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date: 30 October 2020

The Influence of Teacher Education on Teacher Beliefsfree

  • Maria Teresa TattoMaria Teresa TattoArizona State University

Summary

Beliefs defined as the cognitive basis for the articulation of values and behaviors that mediate teaching practice can serve as powerful indicators of teacher education influence on current and prospective teachers’ thinking. Notwithstanding the importance of this construct, the field seems to lack across the board agreement concerning the kinds of beliefs that are essential for effective teaching, and whether and how opportunities to learn and other experiences have the potential to influence beliefs and knowledge in ways that may equip teachers to interpret, frame and guide action, and to fruitfully engage all pupils with powerful learning experiences. Large-scale international comparative studies provide the opportunity to develop shared definitions that facilitate the exploration of these questions within and across nations.

Subjects

  • Educational Psychology
  • Teaching Skills and Techniques
  • Education

Introduction

Equipping teachers with the knowledge and skills that they will need to engage in effective practice once in schools is the central concern of teacher educators. The study of teacher beliefs, with beliefs defined as the cognitive basis for the articulation of values and behaviors that mediate teaching practice (Aguirre & Speer, 1999; Ajzen & Fishbein, 1977), can serve as a powerful indicator of teacher education influence on current and prospective teachers’ thinking. As such, numerous studies about teacher education on beliefs populate the research literature, providing a broad picture of areas that are of most concern for educators.

I refer the reader to extensive reviews of the literature, the first being Sanger’s (2017), in the Handbook of Research on Teacher Education. Sanger presents a comprehensive and succinct review concerning teacher knowledge and beliefs and the influence of teacher education. Other reviews have summarized the state of the art, including the controversial nature of beliefs and their potential to influence or be influenced by action within sociohistorical and cultural contexts (Ashton, 2014; Fives & Buehl, 2012; Richardson, 1996; Tatto & Coupland, 2003). Other reviews continue to highlight concerns with definitional and methodological problems. Indeed the finding from the classical review of Pajares (1992), which declared “beliefs” a messy construct, points to an ongoing and unresolved concern, while others critique measurement approaches (Hoffman & Seidel, 2014; Fives & Buehl, 2012). Sanger (2017) points out that reviews:

continue to recommend greater collaboration among scholars in developing not only shared definitions, but also measures and analytic frameworks, including larger-scale studies that provide a stronger basis for possible generalization, more longitudinal studies to address belief dynamics over periods longer than a semester or year, and greater attention to the linkages between beliefs and conduct. (p. 341)

This conclusion suggests the need to further explore whether and how opportunities to learn, and other experiences that future teachers undergo during their teacher education and beyond, have the potential to influence beliefs and knowledge in ways that may equip teachers to interpret, frame and guide action, and to fruitfully engage all pupils with powerful learning experiences.

Using data collected as part of the Teacher Education and Development Study in Mathematics (TEDS-M), this article responds to concerns that have emerged from diverse reviews of the literature, namely the need to arrive at shared definitions of beliefs seen as key in the development of future teachers, and the construction of valid and reliable measures and methods for analysis. The TEDS-M study is a large-scale, nationally representative study of the outcomes of teacher education in 17 countries. TEDS-M benefited from the collaboration of teacher educators in the different countries that participated in the study, who contributed to the development not only of shared definitions of beliefs, but also valid and reliable measures using questionnaires and knowledge assessments. The questionnaires and assessments were administered in about 500 teacher preparation institutions in the participating countries to 13,907 future primary teachers, to 8,332 future lower secondary teachers close to graduation from their programs, and to 5,505 teacher educators (the details of the study are in Tatto et al., 2008, 2012; Tatto, 2013).

This article considers a particular conception of teacher education influence on beliefs following early work in this area by Tatto (1996, 1998, 1999). In a series of papers, Tatto put forward the notion that teacher education programs may be constructed to produce a significant change on future teachers’ beliefs in ways that challenge naïve views acquired through the apprenticeship of observation and other commonly held societal views about teaching and learning, thus serving as indicators of program outcomes. Tatto’s previous work revealed that when teacher educators in these programs held strong norms about what characterizes good teaching (or notions of the ideal teacher for the ideal students/citizen) they were able to create deliberately planned opportunities to learn (OTLs) and experiences that supported inquiry oriented learning by future teachers (FTs), resulting in significant changes in their system of beliefs. A key indicator of program influence on beliefs used in Tatto’s studies was the magnitude of the difference in means between the aggregated beliefs of program faculty and their FTs relative to the size of the standard deviations (or effect size). We refer to this as the teacher education alignment index.

After a brief overview on ways to conceptualize the influence of teacher education programs on teachers’ beliefs as cognitive constructs and as indicators of program outcomes, this article explores the influence of teacher education on FTs’ beliefs based on analysis of the TEDS-M data (Tatto et al., 2012). Specifically the article examines the degree of alignment on key beliefs between teacher educators and future primary and secondary mathematics teachers as mediated by programs’ opportunities to learn and by FTs’ knowledge of the subject and of the pedagogy of the subject in three countries: Poland, Russia, and the United States. The article concludes by discussing these findings in view of who is shaping teacher education programs’ philosophy and opportunities to learn in an era of market-based approaches to education.

Conceptualizing the Influence of Teacher Education on Future Teachers’ Beliefs

Tatto’s earlier work compared FTs’ beliefs at program entry and exit with the beliefs of their educators, with the aggregated beliefs of those educators representing program norms. Specifically, the studies used samples of U.S. teacher education programs, including some that had undergone a process of reform and some that had remained unchanged, and explored key beliefs about teaching diverse students, beliefs about instructional choice, and beliefs about the purposes of education, teachers’ roles and practices (Tatto, 1996, 1998, 1999).

Tatto found that reformed programs where faculty followed a strong program philosophy (in this case aligned with constructivist principles) also had strongly aligned beliefs, and that these beliefs were reflected on the programs’ graduates with significant changes between entry and exit. Tatto’s research also found that in programs where faculty did not identify with a particular philosophy FTs’ beliefs did not show a significant change between entry and exit; in other words, passage through teacher education seemed to have little or no effect on the beliefs that they held when entering the program. This early work framed the study of beliefs in the TEDS-M study (Tatto et al., 2008, 2012; Tatto, 2013).

Tatto’s research was done at a time when important changes in teacher education were occurring across the United States and globally, including reforms following constructivist principles. Shulman (1987) had been arguing for a complex view of teachers’ professional knowledge, with knowledge of the content as a foundation for other equally important knowledge areas that are unique to and define the teaching profession, much in the way that other kinds of knowledge define established professions such as medicine. One central aspect of Shulman’s knowledge typology unique to the discipline of education is pedagogical content knowledge (PCK). PCK is defined as “a type of knowledge that is unique to teachers, and is based on the manner in which teachers relate their pedagogical knowledge (what they know about teaching) to their subject matter knowledge (what they know about what they teach)” (Cochran, 1997). This knowledge interacts with other knowledge areas also unique to the education discipline (of the curriculum, of pupils, of their communities) and positions the teacher (to follow Bernstein, 1999) as the key recontextualization actor of the school curriculum. The successful acquisition of PCK requires a strong knowledge of the discipline, the ability to make sense of that knowledge in order to recontextualize it in a way that is accessible to pupils, to develop learning opportunities to accommodate different learning needs and styles, and understanding of the social, political, cultural, and physical environments in which students are asked to learn (Cochran, 1997). In short, adoption of a constructivist philosophy as a framework for teacher education aligned well with the development of the different types of knowledge seen as essential in the development of teachers as autonomous professionals. Teacher educators under this frame were seen as part of a learning community able to create opportunities for FTs to encourage reflection, dialogue, critical thinking, knowledge ownership, and understanding in context, including the development of norms to guide program improvement and ensure consistency and continuity (Tatto, 1998). In addition teacher change was seen as requiring learning opportunities that support in-depth examination of theories and practices in light of teachers’ beliefs and experiences within a sociohistorical context to find meaning in what they learn (Ashton, 1992, p. 322).

Cross-national studies have explored important dimensions influencing belief formation on FTs. For instance, Fraser and Ikoma (2015) show how global curriculum regimes tend to favor a constructivist (learner-centered) over a traditional (teacher-centered) teaching orientation in a dynamic that has resulted in increased isomorphism in teacher education. In contrast, others have explored the pervasive nature of traditional beliefs among future mathematics teachers as a result of national-bounded cultural values that are in turn embedded in institutions (Stigler & Hiebert, 1998, 1999); while others have documented how these global forces have an impact not only on teacher beliefs but also on knowledge development (Desimone et al., 2005). Beliefs about what is appropriate for teachers to address, and how they should develop and recontextualize knowledge are likely to be influenced in various degrees by dominant global and national cultural influences.

Because beliefs formation occurs as part of cognitive development and learning and as a function of cultural and social interactions (as formulated by Vygotsky, see Daniels, 2001), a sociocultural approach is useful in understanding the existence of program norms about what makes a professional teacher.

A Sociocultural Approach to Analyze the Influence of Teacher Education on Teachers’ Beliefs: The Interaction of the Macro-, Meso-, and Microlevels

The recent work of Tatto, Burn, Menter, Mutton, and Thompson (2018), which analyzes policy at the macrolevel, as it interacts with teacher education programs and their partner schools at the mesolevel, and as it influences FTs is helpful in explaining the influence of teacher education on teachers’ beliefs. Currently in countries such as the United States, England, and Australia, to name a few, teacher education is increasingly influenced at the macrolevel by policies and regulation mandates, which have tended to emphasize performativity, standardization, and testing (see also Akiba, 2017). At the mesolevel of institutions there has been a gradual shift in the control of teacher education curriculum from teacher educators to external controls (i.e., standards, accreditation guidelines), and an increased tendency to transfer the provision of teacher education to schools or to other vendors in a continuously growing market approach to teacher preparation. Thus, teacher education programs and their partner schools may find themselves at odds as they seek to meet these demands while maintaining a curriculum that aligns with the notion of the teacher as a professional. It is at the microlevel of the individual teacher where sense-making is more complex, especially as individual FTs seek to align their beliefs alongside programs and partner schools in a dynamic that may occur in complex ways. For instance, programs and schools may be internally and externally aligned with regulation mandates; schools may be aligned with external regulations but misaligned with the goals of teacher education programs; or programs and partner schools may be internally and externally misaligned (Tatto et al., 2018). Further, individual FTs may have internal motives that may be aligned or misaligned with all of the above. Our work shows that in some cases alignment is necessary for fruitful learning but not always, thus revealing the complexity entailed in learning to teach (Tatto et al., 2018). In other settings, policy trends have not been so strongly influenced by market approaches. In Japan and South Korea, for instance, the tendency is toward centralized control over teacher education by the federal state. In cases such as these, national cultural values and stronger levels of alignment across all levels may predominate. The hypothesis pursued here is that external controls and increased regulation as a result of rapid-paced reforms have altered in many cases the factors that in the past facilitated alignment among teacher educators at the mesolevel of institutions, such as the necessary time to meet to share understandings and to construct inquiry-based opportunities to learn within programs and in collaboration with schools. Such lack of alignment at the mesolevel may have weakened teacher education influence at the microlevel of the individual, and beliefs are a sensitive indicator of these changes. If this is true, we should see a lack of alignment in beliefs held by faculty and FTs, especially in those areas that are considered important in supporting inquiry-based learning in mathematics (e.g., reasoning around complex concepts and ideas, understanding students’ thinking) and which by definition challenge more traditional beliefs. This may consequently weaken the influence of teacher education programs’ OTL on FTs’ mathematical pedagogical content knowledge (MPCK) and beliefs. In situations such as those in Europe, where the impetus has been to align entire higher education systems to fit one model under the Bologna agreement, traditional systems that were highly coherent (as in Bulgaria, see Bankov, 2007) had to be modified, often quickly, sacrificing core elements that were considered important in learning to teach specially on the pedagogy of the subject. Alignment in beliefs may be found, however, in areas of regulatory pressure, such as the use of assessments to evaluate individual learning and the introduction of standards to regulate teaching practice. Such alignment may indicate program efforts to accommodate external regulations, thereby moving away from cultural values.

Data and Analysis Source

The analysis presented here draws on the analysis by Rodriguez, Tatto, Palma, and Nickodem (2018) of TEDS-M study data from teacher educators and their FTs in primary and secondary programs in Poland, Russia, and the United States. These countries obtained moderately high or high scores in the assessments of mathematics content knowledge (MCK) and MPCK (see Tatto et al., 2012, pp. 130–131), thus representing systems that produce FTs with good knowledge of the subject and of the subject pedagogy along the lines suggested by Shulman and others. Studying the United States is of particular interest in light of the reforms (macrolevel) that shaped the programs initially studied by Tatto in the 1990s and of further efforts to reform programs since then. While following similar regulation trends as other countries, teacher educators for the most part remain in control of their programs. The study of Poland and Russia provides insight into other types of reforms influenced by global forces such as the Organisation for Economic Co-operation and Development (OECD) and the Bologna Process in Europe, which placed control of the higher education system in the hands of Ministries of Education with the goal of ensuring comparability in the standards and quality of higher education qualifications. Poland has been open to implementing the Bologna Accord since its creation in 1999, and to global reforms including those proposed by the OECD for “teacher training programmes that target the teaching or development of 21st century skills” (Ananiadou & Claro, 2009). In contrast, Russia became a signatory of the Bologna Accord in 2003, which started a long process of changing the higher education system while preserving fundamental values and traditions, and the country is not yet an OECD member. Thus, the expectation is that national cultural values would predominate among Russian FTs and their educators, and that global values would predominate amongst U.S. and Polish FTs and their educators. The study focuses on mathematics teacher education because of the strong grammar of mathematics (Bernstein, 1999), which allows finding common definitions and comparisons within and across countries.

In this article, the focus is on the concept of beliefs as cognitive states regarding the teaching and learning of mathematics that FTs and their educators hold to be true. The TEDS-M study focused on those areas of beliefs judged to influence the processes of learning to teach mathematics,1 such as beliefs about:

the role of the teacher in the learning of mathematics; for instance, whether direct teaching is more advisable than students’ active learning.

the nature of learning in mathematics; for instance, whether mathematics learning consists of acquiring the ability to apply a set of rules and procedures that have to be memorized and mastered, or whether mathematics can be learned by following a process of inquiry, such as learning, to solve problems in a variety of ways.

the factors that account for students’ success in learning mathematics; for instance, is one naturally good at mathematics or can one become good at mathematics?

the degree to which the program experienced by FTs across the areas of mathematics pedagogy, pedagogy and school experiences contributed in a significant way to their learning to teach.

FTs’ beliefs (microlevel) in these areas are seen as mediated by the opportunities to learn and other experiences provided by their programs in collaboration with schools (mesolevel). These included opportunities to learn that FTs had in their:

mathematics pedagogy courses, such as (a) the foundations of mathematics education, (b) mathematics instruction, (c) participation in mathematics education courses, (d) doing readings in mathematics education courses, (e) solving problems in class, (f) studying instructional practice, (g) studying instructional planning, and (h) studying the uses of assessment and (i) assessment practices;

pedagogy courses, such as in the areas of (j) the social sciences in education, (k) general educational applications, (l) teaching for diversity, (m) teaching for reflection on practice, and (n) teaching for improving practice; and

school experience, such as (o) connecting classroom learning to practice, (p) the reinforcement of teacher education program goals in the school setting). and (q) the quality of supervising teacher’s feedback.

Other questions asked about the degree to which the program experienced by FTs was coherent; that is, whether there was consistency across courses and experiences offered to FTs, and whether there were explicit standards with expectations for what FTs should learn from their respective programs.

Finally, the results of the MCK and MPCK knowledge assessments for these FTs helped to understand the mediating nature of knowledge in belief acquisition. The MCK assessed knowledge of FTs in the domains of number, algebra, geometry, and data, across three cognitive areas, namely application, knowledge and reasoning. The MPCK assessment measured knowledge for teaching in these four domains (number, algebra, geometry and data) but went beyond to assess in addition mathematical curricular knowledge and knowledge of planning for and enacting mathematics teaching (Tatto et al., 2008, pp. 37–38).

Influence of Teacher Education’s Opportunities to Learn and Knowledge Levels on Future Teachers’ Beliefs

To understand the influence of teacher education on beliefs differences between faculty and future primary and secondary teachers we used a procedure called regression.2 We used a series of Weighted Least Squares (WLS) regressions to model the influence of opportunities to learn on variability in effect sizes (e.g., the difference in beliefs between faculty and their FTs) in programs aggregated at the country level.3 Regressions for future primary teachers (FPTs) and future secondary teachers (FSTs) were run for each country (see Tables 1 to 6). To understand the tables a brief explanation is necessary. The R2 coefficient indicates the proportion of the variance explained by the opportunity to learn variables (OTL) and the knowledge variables included in the model (MCK and MPCK). The magnitude of the regression coefficients in each row across the columns indicate the variability in effect sizes (i.e., the difference in beliefs between FTs and their faculty) in relation to the opportunities to learn provided by the program, and the degree to which these coefficients are significant (*p < .05). R2 values range from 0 to 1 and are commonly stated as 0% to 100%, where 100% represents a model that explains all of the variance. The sign of the intercept at the top of each column and the sign of the regression coefficients in each row for all of the regressions are also key to interpreting these results. A positive intercept indicates that, on average, when all other variables are held constant, FTs had higher scores on the given belief than their educators (i.e., they were more likely to agree with the statements comprising the belief). A significant positive OTL regression coefficient suggests that a one standard deviation increase in the OTL will increase the difference in belief, widening the gap in the level of belief between FTs and their educators. Conversely, if an OTL has a negative coefficient, every standard deviation increase in the OTL will reduce the difference in belief between FTs and their educators. The same applies for the knowledge regression coefficients.

For instance, Table 4 shows that the intercept for future primary teachers (FPTs) in the United States regarding the belief that teaching mathematics should engage students in active learning is –0.12, meaning that, for institutions with average OTLs in that country, FPTs are less likely to believe in teaching as active learning than their educators do. Looking for the influence of programs’ opportunities to learn on differences in beliefs between educators and their FTs, see for instance the regression coefficient for OTL from “instructional practice” (e.g., the opportunity to learn to apply mathematics to real-world problems and to distinguish between procedural and conceptual mathematics when teaching), which is 0.40. This indicates that a 1.0 standard deviation (SD) increase in the OTL from instructional practice is associated with a shift in the difference in beliefs between faculty and FTs of 0.28 (–0.12 + 0.40 = 0.28), essentially reversing the difference in beliefs. In other words, FPTs in U.S. programs offering OTL from instructional practice were more likely to believe in teaching as active learning, and these beliefs were strongly held relative to the beliefs of their faculty.

A simpler way to understand the results in the tables is to look at the intercepts and at the regression coefficients by OTL or knowledge variables. When the regression coefficient is the same sign as the intercept this results in an increased difference in beliefs among FTs and their educators. When the intercept is the opposite sign of the coefficient this will result in a reduction (or reversal) of the difference, to a point where additional OTL or knowledge levels may actually reverse the difference (essentially serving as an indicator of teacher education influence on FTs’ beliefs).

An important finding from the TEDS-M study was the great variability in the way programs organize OTL across and even within institutions in the participating countries (Tatto & Senk, 2011). Because of this variability, we found that OTLs were rarely uniform and significant predictors of the difference in beliefs between FTs and their educators, indicating possible program misalignment. This finding is consistent with that of Hammerness and Klette (2015), who found considerable national sources of variation in teacher education in their study.

The levels of MCK and MPCK demonstrated by FTs in the TEDS-M assessments, however, were often significant predictors of belief differences between educators and FTs (typically, higher levels of MPCK were associated with higher levels of alignment). This finding confirms the cognitive nature of these constructs and the likely conclusion that beliefs are more effectively affected by important changes in cognition of the subjects and of pedagogy.

In the next section six sets of beliefs are examined (mathematics as a process of inquiry, mathematics as a set of rules and procedures, teacher-directed mathematics learning, active learning of mathematics, mathematics as a fixed ability, and preparedness for teaching), together with the influence of OTL and knowledge on FTs’ beliefs, including the degree of alignment between faculty and their FTs as an indicator of program influence.

Mathematics as a Process of Inquiry

Table 1 shows that across each country, for primary and secondary programs, educators were more likely to agree that mathematics learning can be advanced through processes of inquiry than FTs were (note the negative intercepts in Table 1). In Poland, the WLS regression models explained 43% of the variance in difference in beliefs between educators and their FPTs and FSTs. In the Russian Federation, the model explained 55% of the variance in beliefs for FSTs and their educators across institutions. Programs’ OTLs about national or state standards and assessments as related to pupils’ learning (assessment practice), reduced and reversed the difference in this belief for FSTs in Poland and for FPTs and FSTs in the Russian Federation (e.g., with more OTL assessment practice, FTs tend to agree with their educators, reversing the differences and indicating the influence of teacher education on this view). Similarly, OTL from school experiences, such as observing and practicing teaching, and collecting and analyzing evidence about pupil learning as a result of FTs’ teaching methods (classroom learning to practice), also reduced the difference for FPTs in Poland and the Russian Federation and for FSTs in the United States. The associations between the measures of knowledge and beliefs in this case were not consistent across countries and levels of teacher preparation programs. Overall, OTL explained about half of the variation in differences in beliefs.

Table 1. WLS Regression Results for Future Primary and Secondary Teachers on Mathematics Learning as a Process of Inquiry

Primary

Secondary

Predictors

POL

RUS

U.S.

POL

RUS

U.S.

R2

.43

.46

.53

.43

.55

.44

Intercept

−0.68

−0.43

−0.65

−0.59

−0.29

−0.31

OTL Variables

Foundations

0.05

−0.13

Instruction

Class Participation

0.18*

Class Reading

0.08

−0.08

Solving Problems

−0.15

−0.10

−0.15

−0.15*

0.09

Instructional Practice

0.12

0.23*

0.24*

Instructional Planning

−0.15

−0.19

−0.21*

0.40*

Assessment Uses

−0.15

−0.15

−0.31*

Assessment Practice

0.20*

0.29*

0.41*

Social Science

0.06

Application

−0.29*

−0.20*

−0.24*

Teach for Diversity

0.34*

−0.10

−0.09

Teach for Reflection

Teach for Improving

−0.51*

Classroom Learning to Practice

0.16*

0.23*

0.13

0.25*

Reinforcement of Goals

−0.11*

0.19*

Feedback Quality

−0.09

−0.13

Program Coherence

0.15

0.11

−0.32*

Knowledge Variables

MCK

0.28*

−0.07

−0.43*

MPCK

0.38*

−0.18

0.34*

Note: POL = Poland; RUS = Russian Federation; U.S. = United States. MCK = Mathematical Content Knowledge; MPCK = Mathematical Pedagogical Content Knowledge.

* p < .05

Source: Rodriguez, Tatto, Palma, and Nickodem (2018)

Mathematics as a Set of Rules and Procedures

Table 2 shows that in all cases the FTs who participated in our study were more likely to agree that mathematics consists of the application of a set of rules and procedures (consistent with their lower scores on beliefs regarding mathematics as a process of inquiry) relative to their educators (positive intercepts). The WLS regression models explained 23% (Poland primary programs) to 78% (Poland secondary programs) of the variance in differences between FTs and educators. FTs’ opportunity to participate in class (e.g., ask questions, participate in discussion and to teach a class during their program) tended to reverse the difference in beliefs in the Russian Federation primary programs, but increased the differences for secondary programs in all three countries. Similarly, having opportunities to develop instructional plans to accommodate pupils’ diverse learning needs significantly increased the differences in views between teacher educators and their FPTs and FSTs in Poland, and FSTs in the Russian Federation, an outcome that may occur because instructional plans are more attuned to school norms than to program norms, and, in some cases, these norms differ. In most cases, institutions where FTs had higher levels of MCK also had views that were more closely aligned with those of their educators (i.e., they were more likely to reject the view that learning mathematics for the most part means memorizing and applying a set of rules and procedures).

Table 2. WLS Regression Results for Future Primary and Secondary Teachers on Mathematics Learning as a set of Rules and Procedures

Primary

Secondary

Predictors

POL

RUS

U.S.

POL

RUS

U.S.

R2

.23

.54

.42

.78

.50

.47

Intercept

0.50

0.35

0.81

0.29

0.18

0.62

OTL Variables

Foundations

0.12*

0.09

Instruction

−0.45*

Class Participation

−0.23*

0.09

0.38*

0.09*

0.14*

Class Reading

0.13*

Solving Problems

Instructional Practice

0.31*

Instructional Planning

0.18*

−0.23

0.31*

0.16*

Assessment Uses

0.18*

Assessment Practice

−0.17*

−0.17

Social Science

−0.10

−0.09

0.07

Application

Teach for Diversity

−0.24*

−0.15

−0.37*

Teach for Reflection

0.18

−0.11

Teach for Improving

0.26*

Classroom Learning to Practice

0.38*

Reinforcement of Goals

−0.13

−0.14

0.12*

Feedback Quality

−0.10

0.15*

−0.29*

Program Coherence

0.20*

Knowledge Variables

MCK

−0.35*

−0.34*

−0.13*

−0.36*

−0.17*

0.21

MPCK

0.23

0.40*

0.12

−0.44*

Note: POL = Poland; RUS = Russian Federation; U.S. = United States. MCK = Mathematical Content Knowledge; MPCK = Mathematical Pedagogical Content Knowledge.

* p < .05

Source: Rodriguez, Tatto, Palma, and Nickodem (2018).

Teacher-Directed Mathematics Learning

Table 3 shows that in all cases FTs were more likely to believe that mathematics instruction should be teacher-directed relative to their educators (positive intercepts). Regarding variation in these differences, the models produced R2 values ranging from 0.39 (Russian Federation secondary programs) to 0.55 (Russian Federation primary programs), with very few consistent predictors across countries and teacher level. None of the OTL measures were significant predictors for more than two of the six teacher types (primary or secondary) by country combinations. Even then, the direction of the impact varied across country and teacher level. In two cases for MCK and in three cases for MPCK, institutions with FTs with higher knowledge scores were less likely to believe that mathematics instruction should be teacher-directed, toward a view generally more common among their educators. Overall, OTL appears to explain about half of the variation in differences in this belief, although there is variation across countries.

Table 3. WLS Regression Results for Future Primary and Secondary Teachers on Mathematics Teaching as Teacher Directed

Primary

Secondary

Predictors

POL

RUS

U.S.

POL

RUS

U.S.

R2

.54

.55

.41

.43

.39

.50

Intercept

0.55

0.63

0.73

0.44

0.40

0.53

OTL Variables

Foundations

−0.21*

0.18*

0.07

−0.13

Instruction

−0.12

−0.35

0.08

Class Participation

−0.16*

0.06

Class Reading

0.09

Solving Problems

0.24*

−0.15

Instructional Practice

0.28*

0.12

0.21

Instructional Planning

0.38*

−0.27*

−0.15

0.27

−0.21

Assessment Uses

0.34*

−0.21*

Assessment Practice

−0.27

Social Science

0.12

Application

0.27*

−0.16

Teach for Diversity

−0.53*

0.21*

−0.16

Teach for Reflection

0.23*

Teach for Improving

−0.30*

0.36

−0.28*

0.33*

Classroom Learning to Practice

−0.23*

0.19

Reinforcement of Goals

−0.16

Feedback Quality

0.16*

−0.10

0.07

Program Coherence

0.22*

Knowledge Variables

MCK

−0.16*

−0.15*

0.16

MPCK

−0.61*

−0.21*

−0.30*

Note: POL = Poland; RUS = Russian Federation; U.S. = United States. MCK = Mathematical Content Knowledge; MPCK = Mathematical Pedagogical Content Knowledge.

* p < .05

Source: Rodriguez, Tatto, Palma, and Nickodem (2018).

Active Learning of Mathematics

Table 4 shows that in all cases, and relative to their educators (negative intercepts), FTs were less likely to believe that mathematics instruction can be done through active learning (e.g., instruction should allow time for investigations and discussion so that pupils can figure out their own solutions to mathematical problems and to understand why an answer is correct). The model only explained 10% of the variation in the gap in this belief between educators and their FPTs in the Russian Federation, but explained 83% of the variation for FSTs in Poland. However, there was little consistency in the predictors for primary programs in all three countries. Higher quality of feedback provided by the supervising teacher (supervising teacher feedback quality) uniformly increased the differences between FSTs and their educators regarding the notion that mathematics learning can be inquiry-based, indicating a lack of alignment between program and school goals. In addition, having more OTL about standards and assessments, including the analysis of assessment results in relation to pupils’ learning (assessment practice), increased the difference in views among educators and their FPTs in Poland and in the United States. For FSTs, learning how to address the learning needs of diverse students (teaching for diversity) increased the difference in views among educators and FTs in Poland and the Russian Federation on the need for active learning in mathematics. These results indicate the preponderance of performativity and testing concerns over one of the most important core beliefs in the teaching and learning of mathematics under a constructivist approach (Richardson, 2003).

Higher levels of program alignment with standards were related to larger differences between FTs and their educators. This was true for FPTs in the United States and for FSTs in Poland, but this difference was reversed for the Russian Federation’s FSTs (e.g., 1 SD increase in program alignment with standards reversed the difference in beliefs about active learning, –0.26 + 0.25 = –0.01) likely indicating the qualitative difference in standards in the Russian Federation in contrast with those in the United States and Poland. Levels of MCK knowledge did not have a consistent relationship on differences in this belief, but levels of MPCK had significant effects in Poland on primary and secondary programs: greater knowledge of MPCK tended to reverse differences, with FTs supporting the notion that mathematics learning can be inquiry-based, an indication of teacher education influence.

Table 4. WLS Regression Results for Future Primary and Secondary Teachers on Mathematics Teaching as Active Learning

Primary

Secondary

Predictors

POL

RUS

U.S.

POL

RUS

U.S.

R2

.23

.10

.48

.83

.40

.21

Intercept

−0.52

−0.39

−0.12

−0.58*

−0.26

−0.08

OTL Variables

Foundations

−0.20

−0.18*

−0.13

Instruction

0.25*

Class Participation

−0.10

0.88*

Class Reading

0.17*

Solving Problems

Instructional Practice

0.40*

Instructional Planning

Assessment Uses

Assessment Practice

−0.25*

−0.30*

Social Science

Application

−0.08

Teach for Diversity

−0.74*

−0.23*

Teach for Reflection

0.11*

0.12

0.48*

Teach for Improving

Classroom Learning to Practice

0.28*

0.63*

0.22

Reinforcement of Goals

Feedback Quality

−0.23*

−0.22*

−0.17*

Program Coherence

−0.14*

−0.36*

0.25*

Knowledge Variables

MCK

0.15*

−1.47*

MPCK

0.33*

1.74*

0.13*

Note: POL = Poland; RUS = Russian Federation; U.S. = United States. MCK = Mathematical Content Knowledge; MPCK = Mathematical Pedagogical Content Knowledge.

* p < .05

Source: Rodriguez, Tatto, Palma, and Nickodem (2018).

Mathematics as Fixed Ability

Table 5 shows the results of the analysis of the belief that doing well in mathematics can be explained by a natural ability or a mathematical mind (mathematics as fixed ability). In Poland’s secondary programs an R2 equal to 0.94 tells us that the OTL variables explained nearly all of the variation in differences across institutions. On average, Poland’s FSTs believe that mathematics learning is a fixed ability just slightly less than their educators, whereas FTs in the other countries had strong beliefs supporting the fixed ability notion relative to their educators (positive intercepts). The WLS models explained 21% of the variation in the differences of belief that doing well in mathematics can be explained by a natural and fixed ability, with little consistency in the significance of OTL predictors in the models between country and teacher level in the Russian Federation secondary programs. Class participation and instructional planning significantly reversed the difference in this belief between FPTs and their educators in the Russian Federation and FSTs and their educators in the United States. Although the opposite effect was found for FSTs in Poland, opportunities to participate in discussions and teach a class (class participation) and to develop instructional plans (instructional planning) also reversed the difference and indicated the strength of school norms over program norms. Consequently, future secondary teachers were relatively more likely than their educators to believe that mathematics learning is a function of fixed ability, a finding that is consistent with the average differences (given intercepts) of other countries and teacher levels.

Nevertheless, it is important to note that differences in beliefs between FTs and educators narrow across institutions by accounting for variation in OTL and levels of knowledge (MCK and MPCK).

Table 5. WLS Regression Results for Future Primary and Secondary Teachers on Mathematics Learning as a Fixed Ability

Primary

Secondary

Predictors

POL

RUS

U.S.

POL

RUS

U.S.

R2

.58

.48

.38

.94

.21

.55

Intercept

0.23

0.34

0.64

−0.17

0.25

0.43

OTL Variables

Foundations

0.10*

−0.24*

Instruction

−0.06

−0.67*

Class Participation

−0.10*

0.30*

−0.28*

Class Reading

0.16*

Solving Problems

0.18*

−0.20

Instructional Practice

Instructional Planning

−0.08

−0.30*

0.66*

−0.37*

Assessment Uses

0.42*

Assessment Practice

−0.37*

Social Science

0.14

0.31*

Application

0.14*

−0.53*

Teach for Diversity

−0.13

0.19

Teach for Reflection

0.10

0.25*

Teach for Improving

−0.16

0.54*

Classroom Learning to Practice

−0.12

0.56*

0.09

Reinforcement of Goals

0.14*

Feedback Quality

−0.07

−0.46*

−0.09

0.40*

Program Coherence

0.06

−0.18*

0.41*

Knowledge Variables

MCK

−0.11

−0.80*

−0.12*

0.19

MPCK

−0.17*

−0.12

0.65*

0.13*

Note: POL = Poland; RUS = Russian Federation; U.S. = United States. MCK = Mathematical Content Knowledge; MPCK = Mathematical Pedagogical Content Knowledge.

* p < .05

Source: Rodriguez, Tatto, Palma, and Nickodem (2018).

Preparedness for Teaching

Table 6 shows that in Poland, in both primary and secondary programs, FTs were less likely to believe that they were well prepared for teaching than were their educators; in contrast, at both program levels in the Russian Federation and the United States, FTs were more likely to believe that they were well prepared than were their educators. The WLS models produced R2 values ranging from 0.22 (Poland primary programs) to 0.99 (Poland secondary programs) for differences in this belief. Programs offering OTL to teach diverse students, however, significantly increased differences in the perceptions of preparedness to teach among FPTs and FSTs in Poland. Learning in a “coherent” program significantly increased differences in the perceptions of preparedness among educators and their FSTs in Poland and the United States, but in different ways. In the United States, where teacher education is highly variable, FTs felt well prepared to teach in programs that are more coherent and where there is a balance of subject, pedagogical and practical preparation. In Poland, however, because of the Bologna Agreement, new regulations mandated that subject-related training for teachers should be implemented in accordance with the standards for a given field of study. These standards in turn define the general content of the teacher-related subjects and competencies to be developed in teacher education programs. Consequently, teachers for higher grades (FSTs) are trained in mathematical studies with only minimal attention paid to pedagogical studies (Schwille, Ingvarson, & Holdgreve-Resendez, 2013, p. 184). This kind of program coherence resulted in FSTs feeling less prepared to teach relative to the views of their educators. Indeed, in institutions where FTs demonstrated higher levels of MCK, in our assessments of Polish primary and secondary programs differences in perceptions of preparedness were increased; whereas greater MPCK reversed the difference in Polish secondary programs. In the United States, FTs reported more positive perceptions of preparedness than their educators, especially those who did better on the MCK assessment; however, those who obtained higher scores in the MPCK assessment tended to report more negative perceptions of preparedness.

Table 6. WLS Regression Results for Future Primary and Secondary Teachers on Preparedness for Teaching

Primary

Secondary

Predictors

POL

RUS

U.S.

POL

RUS

U.S.

R2

.22

.43

.62

.99

.61

.43

Intercept

−0.35

0.20

0.33

−0.18

0.17

0.11

OTL Variables

Foundations

0.11*

0.25*

Instruction

0.19*

0.19*

0.21

Class Participation

0.12*

0.10*

Class Reading

−0.08

−0.09

Solving Problems

−0.11

−0.11

Instructional Practice

−0.20*

Instructional Planning

0.20*

−0.18

0.17*

Assessment Uses

0.18*

0.95*

Assessment Practice

0.28*

−0.41*

Social Science

−0.09

Application

Teach for Diversity

−0.29*

−0.13*

−0.85*

−0.09

Teach for Reflection

0.23*

Teach for Improving

−0.20

0.10

0.77*

Classroom Learning to Practice

−0.63*

0.15

Reinforcement of Goals

−0.16*

0.52*

Feedback Quality

0.11

0.29*

−0.12

0.23

Program Coherence

0.14*

−0.34*

0.31*

Knowledge Variables

MCK

−0.19*

−0.37*

−0.14*

0.24

MPCK

0.46*

−0.23

Note: POL = Poland; RUS = Russian Federation; U.S. = United States. MCK = Mathematical Content Knowledge; MPCK = Mathematical Pedagogical Content Knowledge.

* p < .05

Source: Rodriguez, Tatto, Palma, and Nickodem (2018).

Discussion

This article began by posing the difficulties involved in defining, measuring, and analyzing the influence of teacher education on FTs’ beliefs. Using the approach originated by Tatto through the TEDS-M study, and aided by more powerful analytical methods (Rodriguez, Tatto, Palma, & Nickodem, 2018), this article shows the ability to arrive at common definitions and measures, and to explain teacher education influence on FTs’ beliefs as mediated by the knowledge levels attained close to graduation. Teaching FTs about standards and assessments and providing structured opportunities to learn from practice in real school settings seem to have an important influence on belief change. Certain beliefs about the nature of mathematics teaching and learning are strongly ingrained, such as beliefs that support the notion that teacher-directed approaches are more effective than active learning approaches, and that there seems to be a natural ability to learn mathematics rather than a learned ability. While some FTs benefit from programs’ OTLs, others do not, given the variability in OTL implementation across programs within countries. The experience of Poland concerning the introduction of subject-based standards above OTL pedagogy or content pedagogy shows mixed results as far as how prepared FTs believe they are. Importantly, acquired levels of MCK and MPCK knowledge seem to exert powerful influences on beliefs in these important areas.

Another finding is the pervasive nature of what seem to be universal norms. We found that averaged differences in beliefs between educator and FTs across institutions within a country (i.e., a cultural norm) are similar across countries. That is, when on average FTs are less likely to agree with their educators on a given belief in one country, similar patterns are found in the other two countries, possibly indicating a tendency toward a universal norm. For example, regarding the belief that learning mathematics is a process of inquiry, FPTs and FSTs were less likely to agree with this belief (i.e., they had lower scores on this belief) than their educators on average across all three countries. This was also true for believing that mathematics teaching should involve active learning (FTs were less likely to agree with this belief than their educators). In contrast, there were beliefs that FTs were more likely to agree with than their educators, including that mathematics is a set of rules and procedures, that learning mathematics should be teacher-directed, and that mathematics ability is fixed. These tendencies indicate a weaker, albeit not generalized, influence of teacher education programs in altering such beliefs, and underscore the influence of cultural beliefs on teacher education.

For instance, we observed significant variation across institutions preparing FPTs in Poland and the United States regarding the belief about mathematics learning as a process of inquiry; the same was true in institutions preparing FPTs in Poland and the Russian Federation with respect to the belief that mathematics learning consists of memorizing a set of rules and procedures. Regarding the belief that mathematics learning should be teacher-directed, significant variation in institutional differences from educators was found for all FPTs and for FSTs in Poland. Regarding mathematics as a fixed ability, only U.S. programs showed significant variation across institutions. Finally, regarding being prepared for teaching, significant variation across institutions was seen in both the Russian Federation and the United States.

In sum, for most countries, as much as half (or even more) of the variation across institutions was accounted for by OTL and mediated by knowledge levels. These findings suggest that the degree to which teacher education programs are able to influence beliefs (e.g., the differences in beliefs between FTs and educators) is a function of the teacher education curriculum and experiences, and in some cases of FT knowledge, which entails a careful balance of MCK and MPCK. These findings are correlational and not causal, corresponding to the design of TEDS-M. While national longitudinal or experimental studies would provide conclusions that are more definitive, these studies are logistically and financially unaffordable.

The evidence presented here, with replication across multiple institutions and countries, provides relevant information regarding the value of exploring alignment between FT and educator beliefs as an indicator of teacher education influence. Higher levels of knowledge, specifically MPCK and carefully designed OTL, as expressed in the teacher education curriculum and in field experiences, are the potential levers that teacher preparation programs can control in an era of increased external regulation and fast-paced reform.

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Notes

  • 1. For more detail on how we measured beliefs, see Tatto et al. (2008) and Tatto (2013).

  • 2. In statistical modeling, regression analysis is a statistical technique to assess the relationships among two or more independent variables (or “predictors,” in this case programs opportunities to learn) and their correlation with a dependent variable (in this case beliefs) and other mediating factors (in this case knowledge: mathematical content knowledge, or MCK, and mathematical pedagogical content knowledge, or MPCK).

  • 3. Weighted Least Squares (WLS) in the regression procedure is a weight that is used to correct for unequal variability or precision in observations, with weights inversely proportional to the relative variability of the data points. The full rationale and procedures used in calculating the weights and in doing the overall analysis is explained in detail in Rodriguez, Tatto, Palma, and Nickodem (2018).