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The Taped-Problems Intervention

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A multiple-probe across-tasks design was used to determine if the taped-problems intervention, a variation of the taped-words interventions (Freeman & McLaughlin, 1984), could be used to enhance division fact fluency in a fourth-grade student. During the taped-problems intervention, the student was given a list of problems on a sheet of paper and instructed to attempt to complete each problem before the answer was provided by an audiotape player. On the tapes, problems were read followed by their answers. Progressive time delay procedures were used as intervals between the problem and answer were adjusted. Initially, the interval between the problem being read and the answer was 1 second. During each session, as problems were repeated, the interval was gradually increased and then reduced. Results showed clear increases in division fact fluency after the intervention was implemented. This enhanced performance appeared to be maintained. Discussion focuses on future research related to the taped-problems intervention.
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Journal of Applied School Psychology
ISSN: 1537-7903 (Print) 1537-7911 (Online) Journal homepage: http://www.tandfonline.com/loi/wapp20
The Taped-Problems Intervention
Elizabeth McCallum , Christopher H. Skinner PhD & Holly Hutchins
To cite this article: Elizabeth McCallum , Christopher H. Skinner PhD & Holly Hutchins (2004)
The Taped-Problems Intervention, Journal of Applied School Psychology, 20:2, 129-147, DOI:
10.1300/J370v20n02_08
To link to this article: http://dx.doi.org/10.1300/J370v20n02_08
Published online: 02 Oct 2008.
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The Taped-Problems Intervention:
Increasing Division Fact Fluency
Using a Low-Tech Self-Managed
Time-Delay Intervention
Elizabeth McCallum
Christopher H. Skinner
Holly Hutchins
University of Tennessee
SUMMARY. A multiple-probe across-tasks design was used to deter-
mine if the taped-problems intervention, a variation of the taped-words
interventions (Freeman & McLaughlin, 1984), could be used to enhance
division fact fluency in a fourth-grade student. During the taped-prob-
lems intervention, the student was given a list of problems on a sheet of
paper and instructed to attempt to complete each problem before the an-
swer was provided by an audiotape player. On the tapes, problems were
read followed by their answers. Progressive time delay procedures were
used as intervals between the problem and answer were adjusted. Ini
-
tially, the interval between the problem being read and the answer was 1
second. During each session, as problems were repeated, the interval
Address correspondence to: Christopher H. Skinner, PhD, The University of Ten
-
nessee, College of EHHS, Claxton Complex A-518, Knoxville, TN 37996-3452
(E-mail: cskinne1@utk.edu).
[Haworth co-indexing entry note]: “The Taped-Problems Intervention: Increasing Division Fact Fluency
Using a Low-Tech Self-Managed Time-Delay Intervention.” McCallum, Elizabeth, Christopher H. Skinner,
and Holly Hutchins. Co-published simultaneously in Journal of Applied School Psychology (The Haworth
Press, Inc.) Vol. 20, No. 2, 2004, pp. 129-147; and: Single-Subject Designs for School Psychologists (ed:
Christopher H. Skinner) The Haworth Press, Inc., 2004, pp. 129-147. Single or multiple copies of this article
are available for a fee from The Haworth Document Delivery Service [1-800-HAWORTH, 9:00 a.m. - 5:00
p.m. (EST). E-mail address: docdelivery@haworthpress.com].
http://www.haworthpress.com/web/JAPPS
2004 by The Haworth Press, Inc. All rights reserved.
Digital Object Identifier: 10.1300/J008v20n02_08 129
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was gradually increased and then reduced. Results showed clear
increases in division fact fluency after the intervention was implemented.
This enhanced performance appeared to be maintained. Discussion fo
-
cuses on future research related to the taped-problems intervention.
[Ar
-
ticle copies available for a fee from The Haworth Document Delivery Service:
1-800-HAWORTH. E-mail address: <docdelivery@haworthpress.com>
Website: <http://www.HaworthPress.com> © 2004 by The Haworth Press, Inc.
All rights reserved.]
KEYWORDS. Tape-problems, time-delay, math fluency, self-manage
-
ment, multiple-probe across-tasks design
Basic mathematics computation facts include solving simple (e.g.,
one-digit plus one-digit) addition, subtraction, multiplication, and divi-
sion problems (Hasselbring, Goin, & Bradsford, 1987). Because basic
computation skills are necessary for completing more complex compu-
tation problems, it may not be sufficient for students to merely acquire
the ability to solve these problems; they should also be able to arrive at
the correct answer rapidly (Deno & Mirkin, 1978; Haring & Eaton,
1978; Shapiro, 1996). Fluency, automaticity, and proficiency are terms
often used to describe rapid and accurate responding (Hasselbring et
al.,1987; Haring & Eaton, 1978; Shapiro, 1996).
Those who can complete basic facts automatically may have more
cognitive resources available to apply to learning more complex com-
putation algorithms or concepts (LaBerge & Samuels, 1974; Wong,
1986). Additionally, the more rapidly students can complete the basic
mathematics facts, the more quickly they can complete complex items
(Skinner, Fletcher, & Henington, 1996). Thus, they receive more op
-
portunities to practice these complex items, which can enhance general
-
ization and discrimination skills (Skinner & Schock, 1995). Finally,
those who can complete basic facts both rapidly and accurately may
find complex mathematics tasks less frustrating and have lower levels
of mathematics anxiety than those who can not complete basic facts au
-
tomatically (Cates & Rhymer, 2003).
Numerous procedures have been used to increase automaticity with ba
-
sic math facts (Greenwood, Delquadri, & Hall, 1989; Rhymer, Dittmer,
Skinner, & Jackson, 2000; Skinner, Turco, Beatty, & Rasavage, 1989).
Perhaps the most important shared characteristic of these procedures is that
they occasion high rates of active, accurate responding (Greenwood,
130 SINGLE-SUBJECT DESIGNS FOR SCHOOL PSYCHOLOGISTS
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Delquadri, & Hall, 1984). Researchers have compared interventions and
shown that interventions that occasion higher rates of accurate academic
responding result in greater increases in fluency than those that occasion
lower rates of responding (Skinner, Bamberg, Smith, & Powell, 1993;
Skinner, Belfiore, Mace, Williams, & Johns, 1997).
TAPED WORDS INTERVENTIONS
An intervention that has been used to enhance rapid, accurate sight-
word reading is the taped-words intervention (Freeman & McLaughlin,
1984). During this intervention, audiotapes are constructed that provide
words in the same sequence as lists. Students are provided with the lists
and instructed to read the lists along with the tape. Results have shown
that this procedure is effective for enhancing word list reading fluency
(i.e., words correct per minute on word lists).
In Freeman and McLaughlin’s study (1984), the audiotapes pre-
sented words at a rapid rate (80 words per minute) because neurological
impress or modeling theories (Cunningham, 1979; Heckelman, 1969)
suggested that rapid rates of presentation may enhance students’ read-
ing rates. Subsequent studies confirmed the effectiveness of the taped
words intervention (Shapiro & McCurdy, 1989; Skinner, Johnson,
Larkin, Lessley, & Glowacki, 1995; Skinner & Shapiro, 1989; Skinner,
Smith, & McLean, 1994; Sterling, Robinson, & Skinner, 1997). How-
ever, in these studies, researchers altered word presentation rates or im-
plemented experimental procedures designed to control for opportunities
to respond embedded within the taped-words intervention. Results from
these studies suggest that neither neurological impress nor students’
modeling the rapid pace of the tape accounted for the increases in stu
-
dents’ accurate reading rates. Rather, these studies suggested that the
opportunities to respond embedded within the intervention and pro
-
vided during assessment procedures caused the increases in reading flu
-
ency.
TIME DELAY
Time delay procedures have been used to enhance accurate respond
-
ing with individuals with various degrees of learning disabilities and
mental retardation (Ault, Wolery, Doyle, & Gast, 1989). Two types of
time delay procedures, constant and progressive time delay, have been
McCallum, Skinner, and Hutchins 131
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used to enhance accurate responding. Both include multiple trials con
-
sisting of (a) the presentation of an antecedent stimulus, (b) an interval
for students to respond to that antecedent stimulus, and (c) an additional
stimulus or prompt that follows the antecedent stimulus when students
fail to respond accurately. Table 1 depicts this process and provides ex
-
amples of how the process would work when students fail to respond
within the response interval, respond inaccurately within the response
interval, and respond accurately within the response interval.
With time delay, the goal is to have the student respond accurately to
the antecedent stimulus. Thus, for a division fact, an antecedent stimulus
may be a printed problem (i.e., 42/7 = __). Following the presentation of
the antecedent stimulus, an interval is provided for the student to respond.
If the student emits a correct response during this interval, then this re
-
sponse is typically followed by reinforcement or praise (see Table 1, ex
-
ample 3). If the student responds inaccurately or fails to respond during
the designated interval, an additional artificial prompt(s) is provided that
is designed to occasion an accurate response (see Table 1, examples 1 and 2).
For a division fact this additional prompt may merely be stating the prob-
lem with the correct answer (e.g., the teacher says “42/7 = 6”).
Time delay procedures provide students with an opportunity to inde-
pendently respond to the initial antecedent stimuli (e.g., 42/7 = __).
However, when students fail to respond or emit inaccurate responses to
the natural antecedent stimuli, the additional artificial prompts are de-
signed to occasion subsequent accurate responses. Thus, all trials typi-
132 SINGLE-SUBJECT DESIGNS FOR SCHOOL PSYCHOLOGISTS
TABLE 1. Graphic Depiction of a Constant Time Delay Procedure with 5 Sec
-
ond Response Intervals and Examples of Procedure When Student Fails to
Respond Within 5 Seconds (i.e., 1), Responds Inaccurately Within 5 Seconds
(i.e., 2), and Responds Accurately Within the 5 Second Response Interval.
1. Natural Antecedent Stimuli--à
(42/7 = ___)
Response Interval--à
5 Seconds and
no student response
Artificial Prompt--à
instructor says
"42/7 = 6"
Student Response
student repeats,
"42/7 = 6"
2. Natural Antecedent Stimuli--à
(42/7 = ___)
Response Interval--à
student provides
inaccurate response
within 5 seconds
Artificial Prompt--à
instructor says
“no 42/7 = 6”
Student Response
student repeats,
“42/7 = 6”
3. Natural Antecedent Stimuli--à
(42/7 = ___)
Response Interval--à
Student responds
accurately within
5 seconds
Reinforcement
instructor says
“Yes 42/7 = 6”
and reinforces
independent accurate
response
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cally involve one correct response and the student’s last response is
almost always an accurate response.
Initially students may fail to respond accurately to the natural ante
-
cedent stimuli. However, after repeated trials, students often begin re
-
sponding correctly to the natural antecedent stimuli prior to the delivery
of the artificial prompts. Thus, stimulus control is transferred from ac
-
curate responding to the artificial prompts to accurate responding to the
naturally occurring antecedent stimulus. Now the student is independ
-
ently emitting desired responses to naturally occurring stimuli.
When using constant time delay the time provided for students to re
-
spond independently (i.e., interval between the natural antecedent stim
-
uli and artificial prompt) remains constant across trials. Although
constant time delay procedures are abundant in the literature, only the
second type of time delay, progressive time delay, was chosen for inte
-
gration into the present intervention. Progressive time delay procedures
involve providing progressively shorter or longer intervals between a
stimulus and a response (Wolery, Ault, Doyle, & Gast, 1986). For ex-
ample, the stimulus is shown and an individual has a very brief amount
of time to respond. As time delay trials continue, this time interval is
gradually increased, allowing more time for responses. When the time
delay is brief, students have little time to respond before the prompt is
delivered. Thus, initially a no-time delay condition can prevent students
from making errors. Gradually increasing the delay during subsequent
trials then allows students to respond independently, before the artificial
prompt is delivered.
In contrast, time delay trials can begin with large delays that are grad-
ually decreased. The large delays may increase errors, but also provide
students with more time to independently emit accurate responses to the
naturally occurring stimuli (McCurdy, Cundari, & Lentz, 1990; Wolery,
Ault, Doyle, & Gast, 1986). Gradually reducing delays then can be used
to occasion automatic responding.
Progressive time delay procedures have been used effectively in pro
-
moting various tasks with various populations. McCurdy, Cundari, and
Lentz (1990) found a progressive time delay procedure to be more ef
-
fective in teaching sight words to students with behavior disorders than
both direct instruction and observational learning. Similarly, Browder,
Hines, McCarthy, and Fees (1984) successfully used a progressive time
delay procedure to teach sight-word recognition and daily living skills
such as answering telephones and doing laundry to a group of adults
with severe handicaps. Progressive time delay procedures also have
been used effectively in teaching language skills (Halle, Marshall, &
McCallum, Skinner, and Hutchins 133
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Spradlin, 1979), food preparation (Schuster, Gast, Wolery, & Guiltinan,
1988), and banking skills (McDonnell & Ferguson, 1989). Most of
these studies have been conducted with students with moderate or se
-
vere handicaps.
Purpose
The current study was conducted to determine if the taped-words in
-
tervention could be adapted to address mathematics division fact flu
-
ency deficits. In the current study, each basic division fact was
presented four or five times. Rather than being encouraged to respond
with the tape (see Freeman & McLaughlin, 1984), students were asked
to try to write the correct math fact answer before it was provided on the
tape.
In addition to altering the target skill, we adapted the taped-words
procedure by employing progressive time delays in an attempt to occa-
sion higher rates of accurate academic responding. In the current study
we employed both forms of progressive time delay. In an attempt to re-
duce error rates, initially each problem was presented on the tape with a
brief time interval or delay (e.g, 1-second) between the problem being
read and the answer being read. These intervals were then increased
(e.g., 5-seconds) to provide opportunities for independent responding
(e.g., responding before the answers were read on the tape). This also al-
lowed students to use the audio cues as feedback to reinforce accurate
independent responding and prompt error correction when responses
were inaccurate (Skinner, Turco et al., 1989). Intervals were then de-
creased to encourage more rapid or automatic responding.
METHOD
Student and Setting
Peter, a 10-year-old male African-American student from a general
education fourth-grade classroom was referred by his teacher because
he had fallen behind his classmates in math class, particularly with re
-
gard to simple division. His teacher indicated that Peter was a good stu
-
dent but that he often used a finger-counting procedure while doing his
division. While this procedure allowed Peter to arrive at accurate an
-
swers, he was unable to complete his assignments or tests quickly
enough to receive passing grades.
134 SINGLE-SUBJECT DESIGNS FOR SCHOOL PSYCHOLOGISTS
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The current study was conducted in an unassigned classroom in Peter’s
school that was used for various purposes on an as needed basis. During the
sessions, the researcher(s) and Peter were alone in the room. Activities
were conducted at a table with the primary researcher seated next to Peter.
Materials
A tape recorder, headphones, and stopwatch were used throughout this
experiment. Baseline and intervention data were collected via experi
-
menter-constructed division fact probes. Basic division facts 2-9 were di
-
vided into three sets (see Table 2) of 22, 21, and 21 problems respectively.
Multiples of one and inversion facts (i.e., either 12 4or12 3 but not
both) were excluded from the probes.
Three audiotapes were made, one for each of the three sets of prob
-
lems. Tapes were constructed for each set by reading the 22 or 21 prob-
McCallum, Skinner, and Hutchins 135
TABLE 2. The Three Sets of Division Problems.
Set A Set B Set C
9 324 648 6
28 712 214 2
16 872 856 8
54 621 315 3
16 420 436 4
40 536 972 9
10 218 28 2
5 515 535 5
64 812 36 3
27 345 520 5
54 956 763 7
28 448 832 8
18 363 945 9
27 924 812 4
36 642 630 6
4 26 242 7
49 732 424 4
40 835 718 9
81 930 512 6
10 514 724 3
18 68 421 7
16 2
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lems and their answers into the tape four or five times. Problems were
numbered and the number of the problem was read immediately preced
-
ing the reading of the problem. The order of problems was randomly se
-
quenced for each of the readings.
Originally, all three tapes were constructed in the same manner based
on a progressive time delay format. Specifically, the series of 22 or 21
problems was read the first time through with no time delay between the
answer and problem. The second series was read with a 3-second time
delay between reading the problem and giving the answer. The third se
-
ries was read with a 5-second time delay between reading the problems
and then reading the answers. The final two readings included 2- and
1-second delays, respectively. Thus, each problem and answer was read
5 times. For each series problem order was randomized.
While working on Set A, Peter complained about the long delay on
the middle series. Therefore, for sets B and C new tapes were con-
structed where the 5-second time delay series was removed, leaving
only four readings per tape: no delay, 3-second, 2-second, and 1-second
delays. The interval between reading the answer to one problem and
reading the next problem remained 3 seconds across all three tapes.
Intervention worksheets were constructed for each tape. These
worksheets contained each problem and a space to write the answer
(e.g., 42 6 = ____). Problems were provided on the worksheets in the
same sequence as on the tape.
Three different assessment sheets were also constructed for each set
of problems. Assessment sheets contained the 21 or 22 problems with
spaces provided for answers. The problems were randomly sequenced
across sheets.
Dependent Measures, Experimental Design, and Conditions
A multiple-probe-across-tasks (i.e., sets of problems) design was
used to evaluate the effects of the intervention (Cuvo, 1979; Horner &
Baer, 1978). Percent correct and digits correct per minute were the de
-
pendent measures used in this study. Both were measured during 1-min
-
ute timed assessment probes. Percent correct was calculated by dividing
the number of correct answers by the total number of problems an
-
swered and multiplying by 100. Unanswered problems were not scored
when calculating accuracy.
Deno and Mirkin’s (1977) scoring procedure was used to calculate
digits correct per minute (DCM) for each assessment probe. To be
136 SINGLE-SUBJECT DESIGNS FOR SCHOOL PSYCHOLOGISTS
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scored as correct, a correct digit had to be written in the correct place.
Thus for the problem 132 11 = ____, an answer of 12 would have
been scored as 2-digits correct because both correct digits are in the cor
-
rect place. An answer of 22, 15, or 1 would have been scored as 1-digit
correct and answer of 21 or 55 would have been scored as 0 digits cor
-
rect. When Peter finished all the problems on an assessment probe be
-
fore the minute was over, the number of seconds he took to complete the
probe was recorded. Digits correct per minute were calculated by total
-
ing digits correct, dividing by the number of seconds it took Peter to
complete the probe, and multiplying by 60.
Procedures
Each day at 9:30 AM the primary experimenter entered the empty
classroom and set up materials. She then escorted Peter from his class-
room and seated him at the table in the experimental room.
Assessment Procedure: Baseline, Probes, and Intervention. During
the first three sessions, assessment procedures were run for each set of
problems. The experimenter used a stopwatch to time each assessment
for 1 minute. Peter was given the assessment probes one at a time in ran-
dom order. Peter was directed to complete as many problems as he
could in 1 minute. When the first minute was up, Peter was instructed to
put his pencil down and wait for the next assessment sheet. No perfor-
mance feedback was given. Following the initial three baseline ses-
sions, Peter’s performance on the target set (i.e., the set of items being
addressed with the taped-problems intervention) was assessed each ses
-
sion. The non-target sets were not assessed each day. Instead assess
-
ments for these items were probed (i.e., administered prior to the
implementation of a new list). This intermittent assessment procedure
was used to decrease the probability of Peter becoming frustrated by
having to work on problems that were not being targeted during the cur
-
rent intervention phase (Cuvo, 1979). Probe procedures also allowed
for the collection of maintenance data.
Intervention Phases: Taped-Problems Intervention. Following the
third baseline session, the first intervention session was run with Prob
-
lem Set A. After the assessment, Peter was given a follow-along packet
for the Set A tape. The packet listed the problems in the numbered order
that they would be heard on the tape. Peter was given a blank sheet of
paper with which to cover the problems below the particular problem
McCallum, Skinner, and Hutchins 137
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being read. Peter was told to use this paper to help him stay with the tape
and not skip ahead.
Peter was told that he was going to listen to a tape-recorder. He was
instructed to look at his intervention packet and follow along with the
tape that would supply the problems and answers. He was instructed to
try to write the answer to each problem following its reading but before
the reading of the answer. Thus, he was encouraged to try to beat the
tape. When he wrote an incorrect response, Peter was instructed to write
a slash on the incorrect answer and write the correct response as heard
on the tape. If he failed to beat the tape, he was instructed to write the
correct answer after its reading. After Peter indicated that he understood
the instructions, he was told to put on the headphones and press the
‘play’ button to begin. When he finished the intervention sheets, he was
instructed to stop the tape.
Following the tape, Peter was given another assessment probe for the
specific problem set he was working on. This probe was randomly se-
lected, with one exception; the probe given during the pre-intervention
assessment was excluded from the selection process. The same timing
procedures used during baseline were used with this probe. Data from
probes following intervention sessions (listening to the tapes) were not
used as the dependent variable for this study. Instead, this assessment
probe was designed to allow Peter the opportunity to independently
practice items just drilled. Following the first intervention session, each
session included (a) assessment procedures, used to collect data for the
dependent variable, (b) the taped-problems intervention, and (c) an-
other assessment to allow Peter to practice problems he had just been
exposed to. Thus dependent variable assessment probes occurred be
-
tween 24, 48, or 72 (weekends and absences) hours after the interven
-
tion sessions.
After Peter demonstrated improved performance with one set of
problems, the tape was switched and similar procedures were run with
subsequent tapes. On most days, before beginning the taped-problems
intervention, assessment procedures were run for only the set targeted.
However, after Peter achieved stability on one set of items, the follow
-
ing day assessments were conducted for all three sets of problems (mul
-
tiple-probes, see Cuvo, 1979) and the intervention for the subsequent
set was implemented. On the last session, all three sets were again as
-
sessed to check for maintenance of set A and B items.
In order to enhance cooperation, each day Peter earned a star on a cal
-
endar for following directions throughout the intervention phase. After
receiving 4 stars, his teacher allowed him to choose a “treasure” (pencil,
138 SINGLE-SUBJECT DESIGNS FOR SCHOOL PSYCHOLOGISTS
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stickers, etc.) from her class “treasure box.” Peter earned a star each
day. Additionally, during each session Peter was praised for trying his
best. However, no mathematics performance-based feedback or re
-
wards were delivered during this study.
Interobserver Agreement and Procedural Integrity
A second observer sat in the room approximately 8 feet from the table
and collected procedural integrity data during five of the 15 (33%) inter
-
vention sessions. During these intervention sessions, the independent
observer recorded the presence or absence of 21 experimenter behav
-
iors (see Table 3). Results showed 100% integrity. Additionally, during
a baseline session, the observer recorded the experimenter completing
steps 1-7 three consecutive times and step 21 at the end of the session.
These data suggest strong procedural integrity.
McCallum, Skinner, and Hutchins 139
TABLE 3. The Treatment Integrity Checklist.
1. ____ Place probe face-down in front of student.
2. ____ Set timer to zero.
3. ____ Instruct student to turn paper over and begin working.
4. ____ Start timer.
5. ____ When timer reaches 1 minute, say "time's up" and stop timer.
6. ____ Collect probe.
7. ____ If student finishes before 1 minute, write exact time at top of probe.
8. ____ Give student headphones and appropriate Follow-Along sheet.
9. ____ Instruct student to keep up with tape but not to work ahead.
10. ____ When student is ready, start tape.
11. ____ When tape ends, collect Follow-Along sheet.
12. ____ Repeat assessment procedures with set of problems.
13. ____ Place probe face-down in front of student.
14. ____ Set timer to zero.
15. ____ Instruct student to turn paper over and begin working.
16. ____ Start timer.
17. ____ When timer reaches 1 minute, say "time's up" and stop timer.
18. ____ Collect probe.
19. ____ If student finishes before 1 minute, write exact time at top of probe.
20. ____ Give student a star on corresponding date on calendar.
21. ____ Escort student back to classroom with no performance feedback delivered.
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The second experimenter also independently scored digits correct for
one baseline session and these five intervention sessions (13 or 34% of
the probes). Interscorer agreement was calculated by dividing the num
-
ber of agreements on digits correct by the number of agreements plus
disagreements and multiplying by 100. Interscorer agreement on digits
correct was 100%. Finally, this independent observer also recorded the
number of seconds the student spent working on assessment across the
same 13 assessments. The two observers recorded the identical number
of seconds for all 13 assessments.
RESULTS
Figure 1 displays the percentage of accurate completed problems per
minute for the student during baseline and intervention phases. Figure 1
confirms teacher reports indicating that Peter’s division accuracy was
high prior to implementing the intervention. These high levels of accu-
racy prevent us from drawing conclusions regarding the intervention’s
impact on this dependent variable.
Figure 2 displays the data on digits correct per minute across condi-
tions and sets of problems. During baseline, Peter’s digits correct per
minute for each set were fairly stable. Baseline digits correct per minute
ranged between 11-16 for set A and 7-13 for set B. Baseline perfor-
mance on Set C appeared to contain one outlier during the first probe
session (session 7) where he only got 3 digits correct per minute. Ex-
cluding this data point, baseline digits correct per minute on set C
ranged from 10-18.
For all three sets of lists, Peter showed a rapid increase in digits correct
per minute after the intervention was applied. Mean digits correct per min
-
uteforsetsA,B,andCincreasedfrom13to26,10to25,and12to28re
-
spectively. Additionally, data show that after three intervention sessions
Peter appeared to reach a ceiling, with little or no additional improvement
in digits correct per minute. The maintenance checks completed on the last
session for Sets A and B showed that Peter’s enhanced fluency was main
-
tained over time (12 days for set A, 7 days for set B).
DISCUSSION
Previous researchers have shown that the taped-words intervention is
an effective procedure for enhancing word list reading fluency (e.g.,
140 SINGLE-SUBJECT DESIGNS FOR SCHOOL PSYCHOLOGISTS
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Freeman & McLaughlin, 1984; Shapiro & McCurdy, 1989). In the cur
-
rent study, we modified the taped-words procedures to target division
fact fluency and incorporated two forms of progressive time delay pro
-
cedures. Results showed rapid increases in digits correct per minute
across sets of problems following the application of the taped-problems
procedure. Additionally, data from Sets A and B suggest that enhanced
fluency was maintained. These data suggest that the taped-problems in
-
tervention was successful in increasing Peter’s division fact fluency.
While the data suggest that the taped-problems procedure was effec
-
tive, future research on this intervention is needed. Researchers should
assess the external validity of the taped-problem interventions by running
similar procedures across students (e.g., students with learning disabili
-
ties) and tasks (e.g., multiplication problems). Prior to the intervention,
Peter used a finger-counting procedure to reliably, but slowly, arrive at
McCallum, Skinner, and Hutchins 141
Percent Correct
100
95
90
85
80
75
70
65
60
Percent Correct
100
95
90
85
80
75
70
65
60
Percent Correct
95
100
90
85
80
75
70
65
60
Set A
Set B
Set C
1 2 3 4 5 6 7 8 9 10 11 12 13 14 150
1 2 3 4 5 6 7 8 9 10 11 12 13 14 150
1234567891011121314150
Session
FIGURE 1. Percent Correct of Problems Completed Across Conditions
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correct answers. Future researchers should assess the effects of the
taped-problems procedure with students who are currently responding in
-
accurately to problems and/or have not developed such strategies to solve
problems.
Although researchers were present throughout the intervention, the
taped-problems intervention is designed so that students need little if
any assistance implementing the intervention. Thus, future researchers
142 SINGLE-SUBJECT DESIGNS FOR SCHOOL PSYCHOLOGISTS
Digits Correct/Minute
0123456789101112131415
Set A
Set B
Set C
Digits Correct/Minute
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Digits Correct/Minute
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
34
30
26
18
14
10
6
2
22
34
30
26
18
14
10
6
2
22
34
30
26
18
14
10
6
2
22
Session
FIGURE 2. Digits Correct per Minute Across Conditions
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should also conduct studies under conditions that may be more reflec
-
tive of typical educational environments. For example, future research
-
ers should determine if the taped-problems intervention would be
effective when used with an entire class or in learning centers where stu
-
dents work independently.
During the current study, we employed a progressive time delay pro
-
cedure, starting with a brief delay, increasing the delay, and then de
-
creasing the delay. The initial brief interval (i.e., 1-second) between the
problem and answer being delivered prevented Peter from using his
count-by procedure to arrive at correct answers. The increase in delay
was designed to allow Peter to respond independently and use the tape
for feedback. Subsequent decreases were used to encourage rapid re
-
sponding. Future researchers should alter the time delay procedures to
determine which procedures are most effective and to determine if spe
-
cific procedures are more effective depending upon students’ level of
skill development.
In the current study, Peter reported that he did not like the 5-second
delay condition. Thus, we altered the tapes by eliminating this long de-
lay series for Sets B and C. This suggests that future researchers should
assess student acceptability with different time delay procedures (Turco &
Elliott, 1986). Because students may be less likely to implement an in-
tervention that they find unacceptable (Skinner & Smith, 1992), these
acceptability studies may prove critical for developing taped-problems
procedures that are self-managed in learning centers or similar situa-
tions (e.g., class-wide). Additionally, more advanced technologies
(e.g., computers and software) may be used to alter time delays on an
item-by-item basis as student responding improves.
Researchers have found that rate of word presentation during the
taped-words intervention may impact learning. Specifically, in some in
-
stances the longer the delay between word presentations, the greater
number of words learned. However, because this procedure lengthened
the time required to complete the intervention, actual learning rates
were depressed when the intervals between words were increased
(Skinner, Belfiore, & Watson, 1995/2002). In the current study, when
the 5-second delay series was eliminated on tapes for Sets B and C, the
number of opportunities to respond decreased by 20%. However, the
data suggest that this reduction had little impact on increases in fluency
(i.e., had little impact on learning levels). Additionally, the time re
-
quired to run the intervention was decreased by over 30% (a decrease of
over 3 minutes). Thus, learning rates were higher for sets B and C when
the long series was eliminated. Future researchers should conduct stud
-
McCallum, Skinner, and Hutchins 143
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ies where both the time delay and the number of opportunities to re
-
spond are manipulated to determine procedures that result in the
greatest increase in learning rates.
In the current study, Peter wrote his responses. Thus, new interven
-
tion packets with problems were required for each session. Future re
-
searchers should determine if altering the taped-problems response to a
verbal or sub-vocal response would be equally, or more effective (Skinner,
Bamberg, Smith, & Powell, 1993; Skinner, Belfiore, Mace, Williams, &
Johns, 1997), as such procedures would take less time and reduce the
need to prepare multiple packets that allow students to provide written
response.
In the current study, assessment procedures were run to provide Peter
an opportunity to independently practice items following the taped-
problems intervention. Researchers should conduct component analysis
studies to determine the degree to which these procedures enhanced the
effectiveness of the intervention.
CONCLUSION
School psychologists have been charged with preventing and reme-
dying student problems through the application of empirically validated
interventions (Kratochwill & Stoiber, 2002; Stoiber & Kratochwill,
2000). The current study showed that the taped-problems intervention
was an effective procedure for enhancing division fact fluency. School
psychologists should continue to contribute to the development of more
effective interventions by conducting future research on the taped-prob
-
lems intervention designed to assess the external validity of this inter
-
vention and enhance the effectiveness and efficiency of the taped-
problems procedure.
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The aim of this study is to determine the effect of Cover-Copy-Compare (CCC) interventions to increase the level of fluency in basic multiplication facts of a student having low performance in math, whether the student can maintain the level of fluency that she attained after a period of time and the social significance of the obtained data. A multiple-probes-across tasks (sets) design was employed in this study. The participant is a 9-year-old female student who is attending the second grade in general education (in the last two months of the second semester). Besides, she receives four hours of individual special education per week in a research center providing special education services for students with developmental disabilities at a state university. The findings of the study indicate that the education done with the CCC technique is effective in increasing the level of fluency of the student in basic multiplication operations in all sets, and she maintains the fluency performance after a certain period of time. The subjective evaluation findings of the study on social validity suggest that the student and the implementer who participated in the study had positive opinions about the effects and the obtained results of the CCC technique on the student. In addition, the social comparison findings of the study regarding social validity show that the student's level of fluency in multiplication facts reached the level of her peers. These findings were discussed together with the findings of other studies. Bu araştırmanın amacı, Keşfet-Kopyala-Karşılaştır (KKK) ile yapılan öğretim uygulamalarının matematik başarısı düşük bir öğrencinin temel çarpma işlemlerinde akıcılık düzeyini artırmaya olan etkisini, öğrencinin ulaşmış olduğu akıcılık düzeyini aradan belli bir süre geçtikten sonra da sürdürüp sürdürmediğini ve elde edilen sonuçların sosyal açıdan önemini belirlemektir. Araştırmada tek denekli desenlerden beceriler (setler) arası çoklu yoklama modeli kullanılmıştır. Katılımcı, 9 yaşında, genel eğitimde ikinci sınıfa devam eden (ikinci dönemin son iki ayında) bir kız öğrencidir. Aynı zamanda bir devlet üniversitesinde gelişimsel yetersizliği olan öğrenciler için özel eğitim hizmeti veren bir araştırma merkezinde haftada dört saat bireysel özel eğitim hizmeti almaktadır. Araştırma bulguları, KKK tekniği ile yapılan öğretimlerin tüm setlerde öğrencinin temel çarpma işlemlerindeki akıcılık düzeyini artırmada etkili olduğunu, öğrencinin ulaşmış olduğu akıcılık performansını aradan belli bir süre geçtikten sonra da sürdürdüğünü göstermektedir. Araştırmanın sosyal geçerliğe yönelik öznel değerlendirme bulguları, araştırmaya katılan öğrenci ve uygulamacının KKK tekniği ve elde edilen sonuçların öğrenci üzerindeki etkilerine yönelik olumlu
... Researchers have investigated procedures designed to enhance S-R-S learning trials by increasing learning trial rates (e.g., using briefer response intervals) and/or rates of accurate responding (Skinner, Fletcher, & Henington, 1996). These procedures include altering fixed response intervals (e.g., McCallum, Skinner, & Hutchins, 2004;Yaw et al., 2014), allowing the learner to self-determine response intervals (e.g., Cazzell, Skinner, et al., 2017;Cazzell, Taylor, et al., 2017), and providing additional opportunities for the learner to respond after each learning trial (e.g., Belfiore et al., 1995;Ferkis, Belfiore, & Skinner, 1997). Some findings from researchers investigating perceptual fluency suggest merely altering the manner in which stimulus words are presented could enhance learning (e.g., Sungkhasettee, Friedman, & Castel, 2011). ...
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