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Math Peer Tutoring for Students with Specific Learning Disabilities

Math Peer Tutoring for Students with Specific Learning Disabilities
April D. Miller
The University of Southern Mississippi
Patricia M. Barbetta
Florida International University
Gregg E. Drevno
Talbot County Public Schools
Stacy A. Martz and Timothy E. Heron
The Ohio State University
Students with specific learning disabilities (LD) often have problems with mathematics
that begin in elementary school and continue throughout their secondary years. For these
students, growth in mathematics knowledge is estimated to be approximately one year for
every two years of schooling (Cawley & Miller, 1989). Although hard data on the
percentage of students with mathematics LD are unavailable (Bender, 1992), several
researchers have reported that these students often lack even basic skill proficiency
(Fleischner, Garnett, & Shepherd, 1982; Garnett & Fleischner, 1983; Thornton &
Toohey, 1985). Specifically, McLeod and Armstrong (1982) suggested that high-school
level students with LD perform mathematics operations at only the third- or fourth-grade
level. Even after graduation from high school, challenges related to math continue to
surface in the work place for these individuals (Scheid, 1990).
While some educators have suggested that an overhaul of the entire mathematics
curriculum might be needed to improve skills (Smith, 1989), peer tutoring offers a less
intrusive solution. A well-designed peer tutoring program provides directed repetition,
regular review, and functional practice to overlearn skills, operations, and concepts
(Lerner, 1993). Each of these areas is important to the development of fluent math skills.
Using Students as Math Tutors
Tutoring has been demonstrated to be effective with students of varying skill levels
(Heron, Heward, Cooke, & Hill, 1983) and, of interest in this context, to produce specific
improvement in mathematics (Barbetta & Heron, 1991; Franca, Kerr, Reitz, & Lambert,
1990; Greenfield & McNeil, 1987; Maher, 1984; Pigott, Fantuzzo, & Clement, 1986;
Thurston & Dasta, 1990; Vacc & Cannon, 1991). Table 1 shows other reasons for using
students as peer tutors.
Formats for Tutoring
Commonly used tutoring formats include peer (classwide), cross-age, 1:1, small group,
and home-based tutoring (Miller, Barbetta, & Heron, 1994). Each of these formats is
discussed briefly below.
Classwide peer tutoring. Classwide peer tutoring systems (CWPT) involve all
students working in tutor-tutee pairs simultaneously (Carta, Greenwood, Dinwiddie,
Kohler, & Delquadri, cited in Greenwood, 1991). As such, CWPT has been used to
improve basic skill performance of low-achieving minority, disadvantaged, or students
with LD within the general education classroom setting (Delquadri, Greenwood,
Whorton, Carta, & Hall, 1986), and to increase the number of opportunities each student
has to respond actively to academic materials (Greenwood, 1991).
Cross-aged tutoring. Cross-age tutoring is an effective method to provide
individualized instruction (Schradj & Valus, 1990). In cross-age tutoring arrangements,
the tutor is approximately two or more years older than the tutee and usually from the
same school. In some cases, however, junior-high or high-school students from nearby
campuses have served as tutors of elementary students (Barbetta, Miller, Peters, Heron, &
Cochran, 1991).
One-to-one tutoring. Only select student dyads participate in this format. Usually
students with LD needing remedial assistance work with just one other student, who
serves as the tutor.
Small group instruction. Two procedural variations are possible within a small-
group configuration. First, small-group tutoring may be used for students with LD who
need additional (or remedial) practice with skills. Thus, part of their independent seat
work time might be devoted to tutoring. In the second variation, the whole class
participates, but on a rotating basis. While the teacher works with one instructional group,
a second group is engaged in peer tutoring, while the rest of the class participates in
independent seat work or other cooperative groups. Groups rotate daily (or weekly) to
allow each group to engage in all activities.
Home-based tutoring. In home-based formats, parents (or siblings) serve as
tutors. Although home-based tutoring programs have not been widely studied,
preliminary data show that parents can serve as effective tutors for their children
(Barbetta & Heron, 1991; Elksnin & Elksnin, 1991).
General Training Procedures
Tutors who have received specific tutor training have been found to emit more
appropriate tutoring behaviors than untrained tutors (Greenwood, Carta, & Hall, 1988;
Heward, Heron, Ellis, & Cooke, 1986). However, the procedures used to train tutors vary
(Barbetta et al., 1991; Folio & Norman, 1981; Krouse, Gerber, & Kauffman, 1981).
Generally, training is based on a task analysis of the tutoring role, with the steps trained
sequentially. The extent and type of training relates directly to the goals and complexity
of the tutoring task, and to the skill of the tutor.
In many tutoring programs, a model, lead, and test sequence is used (Barbetta &
Heron, 1991; Barbetta et al., 1991; Cooke, Heron, & Heward, 1983; Heron et al., 1983;
Maheady & Sainato, 1985; Polirstok & Greer, 1986). This sequence ensures that partners
practice all elements of the program, including the critical element of error correction
(Barbetta et al., 1991; Koury & Browder, 1986; Maheady & Harper, 1987). Further, it
provides the teacher with a method for evaluating tutoring. Scripted lessons have also
been used with this model to keep training consistent across groups and to cue trainer
behaviors (e.g., Barbetta et al., 1991; Heron et al., 1983).
Once a tutoring program is implemented, it is important to monitor and evaluate
the performance of both the tutor and tutee (Krouse et al., 1981). Daily and weekly
progress data can be incorporated for this purpose (Heron et al., 1983). Performance
probes can measure tutoring outcomes across time, while generalization measures assess
effects across settings or responses (Stokes & Baer, 1977). Charts and graphs are efficient
ways to gather and display data. In the following section, we take a closer look at
implementing a math peer tutoring program.
Procedures for Implementing Math Peer Tutoring
Successful implementation of a math peer tutoring program involves three major steps:
Getting ready, running the program, and enrichment and extension activities.
Step 1: Getting Ready
The first step, Getting Ready to Tutor, includes identifying the tutoring format to be used,
selecting the tutoring pairs, training the partners, and arranging the environment.
Tutoring format. In determining which tutoring format to implement, teachers
should take into account characteristics of students, resources available, and purpose(s) of
tutoring. For example, if teachers wish to increase the level of active student responding,
they may select classwide peer tutoring. Likewise, if they wish to increase opportunities
for students to interact with students in other classrooms, they may choose a cross-age
Selecting partners. Student dyads can be paired by the teacher, either on a
random basis (Kohler & Greenwood, 1990), by skill levels, or with special considerations
for students with behavior or achievement problems (Cooke et al., 1983). Within tutoring
pairs, students take turns administering instruction, each spending 5 to 10 minutes as the
Training tutors. In addition to the general training procedures described earlier,
within this tutoring model, students must also be trained to use the tutoring folder. Thus,
tutor-tutee pairs are taught to recognize the function of the “Go,” “Stop,” and “Star Card”
pockets on the right side of the folder, and the tracking chart on the left side (see Figure
1). Further, they are taught how to use the X and O elements on the reverse side of the
folder (see Figures 2 and 3). Folders are easily produced using a file folder, three library
pockets, graph paper, and markers.
Arranging the environment. Arranging the environment requires attending to
tutor scheduling, expectations, and the teacher’s role. Tutoring can be implemented as
little as once a week or as often as every day. However, a minimum of two to three days a
week is recommended so that tutors and tutees can use trained behaviors readily.
Tutoring typically lasts 30 minutes, with 20-minutes reserved for tutoring and 10 minutes
for tests, reviews, and transition.
With respect to expectations, the teacher should provide clear and concise
directions to students regarding their level of participation (“Do your best.” “Help your
partner.”). Similarly, if math peer tutoring occurs outside the classroom (e.g., in the
home), the teacher may wish to communicate these expectations to parents in writing.
The teacher’s role in tutoring is that of program developer, organizer, and monitor. In
each of these roles, the teacher develops the actual content to be learned, arranges content
sequentially as student performance dictates, and provides feedback and reinforcement to
students regarding implementation of tutoring procedures and actual achievement.
Step 2: Running the Program
The second step in effective implementation of tutoring programs contains a sequence
that can be used to implement, maintain, and evaluate peer tutoring across any of the
formats described earlier.
Pretest. First, present a list of math facts (or concepts) to students, and ask them
to solve them. Provide time for each response. The first 10 items that the student misses
are used to develop his or her first set of flashcards. Second, conduct the pretest with a
typical assessment protocol, that is, do not provide the student with any assistance in
forming the correct response. After tutoring has been implemented and the student has
mastered 10 flashcards, repeat the pretest procedure to obtain another list of 10 unknown
items (e.g., facts, concepts).
Practice. Direct the tutor to take the math flashcards from the “Go” pocket and
show them to his or her partner one at a time. Tutees should write (or say) the correct
response. If the tutee responds correctly, tutors say “Good” and present the next card
quickly. If the tutee makes an incorrect response or does not respond at all, tutors should
first say, “Try again.” If after this prompt the tutee is still unable to produce the correct
response, the tutor provides the correct answer. The tutee repeats the correct response.
(This 2-part prompting procedure (i.e., Try again/Write or Say response has been an
essential ingredient in previous tutoring programs). The tutor continues to present
practice cards, reshuffling them until the time expires. After 2 to 5 minutes of practice
and after testing, partners switch roles.
Test. Students turn their folders over to expose an O and an X (see Figure 2). The
tutor shows each card once, holding it up for 2 to 3 seconds. If the tutee writes (or says)
the response correctly, the card is placed on the O. If the tutee does not respond correctly,
or makes no response, the card is placed on the X. No corrective feedback is provided.
After all cards are presented, the back of each card is marked depending which pile the
card was placed. Any card with three consecutive O’s moves to the “Stop” pocket. Cards
without three consecutive O’s return to the “Go” pocket and they are practiced the next
session. Once all cards are in the “Stop” pocket, they are removed from the folder and a
new set of 10 cards is placed in the “Go” pocket. No new cards are added to the set until
the tutee has mastered 10 flashcards in a set (i.e., all cards in a set have been moved to the
“Stop” pocket).
Tracking Graph and Star Card. The tracking graph shows a record of the total
number of cards mastered, and provides visual feedback and reinforcement to students
(see Figure 1, left panel). Students mark the number of blocks corresponding to the
number of cards that moved to the “Stop” pocket that day. By alternating colors daily,
progress can be monitored. If no cards move on a given day, students draw a line between
the connected boxes.
Maintenance Probes. Each time a set of cards moves to the “Stop” pocket, they
are placed in an envelope and dated seven days ahead. On the date indicated, a review
test is administered in addition to the daily test. If a maintenance card is identified
correctly, it exits the system. If a maintenance card is identified incorrectly, however, it is
placed with the next set of flashcards to be inserted in the “Go” pocket (9 new cards plus
1 card from the failed maintenance probe). In short, a card exits the system only if it is
identified correctly three consecutive times during daily testing and once during
maintenance testing. Maintenance is essential to ensure retention of skills learned
Step 3: Enrichment and Extension.
Supplemental practice provides enrichment and extension activities related to tutoring
content. For example, if the students practiced math facts, they might use word or
application problems during generalization exercises. Formulae, time, money, fractions,
measurement, conversions, estimation, and many other skills can be included within an
extension program. Teachers are reminded to watch for opportunities where a fact,
application, or concept can be included or extended. This procedure serves as a good
review and facilitates generalization to new situations.
Program adaptations can enrich or extend skills by varying the type of cards
available in the “Go” pocket, or the type of responses expected from students. Figure 4
shows a sample of adaptations that may be used across math applications and grade
levels. Individualization can be further adapted by creating different card sets based on
student ability, adjusting the pace of tutoring, or varying the number of cards per set.
Teachers must recognize that peer tutoring is not an “add on” program. Instead, it is an
instructional methodology that is consistent with most teacher goals. It provides the
opportunity for students with LD to become active learners and offers a functional way
for students to learn mathematics skills. Teachers can manage a tutoring program in the
same way that they manage other small-group activities in their classrooms. In fact, given
the structured nature of tutoring programs, student management concerns are reduced.
Special materials preparation can be minimized by having students prepare
stimulus cards, or by enlisting the aid of parent volunteers. Students only need enough
materials to initiate the program. Replacements can be generated during implementation.
Some teachers might be opposed to tutoring on philosophical grounds, believing
that all instruction should be delivered directly by them. Although, teachers should be
skeptical, a healthy skepticism should not be confused with bias. Given the
overwhelming data demonstrating the effectiveness of tutoring programs for all students,
especially those with LD, even the most hesitant practitioner should concede its efficacy
and provide implementation opportunities consistent with student needs.
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Table 1. Reasons to Use Students as Tutors
Peers can “shape” the behaviors of others (students, teachers, and parents) (Gerber &
Kauffman, 1981; Greenwood, 1981).
Peers have been shown to be effective teachers (Cooke, Heron, & Heward, 1983; Gerber &
Kauffman, 1981).
Peer interventions can increase the chances for success of students with LD in mainstream
activities (Heron, Heward, Cooke, & Hill, 1983; Madden & Slavin, 1983).
Peer tutoring programs can avoid stimulus control problems that may arise when one or
only a few individuals administer contingencies (Cooper, Heron, & Heward, 1987).
When peers are used as behavior change agents, the desired student behavior may be
performed across a wider variety of settings and situations (Anderson-Inman, Walker, &
Purcell, 1984; Goldstein & Wickstrom, 1986).
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... Additionally, Heron et al. (2003), in a second literature review, found that the development of systematic approaches to tutoring can be traced to field-based studies which show the beneficial effects of tutoring on traditional academic subject areas such as math (Allsopp, 1997;Arreaga-Mayer, 1998;Harper, Mallette, Maheady, Bentley, & Moore, 1995;Miller, Barbetta, Drevno, Martz, & Heron, 1996), and reading (Barbetta, Miller, Peters, Heron, & Cochran, 1991;Cooke, Heron, & Heward, 1983). Finally, Vandell and Pierce from University of Wisconsin found many benefits from participation in high quality after school programs for elementary students. ...
Based on the social cognitive learning theory (1997), peer learning can be viewed as an effective way of enhancing learning. In this study, peer tutoring, a form of peer learning, was examined. The current study investigated the influence of a peer tutoring program implemented at Sultan Qaboos University on students’ English self-concept. 125 Omani university students participated in the study. The Students English Self-Concept Scale (SESCS) and the Tutorial Programs Factors Scale (TPFS) were utilized to collect the data. The findings demonstrated that peer tutoring has a positive influence on English self-concept. Three tutorial program factors were found to positively predict English self-concept. Implications for EFL teachers, and recommendations for future research were discussed.
The purpose of this article is to discuss peer tutoring strategies as an effective class of peer-mediated procedures for both classroom behavior management and direct instruction. In this article, we discuss the need for alternative classroom procedures, review relevant research, discuss recent advances in procedures, and identify implications.
In the early years of the nineteenth century, before public education existed, Joseph Lancaster founded a school for working-class children in London (Kaestle, 1973; Lancaster, 1803). Lancaster’s belief that basic education would discipline and morally shape working-class children, together with his dislike for corporal punishment, attracted some financial supporters and hundreds of children. Faced with severe economic constraints, Lancaster devised a system of peer-mediated instruction which had immediate and dramatic international impact upon educational practice (Charconnet, 1975; Kaestle, 1975; Reigert, 1916/1969).
The ethical and philosophical implications of behavioral technology applied to human affairs has been a controversial topic from its earliest formulation as a deterministic psychology (Watson, 1963, pp. 164-165), and recently as a result of Skinner’s writings (1948, 1966a, 1966b, 1971). Adding to this over the last 10 years, undercurrents in American society have created the impetus for methods guaranteeing against misuse of behavioral control. Perhaps the foremost contributing factor has been the proliferation of behaviorally based programs and methodology to nearly every facet of society (Goodall, 1972). For example, behaviorally trained psychologists are using the techniques in schools, homes, businesses, prisons, mental-health settings, vocational settings, rehabilitation settings, medical settings, and so on, touching the lives of literally thousands of individuals. This proliferation undoubtedly is related to the effectiveness of the technology for solving relevant social and behavioral problems. Thus, it seems that legal, legislative, and professional-group policies to control and monitor the quality of behavioral treatments are increasingly being forced upon practitioners as society reexamines the nature of its institutions.
The relationship between automatization ability, as measured by the Rapid Automatic Naming Test (RAN), and proficiency in arithmetic basic fact computation was investigated. Subjects included 120 learning disabled and 120 nondisabled children between 8 and 13 years of age; 60 subjects in each group were designated as either younger or older. Significant correlations were obtained between RAN performance and basic fact proficiency for both the learning disabled and nondisabled groups. In addition, learning disabled subjects were found to be less proficient in basic fact computation and slower on RAN than their nondisabled peers at both younger and older age levels. Correlations were substantial enough to further inquire whether LD youngsters' lack of proficient basic fact skills may be due, in part at least, to weak automatization. The construct of automatization, or automaticity, has applicability to academic skills beyond those previously investigated.
A total of 114 junior-high, middle-grade, and high-school LD teachers responded to a survey concerning various aspects of mathematics disabilities in students presently on their caseload. The most common deficit areas reported included division of whole numbers, basic operations involving fractions, decimals, percent, fraction terminology, multiplication of whole numbers, place value, measurement skills, and language of mathematics. The remediation approach most often utilized consisted of teacher adaptation of mainstream texts, followed by commercial and teacher-made materials. Respondents indicated the need for a commercial mathematics program based on the mainstream mathematics curriculum with an emphasis on systematic, extended practice for students with learning disabilities in mathematics. The results hold implications for teachers working with secondary students with learning disabilities in mathematics.
This study investigated the effects of providing training and practice in helping behaviors to students during peer tutoring in mathematics. Participants were 20 general educators from grades two through four, whose entire classes participated in peer tutoring for 29 weeks. From each class, teachers identified one average-achieving student and one student with a learning disability to participate as a dyad in this videotape study. The 20 classrooms were assigned randomly to two treatments: peer-tutoring experience with additional training in how to help and peer-tutoring experience without training in how to help. Following training in how to help in 10 of the 20 classrooms, each dyad, one from each classroom, was videotaped completing a mathematics peer-tutoring task. Microlevel quantifications and more global descriptions of transcripts of representative pairs in each condition indicated that students who received the helping training engaged in an increased number of directly trained helping behaviors than the untrained students. The nature of students' explanations is also described.
This paper reviews research on the effects of placing students with mild academic handicaps in full-time special education classes, part-time regular classes with resource support, and full-time regular classes. It also reviews research on the effects of programs designed to improve the achievement, social-emotional adjustment, and social acceptance of academically handicapped students by their nonhandicapped classmates. Methodologically adequate studies of placements of academically handicapped students indicate few consistent benefits of full-time special education on any important outcomes. The research favors placement in regular classes using individualized instruction or supplemented by well-designed resource programs for the achievement, self-esteem, behavior, and emotional adjustment of academically handicapped students. Experimental research indicates that cooperative learning and individualized instruction programs can improve the self-perceptions and behavior of mainstreamed academically handicapped students and acceptance by their nonhandicapped classmates.
Traditionally, discrimination has been understood as an active process, and a technology of its procedures has been developed and practiced extensively. Generalization, by contrast, has been considered the natural result of failing to practice a discrimination technology adequately, and thus has remained a passive concept almost devoid of a technology. But, generalization is equally deserving of an active conceptualization and technology. This review summarizes the structure of the generalization literature and its implicit embryonic technology, categorizing studies designed to assess or program generalization according to nine general headings: Train and Hope; Sequential Modification; Introduce to Natural Maintaining Contingencies; Train Sufficient Exemplars; Train Loosely; Use Indiscriminable Contingencies; Program Common Stimuli; Mediate Generalization; and Train “To Generalize”.