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. \ DOCUMEN;RESUME

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Roberts; rank C.A Cost-Bfpe.tive Analysis and Follow Up Study an .aMulti-LeveLM'athematics Instruction .System atAntelope valley College.Antelope Valley Coll.,.Lancaster,'Calif.Jun 7554p. Some page 'in' appendices may reprodude poorlydue to small type' size

EF-$0.83 HC-$3.50 PlusPostage.College Mathematics; Community CollegeivComparativeAnalysis; Ctnventional Instruction; *CostEffectiveness Course .Evaluation; *IndividualizedInstruction; *Junior Colleges; *MathematicsInstruction; Student Hotivation; Student OpinionAntelope Valley College; *Personalized System ofT.nstructioni PSI

Between the spging of 1970 and the summer 9f 1974,1,747 students enrolled.in Math X, a multilevel PSI (PersonalizedSystei of Instruction) type of open-ende$ mathematics instruction,system at Antelope Valley College. Results of a study designedtoevaluate the course by comparing it with the more conventionalmathematici lecture course indicated that: (1) students .0103 hadenrolled in Math X completed fewer unit (2) fewer students feceivedsuccess grades in Math X than in convent nal lecture classes; (3)

Bath 7 students had a higher grade point average; (4) students whoearned-low or nonsuccess grades bin Math X went cn to do better inconvention I classes, whereas students'who earned high grades in Math

1X tended n t to do as well in conventional math classes; .(5) Math'Xinstructi_n cost approximately three percent legs than conventionalinstruct4ion; (6) only 38% of lecture-only students continued to studymath, while over 52% of those ,exposed to bath X did so. Results of aquestiofinaire sent to 300 Math X students (30% response) indicatedthat students believed Math X to be about as difficult as other lathcourses, that most respondents would 'repeat Math X for more advanced'study if such were offered, and that most would :be interested -inclasses in other subjects taught using the same fors t. (DC)

01

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I1O ART/AE/1,0F HEALTH

EOUCATION A WELFARENATIONAL INSTITUTE OF

EOUCATION

TH.s.DoCumENT HAS SEEN REPRO-DvCED ExAcTLY AS RECEIVED FROMTHE PERSON OR ORGANIZAT,ON OR 4(4.AT INC, T POINTS OF VIEW OR OPINIONSSTATED 00 NOT NECESSARILY REPRE-SENT OFFICIAL NATIONAL INSTITUTE OFEDUCATION POSITION OR POLICY

A COST-EFFECTIVE ANALYIS AND FOLLOW UPSTUDY 'ON A MULTI- LEVEL. MATHEMATICS INSTRUCTION

SYSTEM AT ANTELOPE'V=EY COLLEGE

#

Pao

..<7**

,1 - e

I

Prepared by

.erank.C. RobertsDistitutional Researah'

i"4-

4

'June 1975

2 Q.

a4

4

//-

0

411

ABSTRACT

A ,COST-FLFFECTIVE ANALYSIS AND FOLLOW 'UP

STUDY ON A MULTI-LEVEL MATHEMATICS INSTRUCTION 4

' SYSTEM AT ANTELOPE VALLEY COLLEGE

A cost-effective analysis and follow up study was con-..

.

ducted on a mar sample of students after exposure tb

a multi-level PSI system of math instruction. The study

includes comparison of, cognitiVe accomplishment and cost

of instruction under the innovative system to similar

parameters as evidenced in a random sample control group

which received conventional lecture -tye instruction in

mithematics.

gig

o

Title Page

Abstract

Table of Contents.

TABLE OF CONTENTS.

Definition of Symbols and Acronyms

-1

Objectives of the Stud?

Research Hypothesis

xamination of` Hypotheses I

v.

Summary oX Conclusions

Bibliography

Deekriptive-Statistids Sectton-

%

a

19

22

2 If

25.

26 .-

28,

29

I1. Math 'It Statistics

2. Math I X Erirollment

3. Conr droup Statistics

11. 'Math X Sample Statistids.

.-

Appendix Section

Appendix A' ,

.

'

Those Students Who Took Math .. -$.

After Math X 1

r .

Appendix '$ .-1 : 39Those Studnts Who Di,d NotTake math After Math"X .

e .

,

.appendix CStudersuminary. of Stude Response's

From Sap.ig.factionLAdestionnsii-e

. .

414

"s '

I 1 1.

iii

44

.

\z/

(

TABLE OF CONTiN S (CbNTINyTED)

Appendix DCalculation of a.Point-BiseriaiCorrelation: Degree of;plgevsin Math X vs.-The Same etter

! (f ), or Less Success Xfn),

App4ndix ECalculations of..Oosts perADA-Hour.

Appendix/4F-Computer Print-out of CoatrolGroup (Coded N) t.fid MathPopulation (Coded P)

1

.s

4 A

Availablq only to 'authorized persons

I

5

PAGE

146

147.-

'*

. _-__t1

I

-'PSI

DEFINITIONS OF SYMBOLS AND ACRONYMS.

Personalized System of instruction

,6PSI/AT Personalized SYstemAot.Instruciion

Atidio-Tutbrial Made

CIS Coordinateh Instructional System

:

I

6

J

I

A COST-EFFECTIVE ANALYSIS AND FOLLOW UP 4STUDY ON A"MULTI-LEVEL MATHEMATICS INSTRUCTION

SYSTEM AT ANTELOPE VALLEY COLLEGE

A Multi-level PSI type of open4nded- mathematics instruc-

:ticin system was introduced at Antelope VaI19yCollege. j

during the Fall of 9/0. The clasp was named Math X.

1

1

Between the Fall .of 1970 and the SUimer of 1974, 2t1 sec-,

yeons involving as few 'as,32 and as many as 146 students

:had been completed. More recently, over 200 students

ere,enr011edin a single extended-day section.

Unt.l 1974, statistic's' on these sections were included in

the standard gqade'and attrition study with little con-

cern. ome'refleotion on the nature of Math, X caused

concern that. the inclusion of.gnadg and 'attrition figures

from PSI systeks with statistics from conventional-lec-.,.

I

1

.

ture type classes was a Miiing of apples and,. .- .

i i

1

The following-unusual f;.atureS pf the Math X system make .

.

,. ;

,Icdmparisons.with.conventional systems of instruction

. .

I.' Studentsareallowedlo enroll without screening'. ,

difficult:

or consideration ofdarereqUisites. .,

- ,, . . ,' , .

2. -Blacement in. any ],bevel within* Math "Jcis dedided 7',

. .

after inventory 'jesting andlOOn the advice of". . . .

a teacher or, proctor... .. ,

3. After a tuden't is tounseled intb the appropriate

. - --........- 7-- 1......a.:-..-.....-7 4-- ..... - -.-." .. -.....

r 4 oit °. . , s

1 .73

: ..-t

.

re

:level, the instru for or proctoe..advises hi

garding-the obje tives of that level for success.

The student may of have to study all elements if

he exhibits mas ery. of certain elements.

Math X student? are allowed to progress at their

own rate through a sequence of P I materials

(usually a prOgrammed text or a dio-tutorial

Materials) and may complete a evel,atany time,

durinta semester-or may require over one semes-

ter to be successful. Iostructor, pacing is prac-v

ticed in an attempt 'to estab/iA'sound\tudy

habits and to insure as many' successes each se-

mester aspossible.

5. 'No penalty' grades are 'ever awarded, and students,

. sh%

,\,

,'

may enter or drop the clas's or level at ark, time.

They may also transfer. into a lecture section

(if qualified) at ani time.

'6. All tests are repeatable', ie., a student may re-.

study. af.4er a test and retake an alternate form

4:

4

2 of the test as niany'.t'imes as he wishes in an at-

tempt. to obtain 'the grade he desire;.

T. Up. to 19 'Units can be earned in remedial math

topics (levels froth arithmetic phroggh triOno-.

metry) and College Algebra during one semeser.

(Thls has top happened yet -- the maximum number

'completed is 12.)

1

2

r. .

ConSideration of t1T unusuallfeatures fisted above pro7

videp convincing.evidence that the Math X learning scheme

cannot be compared with standard methods of instruction

using conventional gradp and attrition percentage-dethods.

This study was designed to fill the need for accountabil-

ity in the Math X progifam. An 'attempt kill be made to

develop a- cost - effective analysis model l'or comparing

lecture type instruction with Math X. (P/SI) methods. 4

!

A second element of this study will tof the assessment of .

the compaative satisfaction of stud46ts who have been;

t

exposed.to Math X study (follow pp):

The stated objectives of the study are:

To compare student success figures from claSses

taught 'using leithX procedures with iiiUr s from

11-conventional math Masses.

2. To assess and comp e the relative abilities of,

-students fr.= Math classes with students from 1

conventional math ciases,by correlating grades

in classes taken after taking Math X k4.11

,

.

grades made in Math X.

To determine the#0

cost of Math X instruction asu .. .

.

compared. with conventional math instruction on4

a.perstudentlpasis..

4. To set up an accountability model enabling,com-

parisons'betWeen conventionally taught leCture

9

type math classes with the Math X instructional

system (a cost2-effectiveness,model):

5. To assess student satisfaction with the Math

14

Abrogram after the: student has had a chance to be

away from the program.

In generals. the study will provide fee back for '1.&e in

refining and perfecting what seems to e one o± the latest

methods ,oX mathematics instrucioh4strategies.

PSI Instruction Institutional Researth fr m the

,Literature)

Over 46, studies are ,recorded by

. zona '.tate University his

titled "Se .f- Pacing and Instruct

1

While re,thrust of his study

Dr. Robert A'. Reiser of

it ratUre-search study

r /Pacing in PSI--CourseS.,"

c

1 ;tt wardPacing procedures,

opti ion of sucoess is his ma or concern :(as it is the

f this study) : All autlybrs mentioned in Dr.

udy agree that pacing isfnecess belieite in 1

cone

/ser

usi osi:tivemoivatiOnal methodS rather than punitive

-ttac which ma4 include the heat of non-success,

gr e . Most PSI methods con5iidered involve student prof-

onetops der professional. sihe ratio of instructor-,

.

- t

proct r to students is general y absn;tj:20. While'coit-.

'effe"c iveness is mentioned, a model is not iiropoied in

Dr. c eise'r's study. /

'A study done -by Mary A. Golladay and three associates

10

a

t.

. . ,

.

,I

under'the'auspices of the U.S. Offi e ofEducation, pub-.

lishedin May Of 19752, indicates t at .models of tradi-

tionally_structure0 educational experiences arelthapprop-

riate fortuse in assessing individualized instructional-

programs. .!;leir study? titled "Prdblems in Empirical

Research on Individualized Mathebatics Programs;0 includes

a system of "desCriptore and a complex flow- diagram for)

analysis purposes but sheds no light on building a ,cost- !

-

'%

.effnti Model for our study., t -

, i

k i

. 1

7 A studylpublished by Merrill Publishers regarding the use/ .

.

..

.

..1

of th Merrill system of A.T. instruction at-Fullek.ton,

e,

Commun ty College (Project 70)3.siescribes cost ,savings in

'1

_ PSI math .instruction Fullerton. The study reports data!8 :

froM tilhe 197.4.-1972 peripd'and claims a saving of $10,800

1

per yearion a Program involving throe sections of 35 stu

e4ents,each in a "Fundamentals of Algebra" class; (single'it

1 e ' . Modified self pacing is reported and a fair de7,

1

I ..

gre iof success is claimed in. the Merrill analysis.4

ii,;

. ., . iii.

Ai/ hree-part study titled ."Relative Direct Institutional ':

. . ,.

!,i .

sts of Biology Two and'English A Laboratory at Golden I.:

, , ..

:

, ,

i 1

st Oollege" by Dr. Richard W. Brightman; attempts, as

. 1

omparisovof.Costs of instruction par hour in PSI/AT.

,glasses versus conventional instruction: The Golden:

".

College' PSI sympems (many are CIS) are. reportedly very

cost-effective., 'Tile model develop d in the analysis Wa

011 V

r

modifiel3 slightly and used in a report written at Antelope.

,

Vali* ollge ,tit led "Comfaring Instructional Costs of

Selecte Programs at a Junior College."' Fortiohs or the. %

research Models from thesepapers will be combined with a. .

e% .

I

student, success factor called Units Completed' Per Student !

(UCS) to provide a cost-,effective model of analysil for:

'Aviath X.

esearch H othesis

1 y

It is hypothesized -that a cost .redaction, per stu-

4

dent of apprOximately 20% can be realized' using.

. Math X methods of PSI with a staff g formula in-.

voivini Instructors and student a es (iroctors).

The relative'cC:st pei.' ADA will b bated on "the

turrent costs of education " cicula.ted on a 1

. !

median conventional math cl . (A, median con- ' 0

., . .

.,

ventional math class.is defined a* a lecture 5r1),

,

math class staffed by an instructor receiving a'

salary at the median in the salary range.)I

-2. A cursory eirination of data from Math X imp-1

,grams lndkcates a higher proportion of unsuccess-1

. , ful student's than in'conventional math ciaases.. I r

It is' hypothesized that -a cost-effective analysis

will disclose that success versus nonsuccess may

not be a useful c'iterion on vihic4to base the

desirability or rating of the Math X instruction-

al- scheme..aw

12 /

..-.-,,

4

a

4:I

3. .PSI instructional schemes'are tailored to meet,,

the needs of the individual student. Some edu-A

.cators' question the Validity of any scheme thato

does not place hurdles in the ath of success for. ,

L. the purpose of screening the pop lation in order

to.Alter out those letrners who are not abIb to

'adapt.to classicd1 college procedures: It is

hipothesized that the "quantity" Is approximately

Ate same as woild'be learned in lecture and that4

Math X students, succeed as well in the next math

class despite the spe ial handling present in

.Math'.

1.4

* .,

/ Methodology of the Study1

4 4(

Statilt.I6a1 semplip4 procedUres will Ile used in this stt1-

dy.. Two-mainsamples will be used. The first sample w 11

,be, made up pf approximately' 300. students randomly select d

from the Matll X pdpulation. The second group will be se

lected from s udents involved in all types of math study

an'd will be u ed:as a control, group typical of the, gener

f

math student. A subset, o

1

the last group made up of tho e

students who did not encoanter Math X in. any 0 t1Teir.stu7

.dies will 6e examined statistically.moor

Finally, iqmestionnaire will be mailed to the Math X

students asking for their opinion of tale prgram.

0.

, 1 34

V;

4

TIte Research Model.

. -.

.

.-

1. Units completed per student will be compazzec)A /

sdusing the coxtrol group versus the'Math X sample.

42. Cost.of.instrUdtion of a math student in a lec-.

- tore setting niiebe calculated. The cost of 14n-

struction of a Math X student using the factor

."Units Completed Per ttudent'Retion be:com-

pared to the cost of lecture.type instruction on

cost-effeitive basis.

To calplete thp cost-effective accountability

modell,comparison of grades awarded 'in the two'

math tnsti,uational schemes will be made and 4 .

ca cul2tion of the correlation between grade

inadee Math X versus grades made in classes, laf-

ar Math X will be attempted.

The Math X Samole)

' . I

. ; ..

t , A sample of 'approximately 300 s udents front a population

Of 1747 students Who 'had enroll d in Math X between Jlef

spring of 1970 and the summer se sion of-1974 was draWn by

ran.dtim number methods. using anIBM\ystem 3 Model-10.com=

-puter. Alpha numbers. of students in the popUlation were

Placed in the memory of the computer ,and the draw of the ~ 41

sample'.was done by generating six--:digit'rendom numbers.

^, 4

Alpha numbers corresponding to the random numbers from4

the

computer were selected as the Math X sample. .The.sample.

. I. d. i.

14 P

. 4

8

31

A

was then the ked for,va],idity by comparing cerkain charac-,

terieiics of sub-groups in the population with similar

characteriSt cs of the sample (by Percentage). Aftertsome

minor adjustments in the sample, stratification validity

was found to exist and the sample was judged to 'be fiirly :.

i.

representative of the Math X population. f

.1

. . '4The Control Group

i

A.

. i ..

Students in the control group were picked on a stratified.

random sample basis using a random number table to select; . . r.

!section, teacher, and line'number on a roll sheet. Strat-1 \

ification was accomplished by.seleCting the 'number' of stu-i

1 ,' i

Mdents enrollgd from 1970 to' 1974 (the.sae,.period used .

.

With the Math X group), in eachileVeq ofmath,'ie., Math -\, 1

/ r

.1 1

50, Math A, Math B, etc., as t4e proportion these,groups '.

1.

represented to the-total number; of students in the math

9

.dtvision in the semesters ok concern.

The sub-group of students mit'involved in Math X was sep-

arated using the computer t6 match alpha numbers of the

control group with the mat X population.

\

One hundred\porty were selected frbm the roll sheets of

instructors by the random methods mentioned above. The

grades of each of these sample members Igre recorded on

data record cards' and a transcript search provided histor=-

ical oath relords which were alSo recorded. Confidential-

ity wasjpreserved during these procedures ,by using alpha-

15

1

I

I

numberS instead of student names.

Control Group Characteristics

Fifty-nine students in the original sample of 140 had.been

involved in Math X at one time or another. Thirty-four of,

the original sample were purged because of incomplete

.records or because they were still in attendance (our sam-

ple was supposed to be made :up of students enroIled.be-

tween 1970 and the summer session of 1970. Eighty-oho of

the 106-,member final sample had not been involved in Math

X studies and the remaining 26 had taken Math.): as apart

of their math program. (As an aside, a rough calculation

'indicated that about 42% of the students selected in'theI t

original sample had been exposedAo Math X during their

study of mathematics.) "

Data indidates that studenti In the control grdup received

24 W grades, 4 D grades, and no .1()grades. Combining s .

and D s ;(these are considered non-success grades) an com

parin this total with all success grades earned yie ds a- ;

1.

29.6% non-success rate. This agrees, closely with t

percentage of W's and D's reported in non-Math X cl sses

on the attrition an rade study prepared annually by the!

Officio of In ruction. It was also determined that the

.average nUtber of unitsYearned per student in lecture.

clasee4 is 4.05 (the arithmetic mean) i\gth a standard de-

viation' of 2 units. Ninety-one passing trades in 303

-,, -4

16

- . -

10

-un#s were recorded by 76 of the 81 non-Math X studentS..

Slightly over 12,1 o;. the control sample did not receive a

success grade (C.or better) in any math class.o,This group

be compared to the Math X sample in the research mo-,

which follows.

iesults: The Math X ample Vers the Control Grou

by Objectives

OBJECTIVE 1 -- Comparison of Student Success Between

11

Control Group and Math Group .

On a.per-person basis, fewer units e completed in tilth/iit (

than in ,the -Onitentionalllectu setting. In l &cture

classEs, 4.05 units per student ,were 'completed, while.

only 2.55 4its per s 4nt were comp.),eted'inMatli:X.

Among he special group f 95 Math X stunt who took

/conventi:Pna1 math class s'aftei taking; Math X, 4.7i units

pei "student were accumulated. A "t" te'st.of- significance-

disclosed that 4.75 versus 4.05 was not-significantly

r--different and therefore stud who went on after Math .X

were not significantly different from the population (at

least in terms of units completed). Th't

total Math X

sample of 287 with units per person of 2.55 testecisignif-

icantly different from the populatAin at the .001 alpha

level.

A compariscQ cI GPA earned by the control group to the G ?A

of the Math .X sample shows that a significant difference

17Al

/

1.

--,exists;-this difference tests wellin excess of ths,.0/,. 4

alpha level. The Math\X GPA was round t be 2.92'with. 7

s 7 .832 while the cp ntrol group showed's 2.67 GPA with

an s = .87. Higher grades are beinga*ardeeto successful

students in Math X. It is concluded that fewer units pe;,Y r

Student are being completed .by Math X students, and _that- 4

grades awarded to these students are higher. It,shouldbe

1noted that similar standardized final examinations

given in most- similar Math X and non-Math X classes at

College,-so that CPA figure's do have a women base: l

OBJECTIVE 2 -7 Correlation of Grades Receivedin Math X

*.

With%GradeS Earned by 'the Same Students in -

Conventionally Taught Math ClaSses After

Exposure to Math XI

point bispriai corl'elation was attempted-ciee.AppendA...

03. 4n rpb= -.52 was calculatbd., rr this statistic wed

Used to predict degree of success', only a 34% imprpvement

over chance alone would be realized with such ii-triatle...

GIi "

1

however, while not highlysignificante the result does int ''1,

dicate a tiend.. Apparently, students *ho received low or, ,

non - success grades in Math Xwent on to. do better in con-.

ventipnal (lasses. Conversely, those students who're-.

eleived hi la'ades in Math X had a't ency not to do.as

well in ;co ventional classes. A car rul check of the

i H

membdrs of the 95 in the :sample of those Math X students

who went on to conventional classes reveals that very few,

18 4*N.

--=04. ~417.-4,,,,,,,r).--.ria..

made grade point averages varying more than one point

the class following math X (see Appendt /

/

OBJECTIVE An.Approximate Cost Per Student -Hour

Calculated on Conventional Math Class s,

AndMath X Claises

An approximate cost-per student-hour in r/gular mat in-

13

1 ,

> structidn calculates to be $1.56. Costs computed on a

similr 6asis for lath X are about .$.95. An apparent dif-

1;

../. ference Of about 40% existst liow,ever, it must be under- I

stood Ogtjewer stUdents make success grades in Math X

and, therefore, a factor must be used .to adjust,costs,for0 , A

comparlion Purposes. *.s.

,1..1g. -

..

OBJECTIVE.4 -r An.Accountability MOdelEnabling.domparis8ns/

...1

i

.

,..

.

'Of -the, Effectiveness of Conventional Versus ..

i.. ,

. 4PSI _Math 'X-Type ...in Aathemati-ci':

,

tnstruttion

. ' A UDilts COmpleted per Student Factor (UCSF) was developed

by di\iding mean units compl4ted per Math X stuaent by

mean units completed per cOnkentional sti4dent. UCSF 5,1--

/En order to gor ect the cost per hour` ca culated inJOBfEQ-,.

FIVE 3, one muS divide $..95 by the UCSF which yields . 1

.corrected value of $1.51 per hour for Ma h X instruetion.,' 1.

I

The effective d fferenpe seems to be

of the apparent 40% cost percen

(Math X cost figures were calculated

19

about 3% instea4

ag calculated aboIe.

sing the presJnt

ttaffing formula ,which 'calls for one instructor t,

or the

first 45.'students and two aides for each additional 45. .

students,' except after 135, when usually two instructors

are assigned.)

cA first cods deratic3n might lead-bne to conclude thatthe.

.

Math X sche e of instruction fs nopt as cost-effective As

it shouyi. . However, income from.AbA is not based upon

' units comiiet I-1 only on those students who are in atten-;/

1

dance duying he 'fourth week of instruction. Therefore,

income from theADA foisMulais in excess of what'this

cost-effective model indicates. It-shoud also be noted

that some students are' not "paid.for0. under the ADA.ar-

rangement bejbause.

they enter well afeer the fourth week: -

(Census Week).

Aside from costs per ho of instructIon, other factors

about Math X should be considered. The UCSF does not

take into account the services provided' in 'Math X at.

are not provided in conventional math classes. testing4

and guidance functions are provided 10.thin the clats

/

Jstructure. The "stretched semester - concept and "drop-r

in' capabilities meet the needs of si4cial students, who

ot'rer:,rise might not succeed, or even get an ekpOsure to, .

math instruction. A140; le9ture-onl student's coo not con-

'

time in their math studies to the degree which 'those stu-

derts exposed to%MathiX apParently\do.\ Only abbut 38% of

1.4

lecture-only students go on to study math, while over 52%

,of those exposed to Math X go on to enroll again inmath

.4.classes. .This may indicate the existence of a covert

motivational factor inherent in the Math X system.

ConsideVring the added servicei'provided'students in Math0

15,-.

.X,imaybe the UCSF,methodof comparison is a bit harsh.'

OPEctIVE '5 explores student attitudes toward the system. '-

.I

If Math X pleases the students to the extent that its /'

il

enrollment figures 'indicate, probably it is more cost-, / 1

. / 1

effective than this accountability model,indicates. . I 1

e 4

6/

4 ,

4.

OBJECTIVE 5 %-,,An'Assessment of Student Attitudes Toward '

. i

.

Math X Instructional Methods.. '-i 1 .

About 300 questionnaires were mailefto the studentl of ''

the Math X sample. Forty-nine questionnaires were re-"

; i

, ' %.

,

turned undelivered. (Noting the, tabulated dates in :, ,

Appendix C, students in, the earlier sections did not're-

turn the questionnaire -- probably because they had moved

2.

!

f,

out of the area and were not contacted.) Oirer 30%. of the '.'

,

.,.,

.delivered questionnaires were returned before the cut.-off /.:-.

... ,

1. .'

date of th.e survey (triii is flm approximate percentage , 1/4

estimated in the 'design phaseof this mOdell. .

, . 4

The returned" survey forms'indi,cate that student; feel

Math X studies are about as difficult as,n.c5n.-MathX. .

4 .:

.

Sixty -nine percent,,of the.sample indicate that they wou.

,_repeat Maith X for more advanced,study,.if offeredi and-

I.\*

\

4

( 4,

* J .

-2 18

. 0 v

t

.

I

'1

,

. 14.

that they -would also be interested, in classes other than

math classes taught using the same format (PSI). These

Answers indicate positive feelings toward the learning

method, In.answer to the question, "Do you jeel you wouldi

,-have learned more math in a classical lecture type class?",:.)=. . ..'

.1

-

32 said yes while 35 said no. A Likert scale ranging from

0 (.much less) through 5 (about the same) to 10 (much more)

was provided as a validity measure. The mean response on'

- this scale was 5.35, with a standard deviation of 2.95., 4

The most outstanding feature of Math X was the ability to

move as fast through a course as desirable. ,Open -ended, !

,enrollment ranked second in popularity (by GPA rating

comparison-- see Appendix C).

Students rated the-prOgrammed textbooks lowest among the

features, with the role of the teacher (non-lecturing,.

student-helper'molde)next lowest. Many c maients were in-.

eluded regarding the feat es. Prot these comments, it\

is the feeling of the rese cher that stud is are con-

cerned about the s,low'pace through the programmed texts

because of such "little bits" in each frathe, and students'

concerned with the different role of the teacher clearly,0

indicated that they prefer lectures.

.

16

dr.

The tenor of the responses was generally one of positive

'feeling for the system. Those who liked. Math X'liked it!iwg

very much. -Those who did not wish to takeit again seemed

224.

--%00

to desire stroAg pac

type presentations.

doubtedly are not wi

4

ing discipline

,These student

iling.fo be re

success (or failure) .

Examination of HOpotheses

HYPOTHESIS 1

.

procedures with lecture

s are fthe ones who un-

sponsible for their own

Costs per' ADA hgve risen from $762.45 in 1970-71 to

i847..32 ain 1973-74. Calculations using the last figure

yield an average cost per ADA-hour of $1.61 in the Antelope

Valley College District. xIf e uipment costs and amorti-,

zaiion charges ars subtracted (math is a low"-equipment.'r

subject), cost of instructio is about $1.56 ent

hour.

HYPOTHESIS i claimed a minimum ,of a 20% saving could be

realized using Math X methods. A "worst Case" considers-!

1

;

,

.,

tion using the (JCSF comparative method produces a savings,

. .4-

of only 3% -- therefore, this hypothesis .is rejected.

HYPOTHESIS 2

HYPOTHESIS 2 states that success versus non-success may

not,be a useful criterion'on ahich tp base" the desira-

;

hilly of the Math X type of instruct4.on. Up to this

point, "success" in ,a class.has meant' receiving passing

grade. In Math X, many students' eni'oll to study a.portion .

or a topic in math, leaving the class as soon as they have

'mastered that topic. Additionally, passing a class may

23.

17'

18

requirdore than one semester,, in which case a:student

receivesa non-success) grade (W) during the first phase of :

his studies. In either'case, the non-success' vade does

not really mean non-success. A convention discovered in..

1

the literature and practiCed by most PSI proponents allows,

.!

J i

one and one-half semesters for success, in a course of , -

..,.

( 0 .

study before a non-success grade is awarded. Whilethis'

modification in Weinition would have 'contributed pOsi-

tiVely to our results, it -is diffiCult to estiviate the''

c

precise effect.%. '".

On the basis of th responses received on the studentl

i

questionnaire and ,t continuing upward-trend in sAroll-I I

I

1 t .

.ment, HYPOTHES4, 2 Wil..N.be accepted and a'aligent effort! ,

will be made to establish 'a Adw base for .assessment of4 . .

Math X su cceps.. c

'HYPOTHESIS 3.,

comparisonAn objective Comparison of the' amount of math leaimed iii

Math Xiversus the'amount learned in ledture math classes

is difficult to make. HYPOTHESIS 3 stated that about as

.

pitch or*Taybe more mathematics,was learned in the Math 'X\k

system. Apparently .stu'dents are not hurt by the schpme,.

. A .

and marly.do go on t9 do weTi in conventional math' sasses., .

,

.

.(._

-A standard Pearson r was Calculated using the grade rt.om4. '

.0the sample group which went on to more ddvance.d mathWbudy.

\ 1,

12 : -\

An l' = .02 resulted. The point biserial correlation.

,.._ . .

1

.----.\

V ..2 4 .

19

'discussed in OBJECTIVE 2yith the value rpb = -.52 both

pared how well Student's did in Math X with whether th y

did thelaame or better (considered positive) Or woe

(negati e). (The'.""worse".corldition included the condition

unsucce sful.1 This valile of correlation does not yield

any conclusive evidence (refer to,OBJECTIVE 2 for discuS-

sion).

In view of the lo correlations talculated, t his hypothesis'

needs further inv stigation, but will be tent tively a6-

. 1

.cepted because_ o the

i

[needs not met'i conve tional math classe a e being met

ttn, the `Math X c aipSro Without the-Aeo nse or screening,i

rit, is ,speculat d that the initial a:bill les of 'many of theI , .1

Math enroll es may be solliewhat'lower han AbIlities in

tronk'indicati,ons that many studen

1

conventional math classes, indicating .difference in the

----

typ of strudentserved in Math X./

ISummary of Conclusions

O

4. Fewer students receive success grades in Math X

than in conventional letture classes. A "units

completed per

1

student factor" has been developed,1

enabling cost -- effective comparisons. The value

-\cotputed for the UCSF is .62. When this factor

isusea to compare conventional and Math X in-'

straction, 5c reduction in, cost per hour-of

ning a,"successful" math student results.

1 '

...""yY

4'ot

40% reduction in coste is indicated if one .con-

siders.all student's handid.4

2. Grades earne n Math X are found to-be

cantly highdr: -a.GPA or 2s92 in Math X compared

with 2'.67 in the control group has been calculated

(t test. shows 'significance beyond the .01;alPha

level for this difference i-Math X lo;st,e; ed-1,

I .

those students who are to accept 0 t

,

learning* is their, respon qbility?, Of even, ore c '

I

importance is the fact that.52% If the students

h\VI.

N

expOsed-to Mat :X continued to s+dy math,, while

the conventional math group showe a persistence .J %.

percentage of only( 38x.

3. tCpoint'bfse i 1 cdrreiationof -45clier.l.

, 4

tendencY to o better in a ect4ure cl s ditr_. , ,

1 i,

,

taking Mat X', or, .'conversely', y :do, more poorly -/i

in leotIlre after doing airly we 1,14-Math X. A, .

scatter pleat revealed t at most successfUl stu-

dents Iii M th'X went ohlto be successful in con- il

`''Ple

ventional m th classes, but the :blot was suCh:that:. / -

-J 0

. ,..,

.- . -

4 Oho pat n f lineal regres sion -:was prespnt in the

1.1. . , % g.'4' $,ordered pa of grades .-- hence a Fearson r of

only,w.asAund-to exist. -

\

\

4. ConsideriqgtheIaaded services and the individpl.

attention furnished students in the Math X set ing

26

4-

,(the type of individual attention impossible in

.conventional lecture blasses), the PSI scheme of

-,,

i

instruction is judged even more cost-effective .r

,.:

than the 3% decRease,in cost of instruction-per

student hour indicates. Popularity of.: the class I..:

is also indicative of the feelings of students_ '0. 1

towarethe leatni-ng methqid....-

-:. .

. .-

5. ° A. careful study of thel'charaCteristics of .1sut- 1N,

's t,cfssfuln. versus "unsuccessful" Math r i

students

would .Probably reveal differencei in learning ,.,_ .

styles related to maturity. Iiiurther .study of the,

.

4 41` X

I ^

(char acterist ics. . of students and.their success pat-i

terns is. necessary.tA mateihirig;of cognitive-.,' It. ,

styles Of studentstOteacners and pedagogical

.slemes could prove 'useful, in_reducing non- success. ,

ri

ratios .1.n all cis:Ss:es .., Studies of. this type. are I

-called -Cognitiv_e t;ialipixis3 Studies, and perhaps _

should be Undertaken as .next Step.in the- anal ---

7-

.next

. sks of iriSt'Att173434,,sckexestz In ,fint avant, it is'. :

. ..,- ).

,,. -:.- 'tp.r:44,-. .*-- . . i

.1a1 wn that cetta.in students ,succeed in certain " I.

\\\' 11*sings better than in' of ers. dons i ci4ri.ag this. -

aspect, Math X ,is iirofild'in another way to study t 1.11

I

BIBLIOGRAPHY/ .

(1) Reiser, Robert A., "Self-Pacing andPacing in-PSI Courses",,Unpublishedpresented at the 10tionaliConferenceInstruction in Higher Education, Losfornia, March, 1915.1

nstructor4-uscript

do Personalized.Angeles, Cali-

(2) Goliaday, MaryA.ySkuldt, K., Devdult; Vere M.,' Fox, Thomas G:\Jr., "Problems in Empirical Research.

\1

on Individualized Mathematics Programs", Journal forResearch Mathematics. Educatiork,:1975, 5., 155L3.69.

1-

Fast, Hastetllr,-Tpilli, "Fullerterrirogram Co'st.

Data", Unpublished manuscript, Fullerton CommunityCollege; California,. 973. '

\i

\Brightman, Richard W., "Strategies for Change PartIII, ComparingInstructibnaliCoss", UnpublishedManuscript, Coast Community-College District,' CostaMesa, California, 1971.\\ . -, - .

.

.

Robe ts, Frank C., "Comparing In'structionai Costs of

Selec d Programs at g-4'unior,Collegel,,UnpublishedManuscr t, Antelope Valley College, Lancaster, Cali -tori'aa, July; 1974.

..

k

1*

r

g is

DESCRIPTIVE STATISTICS

,

TOPIC . EXHIBIT PAGE

1. Math X Statistics Table 1 .24

2. Math. X Enrollment. Figure 1 25

3. ContrIol Group Statistics Table 2 26

4.. Math X Sample Statistics Table 3 27

.r*

1

23 ic

.T.-- 01.-

4i

1

1

d

I

. 5

4

Table I Math X Statistics

Number of students enrolled at censps weekFt70,through SS174. in Math X classes

Total:enrollment (includes "Drop -ins ")

between. 5

Number of students counting repeaters once

Number of "Drop-ins" (Those students enteringafter the fourth week,. census week)

Number of "Drop44ns" counting repeaters'once

Number,of Math X students that repeated the class.(15% of the population, I t.% of the imdividuals)

0

Percentage of students that repeat more than.twice- (three and more enrollments)

Perentage of non - success grades recorded/.

Percentage'of success grades recorded by level (class )*

Math 50i Arithmetic

Math A

Math B

Math' C

Math D

Math 6,

. Percentagreceived

Elementary Algebra

Geometry

Intermediate Algebra

Trigonometry

College Algebra0

of students that enrolled two times andSuccess grades both times

Percentage of students thatsucceed in Math XJ,

required two semesters to

Percentage of students that enrolled more than onceand received a "W" grade (non-success) for all tries

Percentage of studints completing at least two mathclasses in,a siagletsemester of study in Math X

30

IY .

1610.1

1747

1489

137

114.1.

it

[

124.8%

9.3%

1.6%

6.6%

6.3%

3.3%

I

162'

4:7%.1'

58.9%

3.3%

!

1

4.

I

\

1

14.00

350

300

250

240 .

100

50

0

4

Math X Enrollments By Semester

'Day

Extended Day

(Summer ''Sessionsh416. mim

JP

4

f s1017

1..

I

i70 s71 F71 % S72 F72, `73 *F73 's714.

Semsstir.Table I Math X Enrollments

4

25

r

c

donirol Group Statistics

4

General Information:

U = Population of math students enrolled between Fa 1 1970"and the Summer Session of 1974.

A = Studenti in the'control g *up that.: took math in Math X '1

and in conventional lectut -types sessions

B = Students that took math in conventioital lecture type

sessidins only' ,

NA= 25

,

81

NAtB =

N

s t

..Table 2

characteristic. .

Group.

, No.

B AUBNo x tro.

Students that made Wis inall classes attempted

",Students that completed alecture class and did notto on to another math cies

Students tha,t_completedimath class' =railed i&"'Ssecond math class but wereunsuccessful in the secondclass.

---S-tu deirtsthaimceivid-lower grades .In classesafter cdMplettng a Pre -

requsitesmath cl'ass. . 4 ...

1,1ami:success grades earnedTr (46 WiA, 5 pis, 1 F out of

179 attempt's)

average` numbiTot units..earned per 'student

- -

14. L5% 6 7% 110 9%

,6 23% 46 56%, 52 49%

2 8% 15 18% 17 16%.

1,5

16 19%

4.05

26

4

287,

$

'MATE X SAMPLE STATISTICS

Number -of students in the sample. A return ofabout 30% of.the student questionnaires was anticipated. In order to get a substantial numberof returns, 304 samples weredrawn. Seventeentudents were purged because of present enrollnt'or because their transcript and grades were

pt available. I

95 students in the sample took both Math X andconventional lecture.

192 :

i48 o the 192 Math X-only stude4sccompleted a mathclass and 4id not go on to take another Class.

1

students took Math X -only.

,

54 of the 192 Math X only students completed a mathclass and went on to take another math class.

95 students took Math X and conventional:math.

_52-4 of the 217 students in the sample enrolled inmath 'et least twice.

6

\\2,55 unit rier person are completed with a passing

grade in Math X.

'2-.42 is the mean GPA per student. (NOTE: This is amean of means -- use care in interpreting it.)s = .83.

666

I

66.

33

27

Appendix A

Appen

Appendix

Appendix D

Appendix E

Appendix F'

B

APPENDIX SECTION

PACE

Those Students That ToAk Math 29 .

After Math X

Those Students Who Did Not 39Take Math After Math X-

_Jammtary of Student RespdnsesFrom Satisfaction QuestionnaiDe

Calculation of a Point BisCorrelation: Degree of Succin Math X us. the Same or B(f

p), or Irs'Success.(fn )

CalculatioAs of Costs per'ADA-Hour

ialsstier

Cotputer Print-out of ControlGroup '(Coded N) and Math XPopulation (Coded P)

46

47

* Available only to authcirized persons

34

28

4

I

I.

OPENDIX A

4

Information on Appendix A'

GPA Columns indicate calculated-grade point averagesmade in Math X classes and non-Math X classes.

GF Column Code: ."

1 means greater success in non -Math Xclass after having tried Math X-(andmay have been successful in Math X)

means no success; ie., took math inMath X and inconventional math methodsand did,not receive a success grade' ineither mode. .

means lower aineelneni level in nark-Math X class'aftel4 having -been invglvedinMath X (and was successful in Math X)

29

LISTING OF THOSE STUDENTS THAT TOOK m4fri AFTER'mATH X EiAOLLHEW

ALPHA NO. MANEMATH A -POO.

SEMESTER GAAOEOTHER MATH CLASSESSEMESTER GRACE 6..6. 01, 01400 IN

11,435115135

55 72 A.A 4F 72 76...1

114250 5 71

1142,0 71 A.w7 114250 SS 71 0.10

111250 F 77 2 1

13,624 F 71 4M13,626 7. 74.W 0

156434 S5- 72 4.10

156454 S 76 15w 11.0

157970 S 74 e.5

157970 F /3 LL.4

157970F 74 S 4 1.

166241 S' 74 UIC

16.241 S$ /3 C4166241 $ 73 i A.0 2.67

16.241 5 73 50.8

166241F 71 £408 -C 3 1

166241S 74 44081.1

174104 F 73 44174104 SS 73 4.11 4'

2

174104F 73 CC

' 205713 S 74 4w ,

20,713F 74 74*W

1061115 F 71

20641,S 74 5011

411.1wy.

222629 F 7k, -- A.*

222624 F 2 x.w

222624 F 73 x.4

222624r 73 15.0 2 1

23036. 5 74 D11.4. 3 4 1 4

AM

36

30'

AlPs4

f

SG.

tr

'LISTING ui TKISE STu0ENIS THAT OOK

MATH x INFO. ,

MANE SEMESTER GRADE G.P.A.! ,

MATH AFTER MAN A ENROLLMENT

OTHEA MAT* CLASSESSEMESTER GRADE G..A. GY DROP IN;

I

' 23034. ''\F 74 ILSAA

!

231011 1 S 72 X.M4

234061 SS 72, AAS 2

23.944 SS 73 XM238944 S 72 50,5 03 2

234966 / SS 73 A.0

Ii

!

243+2324,423245+23

F 73

2

Pryf 74 0.41S 74 /A.* 0

24547, S 72 S.C. 2

24,67,74F 75e

245672S 74 7A.6 1

24,472S 73 40114,0C

r

2+3675f 72 406=8 3.05

' 24,7190 S 74 CA24760

S 74 1S.0

249103 SS 74 DA 4 4 1

2+9103F 74 4A

249605 S 73 Raw

249405 IF 7360A. IS 0 Y4 1

256576 74 .0 2 2 1

2,6576f 74 7AC

242031 72 $.W

2.2031 S 71_ 006

262031 f 0 44.C.6

2620313.66 a 711 15.

262031S 73.15.1.

27170527170,

X1.174

0

a251312 k 77. 2 2 1

31

..

,. .

if

i

i

325713325713

AT

I`

la

LISTING OF THOSE STUOENTS THAT TOOK MATH AFTER MATH X ENROLLMENT

MATH X INFO.AL?* NO. NAME SEMESTER GRADE G..A.

211312261312261312

1

I

OTNfA MATH GLASSESSEMESTER 6RAOE G..A. Gl ORO IN

.

F 71 47/ t

S 12 7A.C.S 73 15mM

282696 SS 72 GmA0.4 4 3.4282694 F 72 6.8.15A

287151 S' 74 XmM 0 4

,287751 ' S 74. 50.6

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4 1

31457231457;

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S \I3 AA 4

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360906 F 71 A.M340904 S 72 .X.M

140906 F TI AmW340904 4 F 74 850.m 0

346110346110346110

_346110

3441425'346425

. SS 72Ibi '

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/ S 72 156 3

4

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..........,

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SS 74 50.4

I"

..,

!

I

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7 I

r

r

-e*

I ,

ALPHA pp.

376653

LISTING OF !HOSE STUDENIS THAT TOUR MATH AFTER,NATH A ENHOLLNENT

MATH x INFO.. DIME RATH CLASSESNAME SENESTER GRADE G..A. SENES ER 0RALE u.P.A.

4 F 4 A.6 3

379502374502

$ 71 Amid

F 73 Aw

31139953639653113965333965

F 74 XbiF 73 E40114wS 74 506F 74 esot ' 3.33

363151386151

S 73 Asti /

V.

S 74 50.6 4

394162399132 0

F 7.3 Yo.bi

F 73 50A 4

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F 73 Am bi

S 74 Au'7 .13

409951404951

74 1.IdF 73 A6 3

424000424000424000

1

S 73 AwF 73 A4wS 74 15.o

47988342911113

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SS 74S 74

F 73

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F 74 0.6 3

435221435221

443,22135221

F 72

. SS 7FS 72

S 72F 71

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3.4

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46 72 7A02.

S. 74 76A

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1

39

OP O.IOP IN

0

1

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lu

0

1

1

1

33

1

. #

- .

ALPHA 140.

I

\ 456225\ 45622,

4402424 024244 242

MANE

we'

I

TASTING OF TmUSE SNOWS THAT Tom MATH AFTER MATH X EmicuLkmENT

NAN A INFO: OTHER 747,4 CLASSESSEMESTER GRADE G.P.A. SEMESTER GRADE G.P.A. OmOP IN

SS 7050.0. F 70 C.W

2 1

F 73 1.wF 73 SO.w$ 74 4.0 2 1

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S 74 4410F 74 AC 2 1

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549335549335

LISTING UFITAOSEI

MAT4NA SEAESAE4

S /27"..\_____

1 '

STUDENTS THAT Tubb'" Ifs

X roFki.uRADE C.P.A.

XPli I

4FTE4 04101 A Eh5OLLMCN1

UNE* 44415 C ASSESSVISTEA GA C U.p.A. 010 DROP 1

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1

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35

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LLIO4i NINE

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MATH XsEmtstot G

/

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4113701 73 X11411370

62 3000 1 73 x.w.623000

62'443 50.462443

636743 71 0.01

4347V336743

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447312

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F 7Jl 16.G.

F 74 .50

S 73 TS.*

F 7 4SOW

0r

F 71 SO .WS 72 tSC 2 1

F 70\4.11.44 3 1

$ 71 0.0. 4.6F 74 tA.0 2.8

S 7F 71 7A-C.S 72 76.C. 15.4S 7 A.wSS 74 46 2.4 1

62500642500

'SS .7 X*F '74 A.W 0

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36

y.

ICI11

tLISTING OF HUSE STWENTS THAT TOOK PATH AFTER PATH A E LmENr

0 MATH I Ihr.O. OTHER PATH C SSESALHA W. NAPE SEPtSTEA GRACE G.P.A. SENESTEA s* E u.P.A. WI ux0P IN

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MAN X INFO. OTHER HAIM 0.4SSES

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i

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'

APPENDIX B'1

THO CS4IU0ENTS WHO 010 NOT TAKE MATH CASES AFT MA H X!

,

71

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213000 'X=W

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F 73 518;

S 74 547 i

S 71' 511

S 74 525

/117054 X=4 F 70 519 . 220514 iC F 73 518

11,7906 X= S 73 600 .222319 0=C S /74 . ._,, 25

117906 Xaw F 12 491 2124411 X=W S 1 74 47 !.

1;21900 502kB/ F 7 540

121900 A =C .5 74 47

222441 XaW F, 73 ,1540 .. !

222597 Xagt,i SS 74 074' I

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I

S 600 a25304 X=..k4 5 74 547 !i125468 X=W.

,

12546§ X=w S_ 4 5,47 . 230488\X W S 73 577 li

128078 XaW S 72 550 237,346 X=w 1 F 73 54p; I .%

1. ,...

. - . 1.31376 XaW F 13 5t7 24238/ F 74 Ira*i t' : 1 . I

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,

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1

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: $ , . r I .7.10,

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THOSE sTur.fas 11RO DID NOT TAO MATH CIA,3333 AFTER MATH X

.-

278327 50=C

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29438.7 X =i4/

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303164 18,

316656. X=W

318781 X=

32 100 C=C

SS 72 063

S 73 600

S. 73 54'9

S 74 525

5 74 526

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1

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336658 50=A

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348286.50=it; .

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396716 X=W.

360348 X=W

366380- X:214-___1

F 73, 518

S '73 594

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$ 13 576

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4'0 h61_ X=1t - S 547

407,255"X=W ,y 3 54

408149' X=W F 744

40010 *314 t SS 74 074'

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410171 X=W SS 74 974 11.

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74 5254'

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74 7.418

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40 .

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. THOSE STUDENTS WHO DID NOT MATE C MAIM

.1

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5Q7441 X=i4 F 7, 517 5610.5 =I / F 70 519 1

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F I 0 540 575843 A= i -3q 04

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/

.

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.

47

..

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THOSE STUDATS WHO DID NOT TAKE :MATH: CLASSES AFTER \MATHx

7

696691,0=C,6 SS 74,v0741

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680487 X=W F 73. 518

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to

,

49

,..41.,4

,--

a

?

APPENDIX C SitOtARY OF REPLIES

ANTELOPE VALLEY COLLEGE297 Questionaires mailed

ISSTITUTIONAI: sou= 49. Not delivered.74 Returned (30%)

104 ARE mac A SPEC &WU OF 3133EXT3 CI033111 MUSE 10U OICE ENPOASTELOPE VAULT COLLAGE.

A

IN A MAINgi CUSS AT

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Note:/Seldom did both poxes gechecked by the. lame 31113ple

0 10.1_

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of

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PENDIX:c CONT. SUMMARY Op REPLIESACEIDTE VLLEY C0u.ea1113MUTIONAL

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\owS. Ill 1113SSTICT, M TAY fill MI MOILS ran 8.ulaa om NATI no a

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"GPA" A MT itS41, $ CMS, C 0-.1114T 0 6,04.4 romirogs, I mans .

box UV TAMS (CIS STVOT AT 'MIR .4w5 iArt),Factor of "Range of Opinfpn"sits

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91s trees seiostmese (u sass se All AT AST Tint 1111411/11 ttNLI 3111STINI) 3 =.676

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Iwo 541;14 811111111T ZWiT SI tgrosvoltar I,

6 marked A; B ma.Kked B; 22 markeGovtems 2 marked G: and I mark

i23 did. not mark any

'OT> It I Mg

0; 3 marked D; 11 ma ked E; 1 Mar 4 F;11 in "Item needing greatest impro ement

4

32 ' 1

.

5,marked A4 8 marke4 B; 5 marked C;). marked D;7 marked E; 1 :parked P,and 4 marred E "Other. item'., 39 did not any:

lo

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46 .,

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Po nt*Bisrial elatibn Calculation /i

,

".',

.

chose- students o received higher GPA in lectureclasses (conven tonal math instruction) after

. having succeAsf ily completed Math X,

.

.1.

.

'fn

Thobe students o received lower GPA in lecturein math claspes other than Math Xa.fter haVpgtaken Math X' (and were successful in Math X) , -

.. .

,'Y f.

f- n

f4..

fY fY2 fPY.

,

i

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rpb

. .

The negati oint biserlal value allows one-.

to infer..., \ , , .

that, studettK av4.ing a lo-if GPA in Math X went on 'to ao -..

f,(62)(44)._ (38)(

1,4381(24)(62)09.01.,,.1152

-1680.3196 -.52'

I

'bettenin con

high grades i

math classes-

.

al math elasse4 while i'rocuaents with

.

same in either s

did.not'ao aswe11 in conventional

e students seem to do about the.

1

:.. .,

..

. , I

,

2 I'

7/APiENDIX'E..

Calcufatrns,of Costs per Student Hdur

General InfOrmation.I. ,

Year Costs of Education ADA [ Cost/A A

1970-7I 2,046,45;00 - 2684 tt62. 5

:1971-12- 2,238;378.00., - 2672_ 810,42.

.,

.1972-73- 2,353,307.00' \ 2662 884.04

1973-74 2 78,422.00 .' 2807 847.3 21,

i i

Cost o Educat n-lCurrent co is calculatid b*Y./

combining ateg ries<40..',,

=

phrAgb 80 i'ex ludini 500.

Hou L; of Ihstr4tTo1 '`

1 1

stri t -Wide C

ear

1970-71'

1971772.

-1972-73,

.19731-74

1.

t per Hour of I strUttio

Cost

$..1.54\

1:68

go

1 53' ,.-"....

0

\ . 1.CostDer' Hour in

A

Year

1973714

Ithiction.(

of 45 tudents)

Cokst"

$16

1-

a d, on a. Lecture

.

(Cost of conventional instr tion from report

Comparing Instructional Costs of Selected Programs

'at a Junior College; see listing (5) in BibliograPhy,

page 22 ') 1 r

[

/

,

Cajc416.

'Stith of a

ex,cludin

/ADA gene

. /

48

ns tor.Maih X Ins

categories from

213, d vidpd

383. 47

---/a i Math X-

; '4.

135. x 3 x 35525. .._

383..47, + + 1,56,2 1. 4

496.14525

$.95 Per Student

. Math X 4.

rNs

UNIVERSI3)( OF CALIF.

LOS ANGELES

ffu-N,. AUG 6 S76

.

. CLEARINGHOUSE FOR,Ull.N1013-00j_LEGES

/,

6 4

Hour of Initruction4.0