Assessing Students’ Perceived Learning and Contentment in Physical Education: A Scale Development Study and Structural Equation Modeling Analysis

ABSTRACT

Although students’ perceived learning is central in physical education (PE), few measurements are available. Furthermore, little is known about how students’ perceptions of PE effect students’ perceived learning in PE. Therefore, the aim was to develop a scale to assess students’ perceived learning and a measurement to assess students’ perceived contentment in PE, and furthermore, to analyze the interrelationship between students’ perceived learning and students’ perceived contentment in PE. A total of 1203 students in Sweden who were aged 12–16 years participated. The results from the exploratory (n = 601) and confirmatory (n = 602) factor analyses as well as the validity and reliability analyses showed that there was psychometric support for the one-dimensional model perceived learning in PE and for the three-dimensional model perceived contentment in PE. The structural equation modeling analyses showed that both competence and joyfulness were directly and positively related to students’ perceived learning.

KEYWORDS:

• Physical education
• perceived learning
• perceived contentment
• factor analysis
• structural equation modeling

Introduction

The importance of physical education (PE) and its positive effects on students are well documented (Archer & Garcia, 2014; Ekblom-Bak, Ekblom, Andersson, Wallin, & Ekblom, 2018). PE has profound positive effects in several domains, such as the affective -, the cognitive -, the physical – and the social domain as well as in lifestyle (Bailey, 2006). Students’ physical ability and perceptions of physical activity (PA) are important, not only in PE, but also from a lifestyle perspective (Bailey, 2006). Students’ physical competence, knowledge related to lifestyle and students’ physical abilities – are central in relation to future participation in PA (Organisation for Economic Co-operation and Development [OECD], 2017).

An emphasized focus on students’ learning and knowledge in PE are evident in curriculums in several countries, including Sweden (Hardman, 2008; Hardman & Marshall, 2009; OECD, 2017; Swedish Schools Inspectorate, 2018). Students’ learning in PE has been discussed for decades. For example, Placek (1983) state that it is not enough for students to feel busy, happy, and good during PE – students are supposed to learn something. Recent research emphasize that students are supposed to learn about PA and health in PE (Ennis, 2014; Nyberg & Larsson, 2014). Nevertheless, “developing efficient, easy to use instruments to measure and compile data on students’ learning […] is a challenge to be addressed” (López-Pastor, Kirk, Lorente-Catalán, MacPhail, & Macdonald, 2013, p. 62). The development and validation of measurement to assess students’ learning in PE are an international challenge. This is particularly evident within Swedish PE research where validated measurements are rare and the tradition to develop measurements is weak (Lindwall & Lundqvist, 2004). Furthermore, the lack of measurements is possibly related to the limited knowledge about how students’ perceived learning in PE is related to other aspects of PE, such as students’ perceptions of PE, students participation in PA and the long-term impacts of PE (Green, 2012; López-Pastor et al., 2013; Trudeau & Shephard, 2008).

In this study, data from the Swedish project the School-Sport-Health (SSH) were used (see Thedin Jakobsson, 2015, for more information about the SSH-project). From the large item-pool in the project, items related to students’ learning and perceptions of PE were selected in line with the aim of the current study; to develop a scale to assess students’ perceived learning and a measurement to assess students’ perceived contentment in PE, and furthermore, to analyze the interrelationship between students’ perceived learning and students’ perceived contentment in PE. Identifying how different aspects of students’ perceptions affects students’ perceived learning is important to create meaningful PE experiences that can have meaning and relevance for all students. This study provide, in addition to new measurements, also support for a significant association between students’ perceived learning and contentment in PE.

Students’ perceptions of physical education

Students’ perceptions of PE are a wide concept with several aspects (Taylor, 2012). Several measurements are available to assess different aspects of students’ perceptions of PE. Phillips and Silverman (2012) developed an instrument to assess students’ attitudes toward PE which is based on attitude theory (Ajzen & Fishbein, 1980) with separate factors for affect and cognition. Additionally, Lyyra, Leskinen, and Heikinaro-Johansson (2015) designed an instrument to assess students’ perceptions of curricular goals in Finland based on how students ascribe to curricular goals in PE. Furthermore, Mitchell (1996) developed a frequently used instrument to assess students’ perceptions of learning environment in PE. Moreover, an instrument to assess perceived need support and need satisfaction in PE was developed by Sánchez-Oliva, Kinnafick, Smith, and Stenling (2018).

Instruments to assess enjoyment, fun, and PA during PE lessons have been developed by several researchers (Cunningham, 2007; Barr-Anderson et al., 2008; Kendzierski & DeCarlo, 1991; McKenzie, Sallis, & Nader, 1992; see also Motl et al., 2001; Paxton et al., 2013). Furthermore, several instruments have also been developed to assess students’ perceived competence in PE (see Carroll & Loumidis, 2001; Scrabis-Fletcher & Silverman, 2010).

Students’ learning in physical education

Several ways to operationalize students’ learning in PE have been suggested including grade, students’ estimations of their grade, teachers’ assessment, and different fact-based tests (Chen, Chen, & Zhu, 2012). However, learning in PE can also be operationalized based on the students’ own understanding of PE, as in, perceived learning (O’Sullivan & MacPhail, 2011). Unlike grades or fact-based tests, perceived learning is based on a student-centered perspective. This means that students’ own understanding of learning in PE is in focus. From this perspective, it is possible that students with low grades experience high learning and that students with high grades experience low learning in PE (O’Sullivan & MacPhail, 2011). As mentioned, there are few measurements developed to assess students’ perceived learning in PE (López-Pastor et al., 2013). The limited number of measurements to assess students’ perceived learning in PE could be a limitation in further research. It is possible that the lack of measurements developed to assess students’ perceived learning in PE is related to the lack of knowledge about what, when, and how much students experience that they learn in PE (Rink, 2013).

Students’ contentment in physical education

In this study, students’ contentment in PE – an aspect of students’ perceptions of PE was of particular focus. Students’ contentment in PE is an including term for several aspects of students’ perceptions of PE. In the present study, contentment in PE includes students’ perception of their own capacity in PE (perceived competence), perceptions related to wellbeing in PE (perceived comfort) and perceptions related to engagement in PE (perceived joyfulness). Students’ contentment in PE has been examined in a few earlier studies (Kristjánsson, Sigfúsdóttir, Allegrante, & Helgason, 2009; Metsämuuronen, Svedlin, & Ilic, 2012) and is closely related to one of the main aims in PE described by Hardman and Marshall (2000). However, there are few measurements developed to assess contentment in PE and little is known about how students’ contentment in PE is related to students learning in PE.

The importance of reliable measurements in physical education research

Reliable measurements developed to assess students’ perceptions of PE are a methodological contribution because they constitute a solid ground for further studies (Donovan, Mercier, & Phillips, 2015; Nunnally & Bernstain, 1994). Several researchers emphasize the importance of developing, validating, and using more reliable measurements in PE (Kougioumtzis & Patriksson, 2015; Lindwall & Lundqvist, 2004; Silverman & Subramaniam, 1999). Although there are several reliable and validated measurements developed to assess various aspects of students’ perceptions of PE, more measurements are warranted, mainly for three reasons. First, students’ perceptions of PE are a multifaceted area. In several aspects, reliable and validated measurements are lacking, for example, measurements to assess students’ perceived learning in PE (López-Pastor et al., 2013). Furthermore, even when there are available measurements developed to assess a particular aspect of students’ perception of PE, for example, enjoyment (Barr-Anderson et al., 2008; Cunningham, 2007; Kendzierski & DeCarlo, 1991; McKenzie et al., 1992). New measurements could contribute with the possibility to assess different aspects of enjoyment and also the possibility to assess the same construct from new or different theoretical perspectives. Second, the validity and reliability of measurements could differ depending on the composition of respondents. Several factors, such as the respondents’ age, gender, and national background, could affect the measurements’ psychometric properties (Scrabis-Fletcher & Silverman, 2010; Silverman & Subramaniam, 1999). New or modified measurements, developed for specific contexts or groups of respondents is therefore a methodological contribution. Third, even though there are several measurements developed to assess students’ perceptions of PE for specific aspects, new measurements, developed from existing item-pools could be valuable. Not only, because reliable measurements are a methodological contribution for further studies, but also because it enable analyses to examine how different constructs are related, for example, through structural equation modeling (SEM) analyses (Wang & Wang, 2012). This is particularly relevant in the present study, because the development of measurements and the analyses to examine how the constructs (students’ perceived learning and students’ perceived contentment in PE) are related, is based on an existing item-pool.

The importance of studying students’ perceptions of physical education

Students’ perceptions of PE have shown to be important from several perspectives (Kjønniksen, Fjørtoft, & Wold, 2009; O’Sullivan & MacPhail, 2011). From the student perspective, perceptions of PE are closely related to students’ personal feelings and thoughts about PE. It is an indicator of how PE is perceived based on individual students’ experiences of PE. From the student perspective, students’ perceptions of PE are important not due to future positive outcomes (e.g., high level of PA during leisure time), instead important in direct relation to PE – there and then (Groves & Laws, 2000; O’Sullivan & MacPhail, 2011). Furthermore, students’ perceptions of PE are also important from an outcome perspective (Archer & Garcia, 2014; Kjønniksen et al., 2009), because it could be used to develop PE and improve students’ outcomes in PE (e.g., grade) (Archer & Garcia, 2014). Several researches describe the value of studying students’ perceptions of PE from an outcome perspective and describe that students’ perceptions of PE are a prerequisite for both participation and student learning in PE. In addition, positive perceptions of PE contribute to a lifelong interest in PA (Kjønniksen et al., 2009; Sollerhed, Ejlertsson, & Apitzsch, 2005; Subramaniam & Silverman, 2007; Swedish National Agency for Education [SNAE], 2018). In this study, both perspectives was combined. This means, that the scales in the study were developed with an ambition to capture students’ own experiences of PE, thus, to reflect students’ perceived learning in PE and contentment in PE – from a student perspective. Thereafter, in the construction of the SEM-model, to analyze the interrelationship between students’ perceived learning and students’ perceived contentment in PE, the scale perceived learning in PE was set as the main outcome. From an outcome perspective, this is theoretically justified since students’ learning is, according to several researches, the main objective in PE (Chen & Ennis, 2004; Ennis, 2014; Larsson & Redelius, 2008). The hypothesized model is presented in Figure 1.

Figure 1. Hypothesized model for the relationship between students perceived learning (Le) and perceived competence (Co), comfort (Cf) and joyfulness (Jo).

The aims of physical education

During the last decades, PE has evolved from a strong focus on hygiene and PA, to an emphasized focus on students’ learning, both related to physical movement as well as lifestyle and health (OECD, 2017). There are some clear similarities between several countries regarding the aims of PE (Hardman, 2008; Hardman & Marshall, 2009; OECD, 2017). The aims of PE can be divided into three areas, 1) cognitive (knowledge/knowing), 2) affective (attitudes/values) and 3) psycho-motor (skills/doing) (Hardman & Marshall, 2000). These three areas are closely related to the aims of PE in Sweden (c.f. Hardman & Marshall, 2000). The Swedish National Agency for Education (SNAE, 2018, p. 48) states that the aims of PE are that students can 1) move without restriction in different physical contexts, 2) plan, implement and evaluate sports and other physical activities based on different views of health, movement, and lifestyle, 3) carry out and adapt time recreational and outdoor life to different conditions and environments, and 4) prevent risks during physical activities, and manage emergency situations on land and in water. Furthermore, SNAE states that students should 5) develop their interpersonal skills and respect for others.

As a theoretical framework in this study, we use the (above) described aims in PE by Hardman and Marshall (2000) as well as SNAEs formulated aims in PE in Sweden, however, with a specific focus on two areas, namely 1) cognitive (knowledge/knowing) and 2) affective (attitudes/values). The third area, psycho-motor (skills/doing), is not included in this study. Mainly because other measurements have been developed in this area in Sweden (Ericsson, 2008) and from the same item-pool as the measurements in this study (e.g., Tidén, Lundqvist, & Nyberg, 2015). The two areas 1) cognitive (knowledge/knowing) and 2) affective (attitudes/values) were initially used in the construction of the scales in the present study. The area, 1) cognitive (knowledge/knowing) was used as a theoretical frame in the construction of the one-dimensional scale in the present study (perceived learning). Furthermore, the area 2) affective (attitudes/values) was used as a theoretical frame in the construction of the three-dimensional scale perceived contentment in PE. Thereafter, the two areas (cognitive and affective) were used in the construction of the SEM-model in order to analyze the interrelationship between students’ perceived learning and students’ perceived contentment in PE. The SEM-model was developed based on the theoretical framework in the study; based on previous research (Chen & Ennis, 2004; Ennis, 2014; Larsson & Redelius, 2008; Subramaniam & Silverman, 2007), we hypothesized that students’ positive perceptions of PE has a positive effect on students’ perceived learning in PE – which was considered the main outcome in PE (see Figure 1 for the hypothesized model).

Based on the fact that one primary aim in this study was to develop a scale to assess students’ perceived learning and a measurement to assess students’ perceived contentment in PE, this study is also grounded in psychometric/test theory (Nunnally & Bernstain, 1994). In psychometric theory, one fundamental idea is that the reliability and validity in measurements could be analyzed statistically (Thompson, 2004). Furthermore, the development of reliable measurements is based on psychometric information, which, when simplified, could be described as statistical information about the accuracy, reliability, and stability of the measurements. Psychometric/test theory offers support for several statistical analyses that provide the researcher with psychometric data which may be used to develop reliable measurements in PE (Nunnally & Bernstain, 1994). For example, factor analysis is frequently used to develop measurements. The analyses can provide the researcher with information, for example, about how well items measure the (same) underlying construct(s) (Field, 2016; Nunnally & Bernstain, 1994). Furthermore, several analyses are available to examine the validity and reliability of the instrument (Foster & Cone, 1995). One of the most widely used tests to analyze internal consistency is Cronbach’s alpha (α) (Cronbach, 1951; Tavakol & Dennick, 2011). To analyze construct validity, Fornell and Larcker (1981) provide support for the use of convergent and discriminant validity analyses by calculating composite reliability (CR), average variance extracted (AVE), and the square root of average variance extracted (√AVE). There are also procedures to analyze measurement invariance, which refer to ”the extent to which a measuring instrument is equivalent across two or more independent samples” (Byrne, 2008, p. 872). Several procedures to analyze measurement invariance have been suggested, which include configural, metric and scalar invariance (Byrne, 2008; Muthén & Asparouhov, 2018).

Method

Since 2001, the School-Sport-Health (SSH) study has been an interdisciplinary and longitudinal Swedish project with a focus on PA, health, and sports among children and adolescents. The SSH study consists of a large item-pool with single items/question measures in several areas including PE, PA, psycho-motor skills and medicine. Through the years (2004, 2007, and 2010), data have been collected from the same students at ages 9, 12, and 15 until they were 18, 21, and 24 years old. In this study, only data on students’ perceptions of PE collected in 2016 was used.

Participants

The study participants consisted of 1203 students (girls n = 598, boys n = 594, and 11 students who did not report gender) from grade 6 (n = 562) and grade 9 (n = 641). Students from grade 6 and 9 were selected to capture the variety of experiences students from different age groups could have about PE. The students came from the same schools (N = 24) or the same geographical areas as the randomly selected schools in the first SSH study (see Sundblad, Saartok, Engström, & Renström, 2005, for more details about the process of randomly selecting schools for the first SSH study). The students in grade 6 were aged 12 to 13 years, and the students in grade 9 were aged 15 to 16 years.

Procedure

Before the data were collected, students received written and oral information in accordance with the rules and prevailing ethical practice. The confidentiality of answers was emphasized when informing the students. Throughout all the stages of the analysis, the identity of the students was coded to ensure anonymity. The data were collected by co-authors in accordance with the approved application by the ethical review board at Karolinska Institute, Sweden (ref. no. 00–416).

Questionnaire and coding

The questionnaire developed in the SSH study has remained unchanged to enable comparisons over time, and it has been used both in longitudinal and cross-sectional studies since 2001 (e.g., Tidén et al., 2015). The SSH-questionnaire consists of single items/question measures in several areas including PE, PA, psycho-motor skills and medicine. In this study, only items on students’ perceptions of PE collected in 2016 was used. The items (see Table 1) were developed in order to capture several aspects of students’ perceptions of PE and include students’ perceptions of their own capacity in PE, perceptions related to wellbeing in PE and perceptions related to engagement and learning in PE. The questionnaire was developed in a series of steps that included revising questions after discussions with students and experts (researchers and university teachers in PE teacher education). The questionnaire has demonstrated its validity in construction and high reliability in a test–retest procedure, “when a class (28 students) in grade 9 answered the questionnaire on two occasions with one week in between” (Thedin Jakobsson, 2015, p. 52). In the present study, students answered 24 items based on the question, “How well do these statements describe your idea of PE and how do you feel when you have PE?” The response alternatives were: certainly true (score 3), somewhat true (score 2), not true (score 1) or often/always (score 3), sometimes (score 2), almost never/never (score 1). When negative and positive items were included in the same factor, the negative items were reversely coded.

Table 1. Scales, items, and abbreviations in brackets.

Scale	Items	Abbreviations
Perceived learning	I get stronger and fitter I am getting better at sports I get to learn such that I can benefit from I learn to work together with others I learn about how the body works I learn how different sports are done	(Le1) (Le2) (Le3) (Le4) (Le5) (Le6)
Perceived competence	I can show others that I am good at sports	(Co1)
	Bad	(Co2)
	Good	(Co3)
	I often feel that I am bad at sports	(Co4)
Perceived comfort	Scared	(Cf1)
	Worried	(Cf2)
	Stressed	(Cf3)
	Excluded	(Cf4)
	I feel bad about changing and showering at school	(Cf5) (Cf6)
	I do not like when we split into teams Safe	(Cf7)
Perceived joyfulness	I think physical education in school should be voluntary	(Jo1)
	Happy	(Jo2)
	I would not like to participate	(Jo3)
	I think it is fun	(Jo4)
	Bored	(Jo5)
	I get relaxation from the usual school work	(Jo6)
	Physically tired (sweaty)	(Jo7)

Data analysis

The analyses include exploratory factor analysis (EFA), confirmatory factor analysis (CFA), analyses to examine construct and convergent validity, analyses to examine measurement invariance and finally structural equation modeling analyses (SEM). Of the total number of students in the study (N = 1203), half of the students (n = 601) were used in the EFA and the remaining part (n = 602) in the CFA and SEM-model. The chi-square analysis showed that there were no significant differences between the datasets for gender distribution (χ² (1) = .410, p = .524), grade distribution (χ² (1) = .610, p = .434) or national origin distribution (χ² (1) = .801, p = .372).

Exploratory factor analysis

The EFA was conducted in SPSS (version 24) by an extraction from maximum likelihood (ML) and promax rotation, as we expected a correlation between the factors. No fixed factor assumptions were used, and items with a factor loading < .50 and with communalities (h²) < .30 were excluded from the analysis.

Confirmatory factor analysis

The CFA was conducted in Mplus version 7.4 (Muthén & Muthén, 1998–2017). All available data were used, and the maximum likelihood robust (MLR) estimation method was used in the analysis. Model fit was evaluated from χ²-test and χ²-test divided by degrees of freedom (χ²/df), where the value 2.0 indicates a good fit and 2.0 to 5.0 an acceptable fit (Hair, Black, Babin, & Anderson, 2010). For the comparative fit index (CFI), the value .90 was acceptable and .95 was good. Furthermore, a good model fit for the root-mean-square error of approximation (RMSEA) was < .06, and for standardized root-mean-square residual (SRMR) < .08 (Hu & Bentler, 1999).

Reliability and validity

The reliability of items and scales was evaluated based on reliability coefficients (R²), Cronbach’s alpha (α) (≥ .70) and factor loadings (≥ .50) (Cronbach, 1951; Hair et al., 2010; Nunnally & Bernstain, 1994). Construct validity was evaluated through convergent and discriminant validity. The convergent validity was examined by calculating the average variance extracted (AVE) and composite reliability (CR). The average variance extracted (AVE) “measures the amount of variance that is captured by the construct in relation to the amount of variance due to measurement error” (Fornell & Larcker, 1981, p. 45), and ≥ .50 was used as a guideline value. Regarding CR, the value ≥ .70 indicates an adequate reliability of individual factors (Fornell & Larcker, 1981). To evaluate discriminant validity, which refers to the extent to which the factors differ from other factors, the correlation between factors should preferably be smaller than the square root of AVE (√AVE) (Fornell & Larcker, 1981; see also Hair, Hult, Ringle, & Sarstedt, 2017; Teo, Lee, Chai, & Wong, 2009).

Group invariance

Measurement invariance refers to the consistency of factor structure across different groups, in this study between girls and boys. Analyses to evaluate measurement invariance was conducted in several steps. First, separate models for girls and boys were estimated. Thereafter, measurement invariance was analyzed in three steps, as suggested in earlier research (Byrne, 2008; Muthén & Asparouhov, 2018). The three steps included analyses for configural, metric and scalar invariance. In the first step, the configural invariance model had no restrictions for any of the parameters, thus, not for factor loadings or measurement intercepts. The second step, the metric invariance, holds the factor loadings equal across girls and boys, and is therefore more restrictive. The final step, scalar invariance, holds both measurements intercepts (of items) and factor loadings equal across girls and boys. Therefore, it is also the most restrictive analysis for measurement invariance (Muthén & Asparouhov, 2018).

Structural equation modeling

The SEM analysis was conducted in Mplus version 7.4 (Muthén & Muthén, 1998–2017). The SEM analysis was used to examine the interrelationship between students’ contentment in PE and students’ perceived learning in PE in line with the hypothesized model (see Figure 1). Based on theoretical reasons, students’ perceived learning was the main outcome latent variable and the other latent variables were considered as predictors. In the analysis, the MLR estimation method and all available data were used. Model fit was evaluated based on predetermined criteria. That is, χ²-test and χ²-test divided by degrees of freedom (χ²/df). For the latter, the value 2.0 indicates a good fit and 2.0 to 5.0 an acceptable fit (Hair et al., 2010). A good model fit was indicated by a RMSEA value < .06 and a SRMR value < .08. Furthermore, by a CFI value of .90 (acceptable) and .95 (good).

Results

EFA, dataset 1

The results from Bartlett’s Test of Sphericity (p = < .001) and Kaiser-Meyer-Olkin Measure of Sampling Adequacy (.900) indicate that the data were suitable for EFA. The EFA was conducted with extraction from the maximum likelihood method (ML) and promax rotation. The results showed a four-factor solution (see Table 2). Experts (researchers and university teachers in PE teacher education) discussed adequate names for the factors. The four factors were named learning, competence, comfort, and joyfulness.

Table 2. Factor loadings and communalities (h²) from EFA for four factors and 15 items.

Item	1 (Le)	4 (Cf)	3 (Jo)	2 (Co)	h^2
Le1	.89				.67
Le2	.79				.62
Le3	.63				.46
Le4	.50				.33
Cf1		.82			.61
Cf2		.71			.56
Cf3		.58			.45
Cf4		.53			.36
Jo1			.69		.34
Jo2			.68		.60
Jo3			.63		.61
Jo4			.54		.69
Jo5			.46		.36
Co1				.84	.60
Co2				.79	.60

Note: Le = Learning, Cf = comfort, Co = competence, Jo = joyfulness; All standardized factor loadings are significant (p < .01).

CFA, dataset 2

Based on the theoretical framework in the study, the result from the EFA analysis was discussed by experts and two CFA models were estimated. Factor loadings for the first model, the one-dimensional model perceived learning showed there was psychometric support for the scale. Fit indices for the second model, students’ contentment in PE, a model with three factors, perceived competence, comfort, and joyfulness showed that the model fits the data well: χ² (32) = 105.299, p = < .001; χ²/df = 3.29; CFI = .96; RMSEA = .06; SRMR = .04.

The construct validity and the reliability of items and latent variables (learning, competence, comfort, and joyfulness) were evaluated based on predetermined criteria (factor loadings, α, CR, AVE and √AVE). Table 3 shows that the criteria for all latent variables were met for Cronbach’s alpha (≥ .70) and CR (≥ .70). The criteria for AVE (≥ .50) were fully met for competence and joyfulness but not fully met for comfort (.47) and learning (.49). However, the difference between the predetermined criteria for AVE ≥ .50 and the results (.47 and .49) was small and considered less important. Therefore, the latent variables (learning, competence, comfort, joyfulness) show an overall a good convergent validity. Finally, the criteria for discriminant validity (i.e., that the correlation between factors, preferably should be smaller than the square root of AVE) were fully met for competence and comfort, but not for learning and joyfulness. However, for both learning and joyfulness, the difference between the actual value (learning = .70; joyfulness = .73) and the correlation with the other latent variables were small (≤ .02). Therefore, the latent variables indicate overall a good discriminant validity.

Table 3. Confirmatory factor analysis for latent variables with convergent, – and discriminant validity measures.

Construct	Factor loadings	S.E.	Error variances	R^2	α	AVE	CR
Construct perceived learning
Factor (Le)					.79	.49	.79
Le2	.79*	.03	.37	.63
Le1	.78*	.03	.39	.61
Le3	.62*	.04	.62	.38
Le4	.59*	.04	.65	.35
Construct perceived contentment
Factor (Co)					.82	.69	.82
Co2	.83*	.03	.31	.69
Co1	.83*	.03	.31	.69
Factor (Cf)					.76	.47	.78
Cf1	.75*	.04	.44	.56
Cf2	.69*	.05	.52	.48
Cf3	.62*	.04	.62	.38
Cf4	.66*	.04	.57	.43
Factor (Jo)					.81	.53	.81
Jo4	.81*	.03	.35	.65
Jo3	.71*	.04	.50	.50
Jo5	.58*	.04	.67	.33
Jo2	.78*	.03	.40	.60
Discriminant validity	Factor Le	Factor Co	Factor Cf	Factor Jo
Factor Le	.70 ¤
Factor Co	.60*	.83 ¤
Factor Cf	.32*	.50*	.69 ¤
Factor Jo	.72*	.73*	.53*	.73 ¤

Note. * = All standardized factor loadings are significant (p < .01); R² = 1-item error variance; α = Cronbach’s alpha (Cronbach, 1951); AVE = average variance extracted (Fornell & Larcker, 1981); CR = composite reliability (Fornell & Larcker, 1981); Discriminant validity = the extent to which constructs differ (Teo et al., 2009); vertical/horizontal columns show the correlation between factors, which preferably should be smaller than square root of AVE (¤ = √AVE) (Fornell & Larcker, 1981); Le = learning, Co = competence, Cf = comfort, Jo = joyfulness.

Gender invariance, dataset 2

Measurement invariance was analyzed through several steps. First, the analyses were conducted separately for girls and boys. The results from the separate, girls/boys, models – students’ perceived learning and contentment in PE – indicate a good model fit (see Table 4). Thereafter, invariance analyses were conducted in three steps by analyzing configural, metric and scalar invariance. The analyses were conducted both for the model students’ perceived learning and the model contentment in PE. The results, presented in Table 4, indicate a reasonable fit for all models. Furthermore, based on Satorra and Bentler (2001) Chi-squared difference test, the configural, metric and scalar models were compared. The results indicated that the models remained measurement invariant when 1) the model is unconstrained (configural), 2) factor loadings are held equal across groups (metric) and 3) both factor loadings and measurement intercepts are equal. Overall, the CFA model for the scale perceived learning in PE as well as the CFA model for students’ contentment in PE – were gender invariant based on a high degree of measurement invariance (Meredith & Teresi, 2006; Muthén & Asparouhov, 2018).

Table 4. Result for measurement invariance based on separate models, configural, metric, and scalar invariance.

Model	χ^2(df)	χ^2/df	p	CFI	SRMR	ΔSBχ^2(df)	p
Model Learning
Separate models
Boys	χ^2(2) = .751	.38	.687
Girls	χ^2(2) = 1.810	.91	.405
Model Contentment
Separate models
Boys	χ^2(32) = 66.218	2.07	<.001	.938	.06
Girls	χ^2(32) = 77.722	2.43	<.001	.957	.04
Model Learning
Gender invariance
Configural	χ^2(4) = 2.504	.63	.644			^†χ^2(3) = 6.276	.099
Metric	χ^2(7) = 8.665	1.24	.278	1	.06	^††χ^2(6) = 11.179	.083
Scalar	χ^2(10) = 13.478	1.35	.198	.99	.07	^†††χ^2(3) = 4.871	.182
Model Contentment
Gender invariance
Configural	χ^2(64) = 143.436	2.24	<.001	.95	.05	^†χ^2(7) = 11.464	.120
Metric	χ^2(71) = 153.848	2.17	<.001	.95	.07	^††χ^2(14) = 22.319	.072
Scalar	χ^2(78) = 165.125	2.12	<.001	.94	.07	^†††χ^2(7) = 10.720	.151

Note. ^†Metric compared to configural; ^††Scalar compared to configural; ^†††Scalar compared to metric.

The interrelationship between students’ contentment in PE and perceived learning in PE, dataset 2

In the SEM-model, students’ perceived learning was the main outcome and the three aspects (perceived competence, comfort and joyfulness) of students’ contentment in PE were considered interrelated latent variables and predictors. The first model (presented in Figure 1) showed somewhat low model fit, χ² (72) = 302.204, p = < .001; χ²/df = 4.20; CFI = .91; RMSEA = .07; SRMR = .07. Based on theoretical reasons a relationship between competence and joyfulness was added (presented in Figure 2). The result showed a good model fit, χ² (71) = 180.271, p = < .001; χ²/df = 2.54; CFI = .96; RMSEA = .05; SRMR = .04. Modification index showed that cross loading between some of the manifest and latent variables would improve model fit significantly. The highest cross loading was between the manifest variable Jo3 and latent variable comfort (MImax = 21.62), however, no adjustments were made to preserve the simplicity of the model.

Figure 2. Result from the structural equation modeling with standardized values for the interrelationship between students’ perceived learning (Le) and perceived competence (Co), comfort (Cf) and joyfulness (Jo). Explained variance (R²) and standard error in parenthesis.

The predictors explained the variance in students’ perceived learning with 54%. The effect between students’ joyfulness and students’ perceived learning was positive (.64) as well as students’ competence and students’ perceived learning (.20). Nevertheless, the direct effect between students’ comfort and students’ perceived learning was negative (−.13). However, the indirect effect through the two other latent variables was still positive, students’ joyfulness (β = .14; SE = .04; p = < .001) and competence (β = .10; SE = .04; p = .013). This indicates, that students’ comfort is positively related to students’ perceived learning, through students’ perceived joyfulness (.22) and students’ competence (.50). The result is illustrated in Figure 2.

Discussion

Compared to several other measurements developed to assess students’ perceptions of PE, this study includes a scale to assess students’ perceived learning in PE. Even though learning is described as the main objective in PE (Chen & Ennis, 2004; Ennis, 2014; Larsson & Redelius, 2008), there are few measurements developed to assess student learning in PE (López-Pastor et al., 2013). Several researchers describe that little is known about how students’ perceived learning in PE is related to other aspects of PE, such as students’ perceptions of PE, students participation in PA and the long-term impact of PE (Green, 2012; López-Pastor et al., 2013; Trudeau & Shephard, 2008). The lack of measurements may be due to several reasons. Among others, due to the difficulty of operationalizing learning in PE since the learning objectives are context-driven and vary highly (Groves & Laws, 2000; O’Sullivan & MacPhail, 2011). Therefore, the aim of the current study was to develop a scale to assess students’ perceived learning and a measurement to assess students’ perceived contentment in PE, and furthermore, to analyze the interrelationship between students’ perceived learning and students’ perceived contentment in PE. The scales were developed in line with the theoretical framework in the study, based on the main aims of PE, which can be divided into two areas, 1) cognitive (knowledge/knowing) and 2) affective (attitudes/values) (Hardman & Marshall, 2000). The scales were developed through exploratory and confirmatory factor analyses, thereafter, evaluated based on convergent and discriminant validity measures and finally analyses to assess measurement invariance. The results showed a one-dimensional model (perceived learning) and a three-dimensional model (perceived contentment in PE), with three factors, competence, comfort and joyfulness. Fit indices and factor structure show that the two CFA models fit the data well. With minor exceptions, all predetermined criteria were met for factor loadings, Cronbach’s alpha, and convergent and discriminant validity (Cronbach, 1951; Fornell & Larcker, 1981; Teo et al., 2009). Measurement invariance was analyzed in several steps as suggested in earlier research (Byrne, 2008; Muthén & Asparouhov, 2018). The results showed a high degree of measurement invariance (Meredith & Teresi, 2006).

Although there was psychometric support for all scales in the study, the development of measurements is an ongoing process (Thompson, 2004). This study was conducted in a Swedish context, and the items in the questionnaire were in Swedish. Further development of the scales is important, especially if the instrument is used in countries other than Sweden. A limitation is that the scale perceived competence consists of only two items. However, this is understandable given that the criteria for factor inclusion in the factor analysis were set high. Nevertheless, additional items should be added to improve the scale perceived competence.

The SEM-model was developed based on the theoretical framework in the study; based on previous research (Chen & Ennis, 2004; Ennis, 2014; Larsson & Redelius, 2008; Subramaniam & Silverman, 2007), our hypothesis was that positive perceptions of PE has a positive effect on students’ perceived learning in PE – which was considered the main outcome in PE (see Figure 1 for the hypothesized model). Based on this hypothesis, one latent variable (students’ perceived learning) was the main outcome. The result showed, as expected, that there was a strong positive relationship between perceived learning and perceived competence and joyfulness, however, that there was a direct (weak) negative relationship between comfort and perceived learning in PE. This indicate that, students’ perceived competence and especially students’ perceived joyfulness seems to be important aspects in relation to students’ perceived learning in PE. The importance of enjoyment and fun in PE is established in several studies (Barr-Anderson et al., 2008; Cunningham, 2007). In this study, we show that students’ perceived joyfulness in PE is an important factor in relation to students’ perceived learning in PE – when both students’ perceived competence and comfort in PE is taken into account.

This study offers psychometric support for a scale to assess students’ perceived learning in PE and a measurement to assess perceived contentment in PE. Although that validated and reliable measurements are important, this study also shows that there is a positive relationship between students’ contentment in PE and students’ perceived learning in PE. This indicates that positive perceptions of PE could affect students’ perceived learning in PE. Students’ experiences from PE that strengthen students’ positive perceptions of PE could therefore also positively affect students’ perceived learning in PE.

Additional information

Funding

This study was financed by Malmö University in collaboration with the Swedish School of Sport and Health Sciences in Stockholm.