Peer Mediation The Effects of Program Intervention, Maths Level, and Verbal Ability on Mediation Style and Improvement in Maths Problem Solving ADINA SHAMIR, DAVID TZURIEL and MERAV ROZEN School of Education, Bar Ilan University, Israel
ABSTRACT The objectives of the current study were to examine: (a) the effects of the Peer Mediation with Young Children (PMYC) program on mediators’ and learners’ mediation style in the context of maths teaching; and (b) the interaction effects of the intervention program, children’s verbal ability, and maths level on pre- to postintervention improvement in maths and mediation style. The sample was composed of 108 pupils (54 mediator—learner dyads), equally divided between an experimental and a control group. In each dyad, the mediator was from Grade 3 and the learner from Grade 2. Mediators and learners in each pair were matched in a counterbalanced design (2 × 2) according to their level of maths skills (high versus low). The experimental children received the PMYC program whereas the control children received general preparation for peer-assisted learning only. Following the PMYC intervention, all children participated in a peer-mediation condition where the mediators taught their younger peers how to solve maths problems. The interaction was videotaped for 25 minutes and analysed by the Observation of Mediation Instrument. The main findings showed that the experimental children obtained significantly higher scores on all mediation criteria and improved their pre- to post-intervention scores in maths to a greater degree than did the control children. These findings are explained in relation to Vygotsky’s and Feuerstein’s theories in addition to previous findings on peer mediation. KEY WORDS:
intervention; maths; peer mediations; self-mediation;
Vygotsky
Please address correspondence to: Adina Shamir, School of Education, Bar-Ilan University, Ramat-Gan 52900, Israel. Email:
[email protected] School Psychology International Copyright © 2006 SAGE Publications (London, Thousand Oaks, CA and New Delhi), Vol. 27(2): 209–231. DOI: 10.1177/0143034306064548
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School Psychology International (2006), Vol. 27(2) Introduction In recent years, education policy-makers in the western world have begun to attend to the issues raised by the presence of multicultural students in heterogeneous classes (Mevarech and Kramarski, 1997; Rich, 1990). Constraints imposed by large class size and inclusion policies have likewise generated a search for alternative methods to address the needs this situation has generated among individual learners as well as teachers, especially in mathematics, a subject known for its difficulties (Fuchs et al., 2002; Mevarech and Kramarski, 1997; Stedman, 1997). Given this reality, the purpose of the study presented here was to investigate the effect of a novel intervention program aimed at enhancing children’s mediation style and cognitive skills on their maths achievement, a subject taught in school. Feuerstein’s mediated learning experience theory (MLE; Feuerstein et al., 1979; Feuerstein et al., 1980), as integrated with Vygotsky’s sociocultural theory of learning (1929; 1962; 1978), provided the foundations for Peer Mediation with Young Children (PMYC, Shamir and Tzuriel, 2002; 2004; Tzuriel and Shamir, in press), a cognitive model and intervention program focusing on the interaction aspects of learning among peers. Previous applications of the PMYC program in experimental contexts have shown its effectiveness in enhancing the mediators’ and the learners’ mediational teaching styles (Shamir and Tzuriel, 2004), learning how to learn skills and cognitive modifiability (Shamir, in press; Shamir and Tzuriel, 2002; Shamir and Van der Aalsvoort, 2004; Tzuriel and Shamir, in press). Findings regarding learning how to learn and cognitive modifiability were based on dynamic assessment tests (Feuerstein et al., 1979; Lidz and Elliott, 2000; Sternberg and Grigorenko, 1998; Tzuriel, 2001) that tap problemsolving skills using cognitive operations such as analogical reasoning and seriation (domain generalized). The main goal of the current study was to investigate whether the effectiveness of the PMYC program can be observed with subject matter (domain specific) learned in school, such as maths. The importance of using the PMYC model in a classroom setting thus derived primarily from the need to demonstrate that a cognition-oriented education program can be applied with domainspecific tasks – such as maths – and not exclusively with domaingeneral tasks, as shown in an earlier study (Shamir and Tzuriel, 2002, 2004). It was hypothesized that children who participate in the peer mediation program will improve their learning how to learn skills and, consequently, their achievements in maths. The study’s findings were posited as especially pertinent to multicultural classes, where skills transmission is acutely problematic due to the students’ highly varied learning habits (Fuchs et al., 1997; Maheady et al., 2001). These 210
Shamir et al.: Peer Mediation difficulties are compounded by the children’s vast range of familiarity with the language in which lessons are taught. Other objectives of the current study were, therefore, to examine the relationship between variables such as maths level and verbal ability in relation to mediation style and, consequently, maths level. Paraphrased as questions, we were asking: What is the effect of the mediator’s and learner’s maths level on their mediation style in a peer mediation context? What are the effects of verbal abilities on mediation skills and consequently on maths performance? Responses to these questions are of great importance in view of the extensiveness of the difficulties associated with learning mathematics (Fuchs et al., 2002) and peer-mediation’s potential to improve children’s maths skills. In the remainder of this introduction, we present the PMYC model and intervention program and describe the concept mediation style. Fundamentals of the PMYC model The past 25 years have witnessed a growing interest in Feuerstein’s structural cognitive modifiability and mediated learning experience theory. Researchers who explored the effect of mediational interactions on the child’s intellectual development (e.g. Klein, 1988; 1996; 2001; Tzuriel, 1996; 1999; 2001; Tzuriel and Eran, 1990; Tzuriel and Ernst, 1990) first investigated different forms of mediation as applied by adults, usually parents with their children. However, study of the effect of peer mediation-enhancing interventions on children’s mediation style and cognitive modifiability has commenced only recently (Shamir, 2003; Shamir and Tzuriel, 2004; Tzuriel and Shamir, 2003). According to Vygotsky, as well as Feuerstein, realization of students’ developmental potential is conditioned by their experience of social interaction with a person more competent than themselves, either an adult or a peer. Integration of the two theories invites redefinition of children as individuals capable of learning how to mediate, a process culminating in more competent and experienced persons who can assist their peers in the realization of their developmental potential. Hence, the respective elements taken from these theories, in combination, provide the conceptual and practical tools underlying development of the PMYC model and intervention program. The literature further indicates that Peer-Assisted Learning (PAL) positively affects children’s performance with respect to the structure of the tutorial interaction, specific tutor behaviours, student regulation of the learning process, and status within the tutor–tutee relationship (e.g. Fuchs and Fuchs, 2000; Fuchs et al., 1998; King, 1997; Topping and Ehly, 1998; Verba, 1998). Four points thus characterize the peer mediation model evolved. First, it is a comprehensive theoretical model 211
School Psychology International (2006), Vol. 27(2) that integrates cognitive and affective components to provide the foundations for the design of tutor behaviour. These components, pervasive mediation principles (i.e. mediation style), motivate learning how to learn. Second, the mediation procedures used are both structured and imaginative. They are structured in the sense that children are taught how to apply the respective theoretical principles when teaching peers, yet they nurture creativity by encouraging children to be innovative as they construct mutuality during peer interactions. Within the framework of mediated learning experience theory, mutuality is a fundamental condition because it requires mediators to modify their mediation in response to changes in learners’ behaviour. Third, the status of the mediator is clearly differentiated from the status of the learner in the teaching interaction. Mediators are perceived as more competent than learners not only because of their older age but also because they have learned how to mediate and how to adopt an active, modification-oriented attitude within the interaction. One specific advantage of the peer mediation model and program therefore lies in their potential to tap the learners’ willingness to collaborate with cross-aged peers. Fourth, the peer mediation model is not limited to a specific content domain or learning situation. It can be applied in different contexts ranging from problem-solving tasks (domain general) to learning of school subjects (domain specific). The PYMC intervention program is designed to fulfill the objectives of the PMYC model: to enhance acquisition of a mediation style among young children, develop self-regulation skills and cognitive modifiability among young mediators and facilitate improvement of young children’s performance and learning skills as mediated by moreexperienced peers. The program’s core assumption is that teaching for peer mediation will elicit improved mediation skills from the mediators on one hand, and induce cognitive improvement in both learners and mediators on the other. The subsequent changes in their mediation style and cognitive performance will enable the children to more effectively use these skills in future learning situations. To support this process, the PMYC intervention incorporates basic conditions for effective peer interaction – such as respect for the learner, empathy, and allocation of ‘personal space’ – into the activities associated with Feuerstein’s first five mediation principles, adapted for young children. The children thus learn that these principles can assist them in helping a peer to solve tasks independently. During the experiential phase of the program, children also learn how to extend the mediation principles to different peer-learning situations. Viewed from this perspective, young children are taught how to mediate as preparation for helping other young learners to deal with independent problem-solving and learning how to learn strategies. 212
Shamir et al.: Peer Mediation The PMYC rests on three main ingredients. The first is direct teaching of the basic MLE principles. The second includes observation and discussion of a didactic film to enhance internalization of each mediation principle. The third ingredient entails practicing MLE principles with peers. Multimedia as well as conventional materials – learning aids such as computer programs, games, posters and stickers with the principles’ visual symbols, verbal slogans and work sheets – are used for this purpose. (Each mediation principle has been assigned a visual symbol, a symbol name, and a verbal slogan. For example, ‘Regulation of Behaviour’ is visually represented by a ‘Stop’ sign, the assigned name ‘Stop’, and the slogan ‘Stop and think before and after you drill’. These examples have been translated from the Hebrew.) The intervention program itself is transmitted in seven lessons delivered over a three-week period. Peer mediation: anticipated behaviours Feuerstein et al. (1979; 1980) suggested 12 mediation criteria; only the first five have been operationalized in studies of infants and young children (Klein, 1988; 1991; 1996; 2001; Lidz, 1991; Tzuriel, 1996; 1999; Tzuriel and Weiss, 1998). These criteria, subsequent to their adaptation for peer mediation, were used to observe and evaluate mediation styles in the present study. The five are described here in brief due to their salience to the PMYC program. For a detailed description of all 12 MLE criteria see Feuerstein et al. (1979; 1980). Intentionality and reciprocity. The mediator’s intentional efforts to change the learner’s perceptions, task processing or reactions to the task in response to the learner’s behaviour. Intentionality and reciprocity are observed during peer mediation when the mediator focuses the learner’s attention on an object and the learner responds vocally, verbally, or perhaps nonverbally to the mediator’s actions. Complying with this criterion is essential for the continuation of the entire mediation process. Mediation of meaning. Interactions in which the mediator tries to emphasize the importance of a stimulus by expressing interest and by pointing out its value. Mediation of meaning likewise refers to situations in which the mediator names an object or provides a definition. This principle is demonstrated, for example, by a mediator pointing to an icon on a computer screen and verbalizing its meaning (e.g. ‘This icon’s name is “exit”’). Mediation for transcendence. Those interactions in which the mediator attempts to reach beyond the concrete context or the immediate needs of the learner to achieve goals that are not bound to one specific situation. In peer interactions, the mediator may teach rules and principles that apply to other than the current context (e.g. ‘This flower 213
School Psychology International (2006), Vol. 27(2) blooms every spring’). It should be noted that although mediation for transcendence rests on mediation for intentionality and mediation of meaning, the three, in tandem, are the criteria that most influence the child’s cognitive development and need structure. Mediation of feelings of competence. This criterion refers to those interactions in which the mediator organizes the environment to support the learner’s sense of success. These interactions therefore convey awareness of the learner’s capacity to function independently and successfully, realized through actions such as providing opportunities for success, rewarding the learner for successful problem solving and interpreting the meaning of success to the learner (e.g. ‘Wow, you did a great job!’). Mediation for regulation of behaviour. Interactions in which the mediator regulates the learner’s responses during task performance represent this type of mediation. Regulation is accomplished by controlling negative behaviour such as impulsiveness, inhibiting acting-out behaviour or reinforcing positive behaviour. Examples include statements such as ‘I see that you remembered to check your solution before you continued to the next task’, with each attempt dependent on the task’s demands as well as the child’s individual behavioural style. Mediation for regulation of behaviour can also be achieved by arousing awareness of the task’s characteristics, analysing its components, and motivating review of the child’s own behaviour by delaying immediate responses to initial task completion (e.g. ‘Do you remember what we do once we finish solving a problem?’). In addition to the five MLE criteria already operationalized, two nonmediational behaviours – activation and anti-mediation – observed during episodes of peer interaction, were added as separate measures (Shamir and Tzuriel, 2004). Activation refers to interactions in which the mediator performs the task for the learner (nonverbal interaction) or relates the correct answer to the learner (verbal interaction). During peer mediation, activation is observed, for instance, when the mediator takes the card from the learner or pushes the card into the right place or declares ‘Put this card here’. Anti-mediation refers to interactions in which the mediator acts negatively towards the learner (e.g. he/she expresses indifference, disrespect or rejection). To reiterate, it was anticipated that children’s maths performance would improve after completion of the PMYC intervention program, especially within a multicultural class context. Improvement in cognitive modifiability and basic learning how to learn skills in the area of mathematics was assumed to be the product of an enhanced level of mediation. Hence, the following hypotheses were tested in the current study:
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Shamir et al.: Peer Mediation (a) Experimental mediators will show greater pre- to post-intervention improvement in maths than will control mediators. (b) Improvement in maths among learners taught by experimental peers will be greater than improvement among learners taught by control peers. (c) Experimental mediators will display a higher level of mediation in all mediation criteria than will control mediators. Based on earlier studies, we expect the highest group difference to appear in mediation of competence and regulation of behaviour. In addition to the study’s hypotheses, two questions were asked for which no clear hypothesis could be defined: (a) Does the maths level of the mediator or the learner affect the mediator’s mediation style? Previous findings (Shamir and Tzuriel, 2004) have shown that when the mediator’s cognitive level does not match the learner’s cognitive level (domain general), mediators provide a higher level of mediation. In the current study, however, we investigate whether the same effect will be found with maths levels (domain specific); (b) Does the mediator’s verbal ability have an effect on mediation level? Furthermore, does verbal ability level interact with the treatment to affect the mediator’s mediation style? Methods Sample The sample consisted of 108 pupils (54 mediator–learner dyads); evenly divided between mediators from grade 3 (n = 54) and learners from grade 2 (n = 54). The mediators and learners were drawn from six classes in a primary school (three classes from the third and three classes from the second grade). All children were from families of average socioeconomic status as defined by Israel’s Ministry of Education. The mediator group was composed of 32 boys (60.4 percent) and 22 girls (39.6 percent); the learner group of 30 boys (56.6 percent) and 24 girls (43.4 percent). Chi-square analyses indicated no significant gender differences among the mediators (χ2 = 0.03, p = ns) or learners (χ2 = 0.64, p = ns). The percentages of mixed-gender versus samegender dyads for the entire sample were 44.5 percent and 55.5 percent, respectively (χ2 = 1.35, p = ns). The mediators’ and learners’ mean age (in months) was 95.55 (SD = 3.40) and 83.45 (SD = 3.55), respectively. The next step of the experiment involved random assignment of the mediator–learner dyads into treatment subgroups by maths level. Mediator–learner pairs were first matched in a counterbalanced design, based on their maths achievement level. In order to do this matching, children in each grade were first divided into three 215
School Psychology International (2006), Vol. 27(2) subgroups of low-, medium-, and high-achievement, using the Maths Achievement Test (see Measures); only subjects in the low- and highachievement subgroups were selected to participate in the study. Finally, each high- and low-functioning mediator (by maths level) was matched with a high- or low-functioning learner in a counterbalanced (2 × 2) design. Matching was done separately in the experimental and the control group. In order to control for differences deriving from a subject’s cognitive level, all children were administered the Raven’s Colored Progressive Matrices (Raven, 1956). Comparison of the experimental (M = 23.91, SD = 4.45) and control (M = 23.79, SD = 5.20) groups showed no significant differences between them, t(100) = 0.12, p = ns. Similar group comparisons showed no significant differences in either the mediators, t(52) = 0.29, p = ns, or the learners, t(52) = 0.29, p = ns. It should be stressed that although the learners in the experimental group did not participate in the PMYC program, they did receive mediation by thirdgrade peers who had been assigned to the experimental group. For the sake of clarity, we labelled these learners as experimental learners. The mean maths scores (in percentages) of the high-functioning mediators in the experimental and control groups before the intervention were 88.91 (SD = 6.18) and 92.83 (SD = 12.32), respectively, t(52) = 1.02, p = ns. The mean maths scores of the low-functioning mediators in the experimental and control groups before the intervention were 45.10 (SD = 12.81) and 45.43 (SD = 18.77), respectively, t(54) = 0.04, p = ns. The mean maths scores (in percentages) of the highfunctioning learners in the experimental and control groups before the intervention were 84.24 (SD = 4.61) and 83.69 (SD = 7.05), respectively, t(52) = 0.22, p = ns. The mean maths scores of the low-functioning learners in the experimental and control groups before the intervention were 47.55 (SD = 8.43) and 52.21 (SD = 15.30), respectively, t(54) = 0.98, p = ns. Measures Observation of Mediation Instrument. The Observation of Mediation Instrument (Klein, 1988; 1996; 2001), originally developed for observation of parent–child mediated learning interactions, was later adapted for observation of teacher–child interactions (Tzuriel et al., 1998) and recently for peer-mediation interactions (Shamir and Tzuriel, 2002, 2004). The behavioural categories observed were based on the five mediated learning criteria mentioned previously: intentionality and reciprocity, meaning, transcendence, feelings of competence and regulation of behaviour. Each category had been operationalized in terms of specific behaviours. Behaviours of mediators and learners were coded in relation to the other’s behaviours and the meaning conveyed through 216
Shamir et al.: Peer Mediation these behaviours. This observation method differs from microanalytic, sequential observation procedures (e.g. Ramey et al., 1979) that usually result in an unwieldy number of detailed behaviour codes, thus demanding data reduction for manageability and interpretation. This instrument is based on a macroanalytic rather than a microanalytic approach to the assessment of interaction quality (Klein, 1988; 2001). The advantage of the molar observational approach over other approaches (e.g. Ramey et al., 1979) lies in its allowing identification of meaningful continuities in the mediator’s behaviour along a developmental dimension. The qualitative characteristics of MLE observation not only better reflect interaction in practice, they also allow comparison of behavioural similarities over time. This approach thus complies with others that stress holistic perspectives and the need to look at the meaning of behaviours within psychological contexts rather than as isolated phenomena (Santostefano, 1978; Sroufe and Waters, 1977). For use in this study, the Observation of Mediation Instrument was adapted by changing the type of stimuli presented, prolonging the interaction time to allow for improved sampling of interaction and adding the two non-mediational behavioural categories (Shamir and Tzuriel, 2004). All peer-mediation interactions were videotaped for a period of 25 minutes. The inter-rater reliability coefficients for mother– child mediation with kindergarten and school age children ranged between 0.54 and 0.95 (Tzuriel, 1999; Tzuriel and Ernst, 1990; Tzuriel and Weiss, 1998). These same reliability coefficients were found to range between 0.85 and 0.95 for the different criteria of peer mediation (Shamir and Tzuriel, 2004). Maths achievement tests. Two verbal maths achievement tests were designed and performed before and after the intervention, one targeted at the mediators, one at the learners. The mediators’ maths test contained six verbal problems, two one-stage addition and subtraction computation problems, two problems requiring two-staged computation of addition and subtraction, one multiplication problem and one division problem requiring a one-stage computation. The learners’ maths achievement test contained six one-stage verbal problems. For each of the mediator and learner groups, two versions of the Maths Achievement Test were designed; one for the pre-intervention phase (Version A) and one for the post-intervention phase (Version B). Both versions were similar in terms of the number of problems and content domains but different in terms of difficulty, with the post-intervention versions more difficult than the pre-intervention versions. Previous studies have shown that verbal maths problems are more difficult when the initial condition is unknown (i.e. the question phrase appears at the beginning of the problem; see: Mevarech, 1995) than when the problem includes odd information (i.e. incongruence between the 217
School Psychology International (2006), Vol. 27(2) problem’s logical structure and formulation, see: Nesher, 1993) and when the sentence is complex and requires connectivity. A pilot study on second- and third-grade students (n = 40) revealed that the post-test (M = 59.64, SD = 19.22) was more difficult than the pre-test (M = 72.63, SD = 15.87) by a difference of 12.99 points. In order to compare the pre- to the post-intervention scores, we added 13 points for the sake of comparison to the post-intervention score in the main study. Raven’s Colored Progressive Matrices. Raven’s (1956) test is a standardized non-verbal intelligence test designed for children aged 5 to 11. The test is comprised of tasks that require perceptual skills (i.e. identifying symmetrical relations and Gestalt-like percepts) and inferential skills, especially the last problems in set B (items B8–B12). The test is composed of three sets of visual problems (A, AB, B), with each set containing 12 problems. In each problem, the subject is presented with a matrix with a part missing in addition to six alternative solutions, listed at the bottom of the page; only one solution is correct. The child is asked to find the missing part and point to the correct solution. Each correct solution receives a score of 1; the maximum score obtainable is 36. The Raven test was standardized on a sample of children (n = 628) and found to be reliable (Cronbach-alpha coefficient = 0.80) and valid. The MANN Abstract Verbal Thinking Test. The MANN (Glanz, 1989) test employed is a version for young students (up to grade 5) of the original MANN test, designed for students in grades 6 to 12. The test’s objective is to examine the student’s verbal abstract thinking or verbal intelligence abilities. The test is comprised of nine subscales, four subscales relating to basic thinking skills (synonyms, antonyms, substantive thinking, sorting) and five subscales relating to higher-level components (classification, analogical reasoning, proverbs, definitions, syllogisms). For the present study we chose only two subtests – synonyms and antonyms – found by Glanz (1989) to typify young students’ verbal abilities. The MANN test was standardized on a sample of 2,140 grades 3–5 students displaying normal development (Glanz, 1989). The Cronbach alpha reliability coefficient reported for the entire test was 0.96. Pearson correlations between the MANN subtests and Raven’s Matrices, reported by the authors, ranged between 0.53 and 0.60. Auditory Association Subtest (ITPA). Auditory Association is a subtest taken from the Illinois Test of Psycholinguistic Abilities protocol (ITPA; Kirk et al., 1968) aimed at testing children’s ability to construct verbal analogies according to auditory stimuli (e.g. ‘The bird flies in the sky and the fish swims in the …’). The subtest, designed for 4- to 10year-olds, is constructed of 42 verbal analogies organized by increasing level of difficulty. The Hebrew translation was previously standardized on a sample of 383 children. The Cronbach alpha reliability of this subtest, reported by the authors, was 0.90. 218
Shamir et al.: Peer Mediation Table 1
The study designs for mediators and for learners
Group
PreIntervention
Intervention
Peer-Mediation Interaction
PostIntervention
Videotaping of peer mediation session: Teaching phase of maths for the learners
Maths test
Videotaping of peer mediation session: Teaching phase of maths for the learners
Maths test
Design 1 – Mediators (third Grade) Experimental
Maths Test Raven’s Test Concept Formation
PMYC Program + Practice of teaching maths problems
Control
Raven’s Test Explanation Concept about Formation interaction practice of maths items
Design 2 – Learners (second Grade) Experimental
Maths Test ——— Raven’s Test Concept Formation
Videotaping of Maths peer mediation test session: Learning phase of maths for the learners given by the mediators
Control
Maths Test ——— Raven’s Test Concept Formation
Videotaping of Maths peer mediation test session: Learning phase of maths for the learners given by the mediators
Note: Learners were labelled Experimental or Control based on their being taught by a mediator in either the experimental or control group, respectively.
Design and procedure The study was carried out using two separate designs and procedures, one for the mediators and one for the learners (see Table 1). Each Grade 3 mediator was matched with a Grade 2 learner in a counterbalanced design (2 × 2) of maths level (high versus low) by group (mediator versus learner). Pre-intervention phase. The pre-intervention phase, which was similar for mediators and learners, involved administration of the Maths Test, Raven’s Colored Progressive Matrices (Raven, 1956) and the verbal ability subtests (Auditory Associations from the ITPA, and 219
School Psychology International (2006), Vol. 27(2) Synonyms and Antonyms from the MANN test). The Raven’s Matrices were administered to control for differences derived from the subject’s cognitive level. Comparison of the experimental (M = 23.91, SD = 4.45) and control (M = 23.79, SD = 5.20) children indicated no significant group differences, t(100) = 0.12, p = ns. Similar group comparisons indicated no significant differences among either the mediators, t(52) = 0.29, p = ns, or the learners, t(52) = 0.29, p = ns. Intervention phase. After participating in the PMYC program, mediators in the experimental group were given a lesson in which they were taught the rules of teaching verbal maths problems. The maths problems were then practiced. The lesson and the practice components were essential to prepare the mediators for the peer-mediation session to follow. The PMYC program was delivered in seven lessons, each lasting one hour, during a seven-week period. The mediators in the control group received a substitute intervention in six lessons, each lasting for one hour, during a six-week period. The substitute program focused on general conditions of peer interaction, together with a similar demonstration and practice of the verbal maths problems. The control mediators were not, however, taught the mediation principles transmitted to the experimental children. It should be noted that both the experimental and control children received the same preparation for teaching verbal maths problems (i.e. how to assist learners by considering task demands and the learners’ specific needs). Peer-interaction phase. Following the intervention stage, the experimental and control children participated in a peer-mediation condition that was videotaped for 25 minutes. The mediators were instructed to assist their young counterparts to solve the verbal maths problems with the aid of a work sheet. Each learner had to solve six maths problems with the mediator’s help. The difficulty of the problems at this phase was similar to that of the pre-intervention test (e.g. ‘A house has 11 windows, 9 of them are closed; how many are open?’). The teaching phase was meant to serve three goals: (a) to provide the mediators an actual teaching experience with peers; (b) to assess the level of mediation by videotaping the interactions and later analysing them (this enabled us to evaluate the effects of the PMYC program on the mediators’ mediation strategies) and (c) to assess the learners’ achievements in maths following interactions with peers who had participated in the PMYC program. It should be noted that the experimental learners, although taught by experimental mediators, did not directly receive the PMYC program. During the peer mediations, no guidance other than the most minor technical assistance was given, and that only when necessary. Post-intervention phase. The final stage of the procedure involved testing the mediator and learner groups with the Maths Achievement 220
Shamir et al.: Peer Mediation Test (Version B). The overall time elapsed between the pre- and postinterventions was three months.
Results The results are presented in accordance to the study’s goals, as follows: (a) improvement of maths achievements among both mediators and learners; (b) the effects of the mediators’ and learners’ maths level on their mediation style; (c) the effect of the mediators’ verbal ability on their mediation style and (d) replication of the positive effects of the peer mediation program (Shamir and Tzuriel, 2004) on mediation style using a different sample of children (grade 3 tutoring grade 2 children) and domain-specific tasks (maths). In some analyses, the mediators’ and learners’ initial maths level was treated as an intervening variable that interacted with the treatment effects. Effect of the peer mediation program on mediators’ and learners’ maths scores Preliminary analysis of the pre-intervention maths scores showed no significant differences between the two treatment groups, F(1, 46) = 1.10, p = ns. In order to study the effect of the PMYC program on maths achievement, a repeated measures ANOVA was carried out. The independent variables were treatment, mediator/learner, maths level, gender and time (2 × 2 × 2 × 2 × 2), with time employed as a repeated measures variable. The findings showed a significant main effect of time, F(1,87) = 11.03, p < 0.001, indicating higher post-intervention (M = 73.04, SD = 24.11) than pre-intervention (M = 66.35, SD = 23.59) scores. The main effect of time was modified by the interaction of treatment × time, F(1, 87) = 16.25, p < 0.001, indicating that students in the experimental group (both mediators and learners) improved their preto post-intervention maths scores more than did students in the control group (see Figure 1). The means and standard deviations of the maths scores obtained by the mediators and the learners are presented in Table 2. Table 2 shows that the improvement in maths scores (from pre- to post-intervention) of the experimental group was higher than the improvement of the control group; this overall result was similar for both mediators and learners. Simple main effects analyses indicated that the experimental children significantly improved their maths achievements from pre- to post-intervention phase, F(1, 53) = 9.01, p < 0.001, whereas the control children showed no improvement, F(1, 50) = 0.02, p = ns.
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School Psychology International (2006), Vol. 27(2) 80 Experimental
Math score
77
▲ Control
74
71 ▲
68
▲
65 Pre
Post Time
Figure 1 Pre- and post-intervention maths scores in the experimental and control groups (mediators and learners)
Table 2 Means and standard deviations of pre- and postintervention maths scores (in percentages) of mediators and learners in the experimental and control groups Experimental PrePost-
Group Mediators Learners
M SD M SD
66.19 24.44 65.20 19.86
79.71 22.07 78.97 22.31
Control PrePost67.44 28.81 69.72 20.00
64.57 26.92 69.91 21.79
Mediation style: the effects of treatment, mediators’ and learners’ maths level and mediator’s verbal ability Effect of the treatment on mediators’ mediation style. The effect of the PMYC program on the mediators’ (Grade 3) mediation teaching style was analysed by MANOVA of treatment × mediator’s maths level × learner’s maths level (2 × 2 × 2). The dependent variables were the five mediation criteria. The MANOVA findings showed significant main effects for treatment, F(5, 42) = 8.98, p < 0.001, indicating that the experimental mediators scored significantly higher than did the 222
Shamir et al.: Peer Mediation Table 3 Means and standard deviations of mediated learning criteria among mediators and learners in the experimental and control groups Mediators MLE Criteria
Experimental M SD
Control M SD
Mediators Intentionality and reciprocity Meaning Transcendence Feelings of Competence Self-regulation
6.96 3.33 4.11 8.11 6.56
5.95 2.49 3.53 3.79 3.94
2.63 1.48 2.41 3.62 2.00
1.49 1.22 2.37 2.63 1.27
12.01*** 11.31** 4.79* 29.83*** 33.95***
Learners Intentionality and reciprocity Meaning Transcendence Feelings of competence Self-regulation
3.74 2.67 3.00 2.11 3.67
2.26 2.17 2.97 1.67 2.43
1.78 1.30 2.04 1.48 0.52
1.05 0.87 1.76 0.94 0.80
18.01*** 9.08** 2.27 2.51 19.75***
F
** p < 0.01 *** p < 0.001
control mediators on all the mediation criteria. The means and standard deviations of the mediation scores are presented in Table 3. Univariate analyses revealed that the treatment effect was uniquely significant for each mediation criterion. The largest differences were found in mediation of regulation of behaviour and in feelings of competence. Effect of mediator’s and learner’s maths level on mediation style. One of the questions investigated in this study was whether the maths level of mediators and/or learners as well as the correspondence between the two had any effect on the mediators’ mediation style as observed in a peer-interaction context. In order to examine this question, the data were analysed by a MANOVA of treatment × mediator’s maths level × learner’s maths level (2 × 2 × 2). The findings showed a significant main effect of mediator’s maths level F(5, 42) = 3.13, p < 0.05, indicating that mediators with a high maths level scored higher than did mediators with a low maths level on all the mediation criteria (see Table 4). However, univariate analyses revealed that two mediation criteria contributed significantly to the main effect of maths level: transcendence, F(1, 87) = 10.24, p < 0.01, and feelings of competence, F(1, 87) = 9.37, p < 0.01. No significant main effect was found for learners’ maths level, F(5, 42) = .09, p = ns, nor was a significant interaction found between mediator’s maths level and learner’s maths level, 223
School Psychology International (2006), Vol. 27(2) Table 4 Means and standard deviations of mediated learning criteria among mediators of high and low maths level Maths level of mediators MMLE Criteria Intentionality and reciprocity Meaning Transcendence Feelings of competence Self-regulation
M
High SD
5.35 2.81 4.54 7.19 5.04
5.31 2.68 3.89 4.45 4.44
Low M
SD
F
4.29 2.04 2.07 3.64 3.57
4.35 1.47 1.36 3.01 2.74
0.78 1.84 10.24** 9.37** 3.36
** p < 0.01 *** p < 0.001
F(5, 42) = 0.53, p = ns. The means and standard deviations of the mediation scores for mediators with low and high maths levels are presented in Table 4. Effect of mediator’s verbal ability on mediation style. Another of the study’s question was whether the mediators’ verbal ability had an effect on their mediation style. Correlation analyses among the three abstract verbal ability subtests (Auditory Association, Synonyms and Antonyms) revealed significant positive correlations, ranging from 0.49 to 0.67. Principal factor analyses with varimax orthogonal rotations were carried out for the three subtests in the mediators group. The findings revealed that only one factor (Eigenvalue = 2.19) emerged; a factor that explained 73.1 percent of the variance. It was consequently decided to combine all verbal tests into one global score. All test scores were transformed into percentages and averaged to obtain a verbal ability score. The effect of verbal ability on mediation style was studied by a MANOVA of treatment × verbal ability level (2 × 2), where the dependent variables were the five mediation criteria. The mediators group was divided into high versus low verbal ability by the median score. The MANOVA revealed no significant main effect of verbal ability level, F(5,47) = 0.87, p = ns, and no significant treatment × verbal ability level interaction, F(5,47) = 0.24, p = ns. Effect of treatment on learners’ mediation style. The effect of the peer mediation treatment on the learners’ (grade 2) mediation style was analysed by a MANOVA of treatment × mediator’s maths level × learner’s maths level (2 × 2 × 2). The dependent variables were the five mediation criteria of the learner. The findings indicate that, in general, the mediation score of the experimental learners was significantly higher than that of the control learners, F(4, 42) = 2.52, p < 0.001. The 224
Shamir et al.: Peer Mediation means and standard deviations of the mediation scores are presented in Table 3. Table 3 indicates that the experimental learners scored higher than did the control learners. However, univariate analyses revealed that the treatment effects were uniquely significant for only three mediation criteria: intentionality and reciprocity, meaning and regulation of behaviour. Mediators’activation and anti-mediation behaviour Treatment differences were also investigated in relation to the two non-mediation behaviour criteria: activation and anti-mediation. A MANOVA of treatment × mediator’s maths level × learner’s maths level (2 × 2 × 2) was carried out with activation and anti-mediation behaviours as dependent variables. The findings revealed a significant main effect of treatment, F(1,46) = 21.22, p < 0.001, indicating higher scores for activation in the control (M = 4.33, SD = 3.39 (than in the experimental (M = 1.14, SD = 0.36) group. No significant differences were found for the other main effects or interactions.
Discussion The PMYC program, as a peer-mediation treatment, aims at enhancing a mediation teaching style, developing learning to learn skills and enhancing cognitive modifiability of young mediators as well as learners. While previous research (Shamir and Tzuriel, 2002; 2004; Tzuriel and Shamir, 2004) has shown the effectiveness of the PMYC program using tasks considered to be domain general, the main goal of the current study was to investigate whether the PMYC program is likewise applicable to school subject matter or domain-specific tasks such as maths. Two additional goals guided the current research: (a) to discover whether the maths level of the mediator and the learner and the correspondence between them had any effect on the mediator’s mediation teaching style and (b) whether verbal ability affected the mediators’ mediation teaching style. It was likewise considered important to confirm whether Shamir and Tzuriel’s (2004) previous findings, showing the effectiveness of the PMYC program in enhancing the student’s mediation teaching style, can be replicated with a different sample using a content-oriented rather than a problem-solving task. Similar to the findings obtained in previous research (Shamir and Tzuriel, 2004), the experimental children in the current study showed significantly higher levels of mediation than did the control children for each of the five mediation criteria. The control children, on the other hand, showed higher levels of activation (i.e. solving the maths problem 225
School Psychology International (2006), Vol. 27(2) by directing the learner’s actions or by actually completing the task for him/her and anti-mediation behaviour than did the experimental children. Experimental findings (Shamir and Tzuriel, 2002) have already shown that the most striking group differences were to be found in Mediation for Feelings of Competence, Transcendence and Regulation of Behaviour. It is important to note that the findings of the current study replicate those findings across changes in sample characteristics and tasks employed. The unique findings of the current study are, however, those indicating that both mediators and learners in the experimental group showed higher pre- to post-intervention improvement in maths than did mediators and learners in the control group. These findings indicate the transferability of PMYC program effects. Both the experimental and the control groups studied maths as part of the interaction with the mediators. However, only the experimental children who had been exposed to the intervention program showed a pre- to post-intervention improvement. It is important to note that the learners who did not participate in the PMYC program but were tutored by experimental mediators also showed greater improvement in maths than did learners who were tutored by control mediators. The experimental group’s improvement can be attributed to the training in mediation strategies transmitted during the program and their application for learning maths during the peer interaction session. It seems that the mediation strategies were internalized and used later in another context – maths problem solving. The findings support our hypothesis that a cognition-oriented program aimed at enhancing self-mediation skills, such as the PMYC, can influence children not only in a domain-general task (i.e. problem solving), as reported earlier (Shamir and Tzuriel, 2002; Tzuriel and Shamir, 2004), but also in domain-specific tasks such as maths. Previous findings obtained with the PMYC program have shown that children who learned how to mediate became better self-mediators (i.e. better learners) themselves (Shamir and Tzuriel, 2002; 2004; Tzuriel and Shamir, 2004). We may assume that the experimental mediators, exposed to the rules of mediation within the framework of the PMYC program, became better self-mediators and consequently improved their maths achievement. These findings can be understood in relation to Vygotsky’s theory and its neo-Vigotskian elaborations (i.e. Rogoff, 1990; Wertsch, 1985). Vygotsky conceptualized the social mechanism that nurtures cognitive development as very much like apprenticeship, a relationship in which a novice works closely with an expert in joint problem solving in the zone of proximal development. Children internalize the shared cognitive processes and later use them, independently, in other problem-solving contexts (Rogoff, 1990). Following 226
Shamir et al.: Peer Mediation Vygotsky, Karpov and Haywood (1998) have commented that by regulating peers’ behaviour, children more readily learn to self-regulate and reconstruct their own thinking processes. It appears that in the present case, the experimental mediators who regulated their peers’ behaviours, following exposure to the PMYC program, verily reconstructed their own thinking (learning how to learn rules acquired during the program), a process that subsequently affected their maths performance. To illustrate, these children used more successful mediation strategies in teaching their peers, thereby succeeding in helping learners to internalize the rules of the maths tasks and improve performance in the post-teaching test. These findings demonstrate that peer mediation based on the PMYC program, which is essentially a cognitive education program, can be applied with domain-specific tasks such as maths; it is not limited to ‘pure’ cognitive tasks (general domain) as found previously (Shamir and Tzuriel, 2002; Shamir and Van der Aalsvoort, 2004; Tzuriel and Shamir, 2003). Vygotsky claimed that learning and cognitive change are more effective when the learner interacts with a more experienced adult or peer. Based on this claim, two additional questions were raised in the current study with respect to the applicability of peer mediation of maths tasks in heterogeneous classes. The first question is related to the relationship between a child’s maths level and mediation style. The second question is related to the effect of a mediator’s verbal ability on his/her mediation style. The findings showed that mediators with high maths levels scored higher than did mediators with low maths level on all mediation criteria. However, no significant main effect was found for learners’ maths level, nor was a significant interaction identified between the mediator’s and the learner’s maths level. The findings also revealed no significant main effects or interaction effect between verbal ability and mediation style. These findings have important theoretical and practical implications. In spite of the fact that matched cognitive level between mediator and learner influenced the mediator’s mediation teaching style in an earlier study (Shamir and Tzuriel, 2004), the match in maths level was not significant in the current study. This difference in findings can be attributed to the different type of tasks used in the studies. In Shamir and Tzuriel’s (2004) study, the task was a domain-general task (solving seriation problems) whereas in the present study, the task was domain specific (maths). One might argue that when teaching a domain-specific task such as maths in a peer-mediation context, control of previous knowledge is essential for the mediation process, not for the mediator–learner match in maths knowledge. This idea corresponds with Vygotsky’s idea about the need for an experienced adult or 227
School Psychology International (2006), Vol. 27(2) a peer mediator. When the nature of the task is domain general, it can be argued, the cognitive match emerges as a dominant factor. This post-hoc interpretation requires further research in which the mediator–learner cognitive match and task type will be systematically varied. In the current study, we elaborated Vygotsky’s idea about the necessity to ‘interact with a more experienced adult or peer’ by showing that only the mediator’s maths level – but not necessarily his/her verbal ability – should be taken into account when pairing children for peer interaction in maths. The findings regarding the contribution of the mediator’s maths level and the unimportance of verbal ability to the mediation process are of special significance in multicultural classes. In these classes, skills transmission is problematic due to the different learning habits displayed by the students in addition to the wide range of familiarity with the language in which lessons are conducted (Rich, 1996). In such situations, the positive effect of the program on children’s performance, irrespective of verbal ability, is of special importance, especially regarding maths – a subject considered difficult to teach. Conclusion To conclude, the results of this study show that training young children in PMYC is an effective way to prepare them for a peer mediation style that enhances both the tutor’s and the tutee’s learning how to learn skills and, in consequence, their learning and achievements in maths. We may conclude from these results that the PMYC program promises broad potential for implementation. It is suggested that future studies investigate whether the program can address students’ special needs on the one hand – by opening up an avenue for individuated instruction – and provide a practical solution to the difficulties of teachers required to handle large heterogeneous classes on the other. In conjunction with the variety of instructional methods currently used in schools, the PMYC program demonstrates that a cognitive education-oriented program can also be applied with school subjects. Further studies are needed, however, to examine this effect with different subject matter and populations. References Feuerstein, R., Rand, Y. and Hoffman M. B. (1979) The Dynamic Assessment of Retarded Performers: The Learning Potential Assessment Device, Theory, Instruments, and Technique. Baltimore, MD: University Park Press. Feuerstein, R., Rand, Y., Hoffman, M. B. and Miller, R. (1980) Instrumental Enrichment. Baltimore, MD: University Park Press.
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