Abstract
This study aims to gain insights into the heterogeneity of early childhood teachers’ mathematics teaching efficacy and seek evidence to build their specific profiles, following a person-oriented approach. This approach was chosen to provide combinations of attributes that shape high-risk groups of teachers being globally unconfident/inefficacious in teaching mathematics. We examined whether these profiles differed concerning their sense of responsibility for their students’ achievement, self-efficacy (overall), locus of control, special educational needs, and individual parameters/work-related characteristics. Moreover, the teacher's gender, age, highest degree, educational experience, intention to work as a teacher (in years), monthly income, number of modules related to special education, and seminars in special education (that teachers attended) were evaluated for their contribution in differentiating teachers’ profiles. The sample included 547 in-service typical and special education teachers working in kindergartens. Two cluster analyses (two-step) yielded different profiles for special education teachers, entitled: “Passionate—Confident/Efficacious in Teaching Mathematics,” “Operational—Moderately Confident/Efficacious in Teaching Mathematics,” and “Overworked—Globally Unconfident/Inefficacious in Teaching Mathematics” and typical education teachers, entitled: “Operational—Moderately Confident/Efficacious in Teaching Mathematics,” and “Overworked—Globally Unconfident/Inefficacious in Teaching Mathematics.” Findings are discussed for their implications for designing training programs for teachers at risk.
Keywords
Introduction
The teaching profession is characterized by significant complexity, which can be explained by the classic psychological model and includes cognitive (mental operations to process knowledge), emotional (processes occur between the stimulus eliciting emotion and the resulting physiological and behavioral responses), and action (psychological and physical reactions) processes. Commonly, in literature, these terms are described as declarative knowledge (cognitive process) and procedural learning models (action process) regulated by behavioral control (emotional process). All these components are interrelated and intertwined during teaching (Predescu, 2013).
Students’ well-being, lifelong learning, and development through effective instructional methods and techniques are of main importance. Additionally, students’ behavioral regulation in developing competencies and the adaptation of their instructional methods and techniques to meet their students’ individual educational needs through using differentiated or individualized teaching constitute a demanding area of intervention for preschool education teachers. Consequently, preschool teachers should be characterized with high professionalism. They should embrace the cultural diversity of their classroom and work to promote their students’ self-esteem and self-development (Nasiopoulou et al., 2017; Predescu, 2013). From the students’ perspective, the preschool teacher competence profile is a multidimensional construct composed of interrelated dimensions including competencies needed to lead and organize playful and interactive learning activities with children. In addition, preschool teachers should be aware of the specific content competence they introduce to teach which involves a greater emphasis on literacy, mathematics, science, and technology. Students want their teachers not only to be responsible, flexible, and emphatic, but also to have didactic, cultural, creative, collaborative, and social competencies (Lillvist et al., 2014; Sheridan et al., 2011).
Concerning teachers’ mathematics competence has been considered a multidimensional construct including subject-specific and generic facets of mathematics teachers’ knowledge, skills, and beliefs (Blömeke et al., 2020). The quality of teaching mathematics instruction varies considerably among early childhood teachers. Some teachers are identified as delivering high-quality mathematics instruction because they provide students with opportunities to fully and purposefully engage in deepening their understanding of important mathematics concepts. Additionally, procedural instructions in an appropriate learning environment seem to play a crucial role in teaching, especially when students need to develop foundational skills or learn to follow processes accurately (Cerezi, 2019).
Blömeke et al. (2020) introduced four competence mathematics teaching profiles that differed not only quantitatively, but also qualitatively. These teachers’ profiles were grounded not only on differentiated mathematics subject-specific knowledge but also on generic knowledge and skills including speed in diagnosing student errors, classroom management, teachers’ disposition, perception, interpretation, and decision-making skills. Moreover, the suggested profiles were related to different types of instruction quality and the relations indicate a need for strong levels of knowledge and skills for high mathematics instruction quality.
In another study, four distinct teacher profiles were identified concerning the methods they used in assessing mathematics (Veldhuis & van den Heuvel-Panhuizen, 2014). The biggest sample was the mainstream assessors’ profile in which teachers regularly used different types of assessment, for example, test-based and observation-based, for both summative and formative purposes. In the enthusiastic assessors’ profile teachers were very aware of the different possibilities assessment offers them, and used them likewise. In the non-enthusiastic assessors’ profile teachers viewed assessment more often in a negative way and used it accordingly less. Teachers grouped in the alternative assessors’ profile had an ambiguous view of assessment. Although they reported a lot of input in assessment and devised their tasks and tests, they did not find assessment important or necessary.
Some studies reveal teachers’ lack of mathematical pedagogical content knowledge. It is also known that teachers’ pedagogical content knowledge levels affect their classroom practices (Dewi et al., 2020). The relationship between preschool teachers’ mathematical pedagogical content knowledge, their attitudes towards mathematics, and their attitudes towards mathematics teaching was investigated recently in Tașkin and Sezer's (2022) study, which suggested statistically significant correlations between the variables mentioned above. In addition, findings showed that the levels of knowledge of mathematical pedagogical content were below average in some content areas (counting) and above average in some content areas (pattern, order, shape, spatial dimensions and comparison, and total score). Lastly, they found that the age of the teachers has an effect on the levels of teachers’ mathematical pedagogical content knowledge and the seniority variable affects teachers’ mathematical pedagogical content and attitudes towards mathematics teaching.
Preschool mathematics teaching profiles and teachers’ self-efficacy
The theory of self-efficacy is based on Bandura's (1977) social-cognitive theory and is described as the belief in one's capabilities to organize and execute the courses of action required to produce given attainments (Bandura, 1977, p. 3). Tschannen-Moran et al. (1998) relate specifically this notion to work-related self-efficacy. Teachers’ high/low self-efficacy beliefs affect their self-empowerment. Every new experience has a positive (strengthening existing beliefs) or negative impact (minimizing and discounting the existing ones) (Reyhing & Perren, 2021).
The current educational environment, in preschool education, in addition to taking good care of and teaching students in their class, provides them with beneficial, age-appropriate learning experiences to properly prepare for their future social, emotional, and academic success (Coplan et al., 2015). Preschool teachers must be characterized with positive psychological resources namely self-efficacy, optimism, hope, and resiliency (Luthans et al., 2007). A study explored 2,790 kindergarten teachers’ psychological profiles in China. The results showed that preschool teachers’ psychological profiles were divided into three types: rich (43.2%), medium (46.3%) and poor (10.5%) type. In this culturally oriented study preschool teachers’ psychological profile is considered an important factor affecting work engagement and includes task-oriented psychological principles: (a) spirit of enterprise and diligence, (b) resiliency and perseverance, (c) optimism and hope, (d) self-confidence and courage, (e) toleration and forgiveness, (f) modesty and prudence, (g) thanksgiving and dedication, and (j) respecting and courtesy and interpersonal-orientated psychological principals: (1) toleration and forgiveness, (2) modesty and prudence, (3) thanksgiving and dedication and (4) respecting and courtesy (Gao et al., 2023).
Different personal characteristics seem to affect teachers’ self-efficacy, for example, teachers’ years of experience, teachers’ length of training and level of education, and teachers’ job satisfaction. But, as Bandura (1977) described, self-efficacy is contextually dependent. One teacher may believe in his or her efficacy when his/her classroom children are occupied with organized learning activities and may doubt his or her self-efficacy beliefs in children's free-choice activities (Reyhing & Perren, 2021). In addition, teachers’ perceptions of school climate and their beliefs about the social-emotional learning of students, perceived student behavior, and students’ achievement motivation, may affect teacher self-efficacy beliefs (Collie et al., 2012; Ross et al., 2004).
Mathematics self-efficacy and mathematics teaching self-efficacy must be investigated in parallel to understand teachers’ beliefs about their teaching capabilities and how these affect the classroom’s learning environment (Kahle, 2008). It seems that there is a positive significant relationship between mathematics teaching efficacy and teachers’ self-efficacy beliefs. Teachers’ mathematics teaching self-efficacy also affects students’ mathematics self-efficacy (Gülburnu, 2023). Experienced preschool teachers expressed mathematics self-efficacy as an internal motivation to improve themselves in mathematics and the strength to face the difficulties that emerge in teaching mathematics. Teachers who pursue to improve themselves in this field try different teaching methods and reflect on these methods’ results. These procedures seem to affect the development of students’ mathematical skills (Çelik, 2017). Mathematics teaching self-efficacy seems to be affected by different parameters, for example, teachers with high self-efficacy in teaching mathematics are less likely to experience stress and believe more in students’ freedom (Brouwers & Tomic, 2003) and teachers with high self-efficacy in teaching mathematics showed more interest in low-ability students (Ross & Bruce, 2007). Preschool teachers who care about children's mathematical perceptions organize playful mathematical activities such as games (Gülburnu, 2023).
Internal factors such as experience and attitude were important in preschool teachers’ mathematics efficacy but also past experiences (such as negative school experiences, fear of mathematics, etc.) affected their perspectives on mathematics. In addition, pedagogical education received at the university affects teachers’ mathematics efficacy (Anders & Rossbach, 2015). Karimi (Allvar) (2011) investigated the influence of teacher self-efficacy on student mathematics achievement. The researchers found that teachers with higher levels of self-efficacy in mathematics teaching were more likely to employ effective teaching strategies and have a positive impact on student achievement in mathematics.
The four mathematics teaching profiles discovered in a study in Germany differentiated quantitatively and qualitatively (each group displayed differential strengths and weaknesses). Teachers with high levels of knowledge and skills (profile 1) support their students’ cognitive activation and proceed with mathematics activities with high instructional quality whereas they implement only a medium level of classroom management. Teachers with high levels of cognitive skills demonstrated medium levels of knowledge (profile 3) and they struggled with classroom management and student support. Teachers with medium levels of all competence facets (profile 2) struggled with mathematics-related quality, cognitive activation, and student support. Teachers with rather low levels of knowledge and skills (profile 4) struggled with all mathematics-related qualities (how teachers address mathematical concepts, interact, explain mathematical procedures, and provide feedback to their student's errors). As we can see, each level of the teacher's profile is characterized by some strengths and weaknesses. In sum, strong cognitive skills may be able to compensate at least partly for some weaker aspects of teacher knowledge. Classroom management seems to be an important parameter but not a sufficient prerequisite for a teacher's competence to implement high mathematics instructional processes in their classrooms (Blömeke et al., 2020).
Preschool mathematics teaching profiles and special childhood needs
Preschool children with learning disabilities face a series of difficulties in early numeracy skills. These difficulties related to the number word sequence, problems with counting as a tool to know the cardinal of a set, and a delay in the logical abilities and cognitive functions, compared with peers good in arithmetic (Desoete & Grégoire, 2006). In addition, children with intellectual disabilities have different strengths and weaknesses in various domains [relational skills (classification, seriation, comparison, and correspondence), counting (ability to perceive quantity, to know and to understand the rules of the counting sequence), and operations (composition and decomposition of sets of objects)]. Screening considerably these numeracy skills allows teachers to fully understand preschoolers’ differences, especially those at risk, and enable them to plan evidence-based and personalized instructions (Antoniou et al., 2022; Charitaki et al., 2022).
Preschool children's learning disabilities in mathematics fall mainly into these four factors: (a) preschool children who entered with difficulties in mathematics such as number-magnitude mapping and symbolic numerical tasks and continued to display difficulties till the end of kindergarten (a severe type of mathematical difficulties [MD]), (b) children who might have performed acceptably in preschool but displayed MD at the end of the kindergarten (strong type of MD), (c) children who might demonstrate difficulties during preschool years but response adequately in mathematical activities in kindergarten (weakest type of MD), and (d) children who did not demonstrate difficulties during either preschool or kindergarten mathematical instructions (non-MD), (Morgan et al., 2009; Wong & Chan, 2019).
In terms of special education, four teachers’ profiles (passionate, workaholic, operational, and overworked) were identified concerning their levels of burnout, work engagement, and job satisfaction (Antoniou et al., 2022; Charitaki et al., 2022). Profiles showed considerable differences concerning these main parameters. The results showed that work engagement is positively correlated with job satisfaction and that both are negatively correlated with burnout. These results were confirmed from all groups except for the second one. The second group showed high work engagement and moderate burnout, but low job satisfaction. These contradictive correlations are based on the fact that special education teachers in Greece haven’t many alternatives to changing their profession, despite their high unemployment, so many of them stay engaged in their work, although they do not feel satisfied with it.
Comparing profiles for typical and special education teachers
Μathematics teaching and instruction includes differentiated mathematics subject-specific knowledge and decision-making through insightful observations to assist properly children's immersion in mathematics concepts (Blömeke et al., 2020). Preschool teachers’ optimism, tolerance, dedication, respect, and courtesy are equally significant for children's balanced development. Lastly, preschool teachers’ pedagogical knowledge and previous experience seem to have a significant effect on their teaching self-efficacy and responsibility for children's mathematics achievement (Anders & Rossbach, 2015). Existing findings in the field revealed that preschool teachers lack mathematical pedagogical content knowledge and are not trained to teach early numeracy through playful activities (Dewi et al., 2020).
On the other hand, previous research in the field suggested that special education preschool teachers should be categorized into profiles including cases from overworked to passionate related to their levels of burnout, work engagement, and job satisfaction (Antoniou et al., 2022; Charitaki et al., 2022). These factors are related to teacher preparation, teacher values about learners’ diversity, teacher-specific competencies in applying effective teaching approaches in heterogeneous classes, teacher attitude related to teamwork collaboration practices in inclusive education, school climate, and working conditions (Billingsley & Bettini, 2019). The high burnout rates include a lack of administrative support, poor teacher team efficacy, and a lack of mentoring or support in the early years of teaching. Other factors that lead to high burnout and stress levels may include the amount of paperwork, large caseloads, emotional exhaustion, and lack of support and collaboration (Scott et al., 2021). Furthermore, teachers who feel more prepared and have pedagogical knowledge are more likely to stay in the field longer than those who have not. In addition, teachers’ emotional stability, extraversion, and consciousness were negatively correlated with burnout. Moreover, teachers working with children with special educational needs typically are responsive to a small number of students, allowing them to provide more focused and tailored instruction to meet the unique needs of each child. They are also better trained, having completed additional postgraduate specialization, which makes them more confident in using differentiated and/or individualized teaching methods to address the specific challenges the children face (Nasiopoulou et al., 2017; Predescu, 2013).
Preschool mathematics teaching profiles, school climate, responsibility for students’ achievements, and teachers’ locus of control
Mathematics teaching profiles, school climate, and students’ achievements
School climate consisted usually of four dimensions: (a) relationships, (b) teaching and learning, (c) safety, and (d) institutional environment. School climate has potential implications for students and teachers in preschool classrooms (Cornell et al., 2016). Researchers found positive associations between classroom emotional support, positive emotional climate, and teacher effectiveness (Rochester et al., 2019). These findings suggest that preschool classrooms in which children feel safe and share a supportive learning environment tend to have teachers who maintain positive relationships with their students. School climate is also related to students’ achievements in various contexts. A positive school climate is characterized as a space where students feel valuable which forces them to increase their academic achievements (Dulay & Karadağ, 2017).
Based on Ecological theory (Darling, 2007) significant relations have been detected between school climate, teacher self-efficacy, and job satisfaction (Aldridge & Fraser, 2016). By this theory, teachers are considered as persons whose internal feelings (e.g., job satisfaction, self-efficacy) are steadily being affected by interaction with the environment (e.g., school climate), (Zakariya, 2020). The school climate plays a crucial role in supporting teachers’ mental health and enhancing students’ educational achievements. A positive and welcoming school climate increases teachers’ job satisfaction and confidence but also fosters better relationships between teachers and students, leading to lower turnover rates and decreased burnout. Additionally, a healthy school climate benefits student by positively impacting their behavior, learning methods, overall well-being, and academic success (Lee & Louis, 2019; Zakariya, 2020).
Researchers introduced four different approaches/profiles in teaching mathematics, which include learner-focused, concept-focused, performance-focused, and classroom-focused profiles. These teaching approaches/profiles are based on two main perspectives: transmissive and constructive. The transmissive perspective emphasizes learning through teacher-led instruction, where knowledge is directly imparted to students. On the other hand, the constructive perspective focuses on student-centered learning, where teachers guide students in creating their understanding and interpretation of knowledge (Tatto, 2013).
Teachers who embody a constructive teaching profile/approach help students in their self-development by involving them in mathematical tasks that promote creativity, exploration, and discovery (Yang et al., 2020). In addition, these teachers are better equipped to offer personalized instruction tailored to meet the individual needs of their students (Pozas et al., 2020). On the other hand, teachers who follow a traditional teaching profile/approach tend to focus more on imparting knowledge directly to students and assigning routine problems for practice, often overlooking the importance of promoting a deeper understanding and independence in the learning process (Wang et al., 2022).
Teacher qualities can play a significant role in influencing student's achievements. Graduate-level coursework can offer teachers valuable learning opportunities related to curriculum materials, classroom activities, and assessment strategies, all of which can impact their teaching methods and, in turn, student performance. Similarly, hands-on teaching experiences can help teachers develop the skills needed to effectively apply these elements in practice. Teacher experience has been consistently linked to improved student outcomes, with the most significant gains occurring in the early years of a teacher’s career (Papay & Kraft, 2015). Additionally, teachers’ attitudes and work habits can affect student's achievements. For example, teachers may perceive mathematics either as an established process to be taught or as an interactive process to engage students, which directly influences how they approach their instruction.
In addition, teachers’ different beliefs of their responsibility for students’ achievements may lead them to expend different levels of effort toward securing positive student outcomes. The National Council of Teachers Mathematics (NCTM, 2000) highlights the important role that teachers’ attitudes and beliefs play in enhancing children’s comprehension of mathematical concepts. According to NCTM (2000), teachers have several key responsibilities to ensure effective mathematics education. These include fostering an environment that supports students’ mathematical learning, setting clear objectives, selecting and designing activities to meet these objectives, encouraging students to verbalize and share their ideas to demonstrate their understanding, and organizing their teaching approach by analyzing students’ learning, the learning environment, and the mathematical activities (Öçal & Işık, 2017).
Jung et al.’s (2014) research demonstrated that collective teacher efficacy appears to impact children’s mathematics achievement by the end of the kindergarten year. The researchers defined “collective teacher efficacy” as the teachers’ belief that the entire faculty can collectively organize and implement the necessary actions to positively influence students. The findings suggest that collective teacher efficacy may indirectly affect student achievement through its connection to individual teachers’ sense of efficacy. In addition, while teacher experiences and preparation are considered important factors in student learning, research has shown inconsistent effects on student achievement (Grieve, 2010).
Some studies emphasize the crucial role of mathematics teacher job satisfaction and stress on mathematics teachers’ dialogic instruction. They highlight that job satisfaction and stress are linked to teachers’ commitment, engagement, emotional exhaustion, student support, self-efficacy, and burnout (Skaalvik & Skaalvik, 2016). Teacher job satisfaction and stress influence their instructional practice. These studies proposed that mathematics teachers with high job satisfaction and low level of stress are more likely to implement dialogic instruction. Mathematics dialogic instructions encourage students’ involvement, argumentation, and research engaging them in reasoning and problem-solving processes (Hwang, 2022).
Despite the growing number of studies on various aspects of early childhood mathematics education, there remains a need to clarify the roles and responsibilities of preschool teachers in children's mathematical achievements.
Mathematics teaching profiles and locus of control
Teachers with an internal locus of control are typically described as proactive, innovative, assertive, adaptable, emotionally stable, and well-rounded. On the other hand, teachers with an external locus of control tend to exhibit lower levels of competence and confidence in specific areas, along with heightened anxiety and a lack of acceptance of life circumstances (Cargnelutti & Passolunghi, 2017). According to the existing literature, both locus of control and research on teachers’ effectiveness that focused on locus of control could impact educational methods. Studies have shown significant connections between locus of control and anxiety. Recent research has highlighted the importance of emotional and cognitive factors in mathematics teaching. When considering emotional factors, such as math anxiety, it is suggested that locus of control plays a role in influencing them (Ciftci, 2019; Gunderson et al., 2018). Having a strong internal locus of control can be beneficial for educators seeking leadership positions in a preschool setting. Those who believe they have the power to influence their environment are more likely to be confident decision-makers and take on responsibilities that come with leadership roles (Smidt et al., 2018).
Teachers’ locus of control was examined concerning motivation, self-efficacy, student's perception of the classroom, academic achievement, teacher's teaching performance, anxiety, attitude and confidence, and developmentally appropriate classroom management styles. These studies showed clear and consistent relationships between internal locus of control and positive characteristics and outcomes (Buluș, 2011). Moreover, a shift in control can lead to increased motivation and engagement among mathematics teachers, as they see themselves as active participants in the teaching process rather than passive followers of external guidelines. By taking ownership of their mathematics lesson planning and instructional strategies, teachers are more likely to put in the effort to ensure that their lessons are effective and successful. When teachers hold themselves accountable for the outcomes of their teaching in mathematics, they are more likely to reflect on their practices and make the adjustments that are needed. This reflective practice can lead to continuous improvement in teaching effectiveness and student mathematics learning outcomes (Lipovec & Podgoršek Mesarec, 2021).
Overall, while there is limited research specifically exploring the relationships between mathematics teaching profiles, students’ achievements, self-efficacy, and locus of control, existing studies suggest that these factors are intricately connected and can have a significant impact on student outcomes in mathematics education. Additional investigation is imperative to delve deeper into these correlations and ascertain efficacious methods for enhancing mathematics instruction and student performance, particularly within the realm of early childhood education, where pertinent research remains exceedingly scarce (Smidt et al., 2018).
Purpose of the study
This study aims to gain insights into the heterogeneity of early childhood teachers’ mathematics teaching efficacy and seek evidence to build their specific profiles. Moreover, we intend to research the profiles association with their responsibility for students’ achievement, self-efficacy, locus of control, and special educational needs. Consequently, this study aims to answer the following research questions:
What are the profiles of special and typical education teachers’ mathematics teaching efficacy? Are there qualitative differences within the groups of special and typical education teachers’ distinct profiles related to school climate, responsibility for student achievement, self-efficacy (overall), locus of control, and other demographic characteristics?
Method
Participants
A representative random sample of early childhood teachers, employed at public kindergartens (population) was employed for the purposes of this study. More specifically, we employed a total number including 547 teachers. The typical process of becoming an Early Childhood Teacher (typical kindergarten) in Greece prerequires a degree of a 4-year graduate program, while the employment in special education prerequires a further master's degree (2-year) in special education. Early childhood teachers teach pre-school children aged from 4 to 7 years old. The vast majority of the sample consisted of female participants, which agrees with the distribution of early childhood teachers across genders in Greece. The teachers of the sample were employed either in typical (n = 325) or special education (parallel support or resource classes) (n = 222). A total number of nine demographic questions were used to assess the teacher's gender, age, highest degree, educational experience, intention to work as a teacher (in years), monthly income, number of modules related to special education and seminars in special education (that teachers attended). The specific characteristics of the two sub-samples are presented in detail in Tables 2 and 4. Through researching the heterogeneity of mathematics teaching efficacy among early childhood teachers in the Greek context, we would be able to build evidence for generalization in a wider audience including a comparative resonance with other European countries with similar educational systems, such as Spain, Italy, and Cyprus.
Measures
Below we present all variables that were used to generate teachers’ profiles in detail. For each construct (Mathematics Teaching Efficacy Scale [MTES], Responsibility for Student Achievement Questionnaire [RSAQ], Ashton Efficacy Vignettes [SE], School Climate—Trust [SC], and Teacher Locus of Control [LC]), we estimated a composite z-score which was integrated into the model.
Demographics
A total number of nine demographic questions were used to assess the teacher's gender, age, highest degree, educational experience, intention to work as a teacher (in years), monthly income, number of modules related to special education and seminar in special education (that teachers attended).
MTES
The MTES is an adaptation of the Science Teaching Efficacy Belief Instrument (Riggs & Knochs, 1990). It is a self-rating questionnaire, adapted appropriately to assess mathematics teaching outcome expectancy and personal mathematics teaching efficacy belief. It consisted of 25 close-ended statements, being rated on a 5-point Likert-type scale ranging from 1 (strongly disagree) to 5 (strongly agree).
RSAQ
The RSAQ (Guskey, 1981) is a self-rating questionnaire, that assesses teachers’ perception of their responsibility for their students’ academic achievement and school-related situations. It consists of 30 close-ended statements, rated on a 5-point system assessing teacher's contribution to student achievement. Each teacher may attribute students’ achievement either (a) to students’ personal motivation or (b) to the teacher's clear instructions regarding the assignment [1: a = 0% and b = 100%, 2: a = 25% and b = 75%, 3: a = 50% and b = 50%, 4: a = 75% and b = 25% and 5: a = 100% and b = 0%]. For example, when a teacher may feel that the students complete assignments more because of personal motivation than because of the teacher's clarity in making the assignment. In that case, a possible answer could be a = 75% and b = 25%. Or when a teacher may feel quite the opposite. The percentage can vary according to how strongly he/she feels about each alternative. The teacher may choose a = 0% and b = 100%.
SE
The SE (Ashton et al., 1982) is a self-rating questionnaire, that assesses teachers’ perception of their effectiveness in handling each situation in their classrooms. It consists of 14 close-ended statements, rated on a 7-point system Likert-type scale ranging from 1 (extremely ineffective) to 5 (extremely effective).
SC—Trust
The Omnibus T-Scale (Hoy et al., 2002) is a self-rating questionnaire, that assesses teachers’ trust in principals, parents, students, and colleagues as a dimension of school climate. More specifically, it assesses benevolence, reliability, competence, honesty, and openness. It consists of 26 close-ended statements, rated on a 6-point Likert-type scale ranging from 1 (strongly disagree) to 6 (strongly agree).
Teacher LC
The LC (Rose & Medway, 1981) is a self-rating questionnaire, that assesses teachers’ beliefs in their control over student outcome (success or failure). It consists of 25 close-ended statements, rated on a 5-point system assessing teacher's locus of control (a = 0% and b = 100%, a = 25% and b = 75%, a = 50% and b = 50%, a = 75% and b = 25% and a = 100% and b = 0%). Each teacher responds to a variety of classroom situations involving students.
Procedure
Firstly, all written permission to translate and adapt the MTES, RSAQ, SE, SC, and LC were granted. Afterward, the English versions of the MTES, PSAQ, SE, SC, and LC were translated and adapted into the Greek language and then back-translated to English. A professional translator in collaboration with the research team implemented the translation (English to Greek). The back-translation of the Greek versions of all scales was implemented by another professional translator. A comparison of the two versions for all scales was made. No potential differences were identified. Three experts (university professors with expertise in the field of special and inclusive education) reviewed the Greek adaptations and provided the research team with specific comments for corrections so that the scales should be appropriate for early childhood education. The research team revised the Greek adaptations with the guidance of the specific comments that the experts provided. A written approval was taken by the Scientific and Ethics Committee of the Department of Early Childhood Education of the Authors’ University. The research tools were shared (MTES, RSAQ, SE, SC, and LC) conjointly with an information letter and a consent form.
All participants were informed regarding the purpose of the research and ethical issues such as anonymity and confidentiality of the data collected from the participants. Each teacher answered the close-ended questions and returned them to the research team. The MTES, RSAQ, SE, SC, and LC were given by the researchers to the teachers. The research team as well as 69 trained undergraduate students participated in the data collection. More specifically, each researcher created a team of 23 students to train them and followed the administration process. There were four sessions with the undergraduate students and additional meetings when needed to support the administration of the questionnaire. The educational regions of Greece were distributed to each one of the trained students, who was responsible to send to all schools of his/her region an invitation so as to recruit randomly the sample of participants. The introduction of the questionnaire informed participants about the aim of the study encouraged them to provide true and unbiased answers and ensured participants’ consent, confidentiality, and anonymity. They were also informed that their participation in the survey was voluntary and that they could stop completing the questionnaire if they wished at any time. In addition, they were informed about the research team and were given contact details for any questions. It was also stressed that at no point would information about their identity be disclosed and that the data would be used exclusively for research purposes. The distribution of the questionnaire took approximately 20–25 min. All data were collected during the spring semester of academic year 2023–2024.
Data analysis
Firstly, we estimated z-scores for all measures, so as to be able to compare different measures. Afterwards, we explored potential cluster solutions through a two-step cluster analysis of the attitudes toward Mathematics Teaching Efficacy, School Climate, Responsibility for Student Achievement, Self-Efficacy (overall), and Locus of Control. We estimated Schwarz's Bayesian information criterion (BIC) and silhouette measures of cohesion and separation to choose the best solution. Next, we performed post-hoc analysis with the use of Tukey's HSD. Finally, we re-estimated the cluster solution and the cluster membership through the hierarchical clustering technique and compared it to the initial one to assess the internal validity of the clusters. Statistical software SPSS v. 21, SPSS AMOS, and SPSS syntax were used for the statistical analysis.
Results
Cluster profiles
Special education preschool teachers
Segmentation analysis through a two-step cluster technique revealed a three-cluster solution for the description of the profiles of special education teachers’ multidimensional mathematics teaching efficacy. For the selection of the appropriate number of clusters we also used Schwarz's BIC. All possible cluster solutions from one to six-cluster solutions were assessed for their fit. The Auto-clustering table summarizes the process by which the number of clusters is chosen. The BIC clustering criterion is computed for each potential number of clusters. Smaller values of the BIC indicate better models, and in this situation, the “best” cluster solution has the smallest BIC. The three-cluster solution offered the most optimal and parsimonious fit (BIC was minimized at the value of 13,453.705). The best solution is supposed to have the largest Ratio of BIC Changes and Ratio of Distance Measures. The ratio of distance measures for the three-cluster solution was formed at 2.116. While the ratio of distance measures was formed at 1.448. Moreover, the silhouette measure of cohesion and separation showed better cluster quality (>0.5) in the case of the three-cluster solution (Table 1). A comprehensive interpretation of the suggested profiles is provided in Figure 1.
Mathematics teaching profiles in kindergarten for the special education teachers (three clusters).
Schwarz’s BIC for number of clusters selection.
The changes are from the previous number of clusters in the table.
The ratios of changes are relative to the change for the two-cluster solution.
The ratios of distance measures are based on the current number of clusters against the previous number of clusters.
A total number of n = 146 special education teachers were enrolled in Cluster 1. These teachers were labeled as “Confident/Efficacious in Teaching Mathematics.” More specifically, the teachers in this cluster expressed the most positive attitudes toward their mathematics teaching efficacy, responsibility for student achievement, self-efficacy (overall), school climate, and locus of control compared to the other participants (Table 2, Figure 1). The specific characteristics of the teachers that were enrolled in the Cluster 1 are presented in detail in Table 3.
Dimensions of attitudes towards mathematics teaching efficacy, school climate, responsibility for student achievement, self-efficacy (overall), and locus of control that predict group membership in the sample of preschool special education teachers.
Dimensions of attitudes towards mathematics teaching efficacy, school climate, responsibility for student achievement, self-efficacy (overall), and locus of control that predict group membership in the sample of preschool special education teachers.
*p = .001.
Sample characteristics within clusters of special education teachers.
A total number of n = 56 special education teachers were enrolled in Cluster 2. These teachers were labeled as “Moderately Confident/Efficacious in Teaching Mathematics.” More specifically, the teachers in this cluster expressed that they face difficulties in being effective in teaching mathematics, while they reported the same level of self-efficacy as the teachers of Cluster 1. Also, they felt less responsible for their students’ achievements. Finally, they reported less positive attitudes for the school climate and locus of control compared to the participants of Cluster 1 (Table 2, Figure 1). The specific characteristics of the teachers that were enrolled in the Cluster 2 are presented in detail in Table 3.
Cluster 3: Overworked—Globally Unconfident/Inefficacious in Teaching Mathematics
A total number of n = 20 special education teachers were enrolled in Cluster 3. These teachers were labeled as “Globally Unconfident/Inefficacious in Teaching Mathematics.” More specifically, the teachers in Cluster 3 expressed that they are both ineffective in teaching mathematics and in teaching (generally). Also, they felt the least responsible for their students’ achievements. Finally, they reported less positive attitudes for the locus of control compared to the participants of Clusters 1 and 2 (Table 2, Figure 1), while they expressed the same attitudes for the school climate with the participants of Cluster 2. The specific characteristics of the teachers that were enrolled in the Cluster 3 are presented in detail in Table 3.
Typical education preschool teachers
Segmentation analysis through a two-step cluster technique revealed a two-cluster solution for the description of the profiles of typical education teachers’ multidimensional mathematics teaching efficacy. For the selection of the appropriate number of clusters we also used Schwarz's BIC. All possible cluster solutions from one to six-cluster solutions were assessed for their fit. The Auto-clustering table summarizes the process by which the number of clusters is chosen. The BIC clustering criterion is computed for each potential number of clusters. Smaller values of the BIC indicate better models, and in this situation, the “best” cluster solution has the smallest BIC. The two-cluster solution offered the most optimal and parsimonious fit (BIC was minimized at the value of 5135.500). The best solution is supposed to have the largest Ratio of BIC Changes and Ratio of Distance Measures. The ratio of distance measures for the two-cluster solution was formed at 1.537. Moreover, the silhouette measure of cohesion and separation showed better cluster quality (>0.5) in the case of the three-cluster solution (Table 4). A comprehensive interpretation of the suggested profiles is provided in Figure 2.
Mathematics teaching profiles in kindergarten for the typical education teachers (three clusters).
Schwarz’s BIC for number of clusters selection.
The changes are from the previous number of clusters in the table.
The ratios of changes are relative to the change for the two-cluster solution.
The ratios of distance measures are based on the current number of clusters against the previous number of clusters.
A total number of n = 296 typical education teachers were enrolled in Cluster 1. These teachers were labeled as “Moderately Confident/Efficacious in Teaching Mathematics.” More specifically, the teachers in this cluster expressed that they face difficulties both in being effective in teaching mathematics and in teaching (generally). Also, they felt less responsible for their students’ achievements. Finally, they reported positive attitudes for the school climate and locus of control compared to the participants of Cluster 2 (Table 5, Figure 2). The specific characteristics of the teachers that were enrolled in the Cluster 2 are presented in detail in Table 6.
Dimensions of attitudes towards mathematics teaching efficacy, school climate, responsibility for student achievement, self-efficacy, and locus of control that predict group membership in the sample of preschool typical education teachers.
Dimensions of attitudes towards mathematics teaching efficacy, school climate, responsibility for student achievement, self-efficacy, and locus of control that predict group membership in the sample of preschool typical education teachers.
Sample characteristics within clusters of typical education teachers.
A total number of n = 29 typical education teachers were enrolled in Cluster 2. These teachers were labeled as “Globally Unconfident/Inefficacious in Teaching Mathematics.” More specifically, the teachers in Cluster 3 expressed that they are ineffective in teaching mathematics, but there were no significant differences in terms of their teaching efficacy (overall) compared to the teachers of Cluster 1. Also, they felt the least responsible for their students’ achievements. Finally, they reported less positive attitudes for the school climate and locus of control compared to the participants of Cluster 1 (Table 5, Figure 2). The specific characteristics of the teachers that were enrolled in the Cluster 2 are presented in detail in Table 6.
Internal validity
In the sub-sample of special education teachers, a total number of 195 participants, comprising 88% remained in the same cluster across clustering techniques. In the sub-sample of typical education teachers, a total number of 360 participants, comprising 91% remained in the same cluster across clustering techniques. Afterward, a random selection of 70% in each of the initial sub-samples was used for the re-estimation of the cluster solution. The solution indicated the stability of the clusters.
Discussion
Through this research, we aimed to identify early childhood teachers’ mathematics teaching efficacy profiles based on parameters such as responsibility for student achievement, self-efficacy (general), school climate, and locus of control in different groups of participants (special and typical education teachers). The two-step cluster analyses revealed differences and similarities regarding the profiles among the two groups of participants. Teachers clustered to “Passionate—Confident/Efficacious in Teaching Mathematics,” “Operational—Moderately Confident/Efficacious in Teaching Mathematics,” and “Overworked—Globally Unconfident/Inefficacious in Teaching Mathematics” in correspondence of the different levels of the parameters examined.
In both samples, analysis revealed statistically significant differences regarding mathematics teaching efficacy, responsibility for student achievement, self-efficacy (general), school climate, and locus of control. A significant finding of the current research is that only special education teachers stated that they were “Passionate—Confident/Efficacious in Teaching Mathematics.” A possible explanation may be attributed to their qualifications (Master in Special Education: 116 (79.5%) and PhD: 2 (1.4%)). Another, factor that may affect the phenomenon is related to Greek educational system, where special education teacher is responsible for less students compared to typical education teacher. Also, they can provide their students with individualized educational interventions. They tend to be effective, adaptive, resourceful, enthusiastic, and innovative. They must try to adapt their teaching in order to meet their students’ special nature using “differentiated” or “individualized teaching.” They are characterized by high professionalism and tend to respect and accept the cultural diversity of their classroom. They work systematically to enhance self-esteem and self-development of their students (Nasiopoulou et al., 2017; Predescu, 2013).
Another matter that may cause the observed differences among special and typical education teachers in terms of their efficacy in teaching mathematics is related to the fact that typical education teachers prioritize school readiness with emphasis in self-regulatory goals. Literature suggests that preschool teachers must be capable in regulating students’ behaviors in developing competences (Nasiopoulou et al., 2017; Predescu, 2013). Early childhood teachers tend to lead and organize playful and interactive learning activities with children. In addition, preschool teachers should be aware to the specific content competence they introduce to teach which involves a greater emphasis on literacy, mathematics, science, and technology (Lillvist et al., 2014; Sheridan et al., 2011). This matter tends to become more difficult as the number of students in class is increasing and teachers are not trained to teach early numeracy through playful activities.
Statistical analysis suggested that there are qualitative differences within the groups of special and typical education teachers’ distinct profiles related to school climate, responsibility for student achievement, self-efficacy (overall), locus of control, and other demographic characteristics. A further exploration of the specific factors that influence each group’s profile in more detail suggested a significant effect of age. We can see that in the sample of special education teachers in Cluster 1, the vast majority (78.1%) belongs to the age group of 22–41 (years). The distribution across the different age groups changes with 50.2% for participants for Cluster 2 and 50% for Cluster 3. Analogous pattern is observed for typical education teachers. The findings are in line with existing findings in the field suggesting significant effect of age in teaching efficacy. Another significant aspect is related to having a master's degree. We can observe that the vast majority 80% of special education teachers in Cluster 1 have a master’s degree. The finding is also in line with previous findings suggesting that teachers with highest degrees tend to experience highest levels of teaching efficacy (Antoniou et al., 2022; Charitaki et al., 2022).
The present study highlights the circumstances that lead early childhood teachers to cope with severe difficulties in teaching mathematics. However, there is a number of limitations that should be discussed. The study is exclusively on self-reports, so a bias may be related to the method employed (Demetriou et al., 2015).
Future studies applying qualitative methodology could include more provide us with more data for all categories of participants (“Passionate—Confident/Efficacious in Teaching Mathematics,” “Operational—Moderately Confident/Efficacious in Teaching Mathematics,” and “Overworked—Globally Unconfident/Inefficacious in Teaching Mathematics”). This could aid in their early identification of the teachers’ specific training needs. It is envisaged that supporting teachers in order to develop their work engagement will have a direct effect on their self-confidence, resilience, and positive attitudes towards inclusive practices, as well (Antoniou et al., 2022; Charitaki et al., 2022).
Footnotes
Contributorship
All authors designed the research. MK and HV collected the data. GC analyzed the data. All authors contributed equally in writing and reviewing the manuscript.
Declaration of conflicting interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The authors received no financial support for the research, authorship, and/or publication of this article.
Informed consent
Informed consent was obtained from all participants involved in the study. More specifically, in the first part of the questionnaire, there was a consent form. All participants gave their consent only after this procedure were able to complete the questionnaire.
