The process carried out to select participants was cluster sampling. This provided a representative sample of Secondary Education (K-8 to K-10) of a city with about 150,000 inhabitants like the city of Badajoz (Spain), where the study has been carried out. Access and convenience sampling have been the implemented inclusion criteria, looking for a homogeneous distribution throughout the city.

The considered sample consisted of 431 students, according to the distribution summarized in Table 1.

Sociodemographically the sample featured 47.1% girls and 52.9% boys with ages ranging between 13 and 17 years old. It is an urban sample, with participant students belonging to middle-class families and working parents.

A quantitative non-experimental or “ex post facto” methodological approach was considered to perform this research. The data acquisition instrument was a questionnaire of the authors’ own elaboration (Supplementary Material), based on the one previously proposed by Borrachero et al. (2014).

In the questionnaire, students are asked first about negative and positive emotions they experience when learning certain topics belonging to five blocks of contents. Those blocks of contents were established according to the current educational curriculum (Real Decreto 83/2007). Namely, the considered blocks of content were “Matter” (block I), “Energy and Electricity” (block II), “Structure and Changes of Matter” (block III), “Kinematics and Dynamics” (block IV) and “Work and Energy” (block V). Blocks I, II, and III were considered in K-8 to K-10, while blocks IV and V were exclusively considered for K-10 students; secondly, they are asked about the felt emotions toward several aspects related to the teacher and the students; and lastly, they are asked how often they feel seven positive and seven negative emotions when learning Physics and Chemistry. Previous research carried out by our research group allowed us to identify the selected emotions as the most representative in the academic field (Brígido et al., 2013; Borrachero et al., 2014). In all cases students are asked to respond according to an 11-points Likert scale (0 = minimum; 10 = maximum).

The reliability of the questionnaire was calculated using the covariation between the items of the different scales making it up in order to verify its internal consistency. The obtained values were all higher than 0.80, which means that the questionnaire is quite good.

The teachers responsible for the K-8 to K-10 levels were asked to hand out the questionnaires to the different groups of students. Data was processed and analyzed statistically using the statistical package SPSS (Statistical Product and Service Solutions) 22.0 and The Unscrambler for Windows.

A Principal Component Analysis (PCA) was performed in order to establish possible correlations between the variables, in this case content (of Physics and Chemistry) and causes (teacher/pupil).

Principal component analysis is a dimensionality reduction technique that has proven to be useful in the extraction of relevant information from complex datasets. This analysis seeks to maximize the variance of a linear combination of the variables. It maps each instance of the given dataset in a d-dimensional space to a k-dimensional subspace so that k < d. The set of k new dimensions are called the principal components (PC) and each principal component is directed toward a maximum variance excluding the variance already accounted for in all the preceding components. The first principal component is the linear combination with maximal variance. The second principal component is the linear combination with maximal variance in a direction orthogonal to the first principal component, etc. The first principal component also represents the line that minimizes the total sum of squared perpendicular distances from the points to the line. The principal components can be represented as:

where:

PC_i: principal component “i”;

X_j: original feature “j”;

a_j: numerical coefficient for X_j.

Van der Wal and Kowalczyk (2013) worked in the measurement of changes in the emotional state of a speaker by analyzing his/her voice and employed PCA to visualize the results to the speaker in the 2-d space. They reported that PCA is a promising technique for visualizing a human’s emotional state. Zhang and Zhao (2013) assayed and compared different dimensionality reduction methods, including PCA, with an aim of improving the performance on spoken emotion recognition.

PCA has been also commonly employed in the field of psychology. For instance, Gray studied the implications of psychological membership in the classroom for achievement motivation and emotions (Gray, 2017). Kroeger et al. (2017) employed PCA for the evaluation of impulsivity and emotion dysregulation in adolescents with borderline personality disorder; and Gondim et al. (2015) employed it to analyze measurements on individual differences in the regulation of emotions.

Figure 1 shows the mean frequencies (Likert scale from 0 to 10) for positive emotions experienced by K-8 to K-10 students when learning Physics and Chemistry, depending on the level. The mean frequency ranges between 4.5 and 6.9. Maxima values are found for K-8 students, namely for emotions joy (6.78), satisfaction (6.42), and tranquility (6.26).

It can be also observed that K-8–K-10 students experienced a decrease in the average frequency of the positive emotions as joy, trust, fun, enthusiasm, and tranquility from K-8 to K-10.

A Student’s t-test was performed and statistically significant differences were found in the positive emotions joy (p = 0.000), trust (p = 0.045), fun (p = 0.000), and tranquility (p = 0.000) between K-8 and the other two levels, which reveals a significant decrease from K-8 to higher levels.

Figure 2 shows the mean frequencies (Likert scale from 0 to 10) for negative emotions experienced by K-8–K-10 students when learning Physics and Chemistry, depending on the level. In this case, the mean frequency for negative emotions ranges between 3 and 7, with maxima in K-10 for boredom (6.25), nervousness (6.02), and worry (6.71). This might be due to the higher amount of Physics contents in K-10, whereas more Chemistry is taught in K-9.

Also, it can be observed that negative emotions such as boredom, anxiety, disgust, fear, nervousness, worry, and sadness increase in the average frequency from K-8 to K-10.

Statistical analysis of the mean frequencies reveals significant differences in boredom (p = 0.000), anxiety (p = 0.010), disgust (p = 0.002), fear (p = 0.000), nervousness (p = 0.014), worry (p = 0.000), and sadness (p = 0.003) between K-10 and the other two levels.

Results were also analyzed by PCA. Firstly, the KMO (Kaiser-Mayer-Olkin) index was calculated and the Bartlett’s sphericity test was applied in order to check the suitability of the considered sample (N = 431) to be analyzed by PCA. When applying Bartlett’s sphericity test a p-value < 0.05 is obtained and a high (≈1) KMO index is calculated, which means that PCA can be efficiently performed in the current dataset, i.e., fourteen emotions measured in three levels K-8–K-10.

Results of PCA are summarized in Figures 3, 4 in the form of loadings and scores plots, respectively, and subsequently discussed.

Figure 3 shows the loadings plot for the plane formed by the first (PC1) and the second (PC2) principal components, which as stated above, explain 35.97 and 18.51% of total variance, respectively. This plot helps to identify correlations among variables. As it can be observed, the emotions enthusiasm, joy, satisfaction, fun, and trust present high loading values for PC1, which means that this PC represents positive emotions. It can also be observed that in the in the plane formed by PC1 and PC2 these emotions are located close to each other, which means that they are positively correlated. Nevertheless, the emotions tranquility and surprise are located apart from the other positive emotions in the plane formed by PC1 and PC2, showing lower loading values for PC1. The small loading values for emotions tranquility and surprise suggest that these emotions might not be further considered in the interpretation of the results, since they contribute in a small extension in PC1 and PC2. On the other hand, the emotions fear, worry, nervousness, sadness, and anxiety present high values of loading for PC2 and they are located close to each other in the plane formed by PC1 and PC2, which means that PC2 represents negative emotions and that the emotions above listed are positively correlated among them. The emotions boredom and disgust are located a bit farther from the cluster formed by the other negative emotions. However, since these two emotions present lower loading values for PC2, it can be concluded that the are not very important in the interpretation of the results. In the plot it can be also observed that both groups of emotions are negatively correlated.

The scores plot for the plane formed by PC1 and PC2 is represented in Figure 4. This plot helps in the identification of sample clusters and it helps also to visualize how different are sample constituents among them. In this case, as it can be observed, there is no a clear separation between students of the different levels.

To sum up, a decrease has been detected in the mean frequency of all the positive emotions and an increase in all the negative emotions from K-8 to K-10. These results can be compared to the ones obtained by Dávila et al. (2016) with a similar sample in which a decrease in the frequency of positive emotions (joy, confidence, happiness, tranquility, surprise, and excitement), and an increase in the negative emotions (worry, shame, disgust, and anger) was detected from K-9 to K-10.

The decrease in the positive and increase in the negative emotions in middle and high school in these subjects agrees with the decline of positive attitudes toward science stated in previous studies (Osborne et al., 2003). The combination of negative attitudes and emotions toward Physics and Chemistry content can influence the choice of subsequent career paths and university degrees that involve these subjects (Custodio et al., 2013) since emotions are fundamental in decision making (Angie et al., 2011). The decrease, observed in many countries, in the number of students pursuing Chemistry degrees, and even more in the case of Physics degrees, might be related to the emotionally difficult context surrounding science learning during their secondary education, when they did not manage to enjoy learning these subjects (Vázquez and Manassero, 2008).

Finally, unlike other studies (Borrachero et al., 2014), in the present one, differences according the gender were not found for any of the considered dimensions.

The part of the dataset containing measures of positive emotions toward Physics and Chemistry content, as well as toward the causes related to the teacher’s evaluation, attitude, and methods, and toward aspects related to the students, such as their ability to learn, motivation to learn, and grades obtained, was also analyzed by PCA. Figure 5 shows the loadings for the first two principal components (PC1 vs. PC2), which explain 76 and 6% of the total variance of the system, respectively. As stated above, the loadings plot resulting from a PCA is particularly useful to detect correlations between variables. Those variables with a high loading on a particular principal component (PC) define the meaning of that PC. To determine the correlation between variables, one must bear in mind that when two variables have high loadings on the same PC, those variables are strongly correlated. If the loadings of the two variables have the same sign then the correlation is positive, and negative if they have different signs.

Considering only the distribution of the various items of the content on the loadings map, it is observed that items 1–15 are grouped in the high part of the first principal component (PC1, horizontal axis), whereas items 16–23 are grouped in the high part of the second principal component (PC2, vertical axis). As items 1–15 are Chemistry content, and items 16–23 correspond to Physics content, the first conclusion that could be reached, given these variables grouping, is that the two disciplines cause in the students different quantities and types of positive emotions, which would contribute to the decoupling of the two disciplines with regard to the students’ emotions. It can also be said that all the Physics items considered in the study are strongly correlated, with this correlation being positive as they were all grouped in the high part of PC2, and that all the Chemistry items were also correlated positively with each other, being grouped in the high part of PC1. Thus, for instance, the students who show positive emotions toward the item “Atoms and molecules” (I1) also show them to the items “The periodic table and periodic properties of the elements” (I11), “Formulation and nomenclature” (I12), and “Chemical reactions and stoichiometry” (I13). Considering not only the items but also the distribution of the various causes studied related with the teacher (pink dots), one observes that all these causes except P3 (“Exclusive use of the textbook”) are in the high part of PC1, very close to the cluster formed by the Chemistry items. This means that these causes of positive emotions related to the teacher are correlated positively with the Chemistry items. For example, a pupil showing positive emotions toward Chemistry items will also show positive emotions toward aspects related with the teacher’s methods, such as doing practical laboratory activities (P1), group work and activities outside the classroom (P2), as well as to aspects related with the teacher’s attitude, such as clarification and resolution of doubts (P6), and the use of new technologies (ICT) (P7). It is logical that pupils with positive emotions toward lab work or activities outside the classroom usually do not show such emotions toward the exclusive use of textbooks (P3).

Considering also the causes related to the students (green dots), one observes that all of them except two are located within or very near the cluster formed by the Chemistry content. The two exceptions are E2 (“Giving oral presentations in class”) and E5 (“Solving physics problems”). It is logical that solving Physics problems correlates with neither the Chemistry content nor oral presentations since this is something scarcely worked during this educational stage. Again, this means that all the considered causes related to students which have been considered in this study except E2 and E5 are positively correlated with the Chemistry content as far as positive emotions are concerned. In view of these results, it can be affirmed that a pupil with positive emotions toward the Chemistry content also shows them toward aspects related to motivation and the capacity to learn, such as relating the content to daily life (E3), using diagrams to understand the content (E7), and participating in science-related debates (E4). As shown in the plot, the correlation of E1 (“Marks obtained”) with the Chemistry content is weaker than that of E3, E4, E6, and E7, probably because facing an evaluation creates uncertainty and fear in the students, regardless of the subject. Regarding the Physics items in this study, no clear correlations were observed with any of the considered aspects related to the teacher or to the students.

The scores plot of the performed PCA on positive emotions and aspects related to teacher and students is represented in Figure 6. The score of a sample on a particular PC describes the characteristics of that sample for the variables with high loadings on that PC. Thus, samples with similar scores on the same PC can be said to be similar with respect to the variables that most contribute to that PC. The score plot is typically used to detect groupings, similarities, and differences between samples.

As it can be observed in Figure 6 most of the samples are clustered along the high part of the horizontal axis (PC1), as Chemistry topics and the causes related to the teacher and the students commented above. This means that most students expressed positive emotions toward the Chemistry content and toward the teacher- and pupil-related causes correlated with that content. But, since the maximum density of points is located in this part of the plot, one can also state that most of the positive emotions expressed by the pupils were toward the content of Chemistry, not Physics, because the density of points at the high part of PC2 is very low.

It is reported in the literature that emotions toward learning content are related to the strategies and activities undertaken in class. King et al. (2015) found that, when classes include stimulating activities and experiments about energy, the students’ emotions were very positive: Amazement, surprise, joy, and happiness. In a study with secondary pupils on physics content, Folashade and Akinbobola (2009) found that the use of methods which encourage the pupils’ active participation, such as a problem-based learning technique, leads to a better understanding of physics concepts as well as increasing the pupils’ confidence, especially for those who show low capacities for learning that content.

In the frame of the current research, internal and external causes could be related to the considered students’ and the teachers’ aspect, respectively. However, the failure attributed to internal causes led to lower self-esteem than the failure attributed to external causes. In the current research, the pupils attributed their negative emotions toward physics content to the use of the textbook in class. In contrast, they attributed positive emotions to themselves when solving a physics problem or giving oral presentations. In the case of chemistry content, the pupils who experienced positive emotions attribute them to aspects related to their ability and motivation to learn. The negative emotions, however, were attributed to the teacher’s methods and attitude.