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

The effects of peer tutoring on students' mathematics self-concepts were examined. The Marsh questionnaire was used to measure students' mathematics self-concepts before and after implementation of a peer tutoring program. A pretest posttest control group design was employed. Study participants included 376 students from grades 7 to 9 (12 to 15 years old). No statistically significant differences were reported between the pretest and the posttest for any of the control groups. Statistically significant improvements were reported for all grades for the experimental groups. An average increment of 13.4% was reported for students in the experimental group, and the overall effect size was reported to be medium (Hedges' g = 0.48). No statistically significant differences were reported across grades for the experimental group. The main conclusion of this study is that same-age and reciprocal peer tutoring may be very beneficial for middle school students' mathematics self-concepts. Several recommendations for field practitioners emanated from the study: use same-age and reciprocal tutoring over cross-age and fixed peer tutoring; schedule tutoring programs for four weeks or less with two to four sessions of 25 minutes or less per week for each tutoring session; and, include a control group in research studies.

RCT Entities:   Population Interventions Outcomes

Introduction

Peer tutoring may be defined as a flexible teaching strategy in which half of the students serve as academic tutors and the other half serve as academic tutees [1]. In this methodology a higher achieving student (tutor) provides assistance with academic content to a lower achieving student (tutee). Several benefits have been documented across the literature for both tutors and tutees during peer tutoring experiences. From an academic perspective, the majority of studies report significant improvements in the students’ mathematics scores [2, 3]. The social implications of peer tutoring are also valuable, as it fosters student inclusion [4] and improves the class climate [5]. Different psychological variables have been widely addressed in the field, such as anxiety or attitude towards mathematics [6, 7, 8, 9]. Most studies reporting promising results for academic, social, and psychological variables showed close to medium effect sizes [10]. One of the variables that has yet to be thoroughly addressed is self-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 significant 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) [15], an alternative definition is the sum total of individuals’ mental and physical characteristics and their own evaluation of them. Hence, self-concept is believed to have a complex structure with different factors comprising it. In this sense, Marsh et al. (2018) [16] identified three main aspects of self-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) [18] and Wolff, Nagy, Helm, and Möller (2018) [19] authored papers in which they described how self-concept can both predict and influence academic achievement in different subjects, such as mathematics, reading, and literature, across different learning levels, including primary and secondary education. Hence, considering that an increase in students’ self-concepts usually results in an increase in their academic achievement [20, 21], it is of interest, from an academic 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 most time studying [22]. Research by Pajares and Miller (1994) [23] and Pietsch, Walker, and Chapman (2003) [24] documented the high correlation between students’ mathematics self-concepts and their mathematics academic achievement from primary education to college. Sax (1994) [25] stated that the direct relationship of this psychological variable with students’ academic performance 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 becoming more distinct with age. Marsh and Shavelson (1985) [27] and Lee (2009) [28] concluded that mathematics was the subject in which students’ academic performance was influenced most by their subject-related self-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 task behavior. If a student truly beliefs he/she can solve a mathematics problem, he/she will have the necessary resilience to persist until he/she can solve it. Students with a high self-concept may see failed attempts as exciting challenges and new opportunities, while students with low self-concept will doubt their own abilities and give up early after few attempts [29, 30]. Besides, 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 school to middle school usually results in a decrease in students’ mathematics self-concept during the first year, that is, 7th grade. Factors such as a higher difficulty in the mathematics contents, substantially more difficult exams, the change of learning environments and methodologies are associated with this decrease. Given the importance of this variable, several validated instruments have been developed to measure it at different educational levels [33].

Peer tutoring

Peer tutoring is an active teaching methodology that fosters student inclusion while enabling students to learn from each other [34]. Topping (2018) [35] defined it as a cooperative learning method based on a pairing of students who share learning objectives. These objectives are achieved through a framework in which students have an asymmetric relationship derived from their respective academic competences. In this sense, in each pair one of the students plays the role of tutor and the other plays tutee [36]. Tutees must ask tutors academic questions in order to acquire curriculum content. The main role of the tutors is to provide feedback and help their tutees during the learning process, as tutors, by design, have higher academic competency than their partners [37]. Both tutors and tutees benefit from this methodology. Tutees benefit from receiving direct instruction from a peer. As students share a similar discourse, tutees usually feel more comfortable, ask more 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 active learning and foster student inclusion, as all students participate in the process [39, 40].

The different forms that peer tutoring takes depend on a series of factors, with participants’ ages and roles being the most important [41]. Experts in the field refer to pairing students of different ages as cross-age tutoring [42]. In this type of tutoring, most often the older student plays the role of tutor. Same-age tutoring have been defined as the pairing of a tutor and tutee of the same age [43]. Same-age tutoring is usually easier to arrange and carry 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 fixed peer tutoring, students do not exchange roles [45]. The benefits of peer tutoring in mathematics have been widely largely documented during the last years [3, 46, 47, 48]. Although psychological variables have not been studied as in depth as academic achievement, several meta-analysis in the field state that the expect effect sizes in a peer tutoring intervention may be considered as small to moderate [49, 50]. Academic and psychological effects of peer tutoring may differ significantly across educational levels. For example, academic effects are usually greater in primary education 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 impact on students’ self-concepts, but the significance of the effect has yet to be proven. During the last several years, the latest studies of peer tutoring and students’ self-concepts in reading [53], writing [54], English as a foreign language [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, King, and Heller (1992) [59], Fantuzzo, Davis, and Ginsburg (1995) [60], Ginsburg-Block and Fantuzzo (1997) [61], and Topping, Campbell, Douglas, and Smith (2003) [62] focused on the effect of peer tutoring on students’ mathematics self-concepts. Half of the studies showed significant improvements regarding self-concepts, while results for the other half were not significant or were inconclusive. Most of them indicated that tutors’ self-concept increased significantly after 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 confidence in his/her own abilities in mathematics increases. In fact, recently, while Zeneli, Tymms, and Bolden (2016) [63] did not find any significant results, Alegre Ansuategui and Moliner Miravet (2017) [2] did find significant improvements regarding mathematics self-concept in this context. Although many articles the research in the field show positive outcomes and improvements in students’ mathematics self-concept, only some of them report statistically significant improvements or significant effect sizes. Authors such as Froiland and Davison (2016) [64], Sáinz and Upadyaya, K. (2016) [65], Westphal, Kretschmann, Gronostai and Vock (2018) [66] indicate that peer helping could be beneficial for students mathematics self-concepts and state that more research is needed to address 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 there is a need for more 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 research was the Valencian Ministry of Education. They approved the research but the obtained consent specified that data had to be analyzed anonymously.

Aim of the study and hypotheses

The main aim of this research was to determine the effect of peer tutoring on middle school students’ mathematics self-concepts. To this purpose, two hypotheses were defined:

Hypothesis 1: Students’ mathematics self-concepts will improve significantly as a result of peer tutoring.

Hypothesis 2: No statistically significant differences will be found between 7th, 8th and 9th grade students’ scores before and after the implementation of the peer tutoring program.

Research design

Stigmar (2016) [68] stated that the research design employed in a peer tutoring experience may significantly affect the results. According to this author, the absence of a control group or just performing a posttest (pretest posttest without control group and posttest only with control designs) may overestimate the effect of the experience. Hence, following the guidelines given by this author, an experimental pretest posttest with control group design [69] was used in this research so that results were not critically affected 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 study were selected through clustered sampling, which is a sampling technique that divides the population into groups (middle schools, in this case) so that they all share similar characteristics [72]. One public middle school was randomly selected, and students participating in this research were accessed after 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

According to the Spanish Educational Government, about 1.5 million students were enrolled in grades 7 to 9 in Spain. The authors of this manuscript sought a study sample representative of the population of middle school 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 9 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 and 49.47% were male. The average age was 14.21 years old with a standard deviation of 1.37 years. Of the total, 210 (56%) were Hispanic, 94 (25%) were Rumanian, 64 (17%) were African, 4 (1%) were Asian and the other 1% were from other ethnic groups. The socio-economic status of the students’ families was average. Students were assigned to the experimental or the control group on a probabilistic basis [75]. Hence, half the students in each course were randomly assigned to the experimental group and the other half to the control group. There were six subgroups in each grade. A draw was performed for each grade so that three subgroups were assigned to experimental conditions and the other three to control conditions. An additional final draw 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 grade [76]. 9 students were randomly excluded due to this procedure.

Academic content

In the study, 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 first-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. Eighth graders refreshed on the contents of the prior year’s course as previously described and also calculated compound probabilities, standard deviations and variances, first degree equations with fractions, second degree equations and surfaces, and volumes of irregular prisms. Ninth graders also refreshed previous content and worked with quartiles, percentiles, and box plots, developed advanced tree diagrams, applied Laplace's rule of succession, calculated complex surfaces and volumes, and solved third- and fourth-degree equations of direct solving (using Ruffini’s rule and factorizing).

Peer tutoring implementation

During the first term, teachers for all courses used traditional teaching methods. That is, contents were taught using a one-way instructional teaching method: students could not interact at any time, and they had to sit individually. During the second term, a peer tutoring program 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 as extremely difficult to implement due to bureaucratic and organizational issues. It was impossible to set several hours in which students from upper courses could tutor students from lower courses, as they had different schedules. Also, the parameters for involvement established through the legal consent were quite restrictive; for example, the tutoring program had to be implemented during school 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 self-concept, as they always receive help from their peers, making them feel 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 affect final study results.

Classroom dynamics during peer tutoring

The classroom dynamic was as follows. First, the teacher checked students’ homework, corrected that homework on the blackboard, and explained new content, which took about 15–20 minutes. Later, all students had to complete two exercises followed by either one or two problems, depending on the difficulty of the content. Students worked individually for approximately 15 minutes. The teacher helped students if they were unsure how to proceed. 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 problems that they had not finished yet together. Students were told to follow the protocols and principles indicated by Topping, Buchs, Duran and Van Keer (2017) [36] including, among other issues, “pause, prompt and praise” techniques. Each teacher monitored their students’ interactions. As Wingate (2019) [79] states, the teacher’s role 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 last 5 to 10 minutes, the teacher 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 self-concepts were measured using the Marsh self-concept questionnaire [80], developed by Marsh and Shavelson. This instrument is based on a Likert scale and includes reversed items. Students must grade each item from 1 (absolutely false) to 8 (absolutely true). The questionnaire contains thirteen 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 because 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 research [83, 84]. The average score for each student was used in this study. The higher the score, the higher the mathematics self-concept of the student was. Students’ completed the questionnaire independently during tutoring hours and it 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 about it.

Organization and scheduling

The length of the program, number of sessions per week, and amount of time per peer tutor session were determined following indications by Leung (2015) [85] to maximize gains in students’ self-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 group continued with the above mentioned one-way instructional teaching method. The same teacher that did the lecture in the experimental group also did it in the control group for the same 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 following the suggestions provided by De Backer, Van Keer, and Valcke (2016) [86]. According to these authors, the teacher must supervise interactions between students and assist 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 teacher must help them until they know how to correctly solve the problem. Students were placed in a hierarchal order from highest to lowest, according to their first-term mathematics marks. Then, in order to pair the students, the first and second students in the list constituted the first pair, the third and fourth students constituted the second pair, and so on until the list was finished. This way, the academic differences between pairs are minimized as the academic gap between tutor and tutee is the least possible. According to Matinde (2019) [87] most of the students feel very comfortable with this way of pairing as they are paired with peers whose knowledge in the subject is similar to them. Aspects such as finishing the task in a similar time or sharing similar academic goals in the subject are crucial when it comes to collaboration between students. The other main option of pairing students implied carrying out a fixed peer tutoring. In fixed peer tutoring students’ are ordered by academic achievement, then the list is split in two halves. The first half are the tutors and the other half serves as tutees so that the most competent tutor is paired with the most competent tutee and so on. This way of pairing was discarded as 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 as half of the students (tutees) are almost always 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 course (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 same teachers that taught them mathematics the whole year. Students participated actively during the training with the help of the teacher, for instance, indicating the qualities and abilities that a good tutor and a good 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 non-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 basis 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 problems. First, the teacher had to check that one of the two 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 not coincide, the student who had the correct answer had to explain to the student whose answer was incorrect how to correctly solve the problem, and both had to try to detect the mistake made. Any questions regarding mathematics content were allowed during the interactions, but always from a perseverance and individual work perspective.

Data analysis

SPSS software version 25 was used to analyze all student data. Means, standard deviations and gain scores were reported. Simple quantitative analysis was also 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 order 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 analyze the differences among grades in the experimental group for the pretest scores, posttest scores and gain scores [89]. Effect sizes were calculated [90], and Hedge’s g was provided in each case.

Results

The descriptive results of this study are shown in Table 1, Fig 1 and Fig 2. Mean scores, standard deviations (SDs), and number of students (n) by grade (7th, 8th, and 9th), group (experimental or control), and phase of the study (pretest or posttest) are reported in Table 1. In order to facilitate readers’ understanding of the results obtained in this study, overall scores for the experimental and control group 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.

Table 1

Means, standard deviations and number of students by grade, group and phase of the study.

	Pretest						Posttest
	Experimental			Control			Experimental			Control
Grade	Mean	SD	n	Mean	SD	n	Mean	SD	n	Mean	SD	n
7th	3.76	1.26	62	3.81	1.31	62	4.26	1.29	62	3.87	1.41	62
8th	3.68	1.40	62	3.74	1.32	62	4.19	1.32	62	3.72	1.29	62
9th	3.53	1.23	64	3.55	1.20	64	3.98	1.21	64	3.60	1.37	64
All	3.65	1.31	188	3.70	1.26	188	4.14	1.28	188	3.73	1.32	188

Fig 1

Pretest and posttest overall scores and standard deviations for the experimental and control group.

Fig 2

Experimental group pretest and posttest scores and standard deviations by grades.

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.

Table 2

Number of students that increase or decrease their scores after the peer tutoring program by grades and group.

	Experimental group		Control group
Grade	Increase (%)	Decrease (%)	Increase (%)	Decrease (%)
7th	50 (80%)	12 (20%)	33 (54%)	29 (46%)
8th	53 (86%)	9 (14%)	30 (48%)	32 (52%)
9th	54 (84%)	10 (16%)	33 (52%)	31 (48%)
All	158 (84%)	30 (14%)	96 (51%)	92 (49%)

The analysis of differences between the pretest and the posttest for the experimental group is shown in Table 3. Statistically significant differences between the posttest and the pretest were found individually for each grade and also overall.

Table 3

Experimental group mean differences between the posttest and the pretest and t-tests by grades and overall.

Grade	Mean difference	t-Value
7th	0.50	2.08*
8th	0.51	1.98*
9th	0.45	1.99*
All	0.49	2.91*

*p < .05

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

Table 4

Control group mean differences between the posttest and the pretest and t-tests by grades and overall.

Grade	Mean difference	t-Value
7th	0.06	0.23
8th	-0.02	0.08
9th	0.05	0.21
All	0.03	0.21

The analysis of gain scores, that is, the difference between the posttest and the pretest scores, comparing the experimental group and the control group is shown in Table 5. Statistically significant differences were reported individually for each grade and also overall.

Table 5

Mean differences between experimental and control group gain scores and t-tests by grades and overall.

Grade	Mean difference	t-Value
7th	0.44	2.01*
8th	0.53	2.28*
9th	0.41	1.99*
All	0.46	3.30*

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

When analyzing the gain scores of the experimental group, an overall increment of 13.4% was found. Calculation of effect sizes showed a Hedge’s g value of 0.40 for 7th graders, 0.41 for 8th graders, and 0.37 for 9th 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 between the pretest and the posttest scores for the experimental group, were revealed for all grades as a result of peer tutoring; therefore, hypothesis 1 (students’ mathematics self-concepts will improve significantly as a result of peer tutoring) was confirmed. In this sense, no significant differences were reported across grades before or after implementation of the peer tutoring program. Hence, hypothesis 2 (no statistically significant differences will be found between 7th, 8th and 9th grade students’ scores before and after the implementation of the peer tutoring program) was also confirmed. Recent previous research in the field is consistent with the results found in this examination. Studies conducted by Tsuei (2012) [91], Ke (2013) [92], and Toh and Kaur (2019) [93] also showed improvements in the mathematics self-concepts of students after peer tutoring. This may be attributable to students feeling more capable and valuable in mathematics as they help each other [94, 95]. Moreover, reciprocal and same-age peer tutoring makes all students feel part of the learning process, as any student may be able to explain content throughout the program [96]. Hence, it seems like this type of tutoring has a greater effect than other types of tutoring on students’ self-concepts [53]. Indeed, the effect sizes reported in the study showed that the magnitude of the effect 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 also confirmed. This fact, also, 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 self-concept may be found across educational levels, that is, between primary, secondary, and postsecondary education, but are more difficult to find within the same educational level [14,15].

Although results in this experience may be seen as 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, there is usually a low percentage of students (about 10–15%) that do not improve academically or psychologically. This may be because some students do not 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 so strong that interactions are not valuable and learning between peers does not take place. Besides, when differences between pairs are very limited, such pairs do not benefit so much from the experience. Moreover, ceiling effects must also be considered as many students already showed high scores in the pretest [101]. In this sense, as Agne and Muller (2019) [102] indicate, the supervision of the teacher plays a key role during peer tutoring. Ensuring that interactions are rich from an academic perspective and that cooperation takes place among peers are keys to ensuring that most of the students are benefiting from peer tutoring [103].

Apart from the inconvenience noted, there are certain limitations that should be 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 viable. 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 middle school students, it is not representative of students outside the country. Future research should address the efficiency of this methodology across different countries and within different educational settings [107]. In this sense, caution is required, as many variables, such as the type of students, the time of implementation of the peer tutoring program, the frequency of sessions, the type of experimental design, and many other issues may affect the final outcome significantly [108, 109]. The fact that only one middle school was selected through the sampling process must also be considered, as a comparison among different schools could add greater value to this research [110].

Conclusion and implications for practice

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. Considering the results of this study 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 7th to 9th grade students (12 to 15 years old) in mathematics. Also, from an organizational point of view, same-age and reciprocal tutoring is easier to implement, as it can take place within the same classroom of students. Given the promising results of this study and considering the previous studies in the field, low duration tutoring programs should be scheduled for four weeks or less with two to four sessions of 25 minutes or less per week for each tutoring session. The use of a control group is also highly encouraged, as its absence may result in an overestimation of effect sizes. Moreover, as a document in the literature, practitioners in the field may find improvements not only in the mathematics self-concept variable, but also in other academic and psychological variables, such as anxiety or attitude towards mathematics.

17 Dec 2019

PONE-D-19-28784

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

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Reviewer #1: Partly

Reviewer #2: Partly

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: No

Reviewer #2: Yes

**********

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Reviewer #1: No

Reviewer #2: Yes

**********

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Reviewer #1: Yes

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: This manuscript reported an empirical study that was conducted in a Spanish middle school with the purpose of investigating the effects of peer tutoring on students’ math self-concept. Considering the school context, the effect sizes reported in the manuscript are not small and I believe may have practical significance. However, the study has one major flaw, which is not having a student achievement related variable. The only variable that the authors looked at was math self-concept. In addition, the statistical analysis reported in the results section were not clearly written and may be redundant. Detailed comments are listed below.

Major issues

1. Some important articles are missing from the literature review part. For example, Roscoe and Chi (2007) “Understanding Tutor Learning: Knowledge-Building and Knowledge-Telling in Peer Tutors’ Explanations and Questions”, Roscoe and Chi (2007) “Tutor learning: the role of explaining and responding to questions”.

2. As the authors stated in the self-concept section, self-concept can influence academic achievement. So why was this not accounted for in the hypothesis formulation?

3. What are the potential causes of research design that affect the results? If random assignment to conditions was implemented successfully, I don’t see any problems for a pretest-posttest, experimental vs. control group design.

4. Please be specific about how students were assigned to different conditions. What did the authors mean by a probabilistic base?

5. What were the subscales for the Marsh self-concept questionnaire? I suggest providing some sample items. Also, were there reversely coded items?

6. Did the teacher do the lecture or provide more problems for students to solve in the control condition?

7. Please provide more details about the peer tutoring training that students received.

8. What if both students who were paired had mistakes in their solved problems? Did they receive help from the teacher until they knew how to correctly solve the problem?

9. Which group was the experimental group? Group A or group B?

10. Line 293, what did the three tests (test 1, 2 and 3) about?

11. I cannot understand Table 3.

12. One major issue regarding the results is that the authors did not specify the independent variables and dependent variable in each statistical test they conducted.

13. Line 315. I suggest clearly stating what significant improvements were revealed.

14. I suggest restating the hypotheses in Discussion section.

15. I did not realize that the authors were also interested in the effects of different grade levels on self-concept until I finished reading the results and discussion. So I suggest including some literature in the literature review section.

Minor issues

16. It is not clear what global effect size means in the abstract.

17. First line on page 5, I think the word primary was missing from “…during the transition from school to…”

18. The sentence from line 148 – 152 is too long and difficult to understand.

Reviewer #2: Effects of Peer Tutoring On Middle School Students’ Mathematics Self-Concept

The Marsh questionnaire was used to measure participating students’ mathematics self-concepts before and after implementation of a peer-tutoring program.

The main aim of this research was to determine the effect of peer tutoring on middle school students’ mathematics self-concepts. The study tested two hypotheses.

Hypothesis 1: Students’ mathematics self-concepts will improve significantly as a result of peer tutoring.

Hypothesis 2: Students enrolled in different grades will not show significant differences regarding mathematics self-concepts before and after peer tutoring. ( This hypothesis is not clear. I had to get to line 328 to get the point of this hypothesis. )

Relevant literature was used to discuss the impact of self-concept on the learning of mathematics. However, it would make the paper more meaningful if the authors could be more expansive how positive self-concept helps with mathematics performance. Line 101 the point that students experience important self-concept changes resulting in a lower mathematics self-concept. Line 101 is circuitous, as it does not explain why there should be changes now and what these changes could affect mathematics performance.

In the section Peer tutoring and self-concept, it would be helpful if the authors could draw upon the literature cited to provide more substantial discussion how peer tutoring improve self-concept of the tutor. In line 144, the evidence is not as conclusive as one would hope. Perhaps the authors could offer reasons why the evidence are not so conclusive and how the current authors’ work could provide data to support the effect of peer-tutoring and tutors self-concept. More hypothesising here would make a better case for the hypothesis 1.

Hypothesis 2 is not clear. Perhaps the authors could provide clearer discussion and draw the reader to the meaning of this Hypothesis.

The data collection process was discussed and easy to follow More discussion could be used to explain the formation of the tutor-tutee pair. Although the authors cited the literature (De Becker et al. ) they drew upon to construct the tutor-tutee pair, what other methods did they consider to form the tutor-tutee pair and why the work of De Becker chosen, In particular how much difference in performance should there be between each member of the pair? Only when the relevant literature has been discussed could the authors use the literature to support their selection of the tutor-tutee pair.

Did the authors conduct a pilot study to help confirm such tutor-tutee pair would be effective? Without such preparation, it is difficult to give much credence to the effects of the study.

In the current paper, the authors explained the formation of the pairs. The students were arranged according to their performance, thus the first student was paired with the second, the third with the fourth, and so on. The authors, however, did not explain how different were the students in each pair. What if the first student was an A+ student (85 marks) and the second student, also an A+ student (83 marks), one would not pair these two students as the peer tutoring process would not be helpful to either one. This may explain the finding why although peer tutoring frequently has a positive impact on students,

“there is usually a low percentage of students (about 10–15%) that do not improve academically or psychologically. This may be because some students do not 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 so strong that interactions are not valuable and learning between peers does not take place.” Line 338 -343

It could be that when the differences between the pairs are so limited, such pairs do not benefit from the experience. Did the authors interview such students to ascertain why they did not benefit from the experience?

Studies exploring the effects of Peer-tutoring and the self-concept of tutors are important as peer-tutoring help students develop understanding of themselves as learners and also how helping others to learn strengthen and deepen their own (i.e. tutors’) knowledge of themselves as learners. In addition, self-concept of the tutors could change if they feel that their work with the tutees was beneficial. Also, peer-tutoring and its positive effects self-concept could have a last impact on how students learn. Currently the authors are looking at how self-concept is a function of peer-tutoring. But improved self-concept could help tutors learn how to learn: by helping others.

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files to be viewed.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.

2 Jan 2020

Dear Editor and Reviewers,

We, the authors, are thankful for your consideration of this manuscript. We really appreciate all the comments and suggestions you made in your reviews as the manuscript has been improved considerably. Please find below our responses to your comments. We hope that now you find our manuscript suitable for publication. If that is not the case, please do not hesitate to tell us what you think should be done in order to improve it.

Thank you very much,

Kind regards,

The authors

Academic Editor requirements

When submitting your revision, we need you to address these additional requirements:

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at http://www.plosone.org/attachments/PLOSOne_formatting_sample_main_body.pdf and http://www.plosone.org/attachments/PLOSOne_formatting_sample_title_authors_affiliations.pdf

We ensured that PLOS ONE’s style requirements were met, including those for file naming

2. You indicated that you had ethical approval for your study. In your Methods section, please ensure you have also stated whether you obtained consent from parents or guardians of the minors included in the study (your manuscript only mentions participants' "families") or whether the research ethics committee or IRB specifically waived the need for their consent.

Now this part is clearly stated in the Methodology section (sample access subsection)

3. Your ethics statement must appear in the Methods section of your manuscript. If your ethics statement is written in any section besides the Methods, please move it to the Methods section and delete it from any other section. Please also ensure that your ethics statement is included in your manuscript, as the ethics section of your online submission will not be published alongside your manuscript.

- In the Methodology section we indicated that Ethical requirements provided by the Ethics Committee of the Spanish National Research Council (CSIC) were met during this research.

Reviewer #1 comments:

This manuscript reported an empirical study that was conducted in a Spanish middle school with the purpose of investigating the effects of peer tutoring on students’ math self-concept. Considering the school context, the effect sizes reported in the manuscript are not small and I believe may have practical significance. However, the study has one major flaw, which is not having a student achievement related variable. The only variable that the authors looked at was math self-concept. In addition, the statistical analysis reported in the results section were not clearly written and may be redundant.

You are absolutely right about the absence of a student achievement related variable. We, the authors, thought about this possibility before starting the research. Nevertheless, we found several legal problems when accessing students’ academic achievement in mathematics. Legal consent for the self-concept variable was not very difficult to obtain, but that was not the case for students’ academic achievement. The administration was reluctant to authorize us to use students’ academic information. We take note of your comment and we hope that we can incorporate this variable in our future studies somehow.

Detailed comments are listed below.

Major issues

1. Some important articles are missing from the literature review part. For example, Roscoe and Chi (2007) “Understanding Tutor Learning: Knowledge-Building and Knowledge-Telling in Peer Tutors’ Explanations and Questions”, Roscoe and Chi (2007) “Tutor learning: the role of explaining and responding to questions”.

Both references and other recent articles were added in the literature review part.

2. As the authors stated in the self-concept section, self-concept can influence academic achievement. So why was this not accounted for in the hypothesis formulation?

As we indicated before, we did not obtain legal consent to use the academic achievement variable in our research. Although we knew that we could not perform an analysis, we wanted to note the importance of self-concept regarding mathematics achievement. If you think we must delete this part, please, just tell us and we will do it.

3. What are the potential causes of research design that affect the results? If random assignment to conditions was implemented successfully, I don’t see any problems for a pretest-posttest, experimental vs. control group design.

Our apologies for the misunderstanding. We clarified this part. What Stigmar (2016) means is that some research designs such as pretest posttest without control group or posttest only with control may overestimate the effects of a peer tutoring experience. That’s why we wanted to note that it was important to select a pretest posttest with control group design, so that reported effects were as realistic as possible.

4. Please be specific about how students were assigned to different conditions. What did the authors mean by a probabilistic base?

We clarified this part. We indicated that half the students in each course were randomly assigned to the experimental group and the other half to the control group. There were six subgroups in each grade. A draw was performed for each grade so that three subgroups were assigned to experimental conditions and the other three to control conditions. An additional final draw 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 grade. 9 students were randomly excluded due to this procedure.

5. What were the subscales for the Marsh self-concept questionnaire? I suggest providing some sample items. Also, were there reversely coded items?

The three subscales were indicated. We also indicated the existence of reversely coded items in the questionnaire and provided some sample items.

6. Did the teacher do the lecture or provide more problems for students to solve in the control condition?

We now have indicated in the subsection “organization and scheduling” that students The same teacher that did the lecture in the experimental group also did it in the control group for the same grade. Students in the experimental and control groups were provided the same problems and exercises during the development of the peer tutoring intervention.

7. Please provide more details about the peer tutoring training that students received.

Further details regarding the peer tutoring training were provided in the “organization and scheduling” section.

8. What if both students who were paired had mistakes in their solved problems? Did they receive help from the teacher until they knew how to correctly solve the problem?

Our apologies for not including this information in the manuscript. Of course, if both students who are paired had mistakes in their solved problems, the teacher had to help them until they knew how to correctly solve the problem. This is now clearly stated in the “organization and scheduling” section.

9. Which group was the experimental group? Group A or group B?

10. Line 293, what did the three tests (test 1, 2 and 3) about?

11. I cannot understand Table 3.

Our apologies for not clarifying enough what group A and group B meant and the analysis we were carrying out in table 3. We have clarified this in the manuscript right now before table 3.

First, analysis of differences for the pretest scores between experimental and control groups were conducted for each grade (tests 1 to 3). Then, analysis of differences between the posttest and the pretest scores were conducted for the experimental group by grade and overall (tests 4 to 7) and, after that, analogous analysis were carried out for the control group (tests 8 to 11). Finally, a comparison of increments, that is, the difference between the posttest and the pretest scores for experimental and control group were carried out by grade and overall (tests 12 to 15). Group A and group B were just named like that so that the reader could understand that two subgroups or groups were being compared and which of them was the minuend and the subtrahend when calculating mean differences in table 3.

12. One major issue regarding the results is that the authors did not specify the independent variables and dependent variable in each statistical test they conducted.

The mathematics self-concept scores acts as the dependent variable and the different groups are the independent variables. This has been clearly stated in the manuscript.

13. Line 315. I suggest clearly stating what significant improvements were revealed.

This has been clearly stated.

14. I suggest restating the hypotheses in Discussion section.

Hypotheses were restated in Discussion section

15. I did not realize that the authors were also interested in the effects of different grade levels on self-concept until I finished reading the results and discussion. So I suggest including some literature in the literature review section.

Some literature regarding effect sizes in the literature review section has been included

Minor issues

16. It is not clear what global effect size means in the abstract.

“Global effect size” was changed by “overall effect size”. We just wanted to mean that this was the effect size for all grades combined and not separately.

17. First line on page 5, I think the word primary was missing from “…during the transition from school to…”

As, in all comments above, you are absolutely right. The word primary was added. Thank you very much.

18. The sentence from line 148 – 152 is too long and difficult to understand.

This sentence was divided in three separate sentences so that readers may understand it better. Thank you very much for your review.

Reviewer #2 comments:

Effects of Peer Tutoring On Middle School Students’ Mathematics Self-Concept

The Marsh questionnaire was used to measure participating students’ mathematics self-concepts before and after implementation of a peer-tutoring program.

The main aim of this research was to determine the effect of peer tutoring on middle school students’ mathematics self-concepts. The study tested two hypotheses.

Hypothesis 1: Students’ mathematics self-concepts will improve significantly as a result of peer tutoring.

Hypothesis 2: Students enrolled in different grades will not show significant differences regarding mathematics self-concepts before and after peer tutoring. (This hypothesis is not clear. I had to get to line 328 to get the point of this hypothesis. )

Our apologies for the lack of clarity regarding hypothesis 2. We have rewritten this hypothesis and we hope that now it looks clearer for the readers.

Relevant literature was used to discuss the impact of self-concept on the learning of mathematics. However, it would make the paper more meaningful if the authors could be more expansive how positive self-concept helps with mathematics performance.

In subsection “self-concept” we explained more how positive self-concepts helps with mathematics performance.

Line 101 the point that students experience important self-concept changes resulting in a lower mathematics self-concept. Line 101 is circuitous, as it does not explain why there should be changes now and what these changes could affect mathematics performance.

The information in this line has been rewritten so that it looks clearer for readers

In the section Peer tutoring and self-concept, it would be helpful if the authors could draw upon the literature cited to provide more substantial discussion how peer tutoring improve self-concept of the tutor.

More substantial discussion was provided from the cited literature in this subsection.

In line 144, the evidence is not as conclusive as one would hope. Perhaps the authors could offer reasons why the evidence are not so conclusive and how the current authors’ work could provide data to support the effect of peer-tutoring and tutors self-concept. More hypothesising here would make a better case for the hypothesis 1.

As in all comments above, you are absolutely right. More reasons on why the evidence are not so conclusive were given in this part and this made a better case for hypothesis 1. Thank you very much.

Hypothesis 2 is not clear. Perhaps the authors could provide clearer discussion and draw the reader to the meaning of this Hypothesis.

As stated above, hypothesis 2 was written.

The data collection process was discussed and easy to follow

Thank you very much for your kindness.

More discussion could be used to explain the formation of the tutor-tutee pair.

More discussion was used in this section.

Although the authors cited the literature (De Becker et al.) they drew upon to construct the tutor-tutee pair, what other methods did they consider to form the tutor-tutee pair and why the work of De Becker chosen, In particular how much difference in performance should there be between each member of the pair? Only when the relevant literature has been discussed could the authors use the literature to support their selection of the tutor-tutee pair.

This was also discussed in the section. The other main option instead of reciprocal peer tutoring was fixed peer tutoring. Fixed peer tutoring implies a different type of pairing than reciprocal peer tutoring. All this is discussed now in the manuscript.

Did the authors conduct a pilot study to help confirm such tutor-tutee pair would be effective? Without such preparation, it is difficult to give much credence to the effects of the study.

A pilot study was carried out one year before. Although only 19 students participated in the study, promising results were found. This study was published and it is referenced in the manuscript.

In the current paper, the authors explained the formation of the pairs. The students were arranged according to their performance, thus the first student was paired with the second, the third with the fourth, and so on. The authors, however, did not explain how different were the students in each pair. What if the first student was an A+ student (85 marks) and the second student, also an A+ student (83 marks), one would not pair these two students as the peer tutoring process would not be helpful to either one. This may explain the finding why although peer tutoring frequently has a positive impact on students,“there is usually a low percentage of students (about 10–15%) that do not improve academically or psychologically. This may be because some students do not 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 so strong that interactions are not valuable and learning between peers does not take place.” Line 338 -343. It could be that when the differences between the pairs are so limited, such pairs do not benefit from the experience. Did the authors interview such students to ascertain why they did not benefit from the experience?

You are absolutely right. We included your reflection about what happens when differences peers are so limited. Besides, ceiling effects were also indicated as some students already had high scores in the pretest. We did not interview students, but we take note of the importance of using qualitative information to contrast these findinds for our future research. Thank you very much for improving our manuscript.

Submitted filename: response_to_editor.docx

Click here for additional data file.

3 Feb 2020

PONE-D-19-28784R1

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

PLOS ONE

Dear Moliner,

I have now received two reviews of your manuscript PONE-D-19-28784R1 entitled “ Effects of peer tutoring on middle school students’ mathematics self-concepts". One of the reviewers recommended a minor revision. In light of this reviewer’s recommendation, I have determined that your manuscript requires another revision before I can consider it for publication in PLOS ONE. Please revise your manuscript and submit a list of responses to the reviewer’s comments.

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We look forward to receiving your revised manuscript.

Kind regards,

Bing Hiong Ngu, Ph.D.

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: (No Response)

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: (No Response)

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: No

Reviewer #2: (No Response)

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: (No Response)

Reviewer #2: (No Response)

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: (No Response)

Reviewer #2: (No Response)

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: I enjoyed reading this manuscript. I appreciate the authors’ effort in addressing the concerns I raised in the previous review and understand the difficulty in obtaining student achievement data. I hope the minor issues listed below could help the authors further improve their manuscript.

1. Last sentence on page 4 may have typos. “…such as motivation oron…”

2. In the section Peer tutoring and self-concept, the authors first stated research related to peer tutoring in math on self-concept, then described related research in other fields. However, the authors stated research in math again at the end of this section. I suggest enhancing the structure of this section.

3. I did not see that the authors elaborated on the peer tutoring literature on how students in different grades, although the authors responded that they did. From my point of view, such elaboration can shadow Hypothesis 2.

4. The results section is not very readable. For example, what type of statistical tests were test 1 to test 3? I suggest the authors refer to APA style guide to get some ideas about how to write a results section.

5. I raised the issue in the previous review that the analysis the authors conducted were somewhat redundant, such as the ANOVA and the t tests. However, the authors did not address this in the revision.

Reviewer #2: (No Response)

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files to be viewed.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.

13 Feb 2020

Dear Editor and Reviewer,

Thank you very much for all the work you are putting in to improve our manuscript. As you suggested, we addressed the minor revisions of one of the reviewers and we hope that our manuscript is now suitable for publication. Our responses to these revisions may be found below.

If you think we must do any additional changes or we must address any other issues, please do not hesitate to contact us,

Thank you very much,

Kind regards,

The authors

Reviewer #1 comments:

I enjoyed reading this manuscript. I appreciate the authors’ effort in addressing the concerns I raised in the previous review and understand the difficulty in obtaining student achievement data. I hope the minor issues listed below could help the authors further improve their manuscript.

Thank you very much for your thorough reviews that are helping us so much to improve our manuscript.

1. Last sentence on page 4 may have typos. “…such as motivation oron…”

Our apologies for that. We accidentally deleted a space between “or” and “on” and it became a typo. This was corrected and now it says what it was intended to say “such as motivation or on task behavior”.

2. In the section Peer tutoring and self-concept, the authors first stated research related to peer tutoring in math on self-concept, then described related research in other fields. However, the authors stated research in math again at the end of this section. I suggest enhancing the structure of this section.

You are absolutely right. We restructured this section by dividing all the information that was on it into two different sections. The first one called “peer tutoring and self-concept” now addresses experiences in subjects different of mathematics. The second one called ““peer tutoring and mathematics self-concept” specifically addresses peer tutoring and mathematics self-concept experiences.

3. I did not see that the authors elaborated on the peer tutoring literature on how students in different grades, although the authors responded that they did. From my point of view, such elaboration can shadow Hypothesis 2.

Sorry for that. We included the following information at the end of the “peer tutoring” section. Academic and psychological effects of peer tutoring may differ significantly across educational levels. For example, academic effects are usually greater in primary education 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].

4. The results section is not very readable. For example, what type of statistical tests were test 1 to test 3? I suggest the authors refer to APA style guide to get some ideas about how to write a results section.

We indicated that tests 1 to 3 refer to analysis of differences for pretest scores between experimental and control groups for each grade. We also looked for APA style guides to report results. APA guide indicates that inferential statistical tests, tables and figures must be included and that effect sizes must be reported. As there were no figures in our manuscript, we included two figures (figure 1. Experimental vs control group overall scores and figure 2. Experimental scores by grades) so that readers of the manuscript could understand better the results section.

5. I raised the issue in the previous review that the analysis the authors conducted were somewhat redundant, such as the ANOVA and the t tests. However, the authors did not address this in the revision.

In the first ANOVA we addressed the differences between the pretest scores for the experimental group across grades and in the second ANOVA we addressed the differences in the increments for the experimental group across grades. These analysis had not been previously performed in the previous t tests, that’s why we did not delete any of these analysis. However, if you think we must delete any of these analysis, please just tell us and we will do it.

Submitted filename: response_to_reviewers.docx

Click here for additional data file.

18 Feb 2020

PONE-D-19-28784R2

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

PLOS ONE

Dear Dr Moliner,

I have now received a review of your revised manuscript PONE-D-19-28784R2 titled “Effects of peer tutoring on middle school students’ mathematics self-concepts. I concur with the reviewer that several aspects of the issues raised has not been adequately addressed. More work is needed to refine the following:

There is a need to provide a more readable presentation of the data analysis using APA guidelines (e.g., the use of APA format to report results). The information in the Tables (e.g., there are redundant words, the layout is awkward) and Figures needs rewording to improve clarity.

An analysis of the difference between the experimental group and the control group for the pretest is redundant given that their mean scores only differ slightly.

Greater clarity is needed to describe Test 1 and Test 3.

The use of ANOVA and the t tests in the data analysis is unclear.

I want to give you an opportunity to revise your manuscript. Your manuscript could be reconsidered for publication if you can successfully attend to the issues raised. When preparing your revised manuscript, you are asked to carefully consider the comments, and submit a list of responses to the comments.

We would appreciate receiving your revised manuscript no later than 35 days from today.  When you are ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter.

To enhance the reproducibility of your results, we recommend that if applicable you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

Please include the following items when submitting your revised manuscript:

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). This letter should be uploaded as separate file and labeled 'Response to Reviewers'.

A marked-up copy of your manuscript that highlights changes made to the original version. This file should be uploaded as separate file and labeled 'Revised Manuscript with Track Changes'.

An unmarked version of your revised paper without tracked changes. This file should be uploaded as separate file and labeled 'Manuscript'.

Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

We look forward to receiving your revised manuscript.

Kind regards,

Bing Hiong Ngu, Ph.D.

Academic Editor

PLOS ONE

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files to be viewed.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.

28 Feb 2020

Dear Editor and Reviewer,

Thank you very much for all the work you are putting in to improve our manuscript. As you suggested, we addressed the minor revisions of one of the reviewers and we hope that our manuscript is now suitable for publication. Our responses to these revisions may be found below.

If you think we must do any additional changes or we must address any other issues, please do not hesitate to contact us,

Thank you very much,

Kind regards,

The authors

Editor comments:

There is a need to provide a more readable presentation of the data analysis using APA guidelines (e.g., the use of APA format to report results). The information in the Tables (e.g., there are redundant words, the layout is awkward) and Figures needs rewording to improve clarity.

We remade the entire results section, following APA format to report results, deleting redundant words and trying to provide a more suitable layout. Figures were also reworded in order to improve clarity.

An analysis of the difference between the experimental group and the control group for the pretest is redundant given that their mean scores only differ slightly.

We deleted this analysis

Greater clarity is needed to describe Test 1 and Test 3.

Test 1 and test 3 referred to the analysis above indicated. As you suggested, we deleted them.

The use of ANOVA and the t tests in the data analysis is unclear.

We tried to provide a clearer explanation about the use of ANOVAs and t tests in the “data analysis” section.

Reviewer #1 comments:

I enjoyed reading this manuscript. I appreciate the authors’ effort in addressing the concerns I raised in the previous review and understand the difficulty in obtaining student achievement data. I hope the minor issues listed below could help the authors further improve their manuscript.

Thank you very much for your thorough reviews that are helping us so much to improve our manuscript.

1. Last sentence on page 4 may have typos. “…such as motivation oron…”

Our apologies for that. We accidentally deleted a space between “or” and “on” and it became a typo. This was corrected and now it says what it was intended to say “such as motivation or on task behavior”.

2. In the section Peer tutoring and self-concept, the authors first stated research related to peer tutoring in math on self-concept, then described related research in other fields. However, the authors stated research in math again at the end of this section. I suggest enhancing the structure of this section.

You are absolutely right. We restructured this section by dividing all the information that was on it into two different sections. The first one called “peer tutoring and self-concept” now addresses experiences in subjects different of mathematics. The second one called ““peer tutoring and mathematics self-concept” specifically addresses peer tutoring and mathematics self-concept experiences.

3. I did not see that the authors elaborated on the peer tutoring literature on how students in different grades, although the authors responded that they did. From my point of view, such elaboration can shadow Hypothesis 2.

Sorry for that. We included the following information at the end of the “peer tutoring” section. Academic and psychological effects of peer tutoring may differ significantly across educational levels. For example, academic effects are usually greater in primary education 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].

4. The results section is not very readable. For example, what type of statistical tests were test 1 to test 3? I suggest the authors refer to APA style guide to get some ideas about how to write a results section.

Following suggestions given by the editor, tests 1 to 3 were deleted as they were not necessary. We also looked for APA style guides to report results. APA guide indicates that inferential statistical tests, tables and figures must be included and that effect sizes must be reported. As there were no figures in our manuscript, we included two figures (figure 1. Experimental vs control group overall scores and figure 2. Experimental scores by grades) so that readers of the manuscript could understand better the results section.

5. I raised the issue in the previous review that the analysis the authors conducted were somewhat redundant, such as the ANOVA and the t tests. However, the authors did not address this in the revision.

The editor raised the same issue as you did. Following your recommendations, we remade the entire results section, following APA style, trying to make it more readable and deleting redundant analysis. We hope that this section looks much better now.

Submitted filename: response_to_editor_and_reviewers.docx

Click here for additional data file.

5 Mar 2020

PONE-D-19-28784R3

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

PLOS ONE

Dear Dr Moliner,

While you have addressed other issues raised by Reviewer 1, the issue about data analysis and presentation remain a serious concern. The following need more work:

The titles of Tables and Figures need to be more explicit so as to reflect the content of Tables and Figures.

There is still a lot of redundant information in the tables. For example, the pre-test and post-test in Table should appear only once rather than multiple times in the table (see Ngu & Phan, 2017, page 888).

What do you mean by students’ t-test? Researchers normally use a t-test to examine the mean difference between two groups. I never heard of a student’s t-test.

The analysis of ANOVA is very confusing. I suggest you re-analyse the data. You can either perform a repeated measures ANOVA or t-test. You may perform a 2 (group: experimental vs. control) x 2 (test: pre-test vs. post-test) ANOVA for each grade separately and then for the all grades combined. The group is a between-group factor, and the test is a repeated measures within-subject factor. Alternatively, perform a t-test between the experimental group and the control group on gain score (i.e., post-test – pre-test) for each grade separately and then for all grades.

I want to give you yet another opportunity to revise your manuscript. If you can successfully address the issues related to data presentation and analysis, your manuscript could be reconsidered for publication in PLOS ONE.

We would appreciate receiving your revised manuscript not later than 35 days from today. When you are ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter.

To enhance the reproducibility of your results, we recommend that if applicable you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

Please include the following items when submitting your revised manuscript:

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). This letter should be uploaded as separate file and labeled 'Response to Reviewers'.

A marked-up copy of your manuscript that highlights changes made to the original version. This file should be uploaded as separate file and labeled 'Revised Manuscript with Track Changes'.

An unmarked version of your revised paper without tracked changes. This file should be uploaded as separate file and labeled 'Manuscript'.

Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

We look forward to receiving your revised manuscript.

Kind regards,

Bing Hiong Ngu, Ph.D.

Academic Editor

PLOS ONE

[Note: HTML markup is below. Please do not edit.]

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files to be viewed.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.

18 Mar 2020

Reviewer #1 comments:

I enjoyed reading this manuscript. I appreciate the authors’ effort in addressing the concerns I raised in the previous review and understand the difficulty in obtaining student achievement data. I hope the minor issues listed below could help the authors further improve their manuscript.

Thank you very much for your thorough reviews that are helping us so much to improve our manuscript.

1. Last sentence on page 4 may have typos. “…such as motivation oron…”

Our apologies for that. We accidentally deleted a space between “or” and “on” and it became a typo. This was corrected and now it says what it was intended to say “such as motivation or on task behavior”.

2. In the section Peer tutoring and self-concept, the authors first stated research related to peer tutoring in math on self-concept, then described related research in other fields. However, the authors stated research in math again at the end of this section. I suggest enhancing the structure of this section.

You are absolutely right. We restructured this section by dividing all the information that was on it into two different sections. The first one called “peer tutoring and self-concept” now addresses experiences in subjects different of mathematics. The second one called ““peer tutoring and mathematics self-concept” specifically addresses peer tutoring and mathematics self-concept experiences.

3. I did not see that the authors elaborated on the peer tutoring literature on how students in different grades, although the authors responded that they did. From my point of view, such elaboration can shadow Hypothesis 2.

Sorry for that. We included the following information at the end of the “peer tutoring” section. Academic and psychological effects of peer tutoring may differ significantly across educational levels. For example, academic effects are usually greater in primary education 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].

4. The results section is not very readable. For example, what type of statistical tests were test 1 to test 3? I suggest the authors refer to APA style guide to get some ideas about how to write a results section.

Following suggestions given by the editor, tests 1 to 3 were deleted as they were not necessary. We also looked for APA style guides to report results. APA guide indicates that inferential statistical tests, tables and figures must be included and that effect sizes must be reported. As there were no figures in our manuscript, we included two figures (figure 1. Experimental vs control group overall scores and figure 2. Experimental scores by grades) so that readers of the manuscript could understand better the results section.

5. I raised the issue in the previous review that the analysis the authors conducted were somewhat redundant, such as the ANOVA and the t tests. However, the authors did not address this in the revision.

The editor raised the same issue as you did. Following your recommendations, we remade the entire results section, following APA style, trying to make it more readable and deleting redundant analysis. We hope that this section looks much better now.

Submitted filename: response_to_editor_and_reviewers.docx

Click here for additional data file.

24 Mar 2020

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

PONE-D-19-28784R4

Dear Dr. Moliner,

I am pleased to inform you that I am accepting your manuscript PONE-D-19-28784R4 "Effects of peer tutoring on middle school students’ mathematics self-concept" for publication in PLOS ONE.

Within one week, you will receive an e-mail containing information on the amendments required prior to publication. When all required modifications have been addressed, you will receive a formal acceptance letter and your manuscript will proceed to our production department and be scheduled for publication.

Shortly after the formal acceptance letter is sent, an invoice for payment will follow. To ensure an efficient production and billing process, please log into Editorial Manager at https://www.editorialmanager.com/pone/, click the "Update My Information" link at the top of the page, and update your user information. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to enable them to help maximize its impact. If they will be preparing press materials for this manuscript, you must inform our press team as soon as possible and no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

With kind regards,

Bing Hiong Ngu, Ph.D.

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

26 Mar 2020

PONE-D-19-28784R4

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

Dear Dr. Moliner:

I am pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please notify them about your upcoming paper at this point, to enable them to help maximize its impact. If they will be preparing press materials for this manuscript, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

For any other questions or concerns, please email plosone@plos.org.

Thank you for submitting your work to PLOS ONE.

With kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Dr. Bing Hiong Ngu

Academic Editor

PLOS ONE