Table Of ContentJOURNALOFAPPLIEDBEHAVIORANALYSIS 2007, 40, 223–237 NUMBER2 (SUMMER2007)
TEACHING MATH SKILLS TO AT-RISK STUDENTS USING
HOME-BASED PEER TUTORING
KRISTIN H. MAYFIELD AND TIMOTHY R. VOLLMER
UNIVERSITYOFFLORIDA
Home-basedpeertutoringwasusedtoteachmathskillsto4girlswithdeficitsinmathematics
andhistoriesofabuseorneglect.Girlslivinginthesamehomeformedtutoringdyads,andeach
participant served as both the peer tutor and the tutee during the course of the study. At the
initiationofthetutoringintervention,anexperttutorprovidedmultiple3-mintutoringsessions
to the designated peer tutor on three or four mathematics skills. The peer tutor concurrently
provided3-mintutoringsessionsonthesameskillstothetuteeusingamultiplebaselinedesign.
Results showed that participants improved their performance on all target skills. Additional
interventionswereimplementedforsomeskillstoimproveaccuracyfurther.Maintenancetests
were also administered after 3 to 5 months of no practice on the skills. Results showed that
tutorsandtutees maintainedtheir accuracy on7 ofthe 12skills assessed.
DESCRIPTORS: maltreated youth, mathematics,peer tutoring
_______________________________________________________________________________
Peer tutoring is an intervention in which one successfully implemented with tutors of various
student provides instruction or academic assis- ability levels, including children with advanced
tance to another student. Research on peer skills and children with learning disabilities
tutoring has demonstrated educational benefits (Fuchs, Fuchs, Yazdin, & Powell, 2002;
for tutors and tutees of various ages and Johnson & Bailey, 1974; Mathes & Fuchs,
abilities, ranging from kindergarten to second- 1994; Telecsan, Slaton, & Stevens, 1999).
ary school, and children with autism to average Taken together, this body of research has
achievers (e.g., Calhoun & Fuchs, 2003; demonstrated a robust effect of peer tutoring
Dineen, Clark, & Risley, 1977; Fuchs, Fuchs, acrossdiverseeducationalsettingsandgroupsof
& Karns, 2001; Kamps, Barbetta, Leonard, & students.
Delquadri,1994;Sideridisetal.,1997).Studies Given the variety of effective peer-tutoring
have shown that peer tutoring can improve interventions, it is likely that key procedural
performance in a variety of subjects including components are responsible for the outcomes.
spelling, mathematics, high school driver edu- One way of identifying key components is to
cation, and functional community skills (e.g., analyze the common features of well-documen-
Bell, Young, Salzberg, & West, 1991; Blew, tedpeer-tutoringmethods.Threesuchmethods
Schwartz, & Luce, 1985; Fueyo & Bushell, are reciprocal peer tutoring (Fantuzzo &
1998;Kohler&Greenwood,1990),andcanbe Ginsburg-Block, 1998; Fantuzzo, King, &
Heller, 1992; Pigott, Fantuzzo, & Clement,
Thisresearchwasfundedinpartbyacontractwiththe 1986), classwide peer tutoring (Arreaga-Mayer,
Florida Department of Children and Families. The
Terry, & Greenwood, 1998; DuPaul, Ervin,
content and opinions expressed herein do not necessarily
reflect the position or policy of the Department of Hook, & McGoey, 1998; Kamps et al., 1994),
Children and Families. We thank Daniel Hackman, andpeer-assistedlearningstrategies(Calhoun&
Anthony Nguyen, Mara Torres, Mara Baker, Linda
Fuchs, 2003; Fuchs & Fuchs, 1995; Fuchs et
Meckler, Taryn Manders, Courtney Ayers, and Cassie
al., 2001, 2002). These successful peer-tutoring
Coble for their assistance. Kristin Mayfield is now at
iLearn,Inc. interventions have been carried out in school
Correspondence concerning this article should be settingsandhavetypicallyprovidedsupplemen-
addressed to Kristin Mayfield, 2715 NW 52nd Ave.,
tal practice for fundamental skills such as
Gainesville,Florida32605(e-mail: [email protected]).
doi:10.1901/jaba.2007.108-05 reading, spelling, or mathematics, but generally
223
224 KRISTIN H. MAYFIELD and TIMOTHY R. VOLLMER
have not been used to replace teacher-directed METHOD
instruction in its entirety during the acquisition
Participants and Setting
of new skills (e.g., Calhoun & Fuchs; Dufrene,
Four childrenhadbeenreferred bycaregivers
Noell, Gilbertson, & Duhon, 2005; Kamps et
who were enrolled in a class that taught
al.). In addition, these interventions often
evidence-based parenting practices. The partic-
involve extensive training (e.g., 4 to 8 hr) prior
ipantswere selectedbecause theywereof school
to implementation, the use of structured
age, had a history of maltreatment, lived with
formats and predesigned materials to guide
another previously maltreated child in an out-
instruction, and precise methods of delivering
of-home placement, and were available for
feedback (Arreaga-Mayer et al.; Calhoun &
experimentalsessions.Twoofthechildrenwere
Fuchs; Dufrene et al.; Fantuzzo et al.; Fuchs &
residing with a relative, and 2 of the children
Fuchs; Fuchs et al., 2001; Sa´enz, Fuchs, &
were residing in a group home. Amelia was a
Fuchs, 2005).
9-year-old girl who was enrolled in general
Although these features of peer-tutoring
education classes in a public elementary school.
programs may be important, peer tutoring
Keesa was a 13-year-old girl who was enrolled
may occur in situations that do not permit
in special education classes in a public middle
a similar amount of structure or training (e.g.,
school. Jada was a 15-year-old girl who was
children helping one another with homework
enrolled in an alternative school during part of
after school). Therefore, it is important to
the study and a public high school during the
determine if peer-tutoring interventions that
remainderofthestudy.Oliviawasa16-year-old
lack some of these structured characteristics can
girl who was enrolled in an alternative school
also produce educational benefits. The current
during part of the study and a general educa-
study was conducted to evaluate whether
tional development program during the re-
academic gains could result from a peer-tutor-
mainder of the study. All children were
ing intervention that did not include many of
concurrently enrolled in mathematics courses
thecommonstructuredcomponentsofeffective
during the portion of the study that coincided
classroom-based peer tutoring.
with the academic calendar year. In addition,
A secondary purpose of the current in-
Amelia and Keesa also participated in one or
vestigation was to implement peer tutoring
two other mathematics interventions that
with previously maltreated children, who rep-
targeted different mathematics skills than those
resent an at-risk population that has not been
required for the current study.
thefocusofacontrolledstudyonpeertutoring.
Pairs of tutors and tutees were formed by
In general, children with a history of abuse or matching the children who lived in the same
neglect demonstrate significantly lower grades home, and all children served as both a peer
in math and reading compared to children tutor and tutee during the course of the study.
without such histories (Eckenrode, Laird, & The tutoring pairs were as follows: Pair 1:
Doris,1993),androughly25%to40%(Burley AmeliaastutorandKeesaastutee;Pair2:Keesa
& Halpern, 2001; Stein, 1997) receive special as tutor and Amelia as tutee; Pair 3: Jada as
education services. Moreover, the negative tutor and Olivia as tutee; Pair 4: Olivia as tutor
effectsofmaltreatmentonchildren’seducation- and Jada as tutee.
al achievement persist even after they are Sessions were conducted in the children’s
removed from an abusive or neglectful environ- homes. The experimenter visited the homes up
ment (Colton, Heath, & Aldgate, 1995). Thus, to 5 days per week and typically conducted one
we attempted to apply the beneficial effects of to three experimental sessions per visit. The
peer tutoring to these students. lengthofthesessionsvariedfromapproximately
HOME-BASED PEER TUTORING 225
5 minto45 mindependingonthephaseofthe fying a problem. Solutions werenot requiredto
study. be written in simplest form (e.g., the fraction
equivalent of .4 could be written as 4=10
Materials instead of 2=5), except for the skill of reducing
Practice worksheets. Ten-item practice work- fractions (because simplification was the re-
sheets were constructed for each of the
sponse being trained). All parts of a solution
arithmetic and prealgebra skills trained in the
had to be solved accurately for the answer to be
study (e.g., multiplying decimal numbers,
scored as correct (e.g., both –15 and 19 had to
solving proportions, simplifying radical expres- be included in the answer to |2 – b| 5 17).
sions;descriptionsandexamplesofeachskillare
The experimenter (the first author) served as
available from the first author). Items on the
the expert tutor and primary observer through-
worksheets were arranged in two columns, with
outtheinvestigation.Asecondobserverregraded
five problems in each column. Different
all of the tests for 32% of sessions conducted
versions of the practice worksheets were created
during the tutoring intervention. If the experi-
bychangingthenumbersandlettersusedinthe
menter had marked any of the problems (e.g.,
problems and by varying specific features of the
with a small dot) while grading the tests during
problem within predetermined criteria (e.g.,
the experimental sessions, all of the items were
changing the placement of the decimal to one
marked to reduce or eliminate potential bias of
of three different locations for problems testing
thesecondobserver.Interobserveragreementwas
the multiplication of numbers with decimals).
calculated by dividing the number of test items
Nineteen to 66 different practice worksheets
scoredthesamebybothobservers(eithercorrect
were created for each skill based on the length
or incorrect) by the total number of test items
oftimerequiredforthetuteetomastertheskill,
and multiplying the quotient by 100%. The
and some worksheets were used more than
averageinterobserveragreementwas99%(range,
once.
90% to 100%) across participants. Reliability
Tests.Ten-itemtestswerealsoconstructedfor
data were also collected for the additional
eachofthe13mathematicsskills.Theformatof
interventions and maintenance phases using
the tests was identical to that of the practice
similar procedures. A second observer regraded
worksheets except for the heading on the paper
allofthetestsfor29%ofthesesessions,andthe
(specifying the test version instead of the
average interobserver agreement for accuracy of
practice version). Between 35 and 65 versions
test performance was 98% (range, 92% to
of each test were created for each skill in the
100%) during the additional interventions and
same manner as the practice worksheets accord-
maintenance phases.
ingtothelengthoftimetheparticipantsneeded
to master the skills, and some versions were
Procedure
used more than once.
Preexperimental skills assessment. Before the
Response Measurement and Reliability study began, the experimenter assessed each
The primary dependent measure was accura- participant’s mathematics skills by administer-
cy on the tests. The number of correct answers ing tests containing arithmetic and prealgebra
on each test was divided by 10 (possible correct problems. The experimenter told the partici-
answers) and multiplied by 100% to generate pant that she could earn one penny for each
a percentage correct. Correct answers were problem she answered correctly, and she could
defined as a written combination of numbers, skip problems if she did not know how to solve
letters, and symbols that represented a mathe- them. Following the pretests, the experimenter
matically accurate method of solving or simpli- selected three or four skills for each tutor–tutee
226 KRISTIN H. MAYFIELD and TIMOTHY R. VOLLMER
pair based on their performance on the skills To illustrate, during the initial 3-min session
assessment. for simplifying radical expressions, the experi-
Baseline. During baseline, each participant menter explained the meaning of radical signs
completed tests of the skills during each session and how to use the index of the radical sign to
but did not receive instruction on how to simplify the expression. The experimenter
performtheskills.Theparticipantwastoldthat modeled the simpplification of at least the first
ffiffiffiffiffiffiffiffiffi
she could earn one penny for each problem she problem (e.g., 4 c6d8 ~ ) by showing the
answeredcorrectly, aswellas abonuspennyfor participant how to divide the index into the
answering all of the problems on the test exponentsofthevariablesundertheradicalsign
correctly. She was also told that she could skip andwritethevariablesoutside(aswellasinside,
problems if she did not know how to solve when appropriate) the radical sign with new
them.Theexperimentertimedhowlongittook exponents. The experimenter prompted the
the participant to complete each test and then participant to provide parts of the solution
graded her answers. (e.g., asking how many times 4 divides evenly
The only feedback provided to participants into 6). The experimenter then assisted the
attheendofeverysessionwasthetotalnumber participant by delivering prompts (e.g., asking
of pennies earned during the session on all of what the remainder would be after the index is
the tests combined. The participants used their divided into an exponent) as the participant
earnings to purchase snacks and prizes (e.g., solved additional problems of the same variety
school supplies, a portable CD player, gift during the remainder of the 3 min. The
cards) from the experimenter. Participants were experimenter provided fewer prompts across
allowed to purchase items at any point during the session as the participant emitted more
the study. correct responses. The experimenter provided
Tutoring. Using a multiple baseline design, additional prompts and assistance to partici-
a tutoring intervention for each skill was pants (i.e., modeling and explanations of
introducedinasequentialfashionafteraccuracy solutions)ifparticipantsemittedmoreincorrect
on the skill stabilized during the baseline responses.
condition. The tutoring intervention consisted Throughout the tutor-training session, the
of two components: tutor training and peer experimenter praised the participant for correct
tutoring. responses and provided corrective feedback for
At the beginning of each tutor-training incorrect responses. When the 3-min session
session, the experimenter provided 3 min of ended, the peer tutor completed a 10-item test
tutoringontheskilltotheparticipantservingas of the tutored skill to assess skill acquisition
the peer tutor. The only materials used during resulting from the tutoring session. Tutor
these sessions were writing utensils, practice training was repeated for each of the target
worksheets (as described above), and a timer to skillsuntiltheyweremasteredbythetutor(i.e.,
measure the length of the tutoring session. The three nonconsecutive scores of 100% accuracy
session ceased when the timer beeped (after on the skill).
3 min) regardless of the interaction in progress. Aftereach3-mintrainingsessionand10-item
During the sessions, the experimenter provided test, peer tutoring was implemented. The peer
explanations of how to solve the problems, tutor provided instruction on the same skill to
modeled correct solutions, and faded instruc- the tutee. This typically occurred within
tional prompts while delivering corrective approximately 0.5 hr of the peer tutor finishing
feedback for the participant’s errors and praise the 10-item test(with tutortraining and testing
for correct responses. of other target skills often occurring during the
HOME-BASED PEER TUTORING 227
time lapse). The experimenter told the peer consecutive scores of 100% accuracy on the
tutor that she had 3 min to teach the tutee the skill), subsequent sessions involved only the
skill the experimenter had taught her, and she administration of the 10-item test on that skill.
would receive one penny for every problem the Terminationoftutortrainingandpeertutoring
tutee answered correctly on the test adminis- were independent events such that a tutor who
tered after the peer-tutoring session. The only scored 100% three times on a skill no longer
materials provided to the peer tutor and tutee received3-mintrainingsessionsonthatskillbut
were writing utensils, practice worksheets (as continued to deliver peer tutoring until the
described above), and a timer. The experiment- tutee metthemasterycriterionon theskill(i.e.,
er did not provide any instructions to the peer three nonconsecutive scores of 100%). In
tutor on how to teach the skills or any a similar manner, a peer tutor who had not
instructions to the tutee on how to perform metthemasterycriteriononaskillcontinuedto
the problems, nor did the experimenter provide receive tutor training sessions but ceased de-
the tutor with feedback on her tutoring or an livering peer tutoring if the tutee reached the
answer key to the practice worksheets used mastery criterion on that skill.
during the tutoring sessions. At the end of the The tutoring intervention was implemented
3-min session, the experimenter told the successively such that each girl served as either
participants that the time was up. The tutee the tutor or tutee and then switched (although
then completed a 10-item test of the skill to therewereasmanyasthreeoverlappingsessions
assess skill acquisition following the tutoring during which 1 participant continued to deliver
session.Thisprocedurewasrepeatedforeachof tutoring on the first set of skills while receiving
the target skills in the peer-tutoring phase until tutoring on the second set of skills). The order
they were mastered by the tutee (i.e., three of presentation of the skills varied across
nonconsecutive scores of 100% accuracy on the sessions, but each skill was tutored (if the
skill). mastery criterion had not been met) and then
General tutoring procedure. The instructions tested on separate worksheets during every
beforethetestsandthemonetaryreinforcement session.
contingencies were the same during the in- Additional interventions. After the tutoring
tervention phase (i.e., tutor training and peer procedure was completed, additional interven-
tutoring) as in baseline. In addition, no tions were implemented for skills that had not
feedback on test performance was delivered beenmasteredbythetutees.Thepurposeofthe
after any tests except for the total number of additional interventions was to provide supple-
pennies earned during the session (as in mental instruction that might lead to perfor-
baseline). Participants were allowed to purchase mance improvements for the tutees beyond the
items from the experimenter using their accuracy achieved through peer tutoring alone.
earnings as described above. Six of the 14 skills received additional inter-
Eight of the tutoring sessions (Sessions 9 to ventions (three skills for Keesa, one skill for
16)forthelongdivisionskill(learnedbyPair3) Amelia, and two skills for Jada). The additional
were10 mininlengthinsteadof3 minbecause intervention for Keesa involved an increase in
ofthecomplexityoftheskillandtheamountof magnitude of the reinforcer provided for
time needed to work through one problem. All scoring 100% on a test (from $0.11 used in
othertutoringsessionsforthelongdivisionskill the tutoring phase to $1.00) across all three
and all other skills, however, lasted 3 min and skills. For Amelia, improvements in calculating
wereimmediatelyfollowedbyatestof theskill. percentages initially occurred after the experi-
Following mastery of a skill (i.e., three non- menter provided brief instructions to the tutor
228 KRISTIN H. MAYFIELD and TIMOTHY R. VOLLMER
(i.e., Keesa) coupled with an unlimited amount mastery criterion are presented in the current
of time for the peer-tutoring sessions (averaging dataanalysisbecausetheprimarypurposeofthe
10 min instead of 3 min). She later met the current study was to determine the effects of
mastery criterion (i.e., three nonconsecutive peer tutoring in isolation.
scores of 100% accuracy) after the reinforcer Maintenance. On the final 2 days that the
magnitude was increased (from $0.11 to $1.00 experimenter provided academic services to the
for 100% accuracy on each test), and she was participants, the students completed tests of all
told she could stop practicing after scoring skills taught during their participation (in-
100% three times (i.e., goal setting). For Jada, cluding skills learned as both the tutor and
solving absolute value equations initially im- the tutee). Maintenance tests were given on 2
proved after introducing a modified error- consecutivedays,withnoperformancefeedback
correction procedure in conjunction with delivered between tests except for the partici-
practice of prerequisite skills and an increase pant’s total earnings during the session (as
in reinforcer magnitude. She later met the during other phases of the study). Maintenance
mastery criterion when goal setting was in- data were obtained on all skills except solving
troduced and the experimenter began imple- absolute value equations and changing percent-
menting the tutoring sessions for this skill. Jada ages to fractions because programmed interven-
also achieved mastery for calculating percent- tionswerestillinplacefortheseskillsonthelast
ages under conditions similar to those used for day of service provision for Pair 4. The
absolute value equations (i.e., modified error- maintenance interval for each skill ranged from
correction procedure, prerequisite skill practice, 3to5 months,dependingonthelengthoftime
increased reinforcer magnitude, goal setting, between the final intervention session for each
and experimenter-delivered tutoring). skill and the service termination date.
Because the goal of the additional interven-
tions was to examine potential supplements to RESULTS
thepeer-tutoringprocedure,theyweregenerally
Pair 1
not implemented for the tutors. Instead, if the
Figure 1 displays Pair 1’s accuracy on the
tutorhadnotmetthemasterycriteriononaskill
tests across sessions. During baseline, the tutor
by the end of the tutoring phase and additional
and tutee performed all four math skills with
interventions were implemented for the tutee
0% or 10% accuracy, except for solving
(i.e., for three of the skills for Pair 1 and one
proportions, which the tutee performed with
skill for Pair 2), the tutor continued to receive
0% to 60% accuracy. The introduction of the
tutortraining.Tutor3(Jada),however,received
tutoring intervention resulted in performance
oneadditionalinterventionforthelongdivision
increases on all skills for both participants,
skill because she demonstrated very low accu-
although only performance on the adding
racy during the tutoring phase, and no signednumbersskillreachedmastery(i.e.,three
additional interventions were implemented for nonconsecutive scores of 100% accuracy).
Tutee 3 (Olivia). The additional intervention Amelia (the tutor) and Keesa (the tutee)
involved corrective feedback on Jada’s previous achieved the masterycriterionon adding signed
test and an increase in reinforcer magnitude numbersaftersixandfoursessions,respectively,
(from $0.11 to $1.00 for a score of 100%). and then did not receive further tutoring. Even
With the exception of long division for Jada, without tutoring (after Session 9 for the tutor
whichconsisted ofeight additional intervention and Session 7 for the tutee), the participants
sessions, only the final five additional interven- maintained high accuracy on adding signed
tion sessions prior to the tutee achieving the numbers through the end of the phase.
HOME-BASED PEER TUTORING 229
Figure1. Pair1’saccuracyonthemathskillsacrossbaseline,tutoring, additionalinterventions, andmaintenance.
The five sessions prior to the tutee achieving the mastery criterion are displayed in the additional interventions phase.
Thefilled squares represent thetutor’s performance, andthe opencircles represent the tutee’s performance.
230 KRISTIN H. MAYFIELD and TIMOTHY R. VOLLMER
Following the conclusion of the tutoring subtracting time after 25 tutoring sessions,
phase, Keesa (the tutee) received additional and Keesa scored 100% on this skill after 10
interventions on the three unmastered skills tutoring sessions but did not reach mastery for
(i.e., multiplying decimal numbers, adding and this skill.
subtracting decimal numbers, and solving Because Amelia (the tutee) met the mastery
proportions). Data from the five additional criterion on three of the four skills during the
intervention sessions conducted prior to Keesa tutoringphase,onlyoneadditionalintervention
achieving the mastery criterion are shown in was conducted to improve her accuracy on
Figure 1 (data from all additional intervention calculatingpercentages.Ameliametthemastery
sessions are available from the first author). criteriononthisskillafterSession60,andKeesa
Keesa reached the mastery criterion on Sessions (the tutor) met the mastery criterion after
56, 70, and 69 for multiplying decimal Session 88, even though she did not receive
numbers, adding and subtracting decimal anadditionalinterventionforthisskill.Thefive
numbers, and solving proportions, respectively. data points collected in this phase prior to
Amelia (the tutor) met the mastery criterion on Amelia achieving the mastery criterion are
Sessions 34, 39, and 51 for the same skills, shown in Figure 2. Amelia’s mean score during
respectively, even though she did not receive these sessions was 76% accuracy, and Keesa’s
additional interventions for these skills. Mean mean score during these sessions was 70%
scores for the additional intervention sessions accuracy. Amelia subsequently demonstrated
shown in Figure 1 were 86%, 94%, and 90% lowaccuracyonallthemaintenancetestsexcept
forAmelia(thetutor)and74%,80%,and82% reducing fractions, whereas Keesa maintained
for Keesa (the tutee), for multiplying decimal comparable performance on at least one of the
numbers, adding and subtracting decimal two tests for all four skills.
numbers, and solving proportions, respectively.
Maintenanceperformancewasgenerallylowfor Pair 3
Amelia, but Keesa maintained a relatively high Figure 3 displays Pair 3’s accuracy on the
level of accuracy on three of the four skills after tests across sessions. Following low accuracy on
approximately 4.5 months of no programmed all skills during baseline, performance increased
practice. when the tutoring procedure was introduced
(though at least five tutoring sessions were
Pair 2 required before performance increased on the
Figure 2 displays Pair 2’s accuracy on the long division skill). The tutor (Jada) and tutee
tests across sessions. Neither the tutor (Keesa) (Olivia) met the mastery criterion for changing
nor the tutee (Amelia) scored above 0% correct percentages to decimals after four and three
on any of the skills during baseline, but both tutoring sessions, respectively, and maintained
improved on all skills after the introduction of accurate performance during the remainder of
the tutoring procedure. They met the mastery the tutoring phase without further tutoring. In
criterion for changing decimal numbers to addition, they both performed the skill with
fractions after four and five tutoring sessions, high accuracy on the maintenance tests admin-
respectively, and after six and 18 tutoring istered after 3.5 months of no practice sessions.
sessions for reducing fractions. Both partici- Olivia (the tutee) met the mastery criterion
pants maintained high levels of performance on for long division after 14 tutoring sessions and
theseskillsduringtheremainderofthetutoring maintained high accuracy during most of the
phase, even though tutoring sessions ceased remaining sessions of the tutoring phase
aftertheymetthemasterycriterion.Ameliaalso without further tutoring. The tutor (Jada),
met the mastery criterion for adding and however, received an additional intervention
HOME-BASED PEER TUTORING 231
Figure2. Pair2’saccuracyonthemathskillsacrossbaseline,tutoring, additionalinterventions, andmaintenance.
The five sessions prior to the tutee achieving the mastery criterion are displayed in the additional interventions phase.
Thefilled squares represent thetutor’s performance, andthe opencircles represent the tutee’s performance.
232 KRISTIN H. MAYFIELD and TIMOTHY R. VOLLMER
Figure3. Pair3’saccuracyonthemathskillsacrossbaseline, tutoring,additionalinterventions, andmaintenance.
Thefilled squares represent thetutor’s performance, andthe open circlesrepresent the tutee’s performance.
on long division because she did not score phase. Jada scored 100% on calculating per-
100%duringthetutoringphase.Afterreceiving centages during Sessions 18 and 21 but did not
eight additional intervention sessions, however, meet the mastery criterion for this skill. Olivia
Jada achieved a score of 100%. Neither she nor scored 0% on the first maintenance test, but
Olivia scored above 0% on the long division both participants demonstrated high accuracy
maintenance tests. on the second maintenance test.
Olivia met the mastery criterion on calculat-
ing percentages after four tutoring sessions and Pair 4
maintained accurate performance with no Figure 4 displays Pair 4’s accuracy on the
further tutoring during the remainder of the tests across sessions. Both participants scored
