Personal epistemology and spontaneous small groups

Abstract

We explore the structure of epistemological beliefs and its relation with the spontaneous formation of study groups in a sample of biomedical engineering students. The sophistication of the beliefs as well as the size and distribution of spontaneous small groups were measured for subjects in three different academic years: junior, intermediate and senior. Through principal components analysis, a four-factor structure was found for the epistemological beliefs, additionally validated with confirmatory factor analysis. The spontaneous small groups were determined by a clustering algorithm with data from a survey applied to 151 participants. Using parametric and non-parametric methods, it was found that the size of the group for junior students was positively correlated to naive beliefs about the source of knowledge. For senior students, however, both size and number of groups were inversely correlated to the passiveness in learning. These results are discussed in the frame of the interplay between group praxis and mental representations in the learning process. In addition, general differences were encountered between learners in spontaneous small groups and lone learners concerning the belief about the speed of learning, which also showed an overall difference across gender.

Keywords:

• Cognitive psychology
• personal epistemology
• small groups
• cooperative learning

Introduction

Cooperative learning is widely recognised as a pedagogical practice that promotes both socialisation and learning (Gillies, 2016). In particular, cooperative groups formed in the study routine of the classroom are largely known to be important structures to potentiate the learning process (Good & Brophy, 1995; Hmelo-Silver et al., 2013; Johnson & Johnson, 1975), and have been extensively studied in the frame of educational and psychological research (Delucchi, 2006; Ucan & Webb, 2015). Since very early works (Bligh, 1972) it has been found that group discussion methods are more effective than lectures for stimulating thought, for personal and social adjustment, and for bringing about changes of attitude. In cooperative groups, students are able to manipulate ideas better, establish links with what has already been learned and improve individual achievement (Delucchi, 2006; Gibbs, 1992; Lou et al., 1996, 2001, 2006; Ucan & Webb, 2015). There is a growing consensus in motivating students to work cooperatively (Delucchi, 2006; Hmelo-Silver et al., 2013; Slavin, 1990, 1991) and promoting discussion and personal exchange as a better way of knowledge acquisition. As a result, modern curricula in schools and universities increasingly insist in the formation of study groups and other forms of collaborative work.

Most of the psychological and educational investigations regarding collaborative learning focus in small groups of subjects whose main function is that of learning. These groups are typically the result of a pedagogical, explicit strategy in which the teacher promotes and mediates the cooperation within groups with the aim of measuring the improvements in learning (Gillies, 2016). In this way, the teacher plays an instrumental role in both the formation and subsequent functioning of the study groups. In some specific environments, however, a different dynamic exists for the creation and operation of study groups that does not involve any action on the teacher’s part. Instead, students spontaneously meet, forming their own well-defined small groups to collectively perform tasks related to learning which do not take place in classroom time and are not necessarily meant to be performed collectively. These spontaneous small groups (SSGs) with relatively stable structures are the focus of this work and constitute a prime ground to investigate collaborative learning from the students’ individual perspective.

Even though there is a large number of environmental variables influencing the spontaneous formation of these groups, the contribution of the students’ conceptions about knowledge and learning cannot be neglected. Since the primary role of the subjects within SSGs is that of learners, cognitive variables are likely expected to have important effects on the constitution of the groups (McCord, 2014; Senior & Howard, 2014; Webb et al., 2006). And also the other way around: the specific characteristics of these groups, like their number and sizes, may also affect the evolution of the students’ perspective. In fact, the general influence of the learning environments on the students’ epistemological beliefs, learning outcomes and thinking styles is well-known, and has received an increasing attention in the literature (Fan & Zhang, 2014; Tolhurst, 2007).

For cognitive and educational psychology, unveiling the students’ perspective in the learning process has been a major challenge in the last decades, both theoretically (Hofer & Bendixen, 2012; Schommer, 1990) and experimentally (Khine, 2008; Scardamalia & Bereiter, 2014; Schommer, 1990; Zimmerman, 2000). In this approach, the student is considered as an active agent of her own learning process (Hofer & Bendixen, 2012; Khine, 2008; Scardamalia & Bereiter, 2014; Zimmerman, 2000). In particular, the multidimensional paradigm in personal epistemology (Schommer, 1990) introduced the idea that each person develops their own system of beliefs about the nature of knowledge and learning (Barzilai & Zohar, 2014; Hofer & Bendixen, 2012).

The construct of epistemological beliefs (EBs) is used to understand the student’s beliefs about learning and knowledge from different perspectives (Hofer & Pintrich, 1997; Schommer-Aikings, 2002). In its more extended version, the specific EBs of a sample emerge through a factorial analysis of the answers to simple questions about knowledge and learning (DeBacker et al., 2008; Schommer, 1990). Following this general procedure, however, different samples do not always lead to the same set of beliefs, and an intense debate has been sustained in the literature concerning the specific form in which the factorial analysis should be done, the existence of core or fundamental beliefs and the domain specificity of them. Within the multidimensional paradigm (Schommer, 1990), EBs have been explored in many experimental works, and are theoretically grouped in a more or less constant set, namely: beliefs about the structure of knowledge, sources of knowledge, certainty of knowledge, speed of learning and ability to learn (Buehl et al., 2002; Schommer-Aikins & Easter, 2008). At the same time, other authors have suggested different sets of core dimensions like beliefs on the certainty of knowledge, the simplicity of knowledge, the source of knowledge and the justification for knowing (Hofer & Pintrich, 1997; Pintrich, 2002).

Once beliefs are determined in a specific study, their individual scores for each subject can be calculated, and so they become a quantitative variable that operationalises the construct. This variable has been extensively reported to have significant correlations with many other learning variables such as comprehension, metacomprehension and academic performance (Barzilai & Zohar, 2014; Mohamed & El-Habbal, 2013; Schommer, 1990, 1993). In the Cuban academic context, the study of personal epistemology is slowly becoming an interesting research topic, and EBs have been successfully linked to academic performance, promotion and metacognitive strategies (Morell & Manzano, 2019; Vizcaíno & Manzano, 2017).

In the present study, we follow a research approach that looks at EBs to investigate the forms in which personal epistemology relates to SSGs. In recent years, many scientific reports have started to include both sociological and cognitive approaches at the same time, becoming a popular topic in the literature on educational research (Isohatala et al., 2017; McCord, 2014; Winne et al., 2013). Clarifying the relation between learning conceptions and actual interactions in the study groups is still an open challenge that can be of extreme importance for a better characterisation and understanding of academic activity. In this paper, we explore the connections between the cognitive concept of personal epistemology and the social structures that students spontaneously establish as informal learning scenarios. Our goal of analysing EBs in SSGs is different than that of the so-called collective epistemology (Gilbert, 2004; Lackey, 2014), in which the ascription of epistemic states to groups focus the analysis on collective beliefs. Instead, in the present study the focus is directed to the characterisation of the EBs of individual subjects and its relation to the characteristics of the groups. In other words, to explore the personal epistemology in a particular context of collaborative learning for which the lack of previous literature becomes a motivating challenge.

Since our sample corresponds to university students in three different levels (second, third and fourth academic year), we consider this another variable in our research and name it level of instruction (LI). From the very beginning of the studies on personal epistemology (Perry, 1970), the way in which students modify their ideas about learning as the level of instruction advances has been of particular interest for researchers. It was demonstrated that, during the early years at university, students think of knowledge as rather certain, simple and transmitted by authority, while on reaching further academic years they develop a more sophisticated vision. These findings have also been reported for EBs as defined here in many occasions within the multidimensional paradigm (Cano, 2005; Schommer, 1993; Schommer et al., 1997). In the same line, sociological studies on small groups suggest that recently-formed groups tend to have a rather authoritative design (Good & Brophy, 1995; Slavin, 1991), but can shift from an authoritative to a democratic character in later academic years (Poole & Hollingshead, 2005). In this way, the LI is expected to be a relevant variable in the relation between EBs and SSGs.

We gathered data from a sample consisting of three academic years of biomedical engineering major at the Technological University of Havana (CUJAE). For our sample, and in general for all the undergraduate spectrum in the country, to study in collaborative small groups is a generalised practice inherited from previous study styles at high-school level. In this way, most university undergraduate students spontaneously form a number of small groups that meet to study all kind of disciplines during the academic year. We hypothesise that in this scenario: H1) There are significant differences in the EBs between subjects that do study in SSGs and those who study individually (lone learners); and H2) The LI is a relevant variable in the relationship between EBs and the size and number of the corresponding SSGs.

While a number of studies on small groups have correlated the group size with a wide scope of variables like problem-solving ability (Laughlin et al., 2006), performance (Cohen, 1994; Curral et al., 2001) and skill development (Chou & Chang, 2018), no previous study has specifically looked at the link between group size and EBs, nor at the SSGs and the number of them. The present attempt to relate the structure of this spontaneous assembly of small groups with the characteristics of the individuals’ personal epistemology can boost further research on this topic. Considering this relationship through the progression of the LI from initial to final academic years may offer new theoretical insights that could help with the implementation of pedagogical strategies designed to optimise the learning process.

Method

Participants

The study included 151 students of biomedical engineering major. From them, 36% corresponded to students of the second academic year, 29% to the third academic year, and 35% to the fourth academic year. Correspondingly, the LI will be referred as junior (second year), intermediate (third year) and senior (fourth year). The age range of the sample was 19–26 years (Mean = 21.4). The males accounted for 58% of the sample and the females for 42%. As a first step, an exploratory interview was implemented. It was known that first-year students did not have a settled small-group dynamic. On the other hand, students of the fifth (final) year dedicated most of the time to specialised individual research, in which small group study is hardly likely. These years were not included in the sample, as the structure of study groups was not reliable for them.

Details of the context

In the context of our sample, the undergraduate period is of five consecutive academic years. Majors of the same specialisation and the same academic year share a common classroom all the time and attend exactly the same courses. Without any demand, suggestion or advice, small groups of classmates form at the beginning of the academic year for collaborative study, particularly in the periods before exams. The composition of these groups remain very stable during the academic year, at least for the classrooms of second to fourth academic year, and the structure is inherited to a large extent, as the same classroom composition keeps relatively similar from one academic year to the next. In this way, every student is very familiar not only with the subjects within her study groups but also with all her classmates.

Expectedly, there are many effects influencing the group formation like neighbourhood of residence, personal affinity, etc., whose characterisation goes beyond the scope of our work. The small groups under study are, however, absolutely spontaneous, and for our sample they emerge after at least one year (first academic year) of daily interactions.

Materials

The small-group survey was implemented by simply asking the students to write down a list of the classmates with whom they studied. The option of returning a void list of study mates was explicitly mentioned as a valid one for those cases in which the student studied alone. In order to determine the SSGs we used the survey responses to find all possible clusters of students for which all members identified the rest of them as study mates.

The EBs were measured based on the epistemological beliefs questionnaire EBQ (Schommer, 1990) in its translation to Spanish made and validated by Malbrán (Malbrán & Pérez, 2012 and references therein). Specifically, we applied a re-crafted version of the EBQ called Epistemological Beliefs Survey (EBS) made by Colbeck (Colbeck, 2007). This version consists of only 34 statements that students rate on a 5-point Likert scale ranging from ‘strongly disagree’ (1) to ‘strongly agree’ (5). This survey has also been adequately validated with Kaiser-Meyer-Olkin measures of 0.768 and Bartlett’s test of sphericity of 0.00, and considered in subsequent works (Colbeck, 2007; Sekret, 2018; Yang, 2016).

Procedure

Students completed each instrument in the classroom at the beginning of a class session. First, we administered the EBS (20 minutes) and, one week later, the small-group survey (10 minutes). The questioning was conducted in the morning, with each student answering the instrument independently.

In order to process the responses to the small-group survey, an algorithm was programmed using the Wolfram Mathematica software to bring up the inner structure of these study-groups. Every SSG was defined as a subset of the sample any two members of which were each included in the other’s list. That is to say, every student in a particular SSG wrote down the name of all the others in it, and her name was also written down by each of the others. This way of defining SSGs allows students to be included in more than one group. Thus, for every student of the sample we defined the two relevant variables n and s, accounting for the number of different SSGs she belonged to, and the size of her largest SSG, respectively. In this way, a student belonging to three different SSGs of 2, 4 and 5 individuals, would have the values n = 3 and s = 5.

For processing the data from EBS, we followed the usual method of grouping the 34 items in 10 subscales: Success is unrelated to hard work, Avoid integration, Do not criticise, Avoid ambiguity, Learning is quick, Knowledge is certain, Depend on authority, Seek single answers, Ability to learn is innate and Learn the first time (Colbeck, 2007; Schommer, 1990). A principal component analysis was then performed on the scores of these subscales using the SPSS software. Additionally, a further confirmatory factor analysis was also implemented in the R programming language to validate the structural model relating the subscales with the derived factors.

Results

EBs

The factorial structure was obtained using the principal components method and Varimax rotation with the 10 subscales of the EBS as initial variables. Four factors were generated with eigenvalues greater than 1, which account for 56,7% of the variance. In Table 1 we show the highest loadings of the factors. We named the factors in naive form as it is the convention: Passive Learning (PL), Certain Knowledge (CK), Knowledge Handed down by Authority (KHA) and Quick Learning (QL).

Table 1. Higher loads for factors with eigenvalues greater than 1, subscales are built from the 34 items of the EBS.

Subscale	Fac. I	Fac. II	Fac. III	Fac. IV
Success is unrelated to hard work	0.708
Avoid integration	0.703
Do not criticise	0.612
Avoid ambiguity		0.671
Learning is quick		0.589
Knowledge is certain		0.568
Depend on authority			0.825
Seek single answers			0.504
Ability to learn is innate
Learn the first time				0.879

Factor I: Passive Learning, Factor II: Certain Knowledge, Factor III: Knowledge Handed down by Authority, Factor IV: Quick Learning.

The confirmatory factor analysis was performed choosing maximum likelihood estimation because the data was normally distributed. We hypothesised a four-factor model, same as the one obtained from the exploratory analysis before. The values of chi-square = 20, df = 22, chi-square/df = 0.9 (<3) and RMSEA = 0.59 (<0.6), as well as the comparative fix index CFI = 1.00 (>0.95) and the Tucker-Lewis fit index TLI = 1.027 (>0.95) indicated a good fit between the model and the observed data.

An exploration of the mean and variances of the factors for different academic and demographic variables was conducted showing no significant differences in the EBs of students of different LIs. Nevertheless, a significant difference (t = 2.3, p < .05) with a medium effect size (Cohen D = 0.38) was encountered in Factor IV (QL) concerning gender: while males believe more that learning is quick, females tend to conceive learning as a gradual process. In Table 2, the mean and standard deviation of the factors across several criteria of interest are shown.

Table 2. Means and standard deviations of the four factors across gender, academic year and group-learning habits.

	Fac. I		Fac. II		Fac. III		Fac. IV
	Mean	SD	Mean	SD	Mean	SD	Mean	SD
Females	–0.12	0.92	0.08	0.98	–0.03	1.02	–0.22	1.06
Males	0.08	1.05	–0.06	0.01	0.02	0.99	0.16	0.93
Lone Students	0.19	1.2	–0.11	1.02	0.02	1.2	0.21	1.09
Group Students	–0.09	0.88	0.05	0.99	–0.01	0.89	–0.1	0.95
2nd Year Students	–0.02	1.16	–0.12	0.95	0.21	1.02	–0.04	1.09
3rd Year Students	–0.07	0.93	–0.13	1.06	0.17	1.04	–0.09	0.88
4th Year Students	0.38	1.07	0.00	1.01	–0.39	0.8	0.27	1.08

SSG

Once the different SSGs were identified, a statistical exploration was done to determine the distribution histograms of their structure and number. The distribution of SSG sizes is shown in Figure 1 (left). As can be seen from the histogram plot, there is a prevalence of SSGs composed by two students, but groups of size 3 or 4 are also representative in the sample.

Figure 1. Statistical analysis of small groups. Left: histogram of group sizes. Right: histogram of the number of subjects pertaining to several groups (0 means individual study, 1 means belonging to only one group, etc.).

The histogram of the number of groups n is presented in the right panel of Figure 1. Lone learners (i.e. students with n = 0), and students included in only one SSG (n = 1), are the most representative configurations. However, students pertaining to more than one SSG also make up an important fraction of the total sample. A significant difference was encountered in Factor IV (t = 2.1, p < 0.05) with a medium effect size (Cohen D = 0.4) for the two subsets regarding the collaborative habits, i.e. n = 0 and n > 0. Students studying alone have naiver beliefs regarding Quick Learning than those who belong to at least one SSG.

Correlations

As can be noticed from Figure 1, ordinal variables n and s move in a rather narrow range. In order to highlight the connection between these variables and the beliefs, we rearrange the value of the factors into three ordinal categories as well: (1) sophisticated, (2) average and (3) naive. By construction, the factors have a normal distribution with zero mean and unit variance. We used cut-points at the 33th and 66th percentiles, so that the sample was equally represented in each of them. Although classifying ratio measures into large categories is somewhat risky, the particular features of the construct of epistemological beliefs makes this practice very likely and common (Norman & Streiner, 2003). Indeed, many authors have pointed out that epistemological beliefs are better characterised by frequency distributions than by continuum values (Schommer-Aikins, 2002).

No significant correlations between SSGs and EBs were found for the intermediate year (third year). However, this was not the case for the LI junior (second year) and senior (fourth year). Kendall Tau tests showed a significant correlation for junior students between s and Factor III (τ = 0.37, p < .05) with a medium effect size estimated via the Spearman’s rank (ρ = 0.4, p < .05). For juniors, the larger the group size to which they belonged was, the more they had the naive belief that knowledge is handed down by authority.

For senior students, the Kendall Tau test evidenced two significant correlations: n with Factor I (τ = −0.41, p < .001), and s with Factor I (τ = 0.28, p < .05). The Spearman’s rank value for the correlation of n with Factor I was ρ = −0.48 with p < .05, while the one corresponding to s with Factor I, though large (ρ = −0.33), was not statistically significant (p = .07). In this case, both the size and the number of SSGs correlated negatively with Factor I, Passive Learning. It means that the larger the number and size of the SSG, the more sophisticated the EBs are regarding learning as an active process.

Discussion

The fact that factorial analysis revealed four EBs factors (PL, CK, KHA and QL) is remarkable. Four-factor structures have been obtained previously in several early studies (Schommer & Walker, 1995; Schommer, 1993; Schommer et al., 1992) and also in recent works with engineering students in the same context of the present study (Morell & Manzano, 2019). Comparing with the foundational works, our measurements confirm the presence of the factors QL and CK, while lacking those of Fixed Ability (the belief in the ability to learn as innate) and Simple Knowledge (the belief in knowledge not being complex). Instead, we obtained two different factors better describing the inner characteristics of our sample: CK and KHA. The latter, however, has already been observed in other contexts in previous studies (Sitoe, 2006) as well as in a recent study of the same context using Schommer’s EBQ, in which the factor QL also emerges (Morell & Manzano, 2019).

Following a straight-forward exploration of these factors in our data (see Table 2), women’s beliefs were found to be more sophisticated than men’s. It was encountered that females were more likely to believe in a gradual, slow learning process. Gender differences of this type have been reported in several studies (Chou & Chen, 2016; Taasoobshirazi & Carr, 2008). Within the multidimensional paradigm, important works have also reported gender differences (Cano, 2005; Schommer, 1993; Schommer et al., 1997), pointing out that women believe in learning as a slow and gradual process significantly more than men, as encountered in our exploration.

As firstly hypothesised in H1, we find significant differences in the EBs and particularly in the belief about the speed of learning, depending on the number of SSGs the subject frequents. Subjects studying alone were found to be more likely to believe in learning as a quick process, in comparison to those who were part of an SSG. This naiver approach lone learners have is consistent with the absence of challenging inter-personal interactions at the time of learning. It is a well-established fact that interactions and cooperation generated in the social context in which learning occurs can boost the individual’s critical reflection on knowledge (De Corte, 2000; Van Merriënboer & Paas, 2003). Our result is also consistent with previous works in which it has been established that, in contrast with individual study, the study within friendship groups facilitate conceptual understanding through discussion, explanation and application to real life contemporary issues (Senior & Howard, 2014).

Hypothesis H2 is also confirmed by the significant correlations encountered between EBs and the characteristics of SSGs in junior and senior years. These correlations were expected, since groups are a preferential scenario for students to show their authentic ways of thinking and learning. We found that SSG size is correlated to both the belief in knowledge as handed down by authority and the belief in passive learning. A large number of studies on small groups have correlated the group size with a wide scope of variables like problem-solving ability (Laughlin et al., 2006), performance (Curral et al., 2001) and skill development (Chou & Chang, 2018). However, as far as we know, no previous studies have specifically looked at the link between SSGs and individual EBs. The same applies to the correlation found between the number of SSGs and the belief in passive learning. In both cases, there is a strong need for further investigation to estimate how universal the relation of the structure of groups with the individual’s personal epistemology is.

The correlations found, however, are non-trivial, and the role of the LI turned out to be instrumental in distinguishing the specific sign of the proportionalities. While for junior students the group size relates to a naiver belief that knowledge is handed down by authority, for senior students the belief in learning as an active process was positively correlated to the size and number of SSGs they belonged to. In short: for the low level of instruction, the larger the groups, the naiver the beliefs; for intermediate level of instruction there is no significant correlation; and for high level of instruction, the larger (and multiple) the groups, the more sophisticated the beliefs. This result confirms our hypothesis in a remarkable way and challenges our comprehension of the role of collaborative learning in shaping personal epistemology.

Clearly, the evolution of EBs with time is a well-replicated fact (Cano, 2005). In that sense, differences in the correlations for beginners and experienced students are expected. However, the association of larger collaborative environments to less sophisticated personal epistemology in junior students is somewhat unexpected, even if it has been shown that, in some contexts, cooperative small groups do not necessarily lead to improved learning (Curral et al., 2001; Mulryan, 1992). In some cases, for instance, one could expect junior students to spread their mostly naive beliefs about learning into the group exchange, in a degree proportional to the group size.

Additionally, social studies on the dynamics within small groups suggest that recently-formed groups, as is the case for juniors, tend to have a rather authoritative design (Good & Brophy, 1995; Slavin, 1991). This fact could, in turn, influence personal epistemology by enhancing naive beliefs through the practice of an authoritative interaction model within the SSG. Correspondingly, these cooperative groups can shift from an authoritative to a democratic character in later academic years (Poole & Hollingshead, 2005). It is then plausible that senior students would be engaged in more democratic SSGs, where the interaction model could reinforce active, critical learning, and so larger SSG sizes may produce more plural viewpoints. In this developmental picture, the correlation of the size and number of SSGs with the belief in learning as an active process can be seen as strongly linked to the changes in social interactions. This interpretation suggests an underlying epistemological evolution related to group dynamics that is hidden in the many analyses on cognitive variables along academic years.

Conclusions and recommendations

We have performed an exploratory study on the structure of personal epistemology and spontaneous small groups in a sample of college students of three different levels of instruction. A four-factor structure was encountered for the set of epistemological beliefs whose sophistication was rated for each student, with the emergence of significant differences regarding gender and habits of collaborative study. Women and collaborative students showed more sophisticated beliefs about learning as a process instead of learning as a quick acquisition. While the outcome regarding gender is somewhat known from studies of epistemological beliefs, the latter is a prime finding of direct links between personal epistemology and collaborative study styles.

We report a non-trivial outcome regarding the correlations between beliefs and groups for different academic years. While for junior students the size of the group correlated with naiver beliefs (about knowledge as handed down by authority), for senior students the size and number of groups correlated with sophistication (in Passive Learning). This counterintuitive result for the junior students is interpreted in a sociological frame, suggesting interesting connections to the internal evolution of small groups. In order to better address this point, the inner structure of the groups has to be properly considered in future research on this subject. To the best of our knowledge, this is the first report showing that larger study groups can boost both sophistication and naivety as a function of the level of instruction.

It would be interesting to extend our study to different contexts to determine to which extent the observed behaviour is universal or specific to spontaneously-formed small groups. This study explores the learning process from the student’s perspective in a new approach, contributing to possible educational interventions aimed to improve collaborative learning in the classroom spaces and beyond.

Disclosure statement

No potential conflict of interest was reported by the author(s).