67
th e se th re e t a b l e s .
I t was a p p a r e n t t h a t o f t h e
m e a s u r e s em p lo y ed i n t h i s s t u d y , t h e s c o r e on t h e
a c h i e v e m e n t t e s t i n e l e m e n t a r y a l g e b r a gave t h e
b e s t i n d ic a t i o n of p ro b ab le su c ce ss or f a i l u r e in
th e s tu d y of i n te r m e d i a t e a lg e b r a .
In te r p r e ta tio n of r e s u l t s .
As i n t h e c a s e o f
th e p s y c h o l o g i c a l e x a m i n a t i o n , page 5 3 , r e s u l t s have
been i n t e r p r e t e d h e re i n term s of th e g ra d e p o i n t ,
i.e .,
one g r a d e p o i n t was e q u i v a l e n t t o 14 p o i n t s on
th e s u c c e s s o r K s c a l e .
(S ee T a b le X V I I ) .
And i n
t h e same m anner a s i n d i c a t e d on pa g e 5 3 , t h e c h a n c e
v a r i a t i o n s o f t h e t r u e s u c c e s s s c o r e w ere c a l c u l a t e d
by c o m p a rin g t h e s t a n d a r d e r r o r , 7 . 7 2 , w i t h t h e number
o f p o i n t s o c c u p i e d by one g r a d e p o i n t on th e s u c c e s s
sc a le ,
14.
T h u s , one g r a d e p o i n t i s e q u a l t o 3.4
d i v i d e d by 7 . 7 2 o r 1 .8 1 t i m e s t h e s t a n d a r d e r r o r .
The
a r e a o c c u p i e d by - 1 .8 1 s ig m a s u n d e r t h e n o r m a l p r o b a ­
b ility
c u r v e i s a p p r o x i m a t e l y 93 p e r c e n t o f t h e
to ta l area.
T h u s, t h e c h a n c e s w ere 93 i n 100 t h a t
t h e d e v i a t i o n fro m a p r e d i c t e d s c o r e w ou ld n o t be more
t h a n one g r a d e p o i n t .
R e su lts.
I t was d e t e r m i n e d t h a t o f t h e s i n g l e
p r e d i c t i v e m e a s u r e s em p lo y ed i n t h i s s t u d y t h e
68
a ch iev e m e n t t e s t i n e le m e n ta ry a lg e b r a gave th e b e s t
in d ic a tio n of su ccess o r f a i l u r e in in te rm e d ia te
a lg e b ra .
The s i g n i f i c a n c e o f t h e i n d i v i d u a l s c o r e
on t h i s t e s t may be i n t e r p r e t e d i n t e r m s o f g r a d e
p o in ts as fo llo w s:
1.
The c h a n c e s w ere 63 o u t o f 100 t h a t t h e
a c t u a l g r a d e i n i n t e r m e d i a t e a l g e b r a w o u ld n o t d i f f e r
fro m t h e p r e d i c t e d g r a d e by more t h a n h a l f a g r a d e
p o in t.
2.
The c h a n c e s w ere 93 o u t o f 100 t h a t t h e
a c t u a l g r a d e i n i n t e r m e d i a t e a l g e b r a w o u ld n o t d e v i a t e
from t h e p r e d i c t e d g r a d e by more t h a n one g r a d e p o i n t .
3*
I t was o n l y s t a t i s t i c a l l y
c e r t a i n t h a t th e
a c t u a l i n t e r m e d i a t e a l g e b r a g r a d e w o u ld d i f f e r from
t h e p r e d i c t e d g r a d e by n o t more t h a n >one a n d tw o t h i r d s grade p o i n ts .
CHAPTER IX
THE COMBINED PREDICTIVE MEASURES
I n C h a p te rs V I, V I I , and V I I I , th e p r e d i c t i v e
p o w e rs o f m e a s u r e s o f i n t e l l i g e n c e ,
s c h o l a r s h i p , and
m a th e m a tic a l a b i l i t y have been in v e s ti g a t e d *
I t was
t h e p u r p o s e o f t h i s c h a p t e r t o r e p o r t u p o n t h e com­
b i n e d p r e d i c t i v e e f f e c t o f t h e s e t h r e e m e a s u re s *
O r,
i n o t h e r w o r d s , t o s p e c i f i c a l l y s o l v e th e p ro b le m a s
s t a t e d i n C h a p t e r I*
I.
RELATIVE SIGNIFICANCE OF THE PREDICTIVE MEASURES
S ig n ific a n c e of in d iv id u a l m easu res*
The r e l a ­
t i o n s h i p b e tw e e n t h e g r o s s s c o r e s on t h e p s y c h o l o g i c a l
e x a m i n a t i o n , G, t h e a v e r a g e s o f s t u d e n t s p r e v i o u s
g r a d e s i n m a t h e m a t i c s , PM, t h e s c o r e s r e c e i v e d u p o n
t h e a c h i e v e m e n t t e s t s i n e l e m e n t a r y a l g e b r a , T-^, a n d
o f t h e o t h e r m e a s u r e s em p lo y ed i n t h i s s t u d y h a v e b e e n
i n d i c a t e d by c o r r e l a t i o n c o e f f i c i e n t s i n T a b le X V I II ,
page 7 0 .
The a v e r a g e s a n d s t a n d a r d s d e v i a t i o n s o f t h e
d i s t r i b u t i o n s o f t h e K, G, PM, a n d T^ s c o r e s , a n d t h e
s ta n d a r d and p ro b a b le e r r o r s f o r e s tim a tin g K o r su c ­
c e s s s c o r e s fro m p r e d i c t i v e s c o r e s G, PM, an d T ^ , h a v e
a ll
70
TABLE XVLII
CORRELATIONS OF THE FOUR MAJOR PROGNOSTIC MEASURES,
THE GROSS PSYCHOLOGICAL SCORE (G) , THE PREVIOUS
GRADE AVERAGE IN MATHEMATICS (PM), THE ACHIEVEMENT
TEST IN ELEMENTARY ALGEBRA ( T l ) , THE COMBINED INDEX
( G f PM
T l ) , WITH VARIOUS PROGNOSTIC AND SUCCESS
MEASURES
g
P r o g n o s tic m easures
PM
Tl
Tl
.6 1
.6 3
.8 4
.58
.6 6
.5 7
.6 0
.9 0
.0 5
.2 1
-.0 9
.52
*50
.5 4
.8 6
.7 6
.3 9
.5 0
.3 4
.8 3
.6 3
.6 1
.9 5
.4 9
.4 8
.4 7
.8 0
.5 6
.4 7
.6 4 2 ,
t
o#
.
.7 7
00
.
.8 0
.
.1 4
*■
PM :
00
.
C rite rio n of success
in te rm e d ia te a lg e b ra
K
1 s t ach iev em en t t e s t i n
e le m e n ta ry a lg e b r a
Tl
2nd a c h ie v e m e n t t e s t i n
e le m e n tary a lg e b r a
T2
Score
d iffe re n c e s
T2--T l
A c h ie v e m e n t t e s t i n
i n t e r m e d i a t e a l g e b r a T3
A v e r a g e s o f g r a d e s on
c la ssro o m t e s t s
T4
A verages of g ra d e s
i n homework
H
Q u a n tita tiv e
p sy c h o lo g ic a l sco res
Q
L in g u istic
p s y c h o lo g ic a l sc o re s
L
G-ross
p sy c h o lo g ic a l sco res
a
P re v io u s g rad e s o th e r
t h a n ma them a t i c s
P
P re v io u s g rad es
PM
i n m a t h e m a ti c s
C h ro n o lo g ic a l
ag e
A
a
CO
—
>3
•JL iUl
-
71
b e e n i n d i c a t e d i n T a b le XIX, page 7 2 .
From t h e c o r r e l a t i o n s b e tw e e n t h e p r e d i c t i v e
m e a s u r e s a n d t h e c r i t e r i o n , -Table X V I II , and fro m
th e r e l a t i v e
s i z e s o f th e s t a n d a r d e r r o r s f o r e s t i ­
m a t i n g s u c c e s s s c o r e s , T a b le XIX, i t was a p p a r e n t ,
t h a t t h e m e a s u r e s G, PM, a n d T ^, w ere n o t o f e q u a l
v a l u e i n p r e d i c t i n g s u c c e s s a s m e a s u r e d by t h e c r i t e r ­
i o n K.
k a was I n d i c a t e d i n C h a p t e r s V I , V I I , a n d
V I I I , th e p s y c h o l o g ic a l e x a m in a tio n and th e p r e v io u s
m a t h e m a t i c s g r a d e a v e r a g e w ere o f a p p r o x i m a t e l y e q u a l
p ro g n o stic v a lu e ;
th e e le m e n ta ry a lg e b r a a ch iev e m e n t
t e s t was o f g r e a t e r v a l u e t h a n e i t h e r .
Com bined s i g n i f i c a n c e .
The p r o b le m h e r e was t o
com bine s c o r e s o f t h e t h r e e p r e d i c t i v e m e a s u r e s i n
s u c h a way a s t o g i v e th e b e s t p o s s i b l e p r e d i c t i o n
of su ccess in in te rm e d ia te a lg e b ra , i . e . ,
as success
was m e a s u r e d b y c r i t e r i o n o r s u c c e s s s c o r e s , K.
It
was a p p a r e n t fro m t h e v a r i a b i l i t y , v a l u e , a n d s i z e o f
s c o r e s t h a t e a c h w ould h a v e to b e a r a d i f f e r e n t w e i g h t .
The p r o b le m w a s , t h e r e f o r e , p u t i n t h e fo rm o f a r e ­
g r e s s i o n e q u a t i o n a n d h a n d l e d a s one o f m u l t i p l e
c o rre la tio n .
T h i s e q u a t i o n w as f i r s t w r i t t e n a s
72
TABLE XIXr
THE AVERAGES, STANDARD DEVIATIONS, STANDARD
PROBABLE ERRORS OF ESTIMATE, FOR THE MAJOR PROG­
NOSTIC MEASURES: AND THE MEAN.'AND STANDARD DEVIATION
OF THE CRITERION
M
G ross p sy c h o lo g i
c a l scores
G
P re v io u s gradesi n m a t h e m a t i c s PM
A c h ie v e m e n t t e s t i n
e le m e n ta ry
Tl
a lg e b ra
S.D*
P .E .
(e s t.K )
S .D .
(e s t.K )
9 2 .2 7
2 3 .4 4
7 .2 4
1 0 .7 3
2 .1 3
.7 2
7 .0 9
1 0 .5 3
2 4 .0 3
9 .5 4
5 .2 1
7 .7 2
4 .4 6
6 .6 1
G + PM + T l*
C rite rio n of success
in te rm e d ia te
a lg e b ra
K
5 0 .0 0
1 4 .0 0
*
= . 1 4Zq + • i 9 Zp^ * .6 4 zT1
73
fo llo w s;
- V o
h
+ V W
+ V
n
* N
(1 )
I n t h i s e q u a t i o n W, W, and W w ere c o n s t a n t te r m s
o r c o e f f i c i e n t s r e p r e s e n t i n g t h e s i g n i f i c a n c e to
be a t t a c h e d t o t h e v a r i a b l e s X^, X^, and X^.
T h ese
v a r i a b l e s , o f c o u rs e , r e p r e s e n te d th e p s y c h o lo g ic a l
s c o r e s , p r e v i o u s g r a d e ' a v e r a g e s i n m a t h e m a t i c s , and
e le m e n ta ry a c h ie v e m e n t t e s t s c o r e s i n th e o r d e r i n d i ­
c a te d .
The v a r i a b l e q u a n t i t i e s
W^, an d
w ere
com puted i n te r m s t h e s t a n d a r d d e v i a t i o n s a n d i n t e r ­
c o r r e l a t i o n s o f th e t h r e e p r o g n o s tic m easu res and th e
c rite rio n .
Thus i t was p o s s i b l e
a s i n d i c a t e d i n C h a p te r I ,
i.e .,
t o s o l v e t h e p ro b le m
g i v e n (1 ) a s t u d e n t ’ s
s c o r e on a p s y c h o l o g i c a l e x a m i n a t i o n , G, ( 2 ) t h e
av e ra g e o f h i s p r e v io u s g ra d e s i n m a th e m a tic s, P I ,
and ( 3 ) h i s s c o r e on a n a c h i e v e m e n t t e s t i n e l e m e n t a r y
a l g e b r a , T^; h i s m o s t p r o b a b l e s u c c e s s i n i n t e r m e d i a t e
a l g e b r a was d e t e r m i n e d by t h e s u c c e s s s c o r e , K, i n t h e
f o l l o w i n g w ay;
Xg = •08XQ> + 3 .7 3 X pM ♦ .91X T1 ♦ 1 2 .8 1
The r e l a t i v e
(2 )
s i g n i f ic a n c e o f each o f th e p r e d i c t i v e
was more a p p a r e n t when t h i s same e q u a t i o n was p u t i n
74
s ta n d a r d form , i . e . :
ZK a #1^ q
* *19ZipM * *^4Z T1
(3 )
The v a l u e o r com bined p r e d i c t i v e pow er o f t h e mea­
s u r e s when w e i g h t e d a s i n d i c a t e d , e q u a t i o n ( 3 ) h a s
b e e n i n d i c a t e d i n T a b l e s X V III a n d XIX.
re la tio n c o e ffic ie n t,
The c o r ­
was r e p o r t e d a s
.8 7 a n d t h e s t a n d a r d e r r o r f o r p r e d i c t i n g s u c c e s s
s c o r e s was 6 . 6 1 .
II.
In g e n e ra l.
RESULTS
As a r e s u l t o f t h i s s t u d y i t was
d e te rm in e d t h a t i n p r e d i c t i n g su c c e ss i n in te r m e d ia te
a lg e b r a ( 1 ) th e r e l a t i v e
t i c m easures,
a lg e b ra ,
s i g n i f ic a n c e of th e p ro g n o s­
th e ach iev e m e n t t e s t i n e le m e n ta ry
t h e p r e v i o u s g r a d e s i n m a t h e m a t i c s , th e
p s y c h o l o g i c a l e x a m i n a t i o n , was i n t h e o r d e r named;
(2 )
t h e b e s t s i n g l e i n d e x was t h e a c h i e v e m e n t t e s t
i n e l e m e n t a r y a l g e b r a ; a n d ( 3 ) a com bined i n d e x o f
th e e le m e n ta ry a lg e b r a a ch iev em en t t e s t , th e p r e v io u s
g r a d e s i n m a t h e m a t i c s a n d t h e p s y c h o l o g i c a l e x a m in a ­
t i o n y ie ld e d th e h i g h e s t c o r r e l a t i o n w ith su c c e ss and
f u r n is h e d th e b e s t p o s s ib l e b a s i s f o r p r o g n o s is .
The g e n e r a l e f f e c t i v e n e s s o f t h e c o m b in ed
75
i n d e x h a s b e e n i l l u s t r a t e d i n T a b le XX, p a g e 7 6 .
In
t h i s t a b l e K o r s u c c e s s s c o r e s l y in g a t th e m id -p o in ts
o f g r a d e s A, B, C, D, a n d F have b e e n s e l e c t e d and
th e p ro b a b le d e v i a t i o n s o f th e t r u e s c o r e s and g ra d e s
have b een i n d i c a t e d i n term s o f th e p ro b a b le and s t a n d ­
ard e rro rs fo r p re d ic tin g K sco res.
The r e l a t i v e
v a l u e o f t h e c o m b ined i n d e x may be e s t i m a t e d by com­
p a r i n g t h i s t a b l e w i t h T a b l e s X I I I , XV, a n d X V II.
I n te r m s o f t h e g r a d e p o i n t .
The c o m p a r a t i v e
s i g n i f i c a n c e o f t h e com bined i n d e x h a s b e e n i n d i c a t e d
i n T a b le XXI, p a g e 7 7 .
The v a l u e o f t h e co m bined
i n d e x was i n t e r p r e t e d i n te r m s o f g r a d e p o i n t s i n
t h e same m an n e r a s h a s b e e n p r e v i o u s l y i n d i c a t e d f o r
t h e i n d i v i d u a l p r e d i c t i v e m e a s u r e s , p a g e 53*
One g r a d e
p o i n t was t a k e n a s e q u a l t o 14 p o i n t s on t h e s u c c e s s
sc a le .
Then by c o m p a rin g t h e s t a n d a r d e r r o r 6 . 6 1 ,
f o r p r e d i c t e d K o r s u c c e s s s c o r e s from t h e com bined
in d e x (e q u a tio n 2 ) th e p ro b a b le ch an ces o f a d e v ia tio n
by a n y num ber o f g r a d e p o i n t s c o u l d be c a l c u l a t e d .
S i g n i f i c a n t r e s u l t s w ere a s f o l l o w s :
1.
The c h a n c e s w ere 71 o u t o f 100 t h a t th e
a c t u a l g r a d e i n i n t e r m e d i a t e a l g e b r a w ould n o t d e v i a t e
from t h e p r e d i c t e d g r a d e by more t h a n h a l f a g r a d e
p o in t.
76
TABLE XX
PREDICTION OF GRADES AND SUCCESS SCORES BY A
COMBINED INDEX OF THE GROSS PSYCHOLOGICAL SCORE ( G ) ,
THE PREVIOUS GRADE AVERAGE IN MATHEMATICS (PM), AND
THE ELEMENTARY ALGEBRA ACHIEVEMENT TEST ( T l)
P re d ic te d
sco re
K
22
F
36
D
50
C
64
B
78
A
P ro b ab le d e v ia tio n of
50 i n 100
68 i n
18 t o 26
15 t o
- - F
32 t o 4o
29 to
— D
46 t o 54
43 t o
■—
G
6 0 t o 68
57 t o
B
74 t o 78
71 t o
A
a c t u a l s c o r e o r & rade
C e rta in *
100
2 t o 42
29
F to D
16 t o 56
43
F to 0
30
t o 70
57
D to B
4 4 t o 84
71
G to A
58 t o 98
85
C to A
K S e a le
22
36
50
64
78
1 29
I 43
| 57
j 71
—-------------- 1—----- _ — I------- — 1------------- 1---------100
77
TABLE XXI
THE RELATIVE SIGNIFICANCE OF FOUR
PROGNOSTIC MEASURES INDICATED
IN TERMS OF THE GRADE POINT
N ever l i k e l y to
C h an ces i n 100 t h a t a c t u a l g r a d e w i l l
n o t d e v i a t e from p r e d i c t e d g r a d e by
d e v i a t e by more
more t h a n one g r a d e p o i n t a n d by more
t h a n num ber o f
t h a n o n e - h a l f o f one g r a d e p o i n t
grade p o in ts
1 /2
in d ic a te d
1
G ross
p sy c h o lo g ic a l sco re
G
48
81
2 .3 3 g r d . o t s .
P re v io u s g rad e s
PM
82
i n m ath em a tics
2 ,3 0 g r d . p t s .
49
A c h ie v e m e n t t e s t i n
e le m e n ta ry a lg e b r a
Tl
92
1 ,6 5 g r d , p t s .
63
Combined i n d e x
G. PM. a n d T l
1 ,4 1 g r d , p t s .
71
97
*" NOTE: T h is t a b l e s h o u l d r e a d (ex a m p le row o n e ) , t h e
c h a n c e s a r e 48 i n 100 t h a t t h e a c t u a l g r a d e i n i n t e r m e d i a t e
a l g e b r a w i l l n o t d e v i a t e fro m t h e one p r e d i c t e d by a g r o s s
s c o r e on t h e p s y c h o l o g i c a l e x a m i n a t i o n by more t h a n 1 / 2 a
g r a d e p o i n t * The c h a n c e s a r e 81 i n 100 t h a t i t w i l l n o t
d e v i a t e by more t h a n one g r a d e p o i n t . I t i s a l m o s t c e r t a i n
t h a t i t w i l l n o t d i f f e r by more t h a n 2 , 3 3 g r a d e p o i n t s .
-
78
2.
The c h a n c e s w ere 97 o u t o f 100 t h a t th e
a c t u a l g r a d e i n i n t e r m e d i a t e a l g e b r a w o uld n o t d i f f e r
fro m t h e p r e d i c t e d g r a d e by more t h a n one g r a d e p o i n t *
3*
I t was s t a t i s t i c a l l y c e r t a i n t h a t t h e
a c t u a l g r a d e i n i n t e r m e d i a t e a l g e b r a w o u ld n o t d i f f e r
fro m t h e p r e d i c t e d g r a d e by more t h a n one a n d o n e h a l f g rade p o in ts *
CHAPTER X
SUMMARY AND CONCLUSION
The s i g n i f i c a n t r e s u l t s o f t h i s s t u d y h a v e b e e n
r e p o r te d i n th e p re c e d in g c h a p te rs *
T h is c h a p te r h as
b e e n d e v o t e d t o a summary o f t h e s e f i n d i n g s and a
g e n e r a l c o n c lu s io n i n r e g a r d to p r o g n o s is i n i n t e r ­
m ed iate a lg e b ra *
I.
MINOR ISSUES
C o n trib u tin g f a c t o r s *
An e a r l y i n v e s t i g a t i o n
was made t o d e t e r m i n e t h e e f f e c t o f c e r t a i n c o n t r i b u t ­
i n g f a c t o r s u p o n t h e s t u d y a s a w hole*
T h ese m in o r
i s s u e s w ere t h e i n f l u e n c e w h ic h a s t u d e n t * s a g e , s e x ,
a n d p r e v i o u s y e a r s o f s t u d y i n m a t h e m a t i c s m ig h t h a v e
upon h is u ltim a te su ccess o r f a i l u r e i n in te rm e d ia te
a lg e b ra .
As a r e s u l t o f t h i s i n v e s t i g a t i o n , i t was
d e te rm in e d ( . . . ) .
1.
T h a t s e x was o f no s i g n i f i c a n c e i n d e t e r ­
m in in g s u c c e s s o r f a i l u r e i n i n t e r m e d i a t e a l g e b r a .
2.
T h a t w i t h i n t h e ag e r a n g e o f t h e s t u d e n t s
i n v o l v e d i n t h i s s t u d y , ag e was n o t a s i g n i f i c a n t
fa c to r.
3*
T h a t t h e num ber o f y e a r s a s t u d e n t h a d
p r e v i o u s l y s t u d i e d m a t h e m a t i c s was o f c o n s i d e r a b l e
s ig n if ic a n c e i n d e te rm in in g h i s u ltim a te g rade i n
in te rm e d ia te a lg e b ra .
T h i s was a m a t t e r c o n s i d e r e d
w o r th y o f f u r t h e r i n v e s t i g a t i o n , b u t f o r r e a s o n s
w h ic h ha v e a l r e a d y b e e n i n d i c a t e d , i t was b e y o n d th e
sc o p e o f t h i s s t u d y .
S u p e rflu o u s p r e d ic tiv e m easu res.
The p r e d i c ­
t i v e m e a s u r e s em p lo y ed i n t h i s s t u d y c o n s i s t e d o f :
S c o r e s on a n a c h i e v e m e n t t e s t i n e l e m e n t a r y a l g e b r a ;
q u a n tita tiv e
s c o r e s on a p s y c h o l o g i c a l e x a m i n a t i o n ;
g r o s s s c o r e s on a p s y c h o l o g i c a l e x a m i n a t i o n ; a v e r a g e s
o f p r e v i o u s g r a d e s i n s u b j e c t s o t h e r t h a n m a t h e m a ti c s
and, a v e ra g e s of p re v io u s g ra d e s in m a th e m a tic s.
As
t h e s t u d y d e v e l o p e d i t was a p p a r e n t t h a t some o f
t h e s e m e a s u r e s w ere o f m in o r o r s e c o n d a r y s i g n i f i ­
cance in p r e d i c t i n g s u c c e s s i n in te r m e d ia te a lg e b r a .
I t was d e t e r m i n e d t h a t :
1.
The g r o s s s c o r e on t h e p s y c h o l o g i c a l exam­
i n a t i o n was a s l i g h t l y b e t t e r i n d e x o f s u c c e s s i n
in te r m e d ia te a lg e b r a th a n e i t h e r th e q u a n t i t a t i v e
or lin g u istic
2.
sco re.
The a v e r a g e o f t h e p r e v i o u s g r a d e s i n
m a t h e m a t i c s a f f o r d e d a much b e t t e r b a s i s f o r p r e d i c t ­
in g su c c e ss o r f a i l u r e i n in te rm e d ia te a lg e b r a th an
81
d id th e a v e ra g e of g ra d e s o t h e r th a n m a th e m a tic s.
I t was s u f f i c i e n t ,
t h e r e f o r e , t o r e p o r t upo n
th e s i g n i f i c a n c e o f o n ly th r e e o f th e p r e d i c t i v e
m easu res.
T h ese m e a s u r e s w ere t h e a c h i e v e m e n t t e s t
i n e le m e n ta ry a lg e b r a ,
th e p re v io u s grad e a v e ra g e s
i n m a th e m a tic s , and th e g r o s s o r t o t a l p s y c h o lo g i­
c a l e x a m in a tio n .
II.
RESULTS IN TERMS OF THE GRADE POINTS
The p s y c h o l o g i c a l e x a m i n a t i o n .
of th is s t u d y t h e
I n C h a p t e r VI',
s i g n i f i c a n c e o f th e p s y c h o lo g ic a l
e x a m in a tio n a s an in d e x to su c c e ss i n in te r m e d ia te
a l g e b r a was r e p o r t e d i n t e r m s o f t h e g r a d e p o i n t a s
fo llo w s:
1.
The c h a n c e s w ere a p p r o x i m a t e l y 48 o u t o f
100 t h a t t h e a c t u a l g r a d e i n i n t e r m e d i a t e a l g e b r a
w o u ld n o t d e v i a t e fro m t h e p r e d i c t e d g r a d e b y more
th an h a l f a g rad e p o i n t.
2.
“The c h a n c e s w ere 81 o u t o f 100 t h a t t h e
a c t u a l g r a d e i n i n t e r m e d i a t e a l g e b r a w ould n o t d i f f e r
fro m t h e p r e d i c t e d g r a d e by more t h a n one g r a d e p o i n t .
3.
I t c o u l d o n l y be s a i d f o r c e r t a i n t h a t t h e
t r u e g r a d e i n i n t e r m e d i a t e a l g e b r a w o u ld n o t d e v i a t e
fro m t h e p r e d i c t e d g r a d e b y more t h a n two a n d o n e t h i r d grad e p o i n ts .
82
A verages o f p r e v io u s g ra d e s i n m a th e m a tic s *
I n C h a p te r V I I ,
th e s i g n i f i c a n c e o f th e p r e v io u s
g ra d e a v e ra g e i n m a th e m a tic s a s an i n d i c a t o r o f s u c ­
c e s s i n i n t e r m e d i a t e a l g e b r a was c o n s i d e r e d .
R e su lts
w e re r e p o r t e d i n t e r m s o f t h e g r a d e p o i n t i n t h e
f o l l o w i n g m a n n e r;
1.
The c h a n c e s w e re 49 o u t o f 100 t h a t t h e
a c t u a l g r a d e i n i n t e r m e d i a t e a l g e b r a w o u ld n o t d i f f e r
fro m t h e p r e d i c t e d g r a d e &y more t h a n h a l f a g r a d e
p o in t•
2.
The c h a n c e s w ere 92 o u t o f 100 t h a t t h e
a c t u a l o r t r u e g r a d e i n i n t e r m e d i a t e a l g e b r a w ould
n o t d e v i a t e fro m t h e p r e d i c t e d g r a d e by more t h a n
one g r a d e p o i n t ,
3.
I t was o n l y s t a t i s t i c a l l y
c e rta in th a t
t h e a c t u a l g r a d e i n i n t e r m e d i a t e , a l g e b r a w o u ld .n o t
d e v i a t e fro m t h e p r e d i c t e d g r a d e by more t h a n two
and o n e - t h i r d g rad e p o i n t s .
The a c h i e v e m e n t t e s t i n e l e m e n t a r y a l g e b r a .
I n C h a p t e r V I I I , a r e p o r t was made u p o n t h e v a l u e
o f th e ach iev em en t t e s t i n e le m e n ta ry a lg e b r a as an
in d e x of su c c e ss i n in te r m e d ia te a lg e b r a .
R e su lts
i n d i c a t e d i n t e r m s o f t h e g r a d e p o i n t s w ere a s
83
fo llo w s:
1.
The c h a n c e s w ere 63 o u t o f 100 t h a t t h e
a c t u a l g r a d e i n i n t e r m e d i a t e a l g e b r a w o u ld n o t d e ­
v i a t e fro m t h e p r e d i c t e d g r a d e by more t h a n h a l f
a grade p o i n t,
2.
The c h a n c e s w ere 92 o u t o f 100 t h a t t h e
t r u e i n t e r m e d i a t e a l g e b r a g r a d e w ould n o t d i f f e r
fro m t h e p r e d i c t e d g r a d e by more t h a n one g r a d e
p o in t.
3.
th e a c t u a l
I t was o n l y s t a t i s t i c a l l y
c e rta in th a t
g r a d e i n i n t e r m e d i a t e a l g e b r a w o u ld n o t
d e v i a t e fro m t h e
p r e d i c t e d g r a d e by more t h a n one
and t w o - t h ir d s g rad e p o in ts #
The co m b ined p r e d i c t i v e i n d e x .
I n C h a p te r IX
a r e p o r t was made u pon t h e e f f e c t i v e n e s s o f a com­
b in e d in d e x o f th e p s y c h o lo g ic a l e x a m in a tio n , th e
p r e v i o u s g r a d e a v e r a g e s i n m a t h e m a ti c s a n d t h e a c h i e v e ­
m ent t e s t i n e l e m e n t a r y a l g e b r a .
S c o r e s fro m t h e s e
m e a s u r e s w ere co m bined i n t h e f o l l o w i n g m an n e r:
K s
.0 8 + 3 . 7 3 PM ♦ .9 1 T 1 «•1 2 .8 1
S .D .,
,
(e s t.K )
z 6 .6 1
The s i g n i f i c a n c e o f t h i s co m bined i n d e x i n p r e d i c t i n g
s u c c e s s o r f a i l u r e i n i n t e r m e d i a t e a l g e b r a was r e ­
p o r t e d i n term s o f th e g rad e p o i n t a s f o llo w s :
1*
The c h a n c e s w ere 71 o u t o f 100 t h a t t h e
a c t u a l g r a d e i n i n t e r m e d i a t e a l g e b r a w ou ld n o t d e ­
v i a t e fro m t h e p r e d i c t e d g r a d e by more t h a n h a l f a
grade p o in t.
2.
The c h a n c e s w ere 97 o u t o f 100 t h a t t h e
a c t u a l g r a d e i n i n t e r m e d i a t e a l g e b r a w o u ld n o t d i f f e r
fro m t h e p r e d i c t e d g r a d e by more t h a n one g r a d e p o i n t .
3.
I t was p r a c t i c a l l y c e r t a i n t h a t t h e a c t u a l
I n t e r m e d i a t e a l g e b r a g r a d e w ould n o t d e v i a t e fro m th e
p r e d i c t e d g r a d e by more t h a n one a n d o n e - h a l f g r a d e
p o in ts .
III.
COMPARATIVE RESULTS
C o m p a r a tiv e s i g n i f i c a n c e o f p r o g n o s t i c m e a s u r e s .
The r e l a t i o n s h i p b e tw e e n e a c h o f t h e p r o g n o s t i c mea­
s u r e s and s u c c e s s i n in te r m e d ia te a lg e b r a h a s been
i n d i c a t e d by c o e f f i c i e n t s o f c o r r e l a t i o n s i n T a b le
X X II, p a g e 85*
The v a l u e o f e a c h m e a su re a s a n i n d e x
o f s u c c e s s w a s, h o w e v e r , more o f t e n i n d i c a t e d b y t h e
sta n d ard e r r o r f o r p r e d ic tin g c r i t e r i o n sc o re s .
c o m p a r is o n o f t h e r e l a t i v e
A
s iz e s of th ese e r r o r s has
b e e n made i n T a b le X X I II , pa g e 8 6 .
T h i s same
85
TABLE XXII
CORRELATIONS OF THE FOUR MAJOR PROGNOSTIC
MEASURES, THE GROSS PSYCHOLOGICAL SCORE ( G ) ,
THE PREVIOUS GRADE AVERAGE IN MATHEMATICS (PM),
THE ACHIEVEMENT TEST IN ELEMENTARY ALGEBRA ( T l ) ,
THE COMBINED INDEX (G ♦ PM ♦ T l ) , WITH VARIOUS
PROGNOSTIC AND SUCCESS MEASURES
PM
Tl
•61
_ . .6 3
.8 4
•58
... .5 6
•57
.6 0
.9 0
.05
.2 1
•**09
.5 2
.5 0
.7 7
.? 4
.8 6
.7 6
•39
.5 0
.3 4
.8 3
.6 3
.6 1
.9 5
.4 9
.4 8
.4 7
.80'
.8 0
.3 8
G
C rite rio n of success
in te rm e d ia te a lg e b ra
K
1s t ach iev em en t t e s t i n
e le m e n ta ry a lg e b r a
Tl
2n d a c h i e v e m e n t t e s t i n
e le m e n tary a lg e b r a
T2
S core
d iffe re n c e s
T2--T l
A c h ie v e m e n t t e s t i n
i n t e r m e d i a t e a l g e b r a T3
A v e ra g e o f g r a d e s on
c la ssro o m t e s t s
T4
A verages o f g ra d e s
- i n homework
H
Q u a n tita tiv e
Q
p sy c h o lo g ic a l sco res
L in g u istic
p s y c h o lo g ic a l sco res
L
G ross
p sy c h o lo g ic a l sco res
G
P re v io u s g rad e s o th e r
t h a n m a t h e m a ti c s
P
P re v io u s g rad es
i n m a t h e m a ti c s
PM
C h ro n o lo g ic a l
age
A
*^ K
=
.4 8
.5 6
.4 7
.0 4
-.1 4
.
6 4 Z rp ^
-.1 9
G
- PM
Tl
.
00
—
•3
*
P ro g n o s tic m easures
86
TABLE X X III
THE AVERAGES, STANDARD DEVIATIONS, STANDARD AND
PROBABLE ERRORS OF ESTIMATE, FOR THE MAJOR PROGNOSTIC
MEASURES; AND THE MEAN AND STANDARD DEVIATION OF THE
CRITERION
M
G 1- PM + T l*
C rite rio n of success
in te rm e d ia te . ;
a lg e b ra
•
K
*
zk
9 2 .2 7
2 .1 3
2 4 .0 3
5 0 .0 0
= - i 4 z g * - i 9Zpm
P .E .
(e s t.K )
^ S .D .
(e s t.K )
2 3 .4 4
7 .2 4
1 0 .7 3
7 .0 9
1 0 .5 3
5 .2 1
7 .7 2
4 .4 6
6 .6 1
OJ
•
G ross p s y c h o lo g i­
c a l scores
G
P re v io u s g rad e s in
m ath em a tics
PM
A c h ie v e m e n t t e s t i n
e le m . a l g e b r a
T1
S .D .
9 .5 4
1 4 .0 0
87
c o m p a r is o n h a s b e e n made i n te r m s o f t h e g r a d e p o i n t
i n T a b le XXIV, p a g e 8 8 .
I n te r p r e ta tio n of r e s u l t s .
From t h e e v i d e n c e
f u r n i s h e d by t h i s s t u d y , t h e n , t h e f o l l o w i n g r e s u l t s
w ere i n d i c a t e d :
1.
The t h r e e p r o g n o s t i c m e a s u r e s , t h e a c h i e v e ­
m ent t e s t i n e l e m e n t a r y a l g e b r a ,
th e p r e v io u s grade
i n m a t h e m a t i c s , t h e p s y c h o l o g i c a l e x a m i n a t i o n , w ere
h e re a rra n g e d i n th e o rd e r of t h e i r v a lu e i n p r e d i c t ­
in g su c c e ss in In te rm e d ia te a lg e b r a .
2.
The a c h i e v e m e n t t e s t i n e l e m e n t a r y a l g e b r a
fu rn ish e d a s ig n if ic a n tly b e tte r b a s is f o r p re d ic tin g
s u c c e s s i n i n te r m e d i a t e a l g e b r a , th a n any o t h e r s i n g l e
m easure.
3.
A com bined i n d e x o f t h e a c h i e v e m e n t t e s t i n
e le m e n ta ry a l g e b r a ,
th e a v e ra g e s o f p re v io u s g ra d e s i n
m a th e m a tic s , and th e p s y c h o lo g ic a l e x a m in a tio n , y i e l d ­
ed th e h i g h e s t c o r r e l a t i o n w ith s u c c e s s i n in te r m e ­
d i a t e a l g e b r a , and f u r n i s h e d th e b e s t b a s i s f o r
p ro g n o sis.
IV .
CONCLUSION
C o n cern in g th e r e s u l t s i n d i c a t e d .
R e su lts in
88
TABLE XXIV
THE RELATIVE SIGNIFICANCE OF FOUR
PROGNOSTIC MEASURES INDICATED
IN TERMS OF THE GRADE POINT
N ever l i k e l y to
C h a n c e s i n 100 t h a t a c t u a l g r a d e w i l l
d e v i a t e by more
n o t d e v i a t e fro m p r e d i c t e d g r a d e by more
t h a n number o f
t h a n one g r a d e p o i n t a n d by more t h a n
o n e - h a l f o f one parade p o i n t
grad e p o in ts
in d ic a te d
1 /2
1
G ross
p sy c h o lo g ic a l sco re
G
81
48
2 .3 3 £ rd . p t s .
P re v io u s g rad es
i n m a t h e m a ti c s
PM
82
49
2 . 3 0 & rd. o t s .
A c h ie v e m e n t t e s t i n
e le m e n ta ry a lg e b r a
92
T1
1.65: & rd. p t s .
63
Combined i n d e x
G. PM. a n d T1
1 .4 1 pcrd. p t s .
97
71
NOTE: T h ia t a b l e s h o u l d r e a d (e x a m p le row o n e ) ,
t h e c h a n c e s a r e 48 i n 100 t h a t t h e a c t u a l g r a d e i n i n t e r ­
m e d i a t e a l g e b r a w i l l n o t d e v i a t e fro m t h e one p r e d i c t e d
by a g r o s s s c o r e on t h e p s y c h o l o g i c a l e x a m i n a t i o n by
more t h a n 1 / 2 a g r a d e p o i n t . The c h a n c e s a r e 81 i n
100 t h a t i t w i l l n o t d e v i a t e by more t h a n 1 g r a d e p o i n t .
I t i s a l m o s t c e r t a i n t h a t i t w i l l n o t d i f f e r b y more
t h a n 2 .3 3 g r a d e p o i n t s .
89
th is
s t u d y w e re r e p o r t e d i n r a t h e r p r e c i s e t e r m s .
They w e r e , s t a t i s t i c a l l y , a s a c c u r a t e a s t h e m e th o d s
e m p lo y ed c o u l d make th e m .
T h ese r e s u l t s , h o w e v e r,
w ere b a s e d on e v i d e n c e f u r n i s h e d by o n l y 64 s t u d e n t s .
M o r e o v e r, t h e c r i t e r i o n o r s t a n d a r d o f s u c c e s s i n
i n t e r m e d i a t e a l g e b r a was o n l y a s s i g n i f i c a n t a s th e
i n v e s t i g a t o r ’ s ju d g m e n t c o u l d make i t .
T h erefo re,
i n d r a w in g c o n c l u s i o n s o n l y th e g e n e r a l t r e n d o f
r e s u l t s has been c o n sid e re d .
G o n c lu sio n s.
As a r e s u l t o f t h i s s t u d y , t h e
f o l l o w i n g g e n e r a l c o n c l u s i o n s w ere d raw n:
1.
Knowledge c o n c e r n i n g a s t u d e n t ’ s g r a s p
o f th e p r i n c i p l e s o f e le m e n ta ry a lg e b r a p ro b a b ly
fu rn is h e s a b e t t e r b a s is f o r p re d ic tin g h is success
o r f a i l u r e i n i n t e r m e d i a t e a l g e b r a t h a n d o e s know­
l e d g e c o n c e r n i n g e i t h e r h i s p r e v i o u s g r a d e s i n m a th e ­
m a t i c s o r h i s g e n e r a l a c a d e m ic i n t e l l i g e n c e .
2.
From t h e s t a n d p o i n t o f t h e s t u d e n t ,
th is
w ou ld i n d i c a t e t h a t a so u n d know ledge o f e l e m e n t a r y
a lg e b r a i s th e b e s t p o s s ib l e p r e p a r a t i o n s f o r th e
stu d y of in te r m e d ia te a lg e b r a .
3.
The more e v i d e n c e w hich i s a v a i l a b l e
90
c o n c e r n i n g a s t u d e n t 1a a b i l i t i e s , m a t h e m a t i c a l a p t i ­
t u d e s , a c a d e m ic b a c k g r o u n d and i n t e l l i g e n c e ,
th e
b e t t e r i s t h e p r e d i c t i o n w h ic h may be made o f h i s
p ro b ab le su c ce ss o r f a i l u r e in in te rm e d ia te a lg e b ra .
B I B L I O G R A P H Y
BIBLIOGRAPHY
E l d e r , H a r ry E . , " P e r c e n t i l e Rank i n I n t e l l i g e n c e a s
a P r o g n o s i s o f S u c c e s s i n A l g e b r a , " S c h o o l R e v ie w ,
34-5 5 4 3 - 5 4 6 , S e p t e m b e r , 1 9 26.
F e i n g o l d , G i s t a v e A . , " C o r r e l a t i o n B etw een I n t e l l i ­
g e n c e a n d S c h o l a r s h i p , " S c h o o l R e v ie w , 3 2 : 4 5 5 - 4 6 9 ,
Ju n e , 1924.
G a r r e t t , H enry E . , S t a t i s t i c s i n P s y c h o l o g y and
E d u c a t i o n . New Y o rk : Longm ans, G re e n a n d
Company, 1 9 2 6 .
G ra y , C l a r e n c e T . , S t a t i s t i c s A p p l i e d t o E d u c a t i o n a n d
P s y c h o l o g y . New Y o rk :
The R o n a ld P r e s s , 1939*
K e l l y , Truman L . , S t a t i s t i c a l M e th o d ♦
M a c M illa n Company, 1 9 2 3 .
New Y ork:
The
L e e , M urray L e e , A G uide t o M e a su re m e n t i n S e c o n d a r y
S c h o o l s . New Y o rk : D. A p p l e t o n - C e n t u r y Company,
1936.
M a r s h a l l , M. V . , "Some F a c t o r s W hich I n f l u e n c e S u c c e s s
i n C o l l e g e A l g e b r a , " The M a th e m a tic s T e a c h e r ,
3 2 :1 7 2 -1 7 4 , A p r i l , 1939.
P a r k e r , P a u l i n e , "A S tu d y o f A l g e b r a P r o g n o s i s . "
U n p u b lish e d M a s te r ’ s t h e s i s , th e U n i v e r s i ty of
S o u t h e r n C a l i f o r n i a , Los A n g e l e s , 1 9 3 4 .
P e r r y , R o b e rt D ., P r e d i c t i o n E q u a tio n s f o r S u ccess i n
C o lle g e M a th e m a tic s . N a s h v i l le :
Collom and
G h e r t n e r Company, 19 34.
R i e t z , H. L . , Handbook o f M a t h e m a t i c a l S t a t i s t i e s .
New Y o rk : H o u g h to n , M i f f l i n Company, 1 9 24.
R o s s , C. E . , "The R e l a t i o n B etw een G rade S c h o o l R e co rd
a n d H igh S c h o o l A c h ie v e m e n t," T e a c h e r s C o l l e g e
C o n t r i b u t i o n t o E d u c a t i o n . No-. 1 6 6 , 1 9 2 5 .
93
V otaw , D a v id F . , S t a t i s t i c s A p p l i e d t o E d u c a t i o n .
New Y o rk : The R o n a ld P r e s s , 1939*
Z i e g e n f u s s , G eorg e Raymond, MAn E d u c a t i o n o f M eth ods
o f P r e d i c t i n g S c h o o l S u c c e s s i n M a t h e m a t i c s . M'
U n p u b l i s h e d M a s t e r *s t h e s i s , t h e U n i v e r s i t y o f
S o u t h e r n C a l i f o r n i a , Los A n g e l e s , 1929*
A P P E N D I X '
APPENDIX
A.
A DESCRIPTION OF TESTS
t
1 . The a c h i e v e m e n t t e s t i n e l e m e n t a r y a l g e b r a
T1 A m e ric a n C o u n c i l on E d u c a t i o n , C o o p e r a t i v e
A l g e b r a T e s t , E le m e n t a r y A l g e b r a T hro u g h Quad­
r a t i c s , R e v i s e d S e r i e s Form P . by J o h n A. Long
a n d T. P . S i c e l o f f • C o p y r i g h t 1939 hy C o o p e ra ­
t i v e T e s t S e r v i c e , 15 A m sterdam A v e n u e , New
Y o rk C i t y ,
2 . The a c h i e v e m e n t t e s t i n i n t e r m e d i a t e
a l g e b r a T , A m e ric a n C o u n c i l on E d u c a t i o n .
Co­
o p e r a t i v e A l g e b r a T e s t , E le m e n t a r y A l g e b r a
t h r o u g h Q u a d r a t i c s . R e v i s e d S e r i e s ; Form P ,
by J o h n A . L o n g , a n d T . P . S i c e l o f f , C o p y r i g h t
1939 b y C o o p e r a t i v e T e s t S e r v i c e , 15 A m sterdam
A v e n u e , New Y ork C i t y .
3* The p s y c h o l o g i c a l e x a m i n a t i o n T^ A m e ric a n
C o u n c il E d u c a tio n , P s y c h o lo g ic a l f o r C o lle g e
F re s h m e n , 1938 E d i t i o n . P r e p a r e d by T. L .
T h u r s t o n e a n d Thelm a Gwinn T h u r s t o n e . P u b l i s h e d
a n d C o p y r i g h t e d by t h e A m e ric a n C o u n c i l on
E d u c a t i o n , 74 4 J a c k s o n P l a c e , W a s h in g to n , D.C.
B.
DEFINITION OF SYMBOLS
T..: S c o r e s r e c e i v e d on a n a c h i e v e m e n t t e s t i n
e l e m e n t a r y a l g e b r a when g i v e n a t t h e f i r s t o f t h e
se m e ste r.
Tg: S c o r e s r e c e i v e d on t h e e l e m e n t a r y a c h i e v e ­
m ent t e s t , i n e l e m e n t a r y a l g e b r a , a b o v e , when
g iv e n a t th e end o f th e s e m e s te r.
^2" ^ ls
s c o r e d i f f e r e n c e s b e tw e e n T2 and T«j_
T^: S c o r e s r e c e i v e d on a c h i e v e m e n t t e s t i n
in te rm e d ia te a lg e b ra .
T 4.: A v e r a g e s o f s c o r e s r e c e i v e d on f i v e c l a s s ­
room t e s t s .
96
H:
A v e r a g e s o f s c o r e s r e c e i v e d on homework*
Q: S c o r e s r e c e i v e d on t h e q u a n t i t a t i v e p a r t
o f a p s y c h o l o g i c a l e x a m in a tio n *
L: S c o r e s r e c e i v e d o n t h e l i n q u i s t i c p a r t o f
a p s y c h o l o g i c a l e x a m in a t io n *
Q-s The g r o s s s c o r e s r e c e i v e d on a p s y c h o l o ­
g i c a l e x a m in a tio n .
P: A verages o f each s tu d e n t* s p r e v io u s g ra d e s
i n a l l s u b j e c t s o th e r th a n m a th e m a tic s.
P .M .: A v e r a g e s o f e a c h s t u d e n t ' s p r e v i o u s
g r a d e s i n m a th e m a tic s *
A:
The s t u d e n t s a g e s .
K:
The s u c c e s s s c o r e s o r c r i t e r i o n o f s u c c e s s .
APPENDIX D DATA SHEET
w
1
1
6
6
3
1
13
79
52
39
92
914
79
A
2
13
80
47
38
94
885
77
B
3
11
92
49
34
88
865
76
B
4
4
96
48
35
86
856
75
B
5
9
60
47
39
87
846
74
B
6
6
75
44
35
91
828
73
B
7
13
80
48
37
72
795
71
B
8
12
75
48
37
67
798
71
B
9
8
89
44
28
79
766
69
B
10
5
75
46
• 22
77
719
65
B
11
12
80
41
29
58
686
63
C
12
5
60
40
27
68
671
62
C
39
53
106
159
3 .6 8
4 .0 0
1 9 /6
34
44
84
128
2 .7 1
2 .3 3
1 8 /i
38
45
92
137
3 .3 8
3 .2 5
1 7 /1 1
44
39
78
117
3 .3 1
3 .2 5
19 /6
38
31
56
87
1 .8 8
1 .8 3
1 9 /5
43
53
76
129
2 .6 3
2 .7 5
1 8 /1
36
37
74
111
3 .1 3
3 .0 0
1 7 /8
35
40
61
101
2 .5 0
2 .0 0
1 8 /6
36
39
103
142
3 .5 0
3 .5 0
19/11
41
34
58
92
2 .2 5
2 .7 1
1 8 /1 0
29
21
47
68
2 .0 0
3 .0 0
1 7 /7
35
34
75
109
2 .1 3
1 .7 5
19/11
13 '
15
55
38
32
63
669
62
C
23
29
81
110
1 .9 3
1 .0 0
2 0 /0
14
. 5
50
40
24
68
643
60
C
16
11
67
38
19
67
621
58
C
35
37
70
107
2 .0 0
2 .0 0
1 7 /7
27
32
70
102
2*40
2 .0 0
1 8 /3
vo
A p p e n d ix D — C o nt*d
Student
V T1
H
T2
T3
T4
T o ta l
K
Grade
T1
Q
L
G
P
PM
Average
17
10
90
32
22
64
616
58
C
18
12
70
31
21
67
595
57
C
19
1
70
34
15
76
593
57
C
20
1
55
38
23
52
578
55
C
21
8
65
39
22
46
577
55
C
22
0
70
37
20
51
565
55
C
23
5
30
35
19
65
554
54
C
24
6
70
28
20
63
553
54
C
25
16
80
33
14
55
543
53
C
26
6
70
36
13
55
535
52
C
27
17
70
36
23
30
531
52
C
28
7
40
32
20
52
515
51
C
29
4
75
35
8
58
511
51
C
30
5
79
30
19
44
510
51
C
22
25
72
97
3*24
3 .2 5
1 9 /0
19
24
48
72
2 .2 5
2 .2 5
1 9 /1 1
33
32
74
106
3 .1 0
2 .0 0
2 1 /3
37
34
61
95
2 .5 0
2 .2 8
1 8 /8
31
35
66
102
3 .4 0
3 .4 0
1 8 /8
37
49
91
140
2 .0 0
1 .8 0
1 9 /0
30
10
39
49
2 .5 6
1 .8 3
19 /1 1
22
27
45
72
2 .6 7
1 .7 5
1 9 /4
17
33
77
110
3 .2 3
3 .0 0
1 9 /0
30
25
49
74
2 .0 0
1 .3 7
1 8 /4
13
27
46
63
2 .4 4
1 .5 0
1 8 /1
25
31
34
65
2 .0 0
1 .8 3
1 7 /3
31
32
74
106
2 .0 0
1 .8 0
1 9 /5
25
27
76
103
2 .5 0
2 .0 0
19/6
32
9
75
26
15
56
498
50
C
33
7
79
27
16
50
494
50
C
16
17
23
26
54
67
90
80
2 .4 3 2 .0 0
1 .7 5 1 .8 0
2 1 /0 17/1 1
21
38
64
102
2 .7 7
2 .0 0
2 1 /3
31
3
75
19
12
79
501
50
C
co
A p p e n d ix D — C o n t*d .
Stu dent
V
H
Ti
T2
T3
T4
T o ta l
K
Grade
*1
Q
L
G
P
PM
A
34
10
45
31
14
55
490
49
C
35
6
20
40
16
37
473
48
C
36
9
79
32
15
34
472
48
C
37
11
44
34
16
31
448
46
C
38
9
75
30
10
40
444
46
C
39
7
63
28
14
39
439
46
C
40
12
40
27
16
41
433
45
C
41
14
50
32
14
31
433
45
C
42
3
45
33
18
26
432
45
C
21
23
43
66
2 .7 9
2 .5 7
1 8 /1
32
28
42
70
2 .0 0
2 .0 0
1 8 /4
23
29
86
115
2 .5 1
2 .0 0
1 7 /1 0
24
35
72
107
2 .3 4
1 .8 0
1 8 /2
21
26
54
80
2 .7 3
2 .2 5
1 9 /2
21
31
50
81
2 .0 9
1 .5 7
1 7 /6
15
17
40
57
2 .0 0
2 .0 0
1 8 /9
18
23
61
84
2 .6 1
2 .2 5
1 9 /0
30
33
66
99
2 .6 8
2 .0 0
1 8 /4
43
7
40
29
18
26
407
43
C
44
2
50
22
17
32
382
42
C
45
7
50
26
13
28
375
41
C
46
4
49
21
8
46
365
41
C
47
3
59
19
12
35
353
40
C
48
1
15
26
17
20
334
38
C
49
6
20
21
8
37
311
37
C
50
2
50
23
6
28
310
37
C
51
-1
50
22
13
17
310
37
C
23
20
30
29
66
45
95
75
2 .0 0 2 .0 0
2 .0 0 2 .0 0
1 8 /4 1 7 /1 0
19
28
72
100
2 .7 3
2 .5 0
1 8 /8
17
39
74
113
2 .0 0
2 .0 0
2 0 /7
16
36
60
96
1 .8 3
1 .2 0
2 0 /5
25
30
41
71
2 .2 2
1 .6 7
1 8 /1
15
33
47
80
2 .7 5
1 .7 5
1 7 /1 1
21
31
52
83
2 .3 1
1 .6 6
1 7 /4
23
32
54
82
1 .9 2
1 .6 0
1 8 /8
vo
vo
A p p e n d ix D — C o n tf d .
S tudent
V T1
H
Q
L
G
P
PM
A
12
28
6 8
96
1 .7 9
1 .5 0
24
13
13
58
71
2 .1 5
1 .0 0
18
54
0
25
23
9
24
289
35
D
23
43
45
■ 88
2 .4 1
2 .7 8
1 9 /1 1
55
9
56
1 0
25
50
19
1 1
1 0
1 0
17
286
35
D
16
31
72
103
2 .8 4
2 .4 0
1 8 /4
14
276
34
D
9
7
30
37
2 .0 6
1 .0 0
1 9 /2
57
4
80
58
3
59
2 0
1 0
12
2 1
23
2
1 0
32
264
33
D
8
33
52
85
2 .7 5
2 .5 0
1 9 /1
18
263
33
D
18
19
43
62
1 .9 4
1 .2 0
1 8 /9
2
2
27
243
32
D
21
36
45
81
1 .7 7
1 .7 5
18
60
7
0
24
1 1
8
241
32
D
61
6
54
19
3
15
237
32
D
1 .6 8
13
25
64
89
3 .4 1
1 .0 0
2 .0 0
1 9 /8
1 8 /7
17
18
37
55
62
4
60
19
3
7
217
30
D
15
24
62
86
63
13
30
15
2
7
166
27
D
2
18
31
49
1 .7 9
2 .0 6
.6 6
1 .4 0
2 0 /1 0 1 9 /9
64
5
5
9
3
2
M s 7 .1 1
M s 60
M - 3 1 .3 4
1 7 .5 0
M s 4 7 .4 2
S
S
S
S
S
Ms
Ms
M»
Ms
Ma
M=
S
S
s
s
s
s
11
T 1
53
5
60
18
10
19
290
35
D
tessj
*8
T3
T
4
T o ta l
K
Grade
52
7
60
19
9
20
295
36
C
- 4 .1 9
3 23
3 1 0 .0 0
3 9 .7 9
3 2 4 .2 1
88
2 1
F
6
23
48
71
.9 3
.2 5
2 4 .0 3
3 0 .7 4
6 1 .4 4
9 2 .1 8
2 .4 4
2 .1 3
3 9 .5 4
9 .0 4
a 1 6 .9 8
s 2 3 .4 4
3
.52
= 72
3
8 /1 1
H
O
O
APPENDIX C — COEFFICIENTS OF CORRELATION BETWEEN ALL
OF THE MEASURES EMPLOYED IN THE STUDY
o?
W
Eh
to
Eh
.48
•61
•34
• 76
.77
-.0 9
•57
.46
.55
♦45
.81
.85
.28
.22
.05
.12
.08
.33
♦20
.37
.50
.36
.52
.48
.48
.45
•78
•05
• 86
.49
.54
.50
.46
•64
•64
-.0 4
• 54
• 56
•32
• 37
.15
Q
.55
-.1 2
•63
•36
• 83
•61
L
•56
• 18
•49
.51
.95
G
.61
•04
•47
•48
P
.44
-.0 6
.80
PM
•63
—.14
A
-•03
s
P-i
T1
• 84
-.1 9
• 56
•38
.58
T2
•92
-.2 5
.60
•44
2"T1
•34
-.1 4
.21
T3
•93
-.1 7
T4
• 92
—
H
-.0 3
.63
.90
.90
-.0 9
.37
.85
.77
.78
♦20
.81
.76
.64
.45
.33
.45
.34
.38
.46
.48
.08
.55
.61
•61
.32
.50
.48
.12
.46
.48
•95
•83
•39
• 54
.52
.05
.57
.58
.48
.51
.36
.33
.49
.36
.22
•44
.38
• 80
•47
•49
.63
• 50
.86,
.50
.21
.60
.56
.04
.18
-.1 2
-.3 8
-.0 5
-.1 4
-.2 5
-.1 9
.44
•61
.56
.55
.64
.92
.93
.34
.92
.84
i—1
.
1
K
-•14
rH
EH
.28
•I
•
CM
Eh
ocr>
<
D-
M
■
I 01
i— i
Eh
1
CM
Eh
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