Validation of a Scale on University Teaching Quality in the Area of Mathematics

Abstract

This study examines the quality of university teaching in Mathematics, focusing on the evolution of teaching performance from students’ perspectives. It highlights the importance of adhering to quality standards to enhance teaching, research, and administrative processes, guided by the Andalusian Knowledge Agency. Key factors analyzed include effectiveness, planning, classroom performance, tutorials, and the use of bibliographic materials, using exploratory and confirmatory factor analyses (EFA and CFA) with structural equations. The research involved 229 students from various programs, such as Physical Activity and Sport Sciences, Primary Education, Early Childhood Education, and a Master’s Degree in Secondary Education with a Mathematics specialization, within an Andalusian university center. The results confirmed the reliability and validity of the questionnaire and demonstrated the effectiveness of structural equation methodologies. The findings underscore the importance of integrating effective knowledge transmission, teacher-led motivation, careful planning, individual attention, and complementary materials to improve Mathematics teaching. It concludes that quality teaching depends on a holistic approach that balances pedagogical strategies with student-centered practices.

1. Introduction

Currently, many higher education institutions have placed great emphasis on improving the quality of their institutional processes, covering both teaching and research areas as well as administrative areas. This responds to the need to meet the new quality standards and criteria demanded by contemporary society (Jacques & Boisier, 2019). In this context, assessing teaching quality has become a priority, as it directly impacts student learning and institutional accreditation. The research supports this process, serving as a basis for future external evaluations conducted by the Directorate for Evaluation and Accreditation-Andalusian Knowledge Agency (DEVA-AAC) in Andalusia. These evaluations verify compliance with the objectives established to accredit the university programs offered, allowing the identification of areas for improvement and the development and the implementation of actions to optimize university education.

Regarding the area of Mathematics, ensuring quality teaching is essential to guarantee that students obtain deep and effective learning (Sánchez-Luján, 2017). Mathematics, as a core discipline in various academic fields, often presents learning difficulties due to its abstract nature and the challenges associated with its didactic approach. Discussing the quality of Mathematics teaching is therefore crucial, as international standardized test results and student attitudes towards the subject highlight persistent challenges in the classroom (Sánchez-Luján, 2017).

According to Galvis (2015), addressing issues in Mathematics teaching requires concrete measures closely linked to the teacher’s role. A high-quality Mathematics teacher must demonstrate mastery of content, effective pedagogical strategies, and the ability to adapt teaching methods to students’ needs (Llinares, 2018; Alsina, 2023). Effective instruction in Mathematics not only fosters conceptual understanding but also strengthens problem-solving skills and logical reasoning, which are fundamental competencies for many professional fields.

Education is a constantly evolving field, with ongoing advances in technology, research, and pedagogical approaches. Therefore, Mathematics teachers must continuously adapt their teaching to the diverse learning styles and cognitive processes of their students. Personalized instruction, supported by innovative methodologies, enhances student motivation and facilitates meaningful learning.

Within the framework of university quality assurance, it is essential to assess students’ perspectives, as they are one of the key stakeholders in higher education. Their opinions on degree programs, course content, and teaching methodologies provide valuable insights for institutional decision-making (Pardo Fernández, 2024). This information enables universities to identify areas for improvement and implement necessary corrective measures (Lancheros et al., 2022).

Student satisfaction is a critical indicator for promoting the continuous improvement of educational quality. Evaluation questionnaires on student satisfaction with teaching performance are widely used in higher education institutions worldwide (Zabaleta, 2007). However, their effectiveness depends on their validity and reliability, as some instruments have been designed without a precise understanding of what constitutes effective teaching (Onwuegbuzie et al., 2009). Ensuring the methodological rigor of these instruments is essential to obtain meaningful and actionable insights.

In this context, various pieces of research conducted in Spain highlights that students consider crucial certain aspects of teaching work, such as the teacher’s ability to explain clearly, motivate students, demonstrate interest in their learning, as well as encourage participation and maintain good communication in the classroom (Castro-Morera et al., 2020; De-Juanas Oliva & Beltrán-Llera, 2014; Fernández-Borrero & González-Losada, 2012; Galván-Salinas & Farías-Martínez, 2018). These factors are essential for the satisfaction of educational quality in the university.

In the specific case of Mathematics, it is crucial to use validated instruments that reflect the unique characteristics of this subject. Unlike other disciplines, Mathematics requires a structured pedagogical approach, where conceptual clarity, problem-solving methodologies, and student engagement are key factors. Therefore, a reliable and valid scale tailored to Mathematics ensures a more accurate assessment of teaching quality and its impact on student learning.

In the field of university teaching assessment, several scales have been developed to measure faculty performance in terms of their impact on student learning. Among these, the Institutional Teaching Performance Scale (EDDI) proposed by Durán-Aponte and Durán-García (2015) evaluates university teaching, considering methodological aspects and student-teacher interaction. The scale developed by Graus (2020) incorporates a statistical approach to analyze didactic coherence in Mathematics teaching, allowing for a detailed assessment of instructional strategies. Similarly, Gutiérrez et al. (2020) designed a scale focusing on the relationship between teaching performance and student achievement in Mathematics. Despite the availability of these instruments, many evaluation tools still lack specificity for Mathematics, leading to potential misinterpretations in assessing teaching effectiveness.

However, after reviewing existing instruments, this study opted to use the official scale of the institution where the research was conducted, ensuring methodological consistency and alignment with internal evaluation standards.

The opinion of students plays a fundamental role in improving educational quality at universities. A comprehensive assessment of teaching effectiveness should go beyond classroom performance and consider additional factors influencing the learning experience, such as instructional clarity, student engagement, and the use of complementary resources (Gargallo-López et al., 2017).

In this context, the general objective of this research is to validate the reliability and validity of the evaluation instrument designed to measure student satisfaction with teaching performance in the area of Mathematics. Specifically, this study aims to (1) determine the psychometric properties (validity and reliability) of the questionnaire used to assess teaching performance in Mathematics and (2) identify the underlying dimensions of the evaluation instrument and analyze their relevance to Mathematics education.

Based on these objectives, this research seeks to answer the following questions: To what extent does the evaluation instrument accurately measure student satisfaction with Mathematics teaching performance? Furthermore, what are the key dimensions that structure the questionnaire, and how do they reflect critical aspects of Mathematics instruction?

By validating a discipline-specific evaluation instrument for Mathematics, higher education institutions can gain deeper insights into faculty performance and implement targeted improvements. This contributes to refining teaching methodologies, enhancing professional development for educators, and ultimately fostering better learning outcomes for students.

Finally, the impact of an effective Mathematics teacher extends beyond the classroom. A teacher who conveys enthusiasm and passion for the subject can inspire students to appreciate Mathematics, fostering interest in related fields and contributing to the development of future professionals in STEM areas (Castilla, 2011).

2. Materials and Methods

2.1. Methodological Design

The present study adopts a quantitative, non-experimental, cross-sectional and instrumental research design, based on the validation of a questionnaire designed to evaluate student perception of university teaching quality in the area of Mathematics.

The quantitative approach was selected due to its ability to provide measurable and objective data, allowing for the application of advanced statistical techniques to analyze the validity and reliability of the evaluation instrument. This approach is widely used in educational quality research, as it ensures replicability and generalization of results (Ruiz et al., 2010; Rodríguez-Sabiote et al., 2023).

The non-experimental design is justified by the fact that no variables are manipulated, and no controlled conditions are established. Instead, student perceptions are analyzed in their natural context, ensuring a realistic approach to the evaluation of teaching quality (Hernández-Sampieri et al., 2014).

The cross-sectional nature of this study refers to the fact that data collection occurs at a single point in time. This allows for an instantaneous assessment of students’ perceptions of Mathematics teaching, providing a representative view of the phenomenon during the study period and enabling future comparisons with similar research (Hair et al., 2010).

Finally, this study follows an instrumental research design, which is used when the main objective is to develop, adapt, or validate measurement instruments (Carretero-Dios & Pérez, 2005). In this case, the study focuses on validating a questionnaire to assess Mathematics teaching quality from the students’ perspective. The validation process included exploratory factor analysis (EFA), confirmatory factor analysis (CFA), and structural equation modeling (SEM) to ensure the instrument’s methodological robustness and applicability in future educational quality studies (Gálvez Gamboa et al., 2024; Guerrero Luzuriaga & García Ancira, 2024).

2.2. Sample

A non-probabilistic convenience sampling was used, selected according to the accessibility and availability of the participants in the study. This sampling strategy is justified by the need to obtain data efficiently within a specific educational context, ensuring the participation of students enrolled in degrees where Mathematics is taught in the institution under study. Since the main objective of the research is the validation of a measurement instrument, the selection of the sample does not seek to generalize the results to the entire university population, but rather to guarantee the representativeness of the group studied in terms of their experience with teaching Mathematics.

It consists of a total of 229 students enrolled in a University Center in the autonomous community of Andalusia in the Degrees of Primary Education, Early Childhood Education, Physical Activity and Sports Sciences and the Master’s Degree in Compulsory Secondary Education and Baccalaureate, Vocational Training and Language Teaching in the specialty of Mathematics. These students have answered the questionnaire of Satisfaction with the teaching performance of the professors of the Mathematics Area. Of which 77 were male and 152 female, with an average age of 22 years. The students were chosen using convenience criteria, selecting them according to their availability to complete the questionnaire (Hernández-Sampieri et al., 2014).

As for the students’ study profile, the vast majority come from the Degree in Primary Education (124 students), the Degree in Early Childhood Education (48 students), Physical Activity and Sports Sciences (30 students) and the smallest sample (27 students) comes from the Master’s Degree in Compulsory Secondary Education and Baccalaureate, Vocational Training and Language Teaching, specializing in Mathematics.

With respect to the degree of interest in the subjects of the area taught in these degrees, 67% of the students find the subjects taught by this area very interesting, however, 65% find a high degree of difficulty in these subjects. 85% stated that they attend more than 75% of the classes given, but 15% of the students attend less regularly. Finally, 70.3% of the students state that they do not attend tutoring throughout the course, 13.9% only attend tutoring once, 7.8% attend between 2 and 3 times and 7.8% attend more than 3 times.

2.3. Data Collection Instrument

For data collection, an ad hoc questionnaire was designed, called “Evaluation and improvement of the quality of teaching and teachers: survey of student opinion on the teaching performance of teachers in the area of Mathematics” (Appendix A). For its elaboration, several studies have been taken as a reference (Marimon-Martí et al., 2022; Seivane & Brenlla, 2021). Each item is measured on a Likert scale of 6 intervals, where 1 represents the minimum value, 5 the maximum value and NS if the student considers that it does not apply or does not have sufficient information to answer the question.

The questionnaire begins with some questions about academic information to be answered by the student, such as the name of the professor to be evaluated, the subject he/she teaches and the degree to which the student belongs. This is followed by several questions about the student’s socio-demographic and academic information, such as gender, age, highest and lowest grade enrolled, etc. (Appendix A). These data allow both to describe the sample and to examine its possible impact on other variables in the study. Subsequently, 18 questions aimed at assessing the students’ perception of the teaching performance of the faculty are presented, as shown in

Table 1. Description of the questionnaire items.

Dimension	Item	Descriptor
Teaching effectiveness	A1	Use of adequate means in teaching.
	A2	Motivation of students in the interest of the subject.
	A3	Respectful treatment of students.
	A4	Achievement of the objectives of the subject helped by the teaching given.
	A5	Adequacy of the evaluation criteria and systems carried out by the teacher.
	A6	Satisfaction with the teaching performance in general.
Teaching planning	B7	Orientations for the teaching project.
	B8	Adjustment of the teaching to the planning of the teaching project.
	B9	Well-organized teaching.
	B10	Interest in the degree of understanding of their explanations.
Teaching performance	C11	Clear explanations.
	C12	Use of examples that put into practice the contents of the subject.
	C13	Resolution of doubts raised.
	C14	Encouragement of participation and work environment.
Tutorials	D15	Adequate attention during tutorial hours.
	D16	Fulfillment of the established schedule for tutoring.
Bibliography	E17	Use of bibliography and other recommended teaching material are useful for the follow-up of the subject.
	E18	The bibliography and other recommended teaching material are available to the students.

.

Following similar models of validation of teacher evaluation instruments, such as the Institutional Teaching Performance Scale (EDDI) developed by Durán-Aponte and Durán-García (2015), the Statistical scale to evaluate didactic coherence in teaching-learning processes in Mathematics proposed by Graus (2020) and the model of Evaluation of teacher performance in learning achievement in Mathematics designed by Gutiérrez et al. (2020), a rigorous process of analysis and validation of the scale used in this study was carried out. From this procedure, it was determined that the items, which are used according to the regulations of the institution where the research is being carried out, make up five competency dimensions, which are detailed below (Table 1)

• Teaching effectiveness: This is a key aspect for the success of the teaching-learning process, as it focuses on the teacher’s ability to transmit knowledge effectively and adapted to the needs of students. This is achieved through continuous professional development and research-based learning (Santelices Etchegaray & Valenzuela Rojas, 2015; Maulana et al., 2023).
• Instructional planning: It is essential to ensure a quality teaching-learning process, where contents, methods and resources must be coherently organized to achieve educational objectives (Gutiérrez et al., 2020; Hernandez et al., 2024).
• Teaching performance: It involves not only the transmission of knowledge, but also the creation of an environment that fosters student participation. Good teaching performance includes pedagogical skills that help students develop complex competencies and attitudes that prepare them for their professional life (Hortigüela Alcalá et al., 2017).
• Tutorials: they play a key role in academic accompaniment, allowing personalized support to students, which improves learning and strengthens the educational bond (Aguilera García, 2019).
• Bibliography: The adequate use of bibliography and support resources is fundamental to strengthen university teaching. The bibliography acts as a complementary tool that enriches the learning process and allows students to deepen the topics covered in class (Seivane & Brenlla, 2021).

2.4. Data Collection and Analysis Procedure

The questionnaire was carried out in digital format, through the Google Forms platform, and was provided to the students through a QR code. Data collection took place at the end of both the first and second semesters, in the months of December and May, respectively. Students were informed of the purpose of the study and invited to participate. At all times, it was ensured that the identity of the participants remained anonymous.

The data matrix was adjusted for operational reasons, which allowed the creation of new variables, named Dim_A, Dim_B, Dim_C, Dim_D and Dim_E. These variables were obtained by adding the items that comprise them, with values ranging from 1 to 5. To evaluate the purpose, discriminant validity and convergent validity of the questionnaire, several research studies in Educational Sciences were used as references (Rodríguez-Sabiote et al., 2023; Aroca Reyes & Llorente Cejudo, 2023; Palacios-Rodríguez et al., 2025). Different coefficients were used, including: Cronbach’s alpha, McDonald’s omega, composite reliability (CR), average variance extracted (AVE) and maximum shared variance (MSV). In addition, to compare these results, an inferential analysis was applied between items and dimensions, using the bivariate correlational analysis technique with Spearman’s correlation coefficient.

On the other hand, construct validity was determined by means of an exploratory factor analysis (EFA), using the principal components method for factor selection. The factors obtained are orthogonally rotated using the Varimax method with Kaiser normalization. After defining the number of factors, a confirmatory factor analysis (CFA) is carried out to verify the consistency of the theoretical measures of the model. This process includes representation by means of diagrams and the use of structural equations, as indicated by Ruiz et al. (2010). In other words, it is checked whether the data fit the hypothetical measurement model proposed by the exploratory factor analysis. The weighted least squares (WLS) method was used to test the theoretical model, since it provides reliable estimates even when the samples do not follow a normal distribution (Ruiz et al., 2010). This analysis was performed with AMOS software V29, which facilitates the study of complex relationships between variables through structural equation modeling (SEM).

Simultaneously, it was verified that the data did not present a normal distribution by means of a descriptive analysis that considered skewness and kurtosis. The Kolmogorov-Smirnov test, used to assess goodness-of-fit, corroborated this observation by yielding a p value of 0.000 for all items, indicating a non-normal distribution.

3. Results

The reliability of the Questionnaire of student opinion on the teaching performance of teachers in the area of Mathematics was calculated using Cronbach’s alpha coefficient. The results show a Cronbach’s alpha index of 0.701. It is established that this index is high (>0.7), indicating a high degree of reliability of the questionnaire (O’Dwyer & Bernauer, 2014). In the same way, we proceed to calculate the reliability of the dimensions considered in the questionnaire: teaching effectiveness (0.944), teaching planning (0.852), teaching performance (0.913), tutorials (0.964) and bibliography (0.919). In this case, all dimensions exceed 0.85, therefore, all dimensions are considered to have very high reliability (Lévy Mangin et al., 2006).

Table 2. Convergent and discriminant validity of the model.

Dimension	CR	Adjustment	AVE	Adjustment	MSV	Adjustment
A	0.963	CR > 0.7	0.815	MSV < AVE	0.631	MSV < AVE
B	0.901		0.698		0.395
C	0.940		0.797		0.593
D	0.977		0.955		0.910
E	0.920		0.852		0.705

presents the reliability indices by dimensions, calculating the composite reliability coefficients (CR), average variance extracted (AVE) and maximum shared variance (MSV).

Table 2 presents the results and the reference values used to fit the model (Hair et al., 2010). All the values obtained are aligned with the reference values, demonstrating the reliability of the model (CR), as well as its convergent (AVE) and discriminant validity (MSV). Next, the simple correlations of each item with the corresponding theoretical dimension or construct are analyzed. The results of this analysis are presented in

Table 3. Item correlations with the associated dimensions.

Item	Dim_A	Dim_B	Dim_C	Dim_D	Dim_E
A1	0.880
A2	0.891
A3	0.917
A4	0.895
A5	0.690
A6	0.895
B7		0.729
B8		0.716
B9		0.777
B10		0.734
C11			0.722
C12			0.732
C13			0.753
C14			0.773
D15				0.930
D16				0.929
E17					0.734
E18					0.774

.

The results obtained were verified by means of the McDonald omega coefficient, calculated from the factorial weights of the matrix of components rotated globally. This result confirms the previously established reliability, with a McDonald omega coefficient of 0.721.

The construct validity of the test was assessed by means of an exploratory factor analysis (

Table 4. Rotated component matrix.

Item	Dim_A	Dim_B	Dim_C	Dim_D	Dim_E
A1	0.673
A2	0.983
A3	0.981
A4	0.983
A5	0.763
A6	0.982
B7		0.887
B8		0.896
B9		0.677
B10		0.861
C11			0.874
C12			0.896
C13			0.918
C14			0.882
D15				0.977
D16				0.977
E17					0.914
E18					0.933

). Previously, the applicability of the factor analysis was confirmed by the KMO test, which yielded a statistically significant coefficient of 0.715 and Bartlett’s test of sphericity, with a p-value of 0.000 (indicating that the factor analysis can be applied).

The results explain 86.92% of the variance, identify the 5 theoretical factors proposed: teaching effectiveness (A), teaching planning (B), teaching performance (C), tutoring (D) and bibliography (E).

The theoretical model proposed by the exploratory factor analysis (EFA) was contrasted by means of a confirmatory factor analysis (CFA). Figure 1 shows the structural diagram with the item-dimension and dimension-dimension correlation indexes. The factor loadings are between 0.69 and 1, indicating high levels of correlation. It is observed that among the factors the relationship is low, such as the relationship between the D-E (0.14) and B–E (0.26) dimensions. These have been considered within the limitations of the study. Nevertheless, the results confirm the theoretical model proposed.

Table 5. Fit indices.

Index	Result	Adjustment
GFI	0.999	GFI > 0.7
PGFI	0.730	PGFI > 0.7
NFI	0.997	NFI > 0.7
PNFI	0.815	PNFI > 0.7

shows the obtained and reference values for model fit according to Lévy Mangin et al. (2006): goodness-of-fit index (GFI), parsimonic goodness-of-fit index (PGFI), normalized fit index (NFI) and normalized parsimonic fit index (PNFI).

4. Discussion

In a framework of increasing demands for universities, where quality is a transcendental aspect, having instruments to measure student satisfaction is key (Gálvez Gamboa et al., 2024). One of the main findings of this research is how students perceive teaching performance, highlighting the importance of several key factors such as teaching effectiveness, planning, classroom performance, tutorials, and the appropriate use of the bibliography. These factors reflect the inherent complexity of the educational process and how each one contributes significantly to the students’ overall perception of the quality of teaching.

Another of the main findings is linked to the confirmation of the validity of the Questionnaire: Evaluation and improvement of the quality of teaching and teachers: survey of student opinion on the teaching performance of teachers in the area of Mathematics, which guarantees the integrity of the research results (Guerrero Luzuriaga & García Ancira, 2024). In this sense, both the reliability and validity of the developed instrument allow generating scientific data with adequate precision and robustness, which contributes to improving the educational quality in the area of Mathematics in training institutions (Gisbert & Lázaro, 2015; Rodríguez-García et al., 2019). These results support the creation of educational systems capable of responding to the demands of the knowledge society (García-Valcárcel Muñoz-Repiso et al., 2015).

A significant advance of this study lies in the validation of structural equation models to assess the quality of Mathematics teaching, which confirms its applicability in this specific educational context and reinforces its use in future research (Ruiz et al., 2010; Rodríguez-Sabiote et al., 2023). Unlike previous studies that focused on qualitative or descriptive methodologies, this work provides a rigorous quantitative approach that allows for more objective and replicable conclusions (Gálvez Gamboa et al., 2024). Thus, it strengthens the theory of learning based on student feedback and continuous teacher improvement (Montenegro, 2020), by demonstrating that student perception is not only a reflection of teaching quality, but also a predictor of academic success.

Furthermore, this study provides evidence that student satisfaction with teaching not only has implications for academic performance, but is also a key indicator for evaluating the effectiveness of the pedagogical strategies implemented by teachers (García-Valcárcel Muñoz-Repiso et al., 2015; Juárez Ruiz et al., 2023). This finding opens new lines of research on the relationship between student perception and learning quality, which could influence future educational policies and teacher training strategies.

The importance of this research lies in the fact that it responds to a growing need to improve teaching in a crucial area of knowledge such as Mathematics, where learning difficulties and student demotivation have been widely documented (Sánchez-Luján, 2017; Rodríguez Duarte & Alay Giler, 2023). By providing a reliable assessment tool, this study allows educational institutions to identify critical points in teaching and design more effective interventions to improve the training of future professionals (Pardo Fernández, 2024). In this sense, the work contributes to the development of educational policies based on empirical data and sets a precedent for future research in the field of university teaching quality.

As future lines of research, a longitudinal study is proposed to analyze how teacher training and professional development have an impact on teaching quality over time. Likewise, we suggest a more detailed analysis of variables such as gender, age or the degree taken to determine their influence on the perception of teaching quality. This would make it possible to adapt pedagogical strategies to different student profiles, thus optimizing the impact of teaching on academic training.

5. Conclusions

The results of this study have shown that students’ perception of teaching quality is influenced by several interrelated factors, among which planning, classroom effectiveness, use of tutorials and complementary bibliography stand out. The validity and reliability of the questionnaire used have been confirmed, which reinforces its usefulness as a tool to evaluate and improve teaching in the area of Mathematics.

In comparison with previous studies, the scale used in this study presents similarities and differences with validated instruments in the evaluation of teaching performance. The Institutional Teaching Performance Scale (EDDI) by Durán-Aponte and Durán-García (2015) addresses the comprehensive evaluation of university teaching, but without a specific segmentation in key dimensions such as teaching effectiveness, planning, use of tutorials and bibliography, aspects that have been incorporated in detail in the present study. On the other hand, the Graus (2020) scale introduces a statistical approach to measure didactic coherence in Mathematics, while our instrument prioritizes student perception as a fundamental indicator of teaching quality. Likewise, the work of Gutiérrez et al. (2020) links teaching performance with academic achievement, an approach shared by this study, but expanded with the evaluation of other pedagogical factors that impact the teaching-learning process. In this sense, the scale validated in this research represents a methodological contribution by integrating and expanding previous approaches, consolidating a structured and statistically validated model for the evaluation of teaching at the university level.

In addition, the findings suggest that teaching should not be limited to the transmission of knowledge but should adopt a comprehensive approach that considers student motivation, the personalization of teaching and the use of innovative pedagogical strategies.

The main limitation of this study lies in the size and characteristics of the sample used, which limits the possibility of obtaining results that are completely representative of the general population. Despite the total population of 370 students, 229 responses were obtained. To determine whether this sample is representative, the minimum sample size necessary was calculated using a confidence level of 95% and a margin of error of 5%, parameters commonly used in educational studies. Applying the formula for finite populations, the minimum sample size required is 189 responses. Given that the number of responses obtained exceeds this threshold, it is concluded that the sample is statistically representative, allowing inferences to be made with a high degree of confidence about the total population. In future research it would be advisable to carry out the study in other universities, both nationally and internationally, to improve the size, representativeness and generalization of the results obtained, as well as to add more items to the dimensions that only contain two items.