Katie, a seventh grader with an identified learning disability, was extremely social. Her friends were her life, and school gave her access to her friends. Friendships were important to her; she was good with people. At the start of the year, Katie wasn't interested in math-she rarely participated. Her stock response to her math teacher was, "Who cares?" As the year progressed, math increasingly engaged her attention and interest. Katie explained, "I like PALS because you can help people understand and if I'm confused about something, or I didn't know what I was doing wrong, my pal would help me." Later in the year, she even prepared a PowerPoint presentation on peer-assisted learning strategies to assist her teachers in a regional middle school educator conference.
Early in the school year, two middle school teachers asked themselves, if one student's attitude about mathematics could be changed, which would it be? They reasoned that the greatest barrier to learning was a student's claim that he or she, no matter what, would never be successful in math. To challenge a mindset of perceived helplessness, both educators sought to locate strategies that increased student response to intervention in mathematics.
This article describes how the addition of a teaching and learning strategy, peer-assisted learning strategies (PALS) in mathematics, had multiple influences on the teachers and students in a middle school mathematics class (see box "Review of the Literature" for additional resources). The plan to use peerassisted learning strategies, although not the only method of instruction, positively influenced student attitudes about mathematics. The classwide peertutoring approach permitted teachers to address a challenging mathematics curriculum and simultaneously attend to a wide diversity of math skills in the classroom. The strategy supported extensive engagement among all students on the team, and facilitated the practice of coteaching. Finally, peerassisted learning strategies supported the use of appropriate social skills in a natural setting.
Educators are challenged to teach mathematical thinking and mathematical sense-making in increasingly complex classrooms with students of widely diverse math abilities. To accomplish such a mission, it is critical that teachers use flexible instructional strategies that engage student interest and learning on multiple levels. Two middle school teachers collaborated on a project that explored peer-assisted learning strategies in order to increase response to intervention and engagement to counter the risk factors found in their math classroom.
The Middle School Context
This project took place in a large middle school near a large city in the Midwest. The middle school was marked by diversity, more in terms of socioeconomic status and culture than in racial characteristics. A team of 150 seventhgrade students with diverse mathematical abilities engaged in a project to learn PALS skills in order to regularly assist one another in mathematical problemsolving. PALS was not the only method of instruction but served as a remediation tool for areas where students demonstrated difficulty with the mathematical concepts. What the teachers found was that negative attitudes and a learned failure response decreased over the course of the project. Working together, Beth, a general education math teacher, and Steve, an intervention specialist, developed strategies that would build on meaningful mathematical knowledge. It is not necessary to have two teachers to carry out PALS-a teacher without an intervention teacher can accomplish this as well.
The middle school team consisted of 150 students, about 14% of whom were identified with a disability. Six of the students with IEPs had behavior plans. Two of the students were identified with Asperger's syndrome. Most of the students with IEPs were identified with specific learning disabilities in math and language areas.
Reciprocity between students with stronger and weaker skills was supported and built into the structure of the lessons. Traditional tutoring practice pairs students with more proficient skills with students with significantly less proficient skills. The tutor, in this one-way relationship, delivers assistance to the tutee. In contrast, PALS procedures reverse the roles of the tutor and tutee. This role reversal allows the student with less expert skills to teach and lead the process, furthermore the reversal allows the student with more proficient skills time to practice and receive feedback. In our classroom, increased student engagement transformed teacher practice, creating a more student-centered classroom.
Peer-Assisted Learning Strategies
Beth, the math teacher, expressed concern about negative attitudes in math and how they affect student motivation and achievement. Steve, the intervention specialist, initially investigated PALS and shared his findings with Beth. Fuchs and Fuchs (2001) developed a process that integrated principles of universal design for learning with effective instructional principles. A set of instructional principles, such as creating clear objectives, presenting one new concept at a time, reviewing prior knowledge, making explanations explicit, utilizing effective instructional time, creating opportunities for adequate practice and review, and providing effective feedback, formed the peer assisted learning strategies (PALS) process. The PALS process used universal design for learning principles by designing quick pace and varied instruction and engagement, adhering to challenging standards, utilizing self-verbalization methods, and making use of physical and visual representations of numbers concepts and problem-solving (Fuchs & Fuchs, 2001). Together Beth and Steve agreed to try it in her seventh-grade math classrooms.
The overall structure of the PALS program creates a climate of reduced anxiety. By providing a safe and supportive environment where peer assistance is immediately available to the student, fear responses are minimized. This occurs because a coach is ready to support any effort that the player makes to solve a problem. Over time, the avoidance response is transformed to a more resilient approach response. However, the PALS program was only designed for the elementary level and the secondary level. There is no middle school level PALS program in place, so Beth and Steve had to create specific materials for their students' needs.
Creating Reciprocal Pairs
Beth, with the assistance of Steve, began using PALS at midterm of the first quarter. This allowed Beth adequate time to get to know her students' strengths and weaknesses which would help later with the pairing process of PALS. Beth and Steve decided to pair students according to assessment procedures. A split-list procedure was used, where the entire class of students is ranked on ability, and then split in half (FuIk & King, 2001). The student with the highest assessment is paired with the highest student of the lower assessment. For example, a class of 20 with the highest assessment being 1 and the lowest assessment being 20 would be paired up in the following order: 1 and 11, 2 and 12, and so on, all the way to 10 and 20. Because of this pairing method, student partners do not experience the significant gaps in their abilities as often found in traditional tutoring relationships. The pairing method supported engagement of many students with varying abilities in a way that did not ostracize them. Throughout the year, about once or twice a quarter, Beth would revise her pairing, as students had strengths and weaknesses in different areas, and students had the opportunity to work with different partners.
Training and Frequency of Use
Beth's team operated on a block schedule for the majority of the time so she saw her students 3 days a week on average and occasionally less or more depending on special circumstances. Her school practiced flexible scheduling for teams. The PALS program recommends that you use PALS three times a week. Beth would have to adjust how often she organized a PALS session to meet her own schedule. Beth decided that she would use PALS as a support to her regular instruction. Any time she felt that after teaching a lesson, her students needed further practice on that skill, or any time she taught a lesson in which she knew in the past her seventh graders had struggled, such as confusing greatest common factor with least common multiple, she would design a PALS session. Thus, Beth used PALS as a supplementary program to support and remediate the learning already going on in the classroom.
The PALS program maps out scripts for 5 training days to prepare students in the PALS process. It is recommended that training sessions take place backto-back. Beth and Steve decided to coteach the training days with Beth's math classes because PALS was new to both of them, and they decided to do it within 5 days of block schedule, over the course of 2 weeks. The training days are used to allow students to grow accustomed to and accurately demonstrate the roles of coach and player. Students use scripts, while mutually supporting each other, in addition to using a point sheet. The PALS routine becomes a clear and supportive structure for peer interaction. Clear procedures, such as monitoring for accuracy, immediate feedback, encouragement to try another strategy, and saying "good job," were monitored, supported, and reinforced with positive supports. Students became teachers.
Student training involved various skills and expectations. Students are trained, for example, in a set of responsibilities such as the following: (a) talk only to your partner and only about PALS, (b.l keep your voice low, (c) cooperate with your partner, and (d) try your best. Each of these involves role playing and modeling to deepen understanding and fidelity to the intervention process (Fuchs et al., n.d.).
The student with more proficient skills of the pair is the first to play the role of coach, while the other student becomes the player. The coach explicitly guides the player through the problem-solving process by reading a script (see Figure 1) word-for-word while the player works out the problems on a handout. Beth and Steve had to create all of their own scripts and handouts because the program did not fit the skills Beth needed to cover. The coach reads this script for each and every problem so that the player hears it repeatedly, thus locking it into memory and building neural pathways (Smilkstein, 2003). The coach also stands ready to offer explanations and encouragement for each step in the process, as the player is allowed to ask questions.
The coach is trained to allow practice to occur as the problem-solving skills are learned. This practice format prepares the student with lower skills to take on the reciprocal role of coach, building a sense of reciprocity and reinforcing the learned skill (Fuchs, Fuchs, Karns, & Phillips, 2002). The coach watches the player's work carefully and puts a triangle around any mistake as he sees it occur. It is the player's job to figure out what he did wrong and correct it on his own if possible. The coach may hint or give clues to assist the player, but is not allowed to simply show the player how to do it. If no mistake is made during a problem, the coach circles the entire problem.
If any partners get through problems earlier than the rest of the class, the coaches are allowed to turn the papers over and make up some problems of their own. After about 15 minutes, Beth would cue everyone to stop where they were and switch roles, if they had finished all their problems or not. This helped move everyone along, especially if partners with lower levels hadn't solved as many problems.
Roles are switched during PALS so that the player gets to take on the role of coach and vice versa. Depending on the skill being reviewed, Beth had her first players do about six problems before switching roles. Then the new player did the same amount of problems. The new coach followed the same procedure of reading the script word-for-word for each problem. Players sometimes got ahead of the coach as they learned what they were doing, but the coaches still consistently read the script.
Removing Scaffolds and Building Independence
After about 15 more minutes of working, Beth would cue the students to stop and again switch roles for the "Think Aloud" (see box, "Example of a Think Aloud"). During this time, the coach has the script in hand in case the player gets stuck, but it is the player's job to talk through the problem without a script being read. The player talks through the steps of the problems she is doing while the coach listens and watches, continuing to encourage and/or point out mistakes. Beth had players do about three problems and then switch roles again, giving the first coach time to do the think aloud for several problems.
During the entire time of the PALS routine, while coaches were reading scripts and after roles were switched, Beth and Steve (when he was in the classroom) walked around the room, observing partners at work and marking points on the score sheets (see Figure 2). The score sheets were a way to encourage students to remain on task and also a way to lead into discussion about the PALS process before moving to individual practice. Points were awarded for things such as following the script word-for-word, helping a partner to accurately figure out what mistake he had made without having to point it out, or for staying on task.
When the think aloud time was over, Beth would have a debriefing session in which she had students raise hands for amounts of points. For example, she would say, "Raise your hands if you and your partner earned at least 10 points; keep hands up if you earned at least 11 points;" and so on. When the "winners" were acknowledged, the entire class would applaud and Beth would mention some things she saw with that pair of PALS that may have given them extra points. After, she would ask if any students had some really helpful tips from their coaches or how did the coach decide a player needed help, or anything they wanted to share. Reflecting on their own practice, students saw they are learning the foundational principles of mathematics.
Following the process of scripted practice and think alouds was individual practice. Every student was given a practice sheet and silently worked on the problems without the help of a coach or a script. After 15 to 20 minutes, Beth would stop the students wherever they were and have them switch papers with their partners. The students would check each other's papers with an answer sheet and only circle problems that were incorrect. Practice sheets were not graded, but students were able to see where they were still having difficulty in a particular process.
Usually, by this time, her class time was over. The next step in PALS was done in the subsequent class period. Beth assessed the students on the skill they had been working on by giving a graded quiz. Students worked alone, without scripts, but as most students told her, they pretty much had the scripts committed to memory by this time.
From Helplessness to Helpfulness
This procedural structure of role play and guided discussion supports a new self-understanding that is at odds with old beliefs, creating dissonance, about math as something over which the individual has no control. The process demonstrates that participation and effort can produce successful results. Not only are peer coaches individuals that the student player can identify with, peer coaches also reinforce the value of the student's efforts because success is practically guaranteed. This builds confidence for independent work later in the process.
There were several other positive outcomes when Beth and Steve used PALS in the classroom. For the first time in her teaching career (of 8 years), Beth saw 100% of her students engaged the entire class time. Beth couldn't believe that even the least motivated students on her team of 150 students were engaged and doing their part! She saw confidence levels rise in many of her lower ability students. When Beth had students write reactions to using PALS, many students wrote that memorizing the scripts helped them so much on tests. Students wrote about feeling more comfortable working with a peer as opposed to asking questions in the whole-class context. Students who were normally afraid to raise their hands in a math classroom were getting their chance to be an active participant.
Besides this, Beth did note that students who had been doing poorly on quizzes were improving their scores and seemed to retain the material longer when retested over this material in combination with additional skills. Overall, Beth saw a greater success rate of more students understanding some of the harder topics of the seventh-grade curriculum than ever before. Overall, Beth and Steve considered PALS such a welcome addition to their teaching repertoire that they would continue to use it. They were invited to present their experiences in subsequent conferences, and other teams in the school began to use the process.
Student Reactions to PALS
Daniel described his reactions to a PALS interaction, "One time Alexis and Aaron helped me work out a problem, and it just really felt good to know that they don't judge me on if I can or can't do it." Kristy speaks from a coach's perspective, "What I like about PALS is that it helps me sometimes to work out and help teach problems with other people so I can learn better."
"I like that we get to read scripts to our partners." Jason explained, "I think that PALS helps a lot of people because if we just told our partner to figure out the answer, we wouldn't be learning much." Katie said, "I like PALS because you can help people understand, and if I'm confused about something, or I didn't know what I was doing wrong, my pal would help me. It's easy to ask for help and not feel embarrassed asking it in front of the class."
As these student responses indicate, the learning process is scaffolded. The coach first models the process using a script (see Figure 1), and then the player attempts the problem-solving process. The script that the coach and player use is a problem-solving protocol designed by the teacher beforehand. The PALS program used in this setting did not have a middle school curriculum. Beth would design protocols, or scripts, and Steve would edit for clarity with an eye for students with less proficient math and reading skills.
"With PALS you have someone there to teach you."
The simple routines of PALS engage both partners. While the player is busy working out the math problem using pencil and paper or manipulatives, the coach is keeping score, using the script to guide and check the player's process. PALS provided a structure to help all students to engage in problem-solving and overcome the overwhelming feeling that they couldn't "do math."
After training 150 seventh graders in peer-assisted learning strategies, and using those strategies consistently for several months, Beth used one of her daily math warm-ups for a short writing exercise to find out students' feelings about PALS and whether they were aligned with her own findings of increased student success. Students, like Gretchen, with math goals in their individualized education programs (IEPs) would agonize over math procedures, sometimes in tears. Later, after learning the PALS skills, Gretchen said, "I like PALS because when I take a test, I can say the script in my head." Another student, Carrie, an extremely social being and a student identified with a learning disability, put it this way, "I really like PALS because I can relate to my partner and help that person in any way I can, and I also like the scripts."
Tavon, though not identified with a disability, required the same level of intervention in math as many other struggling students. Tavon expressed hesitation to ask for assistance. The fear of appearing confused was a significant inhibitor for his participation when he was unsure of a process. Tavon explained, "With PALS you have someone there to teach you and guide you. Plus, the coach is right by you. You can ask the coach questions without raising your hand and feeling embarrassed in front of the whole class."
Not every review of PALS was positive. Alicia, a student with an identified learning disability in math, complained, "What I dislike about math PALS is you have to hear the script over and over again, which kind of gets annoying." Whether the student reviews were positive or negative, the net result was the same-increased engagement and positive response to intervention in a content area notoriously challenging for middle school students in general and certainly for students identified with learning disabilities in mathematics.
Skills Used In Other Contexts
Steve found added benefits for students with IEPs. A number of social skills are built into PALS allowing a number of IEP goals to be addressed simultaneously. At the beginning of the school year, students were reluctant to ask their peers for assistance, and when they did ask a peer for help, it was not clear that the help given was accurate. During class time, because of the method of ranking, students with identified disabilities were working side-by-side with students in the general education setting. With the PALS scripts, students, regardless of skill level, could rely on an easily monitored procedure. Furthermore, during the resource period later in the day, students would assist one another using the procedures they learned in math. The helping role acted as an effective distracter for those who finished work early, and increased natural supports at the end of a seventh grader's busy day. Students now had common grounds to address questions and find where lack of learning had taken place-a common means and language to retrace learning steps and review new skills. Peer-assisted learning strategies was an instructional practice that created greater access to the general curriculum for all students.
Final Thoughts Implications for Practice
Teaching math to middle school students is a challenge. Trying to keep every student engaged and interested, especially in an inclusive setting, can seem an impossible feat. On top of that, there is the issue of many middle school students coming into the classroom with the attitude of "I am terrible at math. I have always been and will always be, and therefore I'm not even going to try because I know I will fail." With PALS, Beth and Steve saw student engagement and response to intervention dramatically increase-a world of students discussing and talking through math problems, regardless of ability levels or past experiences in math classes.
With the demands of No Child Left Behind, it is increasingly important to address differentiation and the needs of ALL students. PALS is an effective intervention to increase engagement and opportunities to respond for all students. Of course, it is not the only teaching method, but is a strong tool to be utilized in the classroom toolbox of instructional methods.
Review of the Literature
Many students face significant barriers to success in math. Repeated failure experiences in math, for example, lead to beliefs about one's own ability. As one student stated, "I can't do this math. I've always failed, I just can't get it." When students make such negative self-concept statements, they tend to create a devastating downward spiral and selffulfilling prophesy. As a result, students increasingly disengage from the learning process and more failure follows (Maheady, Harper, & Mallette, 2001). In conditions where there is decreased expectancy of success and a sense of uncontrolled failure students attribute learning difficulty to themselves, making an assumption that their own abilities are the barriers to success in the mathematics curriculum (Finn, 1989; Gentile & Monaco, 1986; Jarvis & Seifert, 2002). Mikulincer (1994) refers to this reaction as a coping action that frequently interferes with the efforts students make to complete mathematics activities. Coping actions such as task avoidance lead to withdrawal from attempts to solve problems. Withdrawal creates a negative behavioral momentum (e.g., student stops responding in class) that leads to a context of increased risk factors (Gresham, 1991, 2004; Nevin, 1988; Witt, DaIy, & Noell, 2000). Fredricks, Blumenfeld, and Paris (2004) note steep declines in motivation, especially among students that represent minorities and students with disabilities. Stedman (1997) contends that students with disabilities face significant risk in high-stakes learning environments because they frequently enter the learning context with skill levels well below that of their peers. In Stedman's review of international achievement differences, eighth graders in the United States performed more than 2 years behind high-scoring countries in math. Because ineffective learning strategies can actually reinforce characteristics of learned helplessness, it is urgent that educators learn a variety of strategies that make success more likely (Coley & Huffman, 1990).
Diverse Needs and Diverse Strategies
Today's mathematical skills are taught in increasingly diverse classrooms (Maheady et al., 2001). Sapon-Shevin, Ayres, and Duncan (1994) point out that the mere physical inclusion of students with disabilities is not sufficient to ensure social or academic success. Careful planning is required. Murray (1994) concludes that teachers must move beyond their teaching comfort zones when faced with students of markedly different backgrounds from their own. To address the challenge of student engagement and response to intervention, the authors sought instructional strategies that would increase student cooperation, as well as opportunities to respond to the mathematics curriculum (Sutherland & Wehby, 2001). They wanted strategies that would challenge entrenched negative attitudes about mathematical ability and facilitate behavioral momentum of desirable behaviors through the use of adapted peer-learning strategies that integrate principles of universal design for learning with effective instructional principles in the mathematics curriculum (CEC, 2005; Gresham, 1991, 2004; Petty, & Cacioppo, 1996). They wanted strategies that would build meaningful mathematical knowledge in line with national, state, and local district standards and principles of best practice, all measured by high-stakes assessments (Cawley, Parmar, Foley, Salmon, & Roy, 2001; Maccini, & Gagnon, 2002).
Peer-Assisted Learning Strategies
Although the peer-assisted learning strategies (PALS) method is described here, both classwide peer tutoring (CWPT; Delquadri, Greenwood, Whorton, Carta, & Hall, 1986; Greenwood, Arreaga-Mayer, Utley, Gavin, & Terry, 2001) and peer-assisted learning strategies (Fuchs & Fuchs, 2001) were studied. Classwide peer tutoring and peer assisted learning strategies address a common core of instructional learning strategies. Both methods, for example, place significance on the development of reciprocal one-on-one relationships that challenge traditional one-way tutoring relationships (Fuchs, Fuchs, Thompson et al., 2001; Greenwood, Delquadri, & Carta, 1997). Both methods include strategies for error correction, incorporate a fast pace of instruction, and increase opportunities to respond (Fuchs, Fuchs, Kazdan, Mathes, Prentice, & Saenz, n.d.; Mitchem & Young, 2001; Sutherland & Wehby, 2001). Both methods detail explicit roles for teachers and students, utilize written and oral response formats, operate within an inclusive environment, and systematically address social and academic goals (King-Sears, 2001; Montague & Applegate, 1993; Tournaki & Criscitiello, 2003).
Response to Intervention
The authors used PALS as a way to enhance classroom practice, support inclusion, and directly confront what appeared to be a learned helplessness response of several of their students. They witnessed the increased engagement and response to intervention, which mutually reinforced educators and students alike. Because very few materials for PALS exist for the middle school context, the authors designed unique mathematics learning materials using the framework and instructional guidelines for a peer assisted learning strategies system; in the process they observed attitude changes and widespread gains for all students regardless of ability level (Murawski & Swanson, 2001; Walsh & Jones, 2004). The first author, Steve, the intervention specialist, increased his role in the instructional aspects of the class. The second author, Beth, the mathematics content area specialist, had more opportunities to assist individual students struggling with the mathematical process.
The classwide peer tutoring approach permitted teachers to address a challenging mathematics curriculum and simultaneously attend to a wide diversity of math skills in the classroom.
Example of a Think Aloud
The player is asked to explicitly work through a set math problems without the coach reading or guiding the player through the script (see Figure 1 of a coach's script). After having previously had the script read to the player several times, the player is more proficient with the problem-solving process. The player, with the peer coach still listening carefully, might begin solving a dividing fraction problem by saying the following aloud as he works through each step of the problem, "This is a dividing fraction problem. I make each term into a fraction so I have no whole numbers or mixed numbers. I rewrite the first fraction in the problem. I write a multiplication sign instead of division. I flipflop the second fraction in the problem and write it. I multiply numerators. I then multiply denominators. Can I reduce? No, I'm done." The player can ask for or be offered help at any time, but the goal is independent completion of the problem.
Students who were normally afraid to raise their hands in a math classroom were getting their chance to be an active participant.
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Stephen D. Kroeger (CEC OH Federation), Assistant Professor, University of Cincinnati, Ohio. Beth Kouche, Seventh-Grade Math Intervention Teacher, Forest Hills School District, Cincinnati, Ohio.
Address correspondence to Stephen D. Kroeger, University of Cincinnati, 4501 MeIlwood Avenue, Cincinnati, OH 45232. 513556-2729 (email: Stephen.Kroeger@uc.edu).
TEACHING Exceptional Children, Vol. 38, No. 5, pp. 6-13.
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