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Effects of peer tutoring on middle school students' mathematics self-concepts

• Francisco Alegre

Effects of peer tutoring on middle school students' mathematics self-concepts

• Lidon Moliner,
• Francisco Alegre

x

• Published: April 10, 2020
• https://doi.org/x.1371/journal.pone.0231410

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Abstract

The effects of peer tutoring on students' mathematics self-concepts were examined. The Marsh questionnaire was used to measure students' mathematics self-concepts earlier and after implementation of a peer tutoring plan. A pretest posttest control group design was employed. Study participants included 376 students from grades 7 to 9 (12 to 15 years one-time). No statistically significant differences were reported between the pretest and the posttest for whatever of the control groups. Statistically significant improvements were reported for all grades for the experimental groups. An average increment of thirteen.4% was reported for students in the experimental group, and the overall effect size was reported to exist medium (Hedges' g = 0.48). No statistically significant differences were reported across grades for the experimental group. The main decision of this written report is that aforementioned-historic period and reciprocal peer tutoring may be very beneficial for center school students' mathematics self-concepts. Several recommendations for field practitioners emanated from the written report: employ same-age and reciprocal tutoring over cross-age and fixed peer tutoring; schedule tutoring programs for 4 weeks or less with 2 to four sessions of 25 minutes or less per calendar week for each tutoring session; and, include a control group in enquiry studies.

Citation: Moliner L, Alegre F (2020) Furnishings of peer tutoring on middle schoolhouse students' mathematics self-concepts. PLoS Ane 15(4): e0231410. https://doi.org/x.1371/periodical.pone.0231410

Editor: Bing Hiong Ngu, University of New England, AUSTRALIA

Received: October 15, 2019; Accustomed: March 23, 2020; Published: April ten, 2020

Copyright: © 2020 Moliner, Alegre. This is an open up access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted utilize, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: Data are held in a public repository (OSF Storage). doi: 10.17605/OSF.IO/RK43G.

Funding: The authors received no specific funding for this piece of work.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Peer tutoring may be defined as a flexible pedagogy strategy in which half of the students serve as academic tutors and the other half serve as academic tutees [ane]. In this methodology a higher achieving student (tutor) provides help with bookish content to a lower achieving pupil (tutee). Several benefits have been documented across the literature for both tutors and tutees during peer tutoring experiences. From an bookish perspective, the bulk of studies report significant improvements in the students' mathematics scores [2, 3]. The social implications of peer tutoring are also valuable, equally information technology fosters student inclusion [4] and improves the class climate [v]. Different psychological variables take been widely addressed in the field, such as anxiety or attitude towards mathematics [6, 7, 8, nine]. Nigh studies reporting promising results for academic, social, and psychological variables showed close to medium outcome sizes [ten]. One of the variables that has yet to exist thoroughly addressed is cocky-concept. Results from previous studies in the field are inconclusive. While some authors indicate that peer tutoring may be beneficial and that their students showed improvements [11, 12], others state that no meaning improvements or benefits were documented [13]. Hence, given the proven potentiality of these methodologies with academic and psychological variables, it is of interest to test the effects of peer tutoring on students' self-concept.

Theoretical framework

Self-concept

Several authors have defined self-concept through the years. Marsh et al. (2019) [14] defined self-concept as individuals' self-perceptions formed through their own experiences and interpretations of their environment. According to Parker, Marsh, Guo, Anders, Shure, and Dicke (2018) [xv], an alternative definition is the sum full of individuals' mental and concrete characteristics and their own evaluation of them. Hence, self-concept is believed to accept a circuitous structure with different factors comprising it. In this sense, Marsh et al. (2018) [16] identified 3 chief aspects of cocky-concept: the behavioural (action), the affective (feeling), and the cognitive (thinking). The importance of this psychological variable has been broadly documented. Susperreguy, Davis‐Kean, Duckworth, and Chen (2018) [17] Walgermo, Frijters, and Solheim (2018) [eighteen] and Wolff, Nagy, Helm, and Möller (2018) [xix] authored papers in which they described how self-concept tin both predict and influence academic achievement in dissimilar subjects, such as mathematics, reading, and literature, beyond different learning levels, including primary and secondary educational activity. Hence, because that an increase in students' self-concepts usually results in an increase in their bookish achievement [20, 21], it is of involvement, from an bookish perspective, to examine teaching methodologies that may positively influence students' self-concepts.

Mathematics self-concept

This research aims directly at students' self-concepts regarding mathematics, which is the academic subject students spent the near time studying [22]. Research by Pajares and Miller (1994) [23] and Pietsch, Walker, and Chapman (2003) [24] documented the loftier correlation betwixt students' mathematics self-concepts and their mathematics bookish accomplishment from primary education to college. Sax (1994) [25] stated that the direct human relationship of this psychological variable with students' bookish operation increases as they get older. In this sense, according to Marsh and O'Neill (1984) [26], the structure of the mathematics self-concept is multifaceted and hierarchical with facets condign more than distinct with age. Marsh and Shavelson (1985) [27] and Lee (2009) [28] concluded that mathematics was the field of study in which students' bookish performance was influenced about by their bailiwick-related cocky-concept. According to these authors a positive self-concept may help with mathematics performance given the effects that produces in variables such as motivation or on job behavior. If a educatee truly beliefs he/she tin can solve a mathematics problem, he/she volition accept the necessary resilience to persist until he/she tin can solve it. Students with a loftier self-concept may see failed attempts as exciting challenges and new opportunities, while students with low self-concept will doubtfulness their ain abilities and give up early on after few attempts [29, 30]. As well, authors such as Sticca, Goetz, Bieg, Hall, Eberle, and Haag (2017) [31] or Onetti, Fernández-García, and Castillo-Rodríguez (2019) [32] state that the transition from primary schoolhouse to middle schoolhouse usually results in a decrease in students' mathematics self-concept during the first twelvemonth, that is, 7^th form. Factors such as a higher difficulty in the mathematics contents, substantially more hard exams, the modify of learning environments and methodologies are associated with this decrease. Given the importance of this variable, several validated instruments have been developed to measure information technology at different educational levels [33].

Peer tutoring

Peer tutoring is an agile teaching methodology that fosters student inclusion while enabling students to larn from each other [34]. Topping (2018) [35] divers it as a cooperative learning method based on a pairing of students who share learning objectives. These objectives are accomplished through a framework in which students accept an disproportionate relationship derived from their respective academic competences. In this sense, in each pair one of the students plays the office of tutor and the other plays tutee [36]. Tutees must ask tutors academic questions in gild to acquire curriculum content. The master role of the tutors is to provide feedback and help their tutees during the learning process, as tutors, by design, have higher bookish competency than their partners [37]. Both tutors and tutees do good from this methodology. Tutees benefit from receiving direct teaching from a peer. As students share a like soapbox, tutees commonly experience more than comfortable, ask more than questions, and better understand the content [38]. Tutors benefit as they reinforce their knowledge by answering the tutees' questions. These interactions between tutors and tutees promote agile learning and foster pupil inclusion, every bit all students participate in the process [39, 40].

The unlike forms that peer tutoring takes depend on a series of factors, with participants' ages and roles being the nigh important [41]. Experts in the field refer to pairing students of dissimilar ages as cantankerous-age tutoring [42]. In this type of tutoring, near often the older student plays the role of tutor. Same-historic period tutoring have been divers as the pairing of a tutor and tutee of the same age [43]. Aforementioned-historic period tutoring is usually easier to arrange and conduct out from an organizational point of view [44]. Depending on the students' roles, fixed or reciprocal peer tutoring may be defined. During reciprocal peer tutoring, students exchange roles, going from tutor to tutee and vice versa. Conversely, in stock-still peer tutoring, students do not exchange roles [45]. The benefits of peer tutoring in mathematics take been widely largely documented during the terminal years [3, 46, 47, 48]. Although psychological variables have not been studied equally in depth as bookish accomplishment, several meta-assay in the field land that the expect consequence sizes in a peer tutoring intervention may be considered as pocket-sized to moderate [49, l]. Academic and psychological effects of peer tutoring may differ significantly across educational levels. For example, academic effects are usually greater in primary didactics than in secondary education [47, 48]. Nevertheless, effects within the same educational level are expected to be similar and, when analyzing differences across grades, significant differences are rarely reported [49, 50].

Peer tutoring and self-concept

Previous meta-analyses in the field by Ginsburg-Block, Rohrbeck, and Fantuzzo (2006) [51] and Ullah, Tabassum, and Kaleem (2018) [52] noted that peer tutoring usually has a positive touch on on students' cocky-concepts, only the significance of the result has however to exist proven. During the final several years, the latest studies of peer tutoring and students' self-concepts in reading [53], writing [54], English language as a foreign linguistic communication [55], physical education [56], physics [57], and chemistry [58] are promising but far for from being conclusive.

Peer tutoring and mathematics self-concept

The influence of peer tutoring on students' mathematics self-concepts has been addressed over the last three decades. The pioneer studies by Fantuzzo, Male monarch, and Heller (1992) [59], Fantuzzo, Davis, and Ginsburg (1995) [threescore], Ginsburg-Cake and Fantuzzo (1997) [61], and Topping, Campbell, Douglas, and Smith (2003) [62] focused on the consequence of peer tutoring on students' mathematics self-concepts. One-half of the studies showed significant improvements regarding self-concepts, while results for the other half were not meaning or were inconclusive. Most of them indicated that tutors' cocky-concept increased significantly afterward the peer tutoring experience. According to these authors, when a student realizes he/she is able to explain mathematics contents to a peer her/his conviction in his/her own abilities in mathematics increases. In fact, recently, while Zeneli, Tymms, and Bolden (2016) [63] did not find any meaning results, Alegre Ansuategui and Moliner Miravet (2017) [2] did find significant improvements regarding mathematics cocky-concept in this context. Although many articles the research in the field show positive outcomes and improvements in students' mathematics self-concept, merely some of them report statistically meaning improvements or meaning outcome sizes. Authors such as Froiland and Davison (2016) [64], Sáinz and Upadyaya, Grand. (2016) [65], Westphal, Kretschmann, Gronostai and Vock (2018) [66] indicate that peer helping could be beneficial for students mathematics cocky-concepts and state that more than inquiry is needed to accost the benefits of peer support in students' emotions. In this sense, the potentiality of peer tutoring with other variables such as mathematics achievement, mathematics anxiety or attitude towards mathematics has been proved. Besides, results found for some studies regarding the mathematics self-concept are inconclusive and at that place is a demand for more than literature in the field [67]. Hence, a peer tutoring study that addresses students' mathematics self-concept is performed in this research.

Methodology

The institutional review board that authorized this enquiry was the Valencian Ministry building of Education. They approved the inquiry just the obtained consent specified that data had to be analyzed anonymously.

Aim of the written report and hypotheses

The main aim of this inquiry was to decide the effect of peer tutoring on eye school students' mathematics self-concepts. To this purpose, 2 hypotheses were divers:

• Hypothesis i: Students' mathematics cocky-concepts will improve significantly as a result of peer tutoring.
• Hypothesis ii: No statistically significant differences will be found between 7^th, viii^thursday and nine^th grade students' scores before and after the implementation of the peer tutoring plan.

Research design

Stigmar (2016) [68] stated that the research design employed in a peer tutoring experience may significantly touch the results. According to this author, the absence of a control grouping or simply performing a posttest (pretest posttest without control group and posttest only with command designs) may overestimate the effect of the experience. Hence, following the guidelines given by this author, an experimental pretest posttest with control grouping pattern [69] was used in this research so that results were non critically afflicted by the experimental design.

Sample access

Difficulty of getting a proper sample in educational research has been discussed by authors such as Kane (2006) [70] or Micklewright, Schnepf and Silva (2012) [71]. In this sense, students in the written report were selected through clustered sampling, which is a sampling technique that divides the population into groups (heart schools, in this case) and then that they all share like characteristics [72]. One public centre school was randomly selected, and students participating in this research were accessed subsequently written informed consent was obtained from their families (parents or guardians of the minors), the School Council, and the Educational Government. Ethical requirements provided by the Ethics Committee of the Spanish National Research Council (CSIC) were met during this research.

Representativity of the sample

Co-ordinate to the Spanish Educational Government, about ane.5 million students were enrolled in grades seven to nine in Spain. The authors of this manuscript sought a study sample representative of the population of middle schoolhouse students in Spain. According to Krejcie and Morgan (1970) [73] and Johanson and Brooks (2009) [74], at least 368 students were needed to achieve this representation.

Participants

A total of 376 students, ages 12 to 15 years old, enrolled in grades 7 to nine participated in this research: 124 were enrolled in 7th grade, 124 were enrolled in 8th grade, and 128 were enrolled in 9th grade. 50.53% were female person and 49.47% were male. The average age was 14.21 years onetime with a standard deviation of 1.37 years. Of the total, 210 (56%) were Hispanic, 94 (25%) were Rumanian, 64 (17%) were African, 4 (one%) were Asian and the other ane% were from other ethnic groups. The socio-economic status of the students' families was boilerplate. Students were assigned to the experimental or the control group on a probabilistic basis [75]. Hence, one-half the students in each course were randomly assigned to the experimental group and the other one-half to the control group. There were vi subgroups in each grade. A draw was performed for each course so that 3 subgroups were assigned to experimental atmospheric condition and the other three to control conditions. An additional final describe was performed in some subgroups to exclude some students so that the number of students in the experimental group matched the number of students in the control group in each form [76]. 9 students were randomly excluded due to this procedure.

Academic content

In the written report, the content worked on by students, including algebra, geometry, statistics, and probability, corresponded to the third term of the mathematics courses for each grade. Seventh graders worked with basic offset-degree equations, calculated surfaces and volumes of regular prisms, used the Pythagoras' theorem, calculated basic statistical centralization parameters for both qualitative and quantitative variables, used Laplace's rule, and completed basic tree diagrams. 8th graders refreshed on the contents of the prior yr's form as previously described and also calculated compound probabilities, standard deviations and variances, offset degree equations with fractions, second degree equations and surfaces, and volumes of irregular prisms. Ninth graders likewise refreshed previous content and worked with quartiles, percentiles, and box plots, developed avant-garde tree diagrams, applied Laplace'southward rule of succession, calculated complex surfaces and volumes, and solved third- and fourth-degree equations of directly solving (using Ruffini'south rule and factorizing).

Peer tutoring implementation

During the first term, teachers for all courses used traditional didactics methods. That is, contents were taught using a one-fashion instructional education method: students could not interact at any time, and they had to sit down individually. During the 2d term, a peer tutoring programme was implemented in combination with the teachers' lessons. Reciprocal and same-age tutoring structures were selected for this study for several reasons. On one hand, cross-age tutoring was seen every bit extremely difficult to implement due to bureaucratic and organizational bug. Information technology was incommunicable to set several hours in which students from upper courses could tutor students from lower courses, as they had unlike schedules. Besides, the parameters for involvement established through the legal consent were quite restrictive; for example, the tutoring program had to be implemented during schoolhouse hours, and students could not leave their classes. On the other hand, previous research has shown that during fixed peer tutoring, tutees may decrease their cocky-concept, equally they e'er receive help from their peers, making them experience academically less capable and not as useful as their colleagues [77, 78]. Hence, reciprocal peer tutoring was implemented so that students' roles did not negatively impact final report results.

Classroom dynamics during peer tutoring

The classroom dynamic was as follows. Showtime, the instructor checked students' homework, corrected that homework on the blackboard, and explained new content, which took most fifteen–20 minutes. Later, all students had to complete two exercises followed by either 1 or two bug, depending on the difficulty of the content. Students worked individually for approximately 15 minutes. The teacher helped students if they were unsure how to go on. After that, peer tutoring was implemented for 20 minutes. Students were allowed to work in pairs, sharing their results, asking each other questions and solving the exercises and bug that they had not finished yet together. Students were told to follow the protocols and principles indicated past Topping, Buchs, Duran and Van Keer (2017) [36] including, amid other issues, "suspension, prompt and praise" techniques. Each teacher monitored their students' interactions. Every bit Wingate (2019) [79] states, the teacher's part is vital in the process as he/she must ensure that students' interactions are rich in academic language and that students are effectively helping each other. Finally, during the concluding five to 10 minutes, the instructor corrected and explained the exercises and problems on the blackboard. Extra problems were given to those students who finished their work early.

Instrument used to collect information

Students' academic cocky-concepts were measured using the Marsh self-concept questionnaire [80], developed by Marsh and Shavelson. This musical instrument is based on a Likert calibration and includes reversed items. Students must class each item from i (absolutely fake) to 8 (admittedly true). The questionnaire contains xiii items divided into three subscales: competence component, affective component and comparison component. Reversely coded items are included in the questionnaire such as item 3—I feel uncomfortable during mathematics class or item 7 –I'm not good at solving mathematics problems. This instrument was selected considering it was specific for mathematics and its validity and reliability have been widely documented [81, 82] and because it was used in prior peer tutoring inquiry [83, 84]. The average score for each pupil was used in this report. The higher the score, the higher the mathematics cocky-concept of the pupil was. Students' completed the questionnaire independently during tutoring hours and information technology took them between 20 to 30 minutes to complete it. A mathematics teacher was with the students while they were completing the questionnaire to solve any questions they could have well-nigh information technology.

Organization and scheduling

The length of the programme, number of sessions per calendar week, and amount of time per peer tutor session were adamant following indications by Leung (2015) [85] to maximize gains in students' cocky-concepts. Hence, three peer tutoring sessions were held each week in all courses for the experimental group. The program lasted four weeks, and, as indicated previously, peer interactions lasted 20 minutes. It must be noted that, during the peer tutoring implementation, the control grouping connected with the above mentioned one-fashion instructional teaching method. The same teacher that did the lecture in the experimental group also did it in the control group for the aforementioned grade. Students in the experimental and control groups were provided the same problems and exercises during the development of the peer tutoring intervention.

Pairs were distributed post-obit the suggestions provided by De Backer, Van Keer, and Valcke (2016) [86]. According to these authors, the teacher must supervise interactions betwixt students and help student pairs who are not able to finish the task on time. Besides, he/she also has to check the final results for each students. If both students who are paired have mistakes in their solved problems, the instructor must aid them until they know how to correctly solve the problem. Students were placed in a hierarchal gild from highest to lowest, according to their start-term mathematics marks. Then, in order to pair the students, the beginning and 2nd students in the list constituted the kickoff pair, the third and fourth students constituted the 2nd pair, then on until the list was finished. This fashion, the academic differences between pairs are minimized every bit the bookish gap betwixt tutor and tutee is the least possible. According to Matinde (2019) [87] about of the students experience very comfortable with this way of pairing as they are paired with peers whose knowledge in the subject is similar to them. Aspects such equally finishing the task in a like time or sharing similar academic goals in the bailiwick are crucial when information technology comes to collaboration betwixt students. The other main option of pairing students implied carrying out a stock-still peer tutoring. In fixed peer tutoring students' are ordered by academic accomplishment, and so the listing is split in 2 halves. The commencement half are the tutors and the other half serves as tutees and then that the about competent tutor is paired with the almost competent tutee and then on. This fashion of pairing was discarded equally several articles indicate that the academic gap between tutors and tutees is greater than for reciprocal peer tutoring and tutees self-concept is difficult to increase equally one-half of the students (tutees) are almost ever receiving help from their peers (tutors).

The students used the same kind of educational materials during the peer tutoring program they had used previously in the class (textbook, worksheets, and online exercises, for example). Students received training on peer tutoring development and skills days before the program was implemented. They were trained by the aforementioned teachers that taught them mathematics the whole year. Students participated actively during the grooming with the aid of the teacher, for instance, indicating the qualities and abilities that a good tutor and a expert tutee should have. Students were trained on the developing of the sessions and the nature of the interactions. The importance of sharing mathematics contents regarding the provided problems and exercises in each session and not other not-academic issues, trying to find different ways to explain a content to a tutee and valuing the different procedures used to solve a problem was highlighted. Respect and patience were defined as the ground of the interactions when working in pairs. Interactions during the tutoring sessions had to aim strictly to a shared goal: understanding and finishing all exercises and issues. First, the instructor had to check that ane of the 2 students in each pair had solved the tasks using suitable procedures and that the final result was correct. Later, students had to share their results and procedures, checking that results were the same for both. If results did non coincide, the pupil who had the correct answer had to explain to the pupil whose answer was incorrect how to correctly solve the problem, and both had to endeavor to observe the mistake fabricated. Any questions regarding mathematics content were allowed during the interactions, merely always from a perseverance and individual piece of work perspective.

Data analysis

SPSS software version 25 was used to clarify all student information. Means, standard deviations and gain scores were reported. Simple quantitative assay was too carried out in order to determine the percentage of students whose self-concept scores had improved or decreased following implementation of the program. T-test (95% confidence level) was used in gild to analyze the differences in gain scores between the experimental and the control group and also the differences between the posttest and the pretest scores within each group for each grade and overall [88]. Analyses of variance (ANOVAs) were used in order to clarify the differences among grades in the experimental group for the pretest scores, posttest scores and gain scores [89]. Outcome sizes were calculated [ninety], and Hedge'south g was provided in each example.

Results

The descriptive results of this written report are shown in Table i, Fig 1 and Fig 2. Mean scores, standard deviations (SDs), and number of students (n) by course (7th, 8^th, and 9th), grouping (experimental or command), and stage of the study (pretest or posttest) are reported in Table ane. In club to facilitate readers' understanding of the results obtained in this written report, overall scores for the experimental and control grouping are represented through a graph in Fig 1. Moreover, scores by grade for the experimental group are represented through a graph in Fig 2. Standard deviations are included in parenthesis in both figures.

The number of students whose self-concept scores increased or decreased from the pretest to the posttest by grade and group is shown in Table 2.

The analysis of differences between the pretest and the posttest for the experimental group is shown in Table iii. Statistically significant differences between the posttest and the pretest were establish individually for each grade and as well overall.

The analysis of differences between the pretest and the posttest for the command group is shown in Table 4. No statistically significant differences between the posttest and the pretest were plant for any of the grades nor overall.

The analysis of proceeds scores, that is, the divergence between the posttest and the pretest scores, comparison the experimental group and the control group is shown in Table five. Statistically significant differences were reported individually for each grade and also overall.

ANOVAS beyond grades were conducted for the experimental group. No statistically pregnant differences were reported for the pretest scores F (2, 185) = 0.46, p = .63, posttest scores F (ii, 185) = 0.02, p = .98 nor gain scores F (2, 185) = 0.55, p = .47 among grades.

When analyzing the proceeds scores of the experimental group, an overall increase of 13.four% was found. Calculation of issue sizes showed a Hedge's yard value of 0.xl for 7^th graders, 0.41 for 8^th graders, and 0.37 for 9^th graders. The global effect size for the peer tutoring program reported a Hedge's g value of 0.48.

Discussion

As stated previously, significant improvements, that is, statistically significant differences betwixt the pretest and the posttest scores for the experimental group, were revealed for all grades every bit a event of peer tutoring; therefore, hypothesis 1 (students' mathematics cocky-concepts will amend significantly as a issue of peer tutoring) was confirmed. In this sense, no meaning differences were reported across grades before or after implementation of the peer tutoring program. Hence, hypothesis ii (no statistically significant differences will be constitute betwixt 7^th, 8^th and 9^th class students' scores before and afterwards the implementation of the peer tutoring program) was also confirmed. Contempo previous enquiry in the field is consistent with the results institute in this exam. Studies conducted by Tsuei (2012) [91], Ke (2013) [92], and Toh and Kaur (2019) [93] too showed improvements in the mathematics cocky-concepts of students subsequently peer tutoring. This may exist attributable to students feeling more capable and valuable in mathematics every bit they help each other [94, 95]. Moreover, reciprocal and aforementioned-historic period peer tutoring makes all students feel function of the learning process, equally whatsoever student may exist able to explicate content throughout the plan [96]. Hence, it seems similar this type of tutoring has a greater event than other types of tutoring on students' cocky-concepts [53]. Indeed, the effect sizes reported in the written report showed that the magnitude of the upshot was medium [97] and that there was a considerable improvement in the students' self-concepts.

No significant differences were reported among grades. Hence, hypothesis 2 was as well confirmed. This fact, likewise, is consistent with prior studies, including the works of Susperreguy, Davis‐Kean, Duckworth and Chen (2018) [17] and Weidinger, Steinmayr and Spinath (2019) [98]. According to several authors, differences in cocky-concept may be found across educational levels, that is, between primary, secondary, and postsecondary instruction, but are more than difficult to find within the same educational level [14,15].

Although results in this experience may be seen every bit promising, the fact that 14% of the students in the experimental group showed lower self-concept scores must be considered. According to Drago, Rheinheimer and Detweiler (2018) [99] and Sytsma, Panahon, and Houlihan (2019) [100], although peer tutoring frequently has a positive impact on students' self-concepts, at that place is usually a low percentage of students (almost 10–15%) that do not meliorate academically or psychologically. This may be because some students exercise non like to help other peers with academic tasks, and, although the main goal of peer tutoring is to foster collaboration, the reluctance of some students is then strong that interactions are not valuable and learning betwixt peers does not take place. Too, when differences between pairs are very limited, such pairs do not benefit so much from the experience. Moreover, ceiling effects must also exist considered as many students already showed high scores in the pretest [101]. In this sense, as Agne and Muller (2019) [102] signal, the supervision of the instructor plays a key role during peer tutoring. Ensuring that interactions are rich from an academic perspective and that cooperation takes identify among peers are keys to ensuring that near of the students are benefiting from peer tutoring [103].

Apart from the inconvenience noted, there are sure limitations that should exist considered when interpreting the results of this study. First, the sample size was quite limited, and, although some researchers may not consider it trivial, it cannot be described as large, either [104, 105]. Furthermore, although as indicated above Krejcie and Morgan (1970) [73] and Johanson and Brooks (2009) [74] state that 368 were necessary, they referred to the case in which a random sampling is feasible. Authors such as Edgar, Murphy and Keating (2016) [106] state that data collected through other types different from random sampling offer no guarantee of representativity. In any case, although the sample may be representative of the population of Spanish heart schoolhouse students, it is non representative of students outside the land. Future research should address the efficiency of this methodology across different countries and within different educational settings [107]. In this sense, circumspection is required, as many variables, such as the type of students, the time of implementation of the peer tutoring programme, the frequency of sessions, the type of experimental design, and many other issues may touch on the final outcome significantly [108, 109]. The fact that only one middle schoolhouse was selected through the sampling process must also exist considered, as a comparison among dissimilar schools could add greater value to this research [110].

Conclusion and implications for do

The main conclusion that can be drawn from this study is that peer tutoring may be very beneficial for middle school students' mathematics self-concepts. Because the results of this report and previous research in the field, same-age and reciprocal peer tutoring is highly recommended for those field practitioners who want to improve the self-concepts of 7^th to ix^th form students (12 to fifteen years old) in mathematics. Also, from an organizational point of view, same-age and reciprocal tutoring is easier to implement, as it tin can take place within the same classroom of students. Given the promising results of this report and because the previous studies in the field, depression duration tutoring programs should be scheduled for 4 weeks or less with two to iv sessions of 25 minutes or less per week for each tutoring session. The utilise of a command group is also highly encouraged, as its absence may result in an overestimation of outcome sizes. Moreover, as a certificate in the literature, practitioners in the field may find improvements not merely in the mathematics self-concept variable, but besides in other academic and psychological variables, such as anxiety or attitude towards mathematics.

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