The effectiveness of this reward contingency was eval uated by observing the direction of change in three basic measures of behavior: (1) fre- quency (frequency multipliers or jump), (2) bounce (variability), and (3) celeration (celeration multiplier or turn). Chart 1 shows data for two students showing different effects. In moving from the baseline to the reward period, student #1 demonstrated a frequency mu1 tiplier (jump up) , a decrease in bounce and a celerati on di vi der (turn down). Stu- dent #2 experienced a frequency multiplier (jump up), a decrease in bounce and a celeration mu1 tiplier (turn up). Chart 1 also illustrates the summary data for a1 1 7 students, showing the number and direction of changes in frequency, bounce and celerati on. These data indicate that "you get what you reinforce." The contingency was for any daily performance improvement. The summary data for fre- quency and bounce show that the contingency had the desired effect, frequency multipliers (jump ups) with less bounce. However, there was a celeration divider (turn down) on four of the seven charts. Interpretation of these data leads to several conclusions: (1) to get significant celeration multipliers (turn ups), we may have to accept some bounce, (2) if we reinforce small, daily performance improvements, we may inadvertently limit celeration, and (3) i f improved learning and lasting performance is desired, the dai ly performance change reinforced should be large enough to produce significant celeration multipliers (turn ups). BeZinda VitaZe i s a resource room teacher at Chickasaw EZementary SchooZ and Eugene "Skip" Berquam i s the Pmject Ahinistrator, Precision Teach- ing Project, Orange County SchooZs, 800 South De Zaney Avenue, OrZando, FZorida 32801. TRENDS IN EDUCATION: A CELERATION ANALYSIS Robert Bower Lmrence, Kansas METHOD A graphic representation of trends can be obtained by plotting yearly data on the yearly Standard Behavior Chart. In this study the researcher counted the number of yearly references to topic headings in Education Index. I t was assumed that Education Index provided a representative sample of educatiorfal publications, indicating the interests of the edu- cational comnuni ty/. Yearly frequencies were placed on the Standard Be- havior Chart. The "trend-fol lowi ng" cel erati on technique was employed in drawing and analyzing celeration lines. A Histolay was constructed to observe the relationships of 3 educational events and charted educa- tional interests. These 3 events were the National Defense and Education Act of 1958, the Elementary and Secondary Education Act of 1965, and Pub- lic Law 94-142 (the special education mandate) of 1975 (NDEA, ESEA, and 94- 142).
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The effect iveness of t h i s reward contingency was eval uated by observing the direct ion of change in three basic measures of behavior: (1) fre-quency (frequency mul t ip l ie rs o r jump), ( 2 ) bounce ( v a r i a b i l i t y ) , and ( 3 ) celerat ion ( ce le ra t ion mul t ip l ie r o r t u r n ) . Chart 1 shows data f o r two students showing d i f f e ren t e f f ec t s . In moving from the base l ine t o the reward period, s tudent #1 demonstrated a frequency mu1 t i p l i e r (jump up) , a decrease i n bounce and a c e l e r a t i on di v i d e r ( t u r n down). S t u -dent #2 experienced a frequency mul t ip l i e r (jump u p ) , a decrease i n bounce and a ce lera t ion mu1 t i p l i e r ( t u r n up) . Chart 1 a l s o i l l u s t r a t e s the summary data f o r a1 1 7 s tudents , showing the number and d i r ec t ion of changes in frequency, bounce and c e l e r a t i on.
These data indica te tha t "you ge t what you re in fo rce . " The contingency was f o r any da i ly performance improvement. The summary da ta f o r f r e - quency and bounce show t h a t the contingency had t h e des i red e f f e c t , frequency mul t ip l i e r s (jump ups) with l e s s bounce. However, t h e r e was a celerat ion d iv ide r ( t u r n down) on four of the seven c h a r t s .
In terpre ta t ion o f these data leads t o severa l conclus ions : (1) t o ge t s igni f icant ce l e ra t ion mul t ip l ie rs ( t u r n u p s ) , we may have t o accept some bounce, (2 ) i f we reinforce small, d a i l y performance improvements, we may inadvertently l i m i t ce lera t ion , and ( 3 ) i f improved learn ing and l a s t i n g performance i s des i red , the dai l y performance change re inforced should be large enough t o produce s ign i f i can t c e l e r a t i o n m u l t i p l i e r s ( t u r n ups).
BeZinda VitaZe i s a resource room teacher a t Chickasaw EZementary SchooZ and Eugene "Skip" Berquam i s the Pmjec t A h i n i s t r a t o r , Precision Teach- ing Project, Orange County SchooZs, 800 South De Zaney Avenue, OrZando, FZorida 32801.
TRENDS IN EDUCATION: A CELERATION ANALYSIS
Robert Bower Lmrence, Kansas
METHOD
A graphic representation of trends can be obta ined by p l o t t i n g yea r ly data on the year ly Standard Behavior Chart. In this study the researcher counted the number of yearly references t o t o p i c headings i n Education Index. I t was assumed t h a t Education Index provided a r ep resen ta t ive sample of educatiorfal publicat ions, i nd ica t ing the i n t e r e s t s of the edu- cational comnuni ty/. Yearly frequencies were placed on the Standard Be- havior Chart. The "trend-fol lowi ng" cel e r a t i on technique was employed i n drawing and analyzing celerat ion l ines . A His to lay was constructed to observe the re la t ionships of 3 educational events and char ted educa- t ional i n t e r e s t s . These 3 events were the National Defense and Education Act of 1958, the Elementary and Secondary Education Act of 1965, and Pub- l i c Law 94-142 ( t h e special education mandate) of 1975 ( N D E A , ESEA, and 94- 142).
RESULTS
Reinforcement and Behavior ModiJication--After two decades of x4 accelera- t ion, a ce lera t ion turn-down has resul ted in a period of no growth f o r the l a s t e igh t years.
Educational U s and Legislation--Correspondi ng accel era t i on trends pre- ceded the NDEA, ESEA, and PL 94-142. Deceleration trends followed NDEA and ESEA, however an acce le ra t ion trend follows PL 94-142. The s teep de- celerat ion trend following ESEA took the frequency to a level f i t t i n g the overall decelerat ion t rend of a 40 year period, from 1935-1975.
Legal Actions and Defenses--A 12-year deceleration trend was reversed wi t h the ESEA. The acce le ra t ion t rend (x2) , beginning in 1966, i s confirmed w i t h the reaction t o PL 94-142. I t looks 1 ike educators will be preoccu- pied w i t h legal ac t ions and defenses as we enter the next century. Al- though topographically re la ted Legal Actions and Defenses and Educational Laws and Legislat ion a r e funct ional ly independent. They counterbounce, countercelerate, cobounce, and cocelerate.
AccountabiZity--An extremely rapi d i ni t i a1 acceleration ( ~ 1 0 0 ) i s fo l 1 owed by a deceleration t rend. A newer topographical category, Competency Based Education, may have usurped some numbers i n i t s acceleration trend.
Competency Based Education--Begi nni ng accel era t i on i s rapid wi t h some leveling off in the mid-1970's. A new acceleration trend corresponds temporari l y t o PL 94-1 42 and confi rms the overall acceleration trend.
Education EuaZuation--A frequency mu1 t ip1 i e r ( j ump-up) occurred in 1966. However the s h i f t was accompanied by only a s l igh t change in ce lera t ion, as i t remains r e l a t i ve ly f l a t .
Robert Bower is a post-doctoraZ s tuden t a t Kansas University, Room 9, Bailey H a l l , Lawrence, Kansas 66045.
PERFORMANCE AND LEARNING WORLD RECORDS
To emphasi ze performance ai ms/s tandards and to encourage learning above x2.0, Michael Maloney has suggested t ha t we i n i t i a t e th i s world records section. Two (2) performance records follow. They will stand as world records u n t i 1 someone "beats them. " I f you are aware of potenti a1 world records, especi a1 ly l earning records, send them to the edi tor .
Perfomance World Records
Tanya Kelb (Be1 lev i l l e , Ontario) See-think 1470 words per minute ( s i l e n t readi ng)
Vicky Vachon (Be1 lev i 1 l e , Ontario) See-wri t e 146 subtract facts of 18 per minute
Leaivling World Records (ye t t o be submitted)
IE pl'sEgA,V!2R"s:%B,!~&I:-' EN) BEHAVlClR RESEARCH C O CALENDAR DECADES BOX 3351 K A N S A S CITY. K A N S 6 6 1 0 3
C t N T U R Y DECADE DECADE DECADE DECADE DECADE DECADE DECADF DE C A W DECADE DFCAUC C l N l U R Y O L C A D E
500,000 Chart 1. Reinforcement and Behavior M o d i f i c a t i o n 1
SUPERVISOR ADVISER M A N A G E R BEHAVER AGE L A B E L C O U N T E D
REINFORCEMENT AND BEHAVIORP ~ D I F I C A T I O N DEPOSITOR AGENCY T I M E R C O U N T E R C H A R T E R
RESULTS
Reinforcement and Behavior Modification--Af t e r two decades of x4 accel era- t ion, a ce lera t ion turn-down has resul ted in a period of no growth f o r the l a s t e igh t years.
EdacationaZ Laus and Legislation--Correspondi ng accel era t i on trends pre- ceded the NDEA, ESEA, and PL 94-142. Deceleration trends followed NDEA and ESEA, however an acce le ra t ion trend follows PL 94-142. The steep de- celerat ion trend following ESEA took the frequency to a level f i t t i n g the overall decelerat ion t r end of a 40 year period, from 1935-1975.
Legal Actions and Defenses--A 12-year deceleration trend was reversed with the ESEA. The acce le ra t ion t rend ( x 2 ) , begi nni ng in 1966, i s confirmed w i t h the reaction t o PL 94-142. I t looks 1 ike educators wi 11 be preoccu- pied w i t h legal ac t ions and defenses as we enter the next century. Al- though topographically re la ted Legal Actions and Defenses and Educational Laws and Legislat ion a r e func t iona l ly independent. They counterbounce, countercelerate , cobounce, and cocelera te .
Accountability--An extremely rapid i ni ti a1 acceleration (x100) i s followed by a decelerat ion t rend. A newer topographical category, Competency Based Education, may have usurped some numbers in i t s acceleration trend.
Competency Based Education--Begi nni ng accel era t i on i s rapid with some leveling off in the mid-1970's. A new acceleration trend corresponds temporari ly t o PL 94- 142 and confi rms the overall acceleration trend.
Education EvaZuation--A frequency mu1 t ip1 i e r ( junip-up) occurred in 1966. However the s h i f t was accompanied by only a s l igh t change in ce lera t ion, as i t remains r e l a t i v e l y f l a t .
Robert Bower is a post-doctoral s tuden t a t Kansas University, Room 9, Bailey H a l l , Lmrmce, Kansas 66045.
PERFORMANCE AND LEARNING WORLD RECORDS
To emphasi ze performance ai ms/s tandards and to encourage learning above x2.0, Michael Maloney has suggested t h a t we i n i t i a t e th i s world records section. Two (2) performance records follow. They will stand as world records un t i l someone "beats them. " I f you are aware of potential world records, especi a1 ly 1 earning records, send them t o the edi tor .
Performcmce WorZd Records
Tanya Kelb (Bellevi l l e , Ontario) See-think 1470 words per minute ( s i l e n t readi ng)
Vicky Vachon (Be1 levi l l e , Ontario) See-wri t e 146 subtract facts of 18 per minute
Lea~vling Wor Zd Records (ye t t o be submitted)
Bow
er, R
ob
ert. T
rend
s in ed
ucatio
n:
a celeratio
n an
alysis.
JomaZ of
Precision Teaching,
Volum
e I, N
umber
2, July
, 1980.
Bow
er, R
ob
ert. Trends in
edu
cation
: a c
ele
ratio
n a
na
lys
is.
JournaZ of
Precision Teaching, Volum
e I, N
umber 2
, Ju
ly,
1980.
YEARLY BEHAVIOR CHART (YCM-1 EN)6 CYCLE - 1W YEARS (10 OECAOES) BEHAVIOR RESEARCH CO.CALENDAR DECADES BOX 3351 -KANSAS CITY. KANS. 66103
ffNTURY DECADE DECADE DECADE DECADE DECADE DECADE DECADF DECAOI DECADf DFCADL C I N T U R ? DLCADE
ESEA
Chart 4. Accountability
SUPERVISOR ADVISER MANAGER B E H A V E R A G E LABEL COUNTED
ACCOUNTABILIPI DEPOSITOR AGENCY T I M E R C O U N T E R CHARTER
Bow
er, R
obert. T
rends in
edu
cation
: a
cel era
tion
an
aly
sis. Jo
urn
al
of %
ecision
Teaching,
Volum
e I, N
umber
2,
July
, 1980.
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