The More,the Merrier? Roles of Device-Student Ratio in Collaborative Inquiries and Its Interactions With External Scripts and Task Complexity

Abstract

In collaborative learning, the intuition “the more device, the merrier” is somehow widely acknowledged, but little research has investigated the relationship between device-student ratio and the learning outcome. This study aims to investigate not only the main effect of different device-student ratio, also to identify the moderators in the learning context including task complexity, external script availability and students’ familiarity to the collaboration settings. A three-round quasi-experiment was conducted in a primary school in mainland China, 130 fifth-grade students from four classes participated. Group worksheet including conceptual understanding and problem-solving tasks were used to collect participants’ inquiry performance. Repeated measures ANOVA was employed in data analysis. Findings indicate that 1:m device-student ratio could be beneficial, and external scripts, and prior collaboration experience could moderate such effect. The different effect of 1:m device-student ratio to 1:1 is only significant in the situation when students are faced with relatively simple task, and the effect size is larger when external script is present. When the task is more complicated, such effect of device-student ratio would only emerge after a period of collaboration. This finding challenged the intuition that one-to-one device-student ratio could be better. Related discussions and recommendations to teaching were made.

Keywords

computer-supported collaborative learning virtual manipulatives device-student ratio external scripts inquiry learning

With regards to using mobile devices to foster students’ learning in collaborative inquiry learning, studies have found that a 1:1 mobile device-student ratio could enhance primary students’ learning experience and performance through seamless resources acquisition anytime and anywhere (e.g., Hershkovitz, & Karni, 2018; Looi et al., 2011; Varier et al., 2017; L. H. Wong & Looi, 2011). Admittedly, getting each student equipped with a digital device is fruitful. Meanwhile, some researchers investigating Computer Supported Collaborative Learning (CSCL) also adopted the design that a group of pupils share one device (Kapici et al., 2019; Olympiou & Zacharia, 2018), those designs also yielded positive effects.

Consequently, here comes a question: Will the device-student ratio (DSR) have a certain effect on the students’ learning? Will the intuition “the more, the better” still stands in all the instruction conditions? There have been voices within the researcher community to reassess the notion of a 1:1 device-student ratio (Looi et al., 2010), but still little is known regarding how device-student ratio in groups would influence learning performance. As such, this research will investigate the effect of the device-student ratio together with some of the daily factors in real instructions as possible moderators including external scripts availability, task complexity and learners’ familiarity to the collaboration setting. Furthermore, investigating this problem is fruitful for instructors and educational administrators, as 1:1 DSR always means a large expense, undermining the potential good instruction designs available. To investigate such a problem could help the instructors and administrators conduct cost-effective teachings.

Meanwhile, Virtual manipulatives (VM), modeled after the prototypes of physical manipulatives (PM), which had been widely used in science class, VM enables students to conduct inquiry activities in a virtual environment, for example, a virtual lab. Studies have found that VM possesses unique advantages over PMs, including augmentation of experimental phenomena, repeatable operations, and timely feedbacks. This study will take virtual manipulatives as the digital tools in students’ collaboration.

Device-Student Ratio in Collaborative Inquiry Learning

When students collaborate, one determinate factor influencing the effect of using VM in scientific inquiries could be the DSR. On the one hand, studies have found that 1:1 DSR could enhance students’ learning experience because the technology affordance provides advantages in information integration and collaborative knowledge construction (Looi et al., 2011; L. H. Wong & Looi, 2011). On the other hand, one group of students share one digital device is also common in classrooms as this modality of collaboration inherits that of PM (e.g., Fokides & Mastrokoukou, 2018; Ha & Fang, 2018; Zacharia et al., 2008).

One question that emerged from these two modalities of collaboration is that whether more devices are bound to result in better learning performance? There seems to be some evidence challenging this intuition, but current literature is rather limited.

A recent systematic review synthesized evidence from 92 empirical studies published since 2000 to investigate how technology could enhance learning in secondary school math and science, the results indicate that a 1:2 computer-to-student ratio is more beneficial than a 1:1 ratio (Hillmayr et al., 2020). Nevertheless, not all studies in this meta-analysis are designed in collaboration settings, so little could be inferred from that analysis. In a long-term research by Hines (2020), the relationship of students’ academic achievement and the student-to-computer ratio was investigated, but no significant difference in the learning outcomes was reported. Also, Lin et al. (2012) compared two modalities of using tablets in collaboration on concept mapping: half of the groups in the study worked together with only one tablet (1:m); other groups had one tablet per student (1:1). The findings indicate that, in terms of concept mapping outcomes, 1:m ratio works better than 1:1 ratio; however, students under 1:1 condition experience higher perception toward tablet use and collaborative learning. With the complex interactions between devices, subjects, tasks inside the collaboration settings, the amount and type of support offered to students will affect the ability to carry out the task and thus will also affect their collaborative learning experience and performance (Kirschner et al., 2018).

Another quasi-experiment investigated the effect of three different modalities of device-student ratio on students’ learning outcome: one device per student, one device per group and one device per class. Results suggested that one device per group is more beneficial than one device per student, but no significant difference were reported regards the mental load and mental effort (Wang, Ma, et al., 2020).

One possible way of how device-student ratio could influence collaborative learning is that it would vary group members’ interaction. CSCL consists a lot of interactions, shared understandings and construction of knowledge (Kreijns et al., 2002). In science inquiry learning, one groups share one device, members would likely to have more interactions with each other, which makes it possible for high-quality knowledge construction to take place. Meanwhile, the design in a group each student has a device also has advantages, they have more chance to use the device and observe the learning content, which would benefit learning through individuals’ distributed knowledge acquisition.

Given the limited current research, it should be fruitful to investigate that problem. Instead of repeating the experiment in Lin et al. (2012), we argue that it would be more informative if appropriate collaborative learning pedagogy was to be incorporated into the experiment. In Wang, Ma, et al. (2020), the group with the modality that one device per class is in line with traditional teaching methods (e.g. lecturing with PPT), which is quite different from the CSCL settings. This could partly explain why the one device per group modality yielded a larger effect than this group and might have compounded the “true effect” yielded by the device-student ratio. In fact, like the long-lived “media-method debate” in educational media research (Clark, 1983; 1994; Kozma, 1991; 1994), manipulating the media is, somehow, bound to change the teaching method, which could mediate the effect yielded by the media variation. Consequently, experiments which just manipulate the device-student ratio and let the instruction happen “naturally”, without controlling for the teaching methods, are likely to draw limited conclusions as they neglect the underneath mechanisms and the boundary conditions.

Consequently, a new experiment should not only focus on the main effect of the device-student ratio on the learning outcomes but also reveal the boundary conditions including the characteristics of the learners, the learning content as well as the teaching method. In this research, we are interested in collaboration with external scripts, which is a popular teaching method in CSCL.

Virtual Manipulatives in Inquiry Learning

Inquiry learnings are gaining increasing popularity in classrooms. There is empirical evidence that learning with manipulatives can be more effective than merely present the learners with static materials (M. Wong et al., 2015), and inquiry abilities are becoming increasingly important these days. A two-year study conducted by Hsu et al. (2016) showed that students benefited from inquiry activities in class and gained more advanced inquiry abilities compared to those who received conventional instruction.

Inquiry learnings are always incorporated with computer-supported collaborative learning, with the help of virtual manipulative s(VM). VM is software running on digital devices, often designed to simulate physical manipulatives (PM) (Moyer, 2001). Compared to PM, VM has unique advantages. As is summarized by Olympiou and Zacharia (2012), the advantages of using VM in scientific inquiries are as follows: observing phenomena that cannot be observed in real life, making or repeating accurate measurements or operations, and overcoming time-consuming procedures, etc.

Possible Factors to Moderate the Effect of Device-Student Ratio on Collaboration

There could be numerous possible factors that influence collaborative learning, to name just a few: students’ collaboration skills and abilities (L. H. Wong et al., 2009), social readiness (L. H. Wong et al., 2010), students’ familiarity (Janssen et al., 2009), students’ prior knowledge (Zhang et al., 2016). It’s almost impossible to consider all of the factors in one research. This research starts from a pragmatics view and aims to investigate some variables that teachers could easily consider and manipulate in their instructional design: availability of external script, task complexity and students’ familiarity to the collaboration settings.

Collaboration supports and scaffolds are important for students’ learning in CSCL (Shin et al., 2020; Wu, 2020). One of the widely used tools in face-to-face collaboration is an external script. External scripts are normally provided by instructors as scaffolds for groups to facilitate collaboration by means of structuring activity sequence and distributing the functions to each participant (King, 2007).

Technologies often allow for learning experiences that many students have not encountered before. The more collaborative learning is different from traditional teaching, the harder it would be for students to collaborate effectively. One of the efficient tools to cope with such a problem is collaboration scripts (Fischer et al., 2013). Collaboration scripts are scaffolds that aim to facilitate collaboration by structuring the interactive processes (Kollar et al., 2006). As is documented, external scripts could reduce the cognitive load during students’ collaboration as they provide guidelines on procedure execution and workload distribution (Dillenbourg & Betrancourt, 2006).

There are two types of collaboration scripts, namely internal script and external script. An internal script is an internalized configuration of knowledge about collaboration which is developed from learners’ past collaboration instances (Kollar et al., 2005). By contrast, external scripts are designed externally by external sources, explicitly imposed on learners as a guiding structure about how to conduct collaborative learning (King, 2007). External scripts convey instructors’ expectations with respect to the way students should tackle the problem and interact with each other (Dillenbourg, 2002). One of the scaffolding strategies that external scripts use is to display cues that encourage the learners to take their respective roles (e.g. “analyzer” or “critic”) (Dillenbourg & Jermann, 2007).

One way to explain how external scripts work is that they could affect the allocation of cognitive resources of group members learners. Learning effectiveness will be threatened if learners’ cognitive resources are not allocated reasonably (Sweller et al., 1998). In some situations, external scripts play a useful role in reducing cognitive load, via partly offloading interaction management as it provides suggestions on procedure execution and labor distributions (Dillenbourg & Betrancourt, 2006; King, 2007). Nevertheless, overly coercive collaboration scripts, namely over-scripting, could have a negative effect on group process because it includes unnecessary scaffolds at lower hierarchical script level (Dillenbourg, 2002). The extraneous load comes from the necessity to understand, memorize, and execute the script, in the meanwhile students need to pay attention to cooperation tasks (Dillenbourg & Jermann, 2007).

Also, external scripts may gradually be replaced by internal coordination of groups overtime, wherein external scripts could be integrated into internal scripts (Fischer et al., 2007). After an external script is internalized, a similar situation will activate a certain mental structure that guides the individuals to act in the new situation (King, 2007).

Collaborative learning sometimes could have complex dynamics inside the interaction. As regards the interplay of the external script and the main effect of the device-student ratio we want to investigate, the biggest question lies here: In CSCL, students need to interact with both the mobile devices and other group members properly to get a decent learning performance. As is reported in former research, Fleck et al. (2009) and Rick et al. (2011) found that a multi-input tabletop interface sometimes would not promote learning because learners were entirely engaged in their tasks. External scripts seem to have the potential that they could scaffold the group members to achieve effective interaction and collaboration. In that way, if external scripts are provided, groups with a 1:1 device-student ratio might benefit more than the 1:m device-student ratio condition.

Except for the external script, as for the boundary conditions, learners’ familiarity to the collaboration settings and task complexity are another two possible moderators. For learners’ familiarity with the collaboration setting. On the one hand, getting familiar with each other could facilitate members’ communication in the collaboration group, thus would likely to influence learning. For example, Lai and Law (2006) found that experienced learners focus more on meaning negotiation compared to the novices. On the other hand, the effect of external collaboration support might fade away as the students getting more familiar with the collaboration setting (Fisher et al., 2013). Meanwhile, as Kirschner et al. (2011) implies, task complexity is influential to collaborative learning, individual learners are more efficient in learning low-complexity tasks and group learners are more efficient in learning high-complexity tasks.

Purpose of This Study

Given that background, this study aims to investigate the main effect of the device-student ratio on collaborative learning outcomes during students’ collaborative learning when using VMs in science inquires. To be specific, there are two modalities of using VM: 1:1 device-student ratio means each student in a group has access to a tablet, and 1:m device-student ratio means the whole group share one device.

Also, another purpose of this study is to investigate if there are some boundary conditions with regards to this main effect, the factors taken into consideration are external script availability, task complexity, and students’ familiarity with the collaboration settings. To be more specific, this study has two research questions:
Will the device-student ratio influence students’ collaboration performance?

Will the availability of external scripts, task complexity, and prior collaboration experience moderate the above effect?

Method

Sample

Participants in this study were students from a public elementary school in Beijing, PRC. Participants were selected in groups by classes, 4 out of 8 classes were randomly selected. There were 130 participants with their ages ranging from 10-12. Additionally, they were taught by the same science teacher. Participants all had the experience of long-term cooperation. Students in this school have been assigned to a group of 5-6 person in which they take part in daily learning activities since grade 1, scilicet participants were experienced at cooperation meanwhile they were in a familiar, stable cooperative learning situation throughout the study. Furthermore, such a group size of 5-6 is decent for investigating the “true effect” of the device-student ratio, as such a variation would not result in a radical change in teaching method, each group members could have sufficient chance to participate in the collaboration. As shown in Figure 1, the 4 classes were randomly labled A B C, and D under corresponding learning conditions.

Materials

Virtual Manipulative

There were three scientific inquiry themes in this study, which were Refraction of light (RL), Simple circuits (SC), and Electromagnetic induction (EI). These three themes contained the main knowledge contents of three units in the fifth-grade science curriculum, namely, light, electricity, and magnetic, of the selected school. Accordingly, virtual manipulatives of this study are three teaching simulation tools selected from PhET learning platform (phet.colorado.edu), a free online simulation program for physics, chemistry, biology, geography, and mathematics. The interfaces of the three virtual manipulatives are shown in Figure 2.

Figure 1.
Classes and conditions.

Figure 2.
Screenshots of the three VMs. Themes of the VMs: (A) refraction of light (RL); (B) simple circuits (SC); (C) electromagnetic induction (EI).

VMs in this study are standalone programs running on tablets, which does not have collaboration support designs. Students use the VMs to observe the phenomenon but they need to interact with other group members to accomplish the collaboration tasks.

External Scripts

External scripts designed in this study aimed to regulate the collaboration process and prompt interaction among group members. There were two kinds of external scripts adopted before and during collaborative inquiry activities in this study. Before collaborative learning, the teacher clearly conveyed guidance and expectations of how group members interact with each other, such as prompting turn-taking and joint attention. During the inquiry process, participated students were able to play most of the roles in accordance with prompted cues by themselves, however, the play of a few roles required assignation. For example, the role of “inspector” was to regulate the collaborative inquiry process and encourage group members to keep participation, which was assigned to a student based on the consultation of the group leader and other members.

Group Worksheets

Group worksheets support students’ inquiry by providing detailed guidance in terms of inquiry tasks and procedures. Each group was provided a group worksheet. Students took part in inquiry activities with the help of the worksheets, the worksheets created some problem situations meanwhile list some questions for the students. Students were asked to work in groups with the help of mobile devices and fill the worksheet with their collaborative answers to the questions. Researchers and the teacher could estimate the learning outcomes of students’ learning outcomes according to these questions.

Also, worksheets could function as tests. Concerning learning performance of applying VM, previous studies mainly focused on two variables: concept understanding (e.g., Kapici et al., 2019; Zacharia & Michael, 2016), and problem-solving performance (e.g., Yuan et al., 2010). Concept understanding refers to students’ observation and comprehension of experiment phenomena; problem-solving aims to promote students’ problem-solving ability through inquiry experiments design. This study measured these two outcomes. Each worksheet within the corresponding lesson consisted of two tasks (Table 1). In a measurement view, task 1 aimed at measuring participants’ observation and understanding of the phenomena in the experiment (i.e., concept understanding); task 2 aimed at investigating participants’ experimental design (i.e., problem-solving). From a competence perspective, task 2 was relatively more complicated. The questions were compiled by the researchers and teachers.

Table 1.
Inquiry Tasks in Group Worksheets.

Theme Task 1 Task 2

Refraction of light What happens when light enters the water from the air? If change the Angle of the incident light from air, what happens to the Angle of refraction? Find the pattern

Simple circuits Listing the function of the components in a circuit diagram Implement a certain kind of function by simply modifying a circuit diagram

Electromagnetic induction Given an electromagnetic system, figure out in what situation the light goes on and try to find the pattern of the changing of brightness Try to list some hypotheses of the relationship between the characteristics of some components in a given electromagnetic system. Test these hypotheses by observing the phenomenon in the VM by changing some settings.

Each group would hand in one worksheet. To facilitate the participants’ motivation within the collaborative activity, individual scores are in line with group scores according to the responses in the worksheet (Theiner, 2014, pp. 351–353). The total score is 100, tasks 1 and 2 weighted respectively 50%.

Procedure

Participants in groups of four classes, namely Class A, Class B, Class C and Class D, were randomly assigned to 4 conditions (see Figure 2). In the 2 × 2 quasi-experimental design, two treatment factors were manipulated in those conditions, namely the device-student ratio (DSR) (1:1 or 1:m) and external script availability (ESA) (yes or no). As shown in Table 2, the four conditions were: (1) DSR = 1:1 & ESA = yes (Class A); (2) DSR = 1:m & ESA = yes (Class B); (3) DSR = 1:1 & ESA = no (Class C); (4) DSR = 1:m & ESA = no (Class D).

Table 2.
2 × 2 Quasi-Experimental Design.

ESA Yes ESA No

1:1 DSR Class A Class C

1:m DSR Class B Class D

Prior to the study, to avoid systematic selection bias, a statistical test was conducted to eliminate participants’ possible differences in content related competence among the four classes (groups). One-way ANOVA was applied to check if there were significant differences among the groups. Four groups’ pre-test score (F (3,126) = 68.249, p = .894 > .05), as well as the final score of the last semester (F (3,125) = 68.249, p = .167 > .05), showed no significant difference, which implies students in these four classes had a similar level of competence in the science discipline at the beginning of the experiment.

The study was conducted in special classrooms for science class, in which dozens of tablet computers were prepared. Each tablet was identical devices with an Android system and an 8-inch screen of 16:10 aspect ratio. The overall study procedure consisted of a three-round classroom instruction. Each of the lessons was designed to be identical in the process but different in learning themes. The lessons were taught in April, May, and June 2019, with a time interval of one month.

The learning themes were RL, SC, and EI. All these three lessons shared an identical instructional process: at the beginning of the lesson, the teacher gave an introduction of the inquiry activity, the introduction would take approximately 10 minutes. Afterward, students all took part in collaborative inquiry learning activity supported by tablet devices and external script (if provided). VM was integrated into the tablet devices to support the students’ inquiry. As was designed, the collaborative inquiry learning activity would take about 25 minutes. The final summary section lasted about 10 minutes. The collaborative inquiry learning activity was guided by Group Worksheets. The students would try to finish the task listed on the Worksheet in groups while the teacher only offered necessary assistance, Figure 3 gives an overview of such a procedure.

Figure 3.
Inquiry learning procedure.

To investigate the influence of task complexity on students’ learning outcomes, two primary learning outcomes were measured according to the students’ performance in the two tasks with different complexity in the worksheet. Two tasks, namely concept understanding and problem solving are there in a worksheet, problem solving is considered as a more complex task. Details of the worksheet will be described in the following section.

Analysis

This research design was a 3-round quasi-experiment, which constituted a repeated measurement design. The dependent variables here are two learning outcomes, namely concept understanding and problem-solving. DSR and ESA are two between-subject factors, meanwhile, the different themes in each of the 3-round lessons are the within-subject factor, the real variable matters in the different themes is the round of the course (ROC), as it will influence the students’ familiarity to the collaboration settings.

Repeated-measures analysis of Variance (Repeated-measures ANOVA) is applied to investigate the effect of these factors on the dependent variables (von Ende, 2001). It is worth mentioning that bringing external scripts as a moderator could bring some internal validity challenges: if we estimate the effect that the three moderators interact with the device-student ratio independently, we are at a risk that we would omit the possible interactions between the moderators themselves. Because, as is mentioned above, the effect of external scripts is likely to fade away as time goes by, which could be correlated with students’ familiarity with the collaboration, as the familiarity could grow through time. Meanwhile, it is risky to claim that task complexity will not interact with the external scripts. Consequently, in the analysis, the interactions of the moderators themselves were also considered.

Students’ learning outcomes were rated according to their performance in the worksheet. During the collaborative inquiry learning activities, each group received only one paper worksheet. As the learning activities were conducted in real classroom situations, we cannot ensure a consistent scale of the groups. The group size might vary from 4-6. This might impact the rationality if we only analyze the learning outcome from a group level. To address this issue, with reference to former studies (e.g., Kirschner et al., 2009; Wang, Fang, et al., 2020; Zacharia & Olympiou, 2011) in which learning outcomes were measured at the individual level, even though the tasks were collaborative. As such, group members received the same score according to their group worksheet. Another reason for adopting this rating method is that the initiative and responsibility of group members would be improved when the group performance were accounted into individual performance (Theiner, 2014). The teacher and the second author independently rated the performance according to a rubric compiled before the class. Pearson’s r is used to calculate the inter-rater reliability, results showed a decent inter-rater reliability (r = .79 > .7), so the teacher’s ratings were adopted as the students’ performance. Afterwards, all the students’ scores were firstly standardized in terms of the distance from the mean in standard deviation units, the z-score. To avoid the use of negative values, we further standardized the z-score to T scores taking the equation: T = 50 + 10Z, in which Z is the z-score. T scores were taken as the operationalization of students’ learning outcomes and would be taken into statistical analysis.

To get a more comprehensive understanding of the influence of each of the factors, this research reports the effect size as well as the significance of each of the variables. partial η2 is taken as the measurement unit of effect size.

Results

A total of 130 students volunteered to participate in this study, and 120 (92.30%) of them completed the 3-round experiment. The attrition is an approximate random event. 10 Students were absent in at least one of the 3 lessons due to some personal affairs. Repeated-measures ANOVA was conducted to investigate the effect of each factors’ impact on the dependent variable - concept understanding. The independent variables here are round of the course (ROC, here the RL, SC, EI as the first, second and third round), DSR (1:m, 1:1), and ESA (Yes, No). The two dependent variables here are students’ concept understanding and problem-solving performance in science inquiry. The problem-solving task is considered more complex than the concept understanding task, so by comparing the different main effect and interaction effect each independent variable has on the two dependent variables, conclusions could be drawn as regard to how task complexity would moderate the main effect of DSR on learning outcomes.

Concept Understanding

Table 3 gives a descriptive statistic result of students’ concept understanding in the 3-round experiment.

Table 3.
Descriptive Analysis of Concept Understanding.

DSR ESA RL SC EI N

1:m Yes 58.45 ± 5.58 58.45 ± 5.21 55.19 ± 9.69 29

No 47.95 ± 8.98 52.25± 56.39 ± 6.97 31

Total 53.03 ± 9.15 55.25 ± 8.13 55.81 ± 8.35 60

1:1 Yes 44.56 ± 11.44 44.09± 44.18 ± 11.78 31

No 49.68 ± 7.78 44.45 ± 4.80 44.82 ± 4.14 29

Total 47.03 ± 10.10 44.26± 44.49 ± 8.88 60

Total Yes 51.27 ± 11.42 51.03 ± 11.14 49.50 ± 12.08 60

No 48.79 ± 8.40 48.48 ± 8.35 50.80 ± 8.17 60

Total 50.03 ± 10.06 49.76 ± 9.89 50.15 ± 10.29 120

Firstly, Mauchly’s test of sphericity was conducted to test if the data violates the repeated-measures ANOVA’s critical sphericity assumption. The result showed that variances of the differences between all possible pairs of within-subject conditions are equal (χ² = 2.696, p = .260 > .05), the sphericity assumption was not violated. Table 4 shows the between-effect and within-effect of the factors on concept understanding.

Table 4.
Between-Effect and Within-Effect of the Factor on Concept Understanding.

Between-effect F (1, 116) p partial η²

DSR 200.144*** .000 .633

ESA 5.426* .022 .045

DSR* ESA 28.960*** .000 .200

Within-effect F (2, 232) p partial η²

ROC 0.053 .949 .000

ROC * DSR 2.965 .054 .025

ROC * ESA 1.579 .208 .013

ROC* DSR* ESA 5.599** .004 .046

p < .05; p < .01; p < .001.

Between-Effect

As is shown in Table 4 in terms of the main effect, DSR (F (1, 116) = 200.144, p < .001, partial η² = .633) and ESA (F (1, 116) = 5.426, p = .022 < .05, partial η² = .045) both have a significant impact on students’ concept understanding. Students in the 1:m VM condition performed better, Also, a significant interaction effect of these two factors is found. As such, post hoc analysis is done to investigate the interaction effect. Note that to avoid type II error, Bonferroni correction is applied to adjust for significance.

The pairwise comparison shows that the main effect of DSR is moderated by ESA. When external script is present, the 1:m condition yields better performance than the 1:1 condition, the mean difference is 13.091 (p < .001). But when external script is absent, the effect is relatively smaller (mean difference = 5.876, p < .001).

Within-Effect

As for the within-subject effect, the main effect of the ROC on the students’ concept understanding is not significant while significant interaction effects are observed (see Table 4). The interaction effect of ROC and DSR shows a marginal significant result (F (2, 232) = 2.965, p = .054, partial η² = .025). Meanwhile the interaction effect of ROC, DSR and ESA is significant (F (2, 232) = 5.599, p = .004 < .01, partial η² = .046).

The effect of DSR is significant in all the 3-round lessons in the same direction. The ROC moderates such effects. In the RL condition, students in 1:m DSR got better concept understanding scores (Mean difference = 6.080, p < .001, partial η² = .111). While in the SC and EI conditions, such an effect is relatively large. In SC condition, the mean difference is 11.080 (p < .01) and partial η² = 0.331; In the EI condition, the mean difference is 11.290 (p < .01) and partial η² = 0.304.

In addition, all the three factors (ROC, DSR, and ESA) constitutes a rather complicated interaction effect. To get a more intuitive understanding of such an effect, Figure 5 is represented. For the convenience of statistical inference, error bars a plotted. The error bars in Figure 4 show a 95% confidence interval, the estimation of the CIs followed the method proposed by Morey (2008), which adjusts for the presence of the within-subject effect.

Figure 4.
The Interaction Effect of ROC, DSR, and ESA on Concept Understanding.

Problem-Solving

Another learning outcomes, students’ problem-solving, is to investigate in this part. The same as that of concept understanding, 120 students’ data were collected to investigate the influence the three factors have on their problem-solving. Table 5 gives a descriptive statistic of students’ performance on problem-solving.

Table 5.
Descriptive Statistics of Students’ Problem-Solving in the 3-Round Experiment.

DSR ESA RL SC EI N

1:m Yes 47.64 ± 8.74 52.64 ± 6.42 57.45 ± 9.53 29

No 52.72 ± 12.38 49.00 ± 14.19 48.92 ± 10.37 31

Total 50.26 ± 10.99 50.7 ± 11.20 53.04 ± 10.78 60

1:1 Yes 55.1 ± 8.60 55.27 ± 4.37 44.92 ± 6.03 31

No 44.13 ± 5.62 46.9 ± 6.83 48.47 ± 8.72 29

Total 49.84 ± 9.15 51.24 ± 7.03 46.64 ± 7.60 60

Total Yes 51.54 ± 9.40 54.00 ± 5.57 50.98 ± 10.07 60

No 48.57 ± 10.57 48.00 ± 11.21 48.7 ± 9.53 60

Total 50.05 ± 10.07 51.00 ± 9.31 49.84 ± 9.83 120

Repeated-measures ANOVA was conducted. Before that, Mauchly’s test of sphericity showed that the sphericity assumption was violated. As such, Greenhouse-Geisser correction was performed to adjust for the lack of sphericity (Greenhouse & Geisser, 1959). Table 6 shows the between-effect and within-effect of the factors on problem-solving.

Table 6.
Between-Effect and Within-Effect of the Factor on Problem-Solving.

Between-effect F (1, 116) p partial η²

DSR 3.781 .054 .032

ESA 10.985** .001 .087

DSR×ESA 1.600 .208 .014

Within-effect F (1.821, 211.231) p Partial η²

ROC 0.705 .482 .006

ROC * DSR 6.781** .001 .055

ROC * ESA 1.775 .175 .015

ROC* DSR* ESA 24.907*** .000 .177

p<.05; p<.01; p<.001.

Between Effect

As is shown in Table 6, test for the between-subject effect shows that DSR has a marginal significant impact on students’ problem-solving (F (1, 116) = 3.781, p = .054 > .05, partial η² = .032), students in the 1:m condition has a higher problem-solving score (Mean difference = 2.242). Meanwhile, ESA has a significant impact on problem-solving (F (1, 116) = 10.985, p = .001 < .01, partial η² = .087), students with external script has a higher problem-solving score (Mean difference = 3.821). Nevertheless, the interaction effect of these two factors is not significant.

Within Effect

Analysis of the within-subject effect shows that although the main effect of ROC ’s influence on students’ problem-solving is not significant, but a significant interaction effect of ROC and DSR (F(1.821, 211.231) = 6.781, p = .001 < .01, partial η² = .055) as well as a significant effect of ROC, DSR and ESA are observed(F(1.821, 211.231) = 24.907, p < .001, partial η² = .177).

A pairwise comparison shows that the effect of DSR is only significant in the condition where students’ ROC is EI (Mean difference = 6.489, p < .001, partial η² = .123). Figure 5 gives an overview of the effect, with error bars showing the 95% confidence interval.

Figure 5.
The Interaction Effect of ROC, DSR, and ESA on Problem-Solving.

Discussion

Generally, a significant main effect shows that 1:m device-student ratio would yield better learning performance. A possible explanation is that limited devices in a community might in turn leave the members with greater chances to observe others, as their attention is not always allocated to the digital devices. As was noted by Antle (2014), learners become more motivated to coordinate their efforts with others when they monitor what others are doing. Also, they are more likely to initiate negotiation if they notice some differences. In this way, the shared device in the 1:m DSR condition acts as a referential anchor for interaction and shared understanding. Consequently, in the 1:1 DSR condition, students are unable to access a shared interface, or a so-called ‘referential anchor’ in the public space, which undermines the chances that they intend to each other, resulting in a relatively non-ideal learning outcome.

Nevertheless, this conclusion should be drawn carefully with the following boundary conditions.

The Interaction Between External Scripts and Device-Student Ratio

To better control for the possible confounding variables, the external scripts used in this study does not contain any instructions with regards to providing strategical tips on how to better use the devices under different DSR for collaboration. Instead, the scripts recommended strategies on how to better cooperate and achieve the learning objective. When the dependent variable is concept understanding, as is shown in Table 4, the interaction effect of DSR and ESA is significant. To be more specific, when external script is present, the 1:m condition yields better performance than the 1:1 condition, the mean difference is 13.091(p < .001). But when external script is absent, though the effect is still significant, the effect is relatively smaller (mean difference = 5.876, p < .001).

This finding is somehow consistent with Lin et al. (2012), that if students are lack of collaboration skills, the inquiry activity might not have a fruitful outcome in the 1:m condition: some students would become isolated, and effective cooperation could not be achieved. External scripts would help the learners to quickly run into an effective collaboration without demanding too much collaboration skills. That is why the effect of the 1:m device-student ratio is larger when external scripts are present. In the study of Lin et al. (2012), no significant difference was found between the 1:1 and 1:m device-student ratio conditions, but in this research, we do find that 1:m is significantly better even if external scripts were not present. This could be due to those students in this experiment have got a certain degree of collaboration experiences they always do this kind of inquiry activity since the entrance to the primary school.

Familiarity Matters

What makes the story even more complicated is that the time students collaborate with the task also moderates the DSR’s effect on learning performance. As is well documented, prior experience and familiarity with the collaboration settings would influence students’ perception of technology (Jeong & Hmelo-Silver, 2016; Kirschner et al., 2018).

A significant interaction effect of ROC and DSR is observed in the problem-solving task, as is shown in Table 6. Meanwhile, in Figure 5, overlapped error bars are observed at the beginning of the study (in RL, the first round), while in the EI class (the third round), the group with 1:m DSR and external script performed significantly better than the others. This implies that it would take more time for the students to reach such a point at which the group members share a robust, negotiated accessibility of the device. In this study, the students were always on their way to accommodate to the technical settings, and one of the key points of their adaptation is to reach a habitus of using the VM.

Nevertheless, neither the effect of ROC nor the interaction effect of ROC and ESA is significant when the task is simpler, in the concept understanding task. We argue that this could because, in a relatively simpler task, the demand for collaborative skills is lower for efficient collaboration. As is discussed in section 6.2, the problem-solving task involved more observations and operation in the VM, so students in the 1:m DSR condition would likely take more time to negotiate who to observe and who to manipulate with the device. But in a relatively simpler task, the insignificant result somehow implies that students with external scripts showed fast adaptation because the external scripts supported them to play their roles, that making the familiarity factor not important anymore. In the EI class students with 1:m DSR performed better than those in the 1:1 DSR condition, but the two 1:m DSR groups showed no significant difference. This could be possibly explained in this way: another group without external script had also adapted to the collaboration settings, and the effect of the external script had faded away as the roles had been internalized (Fisher et al., 2013). In a more complicated task, only the group with 1:m DSR and external script performed significantly better than the others in the last course.

Task Complexity Might Affect Collaboration

Interestingly, taking problem-solving as the dependent variable, not only the main effect of DSR and the interaction effect between DSR and ESA is not significant, but also a directionally reversed pattern is observed in Figure 5. In the RL and SC lessons, for all the students using external scripts, those in the 1:1 DSR condition have better problem-solving performance, which is not consistent with the pattern in concept-understanding.

Though the insignificant result leaves little space for further inferencing, this study might have touched another side of the coin: Unlike Kirschner et al. (2011), which suggests that in collaborative learning, individual learners would be more efficient in less complicated tasks and collaboration would reap fruits from more complicated tasks. In this study, such a “collective working-memory” effect is somehow reversed. Learners in the 1:1 DSR condition are considered to work more independently and the problem-solving tasks in the worksheet are considered more complicated compared to concept understanding tasks. Students in the 1:m condition benefit from the presence of a referential anchor when facing a relatively easy task, but as the task gets more complicated, the advantage of 1:1 DSR emerges. 1:1 DSR enables every member of the group with unlimited access to the VM. Compared to the 1:m DSR, although students in the 1:1 DSR condition cannot get a shared interface which facilitated learning in a way that they share an external representation (Suthers & Hundhausen, 2003), instead, distributed problem-solving is empowered. A complicated task needs more experiments and observations in the VM, the task would likely be decomposed into subtasks which each member of the group would take some (as they take the roles in the external scripts). Students in the 1:1 DSR condition can freely experiment with their devices to cope with their problems, making it more efficient to accomplish the task.

How Device-Student Ratio Could Affect Learning?

It should be emphasized that device-student ratio would not directly affect learning outcome, but via some casual paths. In our perspective, there are two paths to mediate such an effect.

The first mediator is the collaboration efficiency. Different device-student ratio would affect the communication modality of the group members, which has been discussed above.

Also, there exists another possible mediator: students’ accessibility to learning information. In the 1:1 condition, students have full accessibility to content and information in their own device, but in the 1:m condition, some students’ accessibilities to the device are limited, sometimes what they could do is merely watching others manipulate the device and observe the consequent feedback. Limited accessibility is the antecedent of insufficient information input of those students, they could not enjoy the complete functions and content from the virtual manipulatives, which would certainly undermine their learning outcome.

Given our research design, it is hard to identify via which mediation path is the effect of device-student ratio conveyed, as manipulating the device-student ratio would certainly change the two mediators. But conclusions still could be drawn: Although 1:m condition have certain defect as students have limited accessibility to the learning content, but the 1:m condition still outperformed 1:1 condition as per the main effect. This implies that the positive effect mediated in the “collaboration path” is larger than the negative effect mediated in the “accessibility path”. Meanwhile, in the complicated tasks, the 1:1 condition shows better performance when external script is available, showing that the “accessibility path” might outperform the “collaboration path” when the task is complicated – implying that there could exist a possible moderated mediation.

Nevertheless, it needs to be further investigated in future research, which includes a direct measurement of the two mediators to prove this argument.

Highlights and Implications

From the above discussions, the following implications and suggestions to instruction could be drawn. The main suggestion to learning activity design is: in collaborative inquiry learnings supported by virtual manipulatives, the device-student ratio design should be cautiously considered. Generally, one group share one device is a good choice as it fosters communications with a shared screen, leading to better collaborative construction of knowledge. Past literature reported no significant difference when comparing this design to the 1:1 condition (Lin et al., 2012), showing concerns about whether students could effectively collaborate in this setting. Our study suggests that giving external collaboration support could partly relief this concern. External scripts are good solutions as they could help the students to collaborate better in this setting. Also, external scripts are easy to design and develop, making them suitable for daily classroom instruction.

Before implementing such a design, students’ collaboration skills should also be considered. 1:m student-device ratio will be more effective when students are equipped with good collaboration skills, so for students with decent collaboration skills, this kind of design is better recommended. Furthermore, though the result did not show a valid evidence, but we argue that in complicated tasks, 1:1 student-device ratio would have unique advantages, as it enables distributed inquires. This should also be considered when designing inquiry learning activities in classrooms.

In our knowledge, the intuition “the more, the merrier” is somehow widely adopted by educational administrators, who would like to purchase more devices and encourages teachers to conduct teaching in this expensive way. But somehow our results show that this modality of using devices in collaboration might not be cost-effective. Without proper instructional design, just adding technical input might in turn hinder learning.

To sum up, efficient communication is important. Although 1:1 device-student ratio design could ensure the students with sufficient accessibility to the learning content, but without efficient communications of the group members, learning outcome is still inferior compared to the 1:m condition. Maybe a virtual learning environment with some kind of collaboration support might be a better solution: equip each student with a digital device and they could collaborate in the virtual manipulatives embedded with online collaboration systems could taking account both the efficient collaboration and sufficient accessibility. In this sense, the characteristics of the VM are also important. In our study, the virtual manipulatives are just standalone programs.

Up to now, few studies have deliberately discussed the impact of different DSR to collaboration performance. Our research derives from Lin et al. (2012), which suggested that 1:m DSR setting could generate artefacts with higher quality compared to 1:1 setting, but the difference in learning effect is not significant. Nevertheless, the intervention period of time in this study is short and this study does not consider the possible moderators. We conducted this research to (1) revalidate the main effect and (2) investigate the possible moderators in that main effect. Our results showed that 1:m design could be more effective than 1:1 design, especially when external collaboration supports were given. Also, this main effect could be moderated by task complexity. Evidence is added to this field, but meanwhile, the underneath mechanism of how DSR influence learning performance remains to be investigated in future works.

Conclusion

Despite the complicated results, a major conclusion could be drawn here: 1:m device-student ratio could be more preferred in collaborative learning. But the conclusion should be drawn with the following boundary conditions:
The different effect of 1:m DSR to 1:1 DSR is only significant in the situation when students are faced with a relatively simple task. Also, in the simple tasks, the availability of external script would moderate the effect. We observed a larger effect size when external script is present. But the main effect of DSR and its interaction with ESA is not significant when students are faced with a more complicated task.

Students’ familiarity with the collaboration setting would also moderate the main effect of DSR. When the task is more complicated, students need more time to adapt to the collaborative setting, and the effect of DSR would only emerge after a period of collaboration.

Unlike previous research which reported that device-student ratio did not yield a significant impact on students’ collaborative learning performance (Lin et al., 2012), this research found a significant main effect that 1:m device-student ratio could be more beneficial. Meanwhile, such a conclusion should be drawn in careful consideration with the boundary conditions: the external collaboration support, task complexity, and familiarity with the collaboration settings.

Although the experiment and the results are complicated, if we sum them up, we would see that the only issue we are arguing here, is that 1:m device-student ratio could be more preferred than 1:1 device-student ratio when students are equipped with certain collaborative skills. Compared to 1:1 DSR, 1:m DSR enable more communication among members with common access to a shared interface. The previous studies’ failing to reveal such an advantage might because that the experiment was not designed to make efficient collaboration happen, that some students would get isolated (Lin et al., 2012). But in this study, we see that internal (familiarity to the settings) and external (external scripts) collaborative support could compensate for such defects, making it possible for the 1:m DSR group to perform better than the 1:1 DSR group. Also, the task complexity could also play a role here: the more complicated the task is, the more collaborative support should be needed.

One thing worth to be mentioned is that the samples in this research are students with a certain degree of prior collaboration experience. Also, the devices used in this research are standalone versions, without functions of online collaboration supports (e.g., online chat, collaborative manipulation, etc.). Furthermore, the moderators we investigated in this study are just a part of the possible moderators. Other moderators such as the type of the tasks, students’ prior knowledge, the patterners and instructional design should be considered when applying the results to other contexts.

Another defect of this study is that additional evidence was not collected to support the discussion, it involved only one data source. We could have had better insight in terms of the interactions during the students’ collaboration process, hence the discussion of the potential negotiation and coordination of device usage would be more informative. Additionally, although the contents in the three courses are considered relatively independent, another possible defect could be that the content of the three courses might confound the time effect. Future research focusing on the learning process could be done to compensate for these defects through video data collection and analysis.

Theme	Task 1	Task 2
Refraction of light	What happens when light enters the water from the air?	If change the Angle of the incident light from air, what happens to the Angle of refraction? Find the pattern
Simple circuits	Listing the function of the components in a circuit diagram	Implement a certain kind of function by simply modifying a circuit diagram
Electromagnetic induction	Given an electromagnetic system, figure out in what situation the light goes on and try to find the pattern of the changing of brightness	Try to list some hypotheses of the relationship between the characteristics of some components in a given electromagnetic system. Test these hypotheses by observing the phenomenon in the VM by changing some settings.

	ESA Yes	ESA No
1:1 DSR	Class A	Class C
1:m DSR	Class B	Class D

DSR	ESA	RL	SC	EI	N
1:m	Yes	58.45 ± 5.58	58.45 ± 5.21	55.19 ± 9.69	29
	No	47.95 ± 8.98	52.25±	56.39 ± 6.97	31
	Total	53.03 ± 9.15	55.25 ± 8.13	55.81 ± 8.35	60
1:1	Yes	44.56 ± 11.44	44.09±	44.18 ± 11.78	31
	No	49.68 ± 7.78	44.45 ± 4.80	44.82 ± 4.14	29
	Total	47.03 ± 10.10	44.26±	44.49 ± 8.88	60
Total	Yes	51.27 ± 11.42	51.03 ± 11.14	49.50 ± 12.08	60
	No	48.79 ± 8.40	48.48 ± 8.35	50.80 ± 8.17	60
	Total	50.03 ± 10.06	49.76 ± 9.89	50.15 ± 10.29	120

Between-effect	F (1, 116)	p	partial η²
DSR	200.144***	.000	.633
ESA	5.426*	.022	.045
DSR* ESA	28.960***	.000	.200
Within-effect	F (2, 232)	p	partial η²
ROC	0.053	.949	.000
ROC * DSR	2.965	.054	.025
ROC * ESA	1.579	.208	.013
ROC* DSR* ESA	5.599**	.004	.046

DSR	ESA	RL	SC	EI	N
1:m	Yes	47.64 ± 8.74	52.64 ± 6.42	57.45 ± 9.53	29
	No	52.72 ± 12.38	49.00 ± 14.19	48.92 ± 10.37	31
	Total	50.26 ± 10.99	50.7 ± 11.20	53.04 ± 10.78	60
1:1	Yes	55.1 ± 8.60	55.27 ± 4.37	44.92 ± 6.03	31
	No	44.13 ± 5.62	46.9 ± 6.83	48.47 ± 8.72	29
	Total	49.84 ± 9.15	51.24 ± 7.03	46.64 ± 7.60	60
Total	Yes	51.54 ± 9.40	54.00 ± 5.57	50.98 ± 10.07	60
	No	48.57 ± 10.57	48.00 ± 11.21	48.7 ± 9.53	60
	Total	50.05 ± 10.07	51.00 ± 9.31	49.84 ± 9.83	120

Between-effect	F (1, 116)	p	partial η²
DSR	3.781	.054	.032
ESA	10.985**	.001	.087
DSR×ESA	1.600	.208	.014
Within-effect	F (1.821, 211.231)	p	Partial η²
ROC	0.705	.482	.006
ROC * DSR	6.781**	.001	.055
ROC * ESA	1.775	.175	.015
ROC* DSR* ESA	24.907***	.000	.177

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by Fundamental Research Funds for the Central Universities (2020NTSS04).

ORCID iD

Huixiao Le

Author Biographies

Cixiao Wang is a lecturer at the School of Educational Technology, Faculty of Education in Beijing Normal University. Her research interests include mobile learning and collaborative learning.

Huixiao Le is a PhD candidate at the Graduate School of Education in Peking University. His research interests include collaborative learning and intelligent tutoring systems.

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