The relationship between opportunities to learn in teacher education and Chinese preservice teachers’ professional competence

ABSTRACT

Although research on the relationship between opportunities to learn (OTL) in teacher preparation and preservice teachers’ learning outcomes, including aspects of their knowledge, has significantly increased in recent years, the relationship between OTL and preservice secondary school teachers’ cognitive competence and, particularly, the situated aspect of competence, in Mainland China remain poorly understood. This paper examines this association based on a study involving 583 preservice teachers chosen from four preservice teacher education institutions. The results revealed that the preservice teachers received adequate OTL in various domains, such as tertiary-level mathematics and mathematics education pedagogy. However, mainly due to the influence of academically oriented teacher preparation models in Mainland China, there were quite weak overall connections between OTL and the four examined aspects of teachers’ professional competence (mathematics content knowledge, mathematics pedagogical content knowledge, a mathematics instruction-related perspective on noticing, and a general pedagogy-related classroom perspective on noticing). Comparatively speaking, relatively strong associations existed between OTL in teaching methods, school-based teaching practicums, and the situated aspect of competence (e.g. noticing). These findings show that, to a great degree, initial teacher preparation in Mainland China does not relate closely to preservice teachers’ professional competence.

KEYWORDS:

• Mathematics content knowledge
• mathematics pedagogical knowledge
• noticing
• preservice secondary school teachers

1. Introduction

Due to the consistently outstanding achievement of East Asian students in mathematics and science identified in large-scale international studies, such as Trends in International Mathematics and Science Study (TIMSS) and Programme for International Student Assessment (PISA), in recent decades, countries within such area such as China have been named as the high-performing education systems in the literature (Deng & Gopinathan, 2016). Researchers have therefore made tremendous efforts to investigate the possible factors, such as culture, language, curriculum, and teaching practices, that may influence Chinese students’ high achievements (Leung, 2017). It is assumed that the factor that has the greatest direct influence on students’ learning is teacher quality, particularly teachers’ professional competencies, such as their subject content knowledge (SCK) and pedagogical content knowledge (PCK), because teachers with strong professional competencies are expected to positively influence students’ learning outcomes. Indeed, previous cross-cultural comparative studies have identified large differences between the SCK and PCK levels of preservice and in-service teachers in East Asian and Western countries (e.g. Blömeke et al., 2014; Kleickmann et al., 2015; Ma, 1999).

Therefore, it seemed appropriate to systematically investigate how East Asian mathematics teachers acquired and developed their professional competencies. Several previous studies have investigated teachers’ professional development at both preservice and in-service stages of teaching in East Asian contexts, including China (e.g. Li & Huang, 2018; Li, Zhao et al., 2008). However, these studies have focused mainly on the acquisition and development of teachers’ individual knowledge, such as their SCK and PCK, which reflects the cognitive aspect of teachers’ professional competencies. Professional knowledge has been described as ‘more distal’ (Charalambous, 2020, p. 221) to teachers’ teaching practices. That is, decontextualized knowledge, such as SCK and PCK, does not simply and directly transform into teaching practices (Blömeke et al., 2015). Other, more situation-specific and proximal cognitive skills related to complex classroom situations, such as noticing skills, have been deemed to extend teachers’ competence (Kaiser et al., 2017). Currently, combined cognitive and situated approaches have become the dominant approaches for conceptualizing teachers’ competencies in teacher education research (Depaepe et al., 2020). Therefore, it is necessary to investigate the effectiveness of teacher education programmes in facilitating the situation-specific aspects of teachers’ competencies.

Teachers’ professional competencies, including knowledge and teacher noticing, are situationally and culturally determined (Blömeke et al., 2017; Louie, 2018). Indeed, it has been argued that teacher education is embedded in a sociocultural context that makes ‘certain assumptions about which knowledge, skills, and affective-motivational attributes are needed to succeed as a teacher’ (Blömeke et al., 2017, p. 796). Within the East Asian context in general, and the Chinese context in particular, teachers are generally expected to have a profound knowledge of the subjects they need to teach (Hsieh et al., 2018; Kim & Ham, 2017; Paine, 1990). In other words, a teacher should first become ‘an expert or a learned figure (a scholar)’ (Leung, 2001, p. 45) in the subject before assuming the role of teacher. Due to the influence of this tradition, academically oriented teacher preparation programmes, which emphasize the acquisition of subject-matter knowledge but with less focus on practice-related skills, are the dominant model of teacher education in this context (Liao & Hu, 2017; Paine, 1990). We therefore expected that this tradition would provide different opportunities to learn (OTL) to enable preservice teachers to develop their professional competencies.

Evaluating the effectiveness of teacher preparation programmes by investigating the OTL of preservice teachers during the initial teacher training stage has become a prominent topic in teacher education research (Blömeke et al., 2014). In particular, regarding mathematics education, OTL has been included as a main variable in the Teacher Education and Development Study in Mathematics (TEDS-M)—the largest international study on teacher education—conducted under the auspices of the International Association for the Evaluation of Educational Achievement (IEA). Examinations of the relationship between OTL and various types of preservice mathematics teachers’ knowledge have provided empirical evidence of the effectiveness of initial teacher education. However, the findings of these studies have been inconsistent across different contexts and cultures.

Furthermore, some researchers have investigated the relationship between OTL and preservice teachers’ knowledge in Singapore and Taiwan (because they both participated in TEDS-M; Wang & Tang, 2013) or at the primary school level in mainland China (e.g. Youngs & Qian, 2013). However, so far, the relationship between OTL and preservice teachers’ professional competencies, including the cognitive and situated aspects of competencies in Mainland China at the secondary school level, remains largely unknown. In light of this situation, we conducted the current study to systematically investigate the relationship between preservice mathematics teachers’ OTL and their professional competencies, including their professional knowledge and noticing, with the main aim of understanding teacher education effectiveness within the sociocultural context of Mainland China.

2. Literature review and theoretical framework

As the current study refers strongly to the international comparative study on teacher education TEDS-M, our own theoretical framework is described within the literature review.

2.1. Mathematics teachers’ professional competence

Research on teachers’ professional competence has increased in recent decades, especially in the field of mathematics education. Teachers’ professional competence has been widely investigated as both an explanatory or independent variable and as a dependent variable in previous empirical studies (Kaiser & König, 2019) as the basis for proposing various frameworks for the construct of teachers’ professional competencies. It has been widely accepted that teachers’ professional competence is a multidimensional construct that includes cognitive factors, such as various facets of knowledge, and affective factors, such as various beliefs (Weinert, 2001).

In terms of the cognitive aspects of teachers’ professional competence, SCK and PCK have been commonly proposed by researchers as the main components of teachers’ competence based on the teacher knowledge classifications developed by Shulman (1986). Similarly, the theoretical framework that underpins TEDS-M includes three facets of knowledge: mathematics content knowledge (MCK), mathematics pedagogical content knowledge (MPCK), and general pedagogical knowledge (GPK) (Blömeke & Kaiser, 2014; Tatto et al., 2008). In the current study, we specifically investigated MCK and MPCK as cognitive aspects of teachers’ professional competence to evaluate the effectiveness of initial teacher preparation in Mainland China.

According to Shulman (1986), content knowledge mainly refers to teachers’ knowledge of the subject matter they need to teach and its organization. In TEDS-M, MCK was conceptualized as basic factual knowledge about various content domains of mathematics, such as numbers, algebra, geometry, and data, as well as conceptual knowledge of mathematics structures and organizing principles (Blömeke & Delaney, 2012). PCK, however, mainly refers to subject-specific knowledge for teaching, which helps teachers make subject matter more accessible to students (Shulman, 1986). In TEDS-M, two categories of MPCK were investigated: knowledge of curricula and planning for mathematics teaching and learning, and knowledge of how to enact mathematics for teaching and learning (Tatto et al., 2008).

However, more recently, Blömeke et al. (2015) argued that such decontextualized knowledge (i.e. SCK and PCK) cannot be simply and directly transformed into effective teaching practices. Instead, the relationships between the cognitive aspects of teachers’ professional competence and complex classroom teaching practices should be mediated by other, more context-specific or situation-specific skills (Kaiser et al., 2017; Depaepe et al., 2020). Therefore, situational skills, such as teacher noticing, have been proposed by researchers to extend the framework of teachers’ professional competence and have been included in the German follow-up study of TEDS-M, the TEDS-FU study (Kaiser & König, 2019). Blömeke et al. (2015), in a widely quoted paper, conceptualized the construct of teachers’ professional competence as a continuum (see Figure 1) with situation-specific mediators between dispositions, such as knowledge, and situated performance in the classroom. Therefore, cognition and situation-specific skills should be investigated simultaneously to gain a more comprehensive understanding of teachers’ professional competence.

Figure 1. Modeling competence as a continuum (Blömeke et al., 2015, p. 7).

In the model by Blömeke et al. (2015), the situation-specific components of teachers’ professional competence were described with reference to the discourse on noticing (e.g. Jacobs et al., 2010; Sherin et al., 2011); thus, situation-specific skills were conceptualized as consisting of three facets of teacher noticing, namely perception, interpretation, and decision-making (PID) (Kaiser et al., 2015, 2017). Similar to other influential definitions in the field, the PID model of teacher noticing mainly includes: 1) perceiving particular events within a specific complex teaching setting, 2) interpreting the perceived activities within such a setting, and 3) decision-making, which can take the form of anticipating responses to students’ activities or proposing alternative instructional strategies (Kaiser et al., 2015, 2017). In addition, in TEDS-FU, the PID noticing facet was further differentiated into two perspectives: a mathematics instruction-related perspective (M_PID) and a general pedagogy-related classroom perspective (P_PID).

2.2. OTL in teacher preparation

OTL have been examined in various educational contexts for several decades. Originally, OTL was used as a main indicator to investigate students’ learning; for example, it was conceptualized as the degree to which a student had OTL regarding the specific content of a course in the First International Mathematics Survey conducted by the IEA (McDonnell, 1995). However, the investigation of OTL has recently become an increasingly hot topic in teacher education. Researchers across the world have employed OTL as the main means to investigate the effectiveness of initial teacher preparation programmes and establish connections between OTL and preservice teachers’ SCK, PCK, and/or GPK in the fields of language education and preschool education (e.g. Blömeke et al., 2017; König, Tachtsoglou et al., 2017). In particular, OTL has been even more widely investigated in the mathematics teacher education field since it was a main variable included in TEDS-M.

Although the measures of OTL in previous studies varied, most of the studies defined OTL as ‘the content to which future teachers are exposed as a part of their teacher preparation’ (Schmidt et al., 2011, p. 140). That is, OTL mainly refers to the content coverage of the intended curriculum for a specific initial teacher preparation programme. Normally, subject-specific content-related courses, subject-specific pedagogical courses, general pedagogy and psychology courses, and teaching practice experience are included to investigate OTL during the initial teacher preparation period (Blömeke et al., 2014; Kaiser & König, 2019). However, researchers have also argued that teacher educators do not always implement the curriculum uniformly, and that how teacher educators teach courses certainly influences preservice teachers’ learning (Kavanagh & Rainey, 2017). What actually occurs in these courses during the teacher preparation period, and the quality of teaching methods experienced by preservice teachers, should be considered when investigating the effectiveness of initial teacher preparation (Blömeke, 2012). Both the coverage of content and pedagogy should be included to provide a more complete picture of OTL in a specific teacher preparation context (Cohen & Berlin, 2020).

It has also been clearly pointed out in the literature that OTL ‘may be influenced by cultural characteristics’ (Blömeke, 2012, p. 686) within a specific context. That is, OTL reflects certain beliefs about teaching and the role of the teacher in the context. Indeed, in previous studies, such as TEDS-M, a wide variety of teacher education curricula were identified in East Asian and Western contexts (Blömeke, 2012; Wang & Tang, 2013). Generally speaking, previous studies have reported that preservice teachers in East Asian contexts learn more about tertiary-level mathematics, while their Western counterparts learn more about general education.

In Mainland China, teacher education curricula focus greatly on the learning of SCK at the tertiary level but less on subject-specific pedagogical knowledge and general pedagogy (Li, Huang et al., 2008; Wu & Huang, 2018). Due to the influence of the former Soviet Union, mathematics teacher education in Mainland China ‘was heavily influenced by Russian mathematics philosophy, mathematics curriculum, and pedagogy of mathematics’ (Li, Huang et al., 2008, p. 67), with an emphasis on the abstractness, rigorousness, and reduction of formal mathematical operations. Due to this tradition, preservice mathematics teacher education in Mainland China has tended to be academically oriented, with most preservice teachers’ credit hours or time being devoted to the study of their major academic discipline (Liao & Hu, 2017; Paine, 1990; Wu & Huang, 2018). Therefore, we expected preservice teachers in Mainland China to have more OTL for subject-matter-related courses, but with limited OTL for pedagogical preparation (Liao & Hu, 2017; Paine, 1990). However, very little empirical evidence is available in Mainland China for preservice teachers’ self-reported OTL because most previous studies have analysed intended curricula, such as the course syllabi or course requirements for initial teacher preparation, which only reflect ‘desired learning opportunities’ (Cohen & Berlin, 2020, p. 3).

2.3. The relationship between OTL and preservice teachers’ professional competence

The discussion of how preservice teachers’ overall university learning experiences influence their learning outcomes has attracted researchers’ interest in teacher education in recent years (e.g. Wasserman et al., 2023). In previous studies, a common finding was the disconnection between theoretical university courses and real practice in schools or the discontinuity between university mathematics and the reality of school mathematics practices (Brouwer & Korthagen, 2005; Klein, 1932/2016). More recently, researchers have tried to empirically investigate the relationship between preservice teachers’ self-reported OTL and the cognitive aspects of their professional competence, such as PCK and GPK, in various fields, such as language education, preschool education, and mathematics education (Blömeke et al., 2017, König, Tachtsoglou et al., 2017; Schmidt et al., 2011).

Based on a large number of participants, researchers have quantitatively analysed the relationship between OTL and preservice teachers’ professional competence. They have shown that various types of OTL influence preservice teachers’ professional competence quite differently. Compared with specific content or pedagogical courses, teaching practice in schools acts as a relatively stronger predictor of preservice teachers’ competence. For example, König, Bremerich-Vos et al. (2017) found that for preservice language teachers in Germany, only teaching practice experience in schools could significantly and positively predict their lesson planning competence. In contrast, learning experiences focusing on subject matter, subject-specific didactics, and general pedagogy only weakly or even negatively predicted preservice teachers’ lesson planning competence. Similarly, the authors found that teaching practice in schools was strongly related to preservice language teachers’ GPK and PCK (König, Ligtvoet et al., 2017; König, Tachtsoglou et al., 2017).

In mathematics education, there is a long tradition of examining how university mathematics courses influence preservice mathematics teachers’ learning and their school teaching practices. Roughly a century ago, Klein (1932/2016) pointed out the problem of the ‘double discontinuity’ between school mathematics and university mathematics for preservice mathematics teacher education, describing the disconnect between the mathematics preservice teachers learned in school and the university-level mathematics taught to preservice teachers within teacher education. This missing connection between school and university mathematics meant that preservice teachers relied on their school knowledge during their teaching practice in schools and hardly used university-level mathematics. Many researchers in mathematics education have investigated this problem with the aim of strengthening the relationship between university and school mathematics. For example, Leikin et al. (2018) found that research mathematicians who also worked as teacher educators greatly emphasized the importance of robust mathematical knowledge. In their courses, they mainly focused on expanding preservice mathematics teachers’ mathematical knowledge and the meta-mathematical aspects of mathematics, such as proof and the rigorous and accurate use of mathematical terminology. Similarly, Hoffmann and Even (2023) found that the mathematicians in their study considered knowledge about the discipline of mathematics highly important but did not attempt to teach preservice mathematics teachers how to integrate such knowledge into their future classroom teaching. Many other studies have found that the emphasis on tertiary mathematics may improve preservice mathematics teachers’ understanding of mathematics but not necessarily support them in reconceptualizing relevant school mathematics topics (Liang et al., 2023; Wasserman et al., 2023).

In addition, regarding mathematics education, previous researchers have analysed the associations between OTL and preservice mathematics teachers’ knowledge. For example, Schmidt et al. (2011) found that in those places where preservice lower secondary school mathematics teachers performed well in TEDS-M, around half of the courses were allocated to mathematics. However, the connections between OTL and MCK scores were not always direct or clear-cut. For example, based on TEDS-M data, Qian and Youngs (2016) found that the coefficients for the number of mathematics content courses taken by preservice primary school teachers and their MCK scores were only statistically significant for Taiwan and Switzerland, but not for Singapore, Spain, or the United States. Similarly, Blömeke et al. (2017) did not identify significant relationships between OTL in mathematics and preservice preschool teachers’ MCK, but they found significant relationships between OTL, MPCK, and GPK.

For MPCK, Blömeke et al. (2017) found that OTL in mathematics pedagogy was quite strongly related to MPCK but not to OTL in mathematics. Similarly, Youngs and Qian (2013) found that the overall number of university-level mathematics courses taken had little impact on preservice primary school mathematics teachers’ mathematical knowledge of teaching in Mainland China. In contrast, they identified a significant relationship between the number of topics in mathematics pedagogical methods courses and preservice teachers’ mathematical knowledge for teaching but not for the length of teaching practice in schools. Torbeyns et al. (2020) found that theoretical courses on PCK in mathematics methods courses played a pivotal role in the development of preservice preschool teachers’ MPCK.

In terms of the relationship between OTL and preservice teachers’ professional competence, most of the currently available studies have investigated the relationship in Western contexts (e.g. König, Bremerich-Vos et al., 2017) or at the primary school or preschool level (e.g. Blömeke et al., 2017; Youngs & Qian, 2013). In addition, most studies have focused on a single specific facet of the cognitive component of competence, such as GPK or PCK, despite it being clear that ‘it is important to address the different facets of teacher competence’ (Torbeyns et al., 2020, p. 277). Moreover, to date, very few studies have explored the relationship between OTL and situation-specific skills as further components of teachers’ competence.

3. Methodology

3.1. Research context and participants of the study

In Mainland China, preservice teachers at the secondary school level are mostly educated in a specific type of university (normal university) over four years. There are six normal universities under the direct control of the Ministry of Education of China (national-level normal universities). These six universities normally receive relatively strong support from the Ministry of Education of China and admit candidates with strong academic backgrounds. Therefore, it has been generally assumed that the quality of preservice training in these six universities is quite high (Wu et al., 2017). In addition, there is usually one normal university in each province (province-level normal university) and a local normal college or university for each district within a province (local-level normal university). Normally, support for normal universities at the province and local levels is relatively weaker, and they admit candidates with relatively less strong academic backgrounds. However, the curricular structure, such as the number of courses, is quite similar in all normal universities because of the centralized system of teacher education in Mainland China.

Currently, secondary school teacher programmes in Mainland China are dominated by a concurrent curriculum model of teacher preparation that is still specialized and discipline-based. That is, the majority of preservice teachers at the secondary school level are educated in departments for specific academic subjects, where the studies of specific disciplines and pedagogy are integrated and taught at the same time over four years (Musset, 2010). Normally, the first two years of preservice education in university focus on the learning of subject content at the tertiary level and general education content. In the third year, some subject-related educational courses are offered but only occupy a very small portion of teaching time (providing around 10–30% of the total credits; Wu & Huang, 2018). In addition, preservice teachers are currently required to participate in one-semester teaching practicums in schools within their preservice education period. Experienced teachers majoring in the same subject who work in the schools are assigned as school supervisors to mentor one or two preservice teachers each and support them in acquiring teaching-related skills. Simultaneously, teacher educators at the university level provide supervision during the school-based teaching practicum period.

We selected 583 preservice secondary school mathematics teachers at the end of their initial teacher education (i.e. in Year 4) in Mainland China to participate in this study, which aligned with the selection criterion for participation in TEDS-M. Of these 583 teachers, 432 were chosen from one national-level normal university, 99 were chosen from two province-level normal universities, and 52 were from one local normal university. All participants had already completed approximately one semester (18 weeks) of teaching practicums in schools. Roughly 40% of them had completed their teaching practicums in junior secondary schools (Grades 7–9), while the others did so in senior secondary schools (Grades 10–12).

3.2. Instruments

3.2.1. MCK and MPCK

We used the instruments developed for TEDS-M to measure preservice secondary school mathematics teachers’ MCK and MPCK and to examine the cognitive aspects of their professional competence. Based on agreement with the IEA, we directly employed the Chinese version of the instruments used in Taiwan, with only slight modifications to make a few expressions closer to current language usage in Mainland China (Tatto et al., 2008). After these slight modifications, the whole instrument was further checked by two mathematics education professors with expertise in mathematics educational assessment and two experienced secondary school mathematics teachers in Mainland China. Modifications were made before the instruments were finalized.

In total, the instruments comprised 103 items, 76 of which were MCK items and 27 were MPCK items. In TEDS-M, these items were allocated to three booklets with a balanced-incomplete-block design to capture adequate domain coverage of teachers’ knowledge within a reasonable administration time (Blömeke et al., 2014; Tatto et al., 2008). The items for assessing MCK covered four content areas (numbers, geometry, algebra, and data) and were further classified into three cognitive dimensions (knowing, applying, and reasoning). The MPCK items included aspects of curricular and planning knowledge and knowledge about how to enact mathematics in the classroom. The majority of the items in both the MCK and MPCK tests were complex multiple choice items with a few open-response items. The participants were given 60 minutes to complete both the MCK and MPCK tests in paper-and-pencil format. Item examples can be found in Blömeke et al. (2014).

3.2.2. Noticing

The instruments we used to examine preservice mathematics teachers’ professional noticing skills were adapted from the instruments originally designed for the TEDS-M follow-up studies (TEDS-FU and TEDS-Instruct/Validate; for detailed information on the adaptation and validation process, see Yang et al., 2018, 2019). For TEDS-FU and TEDS-Instruct/Validate, three video vignettes were developed to assess German secondary school mathematics teachers’ professional noticing. The video assessment consisted of items for examining two perspectives on teacher noticing: 1) mathematics instruction-related noticing (labelled as M_PID) and 2) general pedagogical noticing (labelled as P_PID). The items focused on the three facets of noticing distinguished in TEDS-FU: perception, interpretation, and decision-making. All items required teachers to notice the entire process of mathematics classroom teaching and almost all aspects of a mathematics lesson.

The three video vignettes were based on scripted plots, which included critical incidents of typical mathematics teaching that reflected different teaching phases in a mathematics lesson. The content of the three videos included typical teaching topics in secondary school mathematics, such as functions, volumes, and surfaces of geometrical solids. Each video vignette lasted around three to four minutes. In addition, detailed background information, such as information about the class and lessons, was given to help the participants gain a more comprehensive understanding of the exhibited teaching.

After the participants watched each of the three videos, they were given around 15 minutes to answer a few items related to each video (not exceeding 60 minutes for all three videos). There were two types of items for this exercise: 1) 38 items (22 P_PID and 16 M_PID) based on Likert scales (four choices from ‘fully correct’ to ‘not correct’) to assess the participants’ noticing (mainly related to the perception facet), and 2) 36 constructed-response items (18 P_PID and 18 M_PID) to assess the participants’ noticing regarding the interpretation and decision-making facets. In addition, an extensive coding manual was developed to evaluate the participants’ answers. Item examples can be found in Kaiser et al. (2015). Although the instrument was originally developed for in-service teachers, a further study showed that it could also be used for preservice teachers (Weyers et al., 2023).

3.2.3. OTL

We adapted five scales of the instruments developed for TEDS-M to survey preservice mathematics teachers’ OTL, which included tertiary-level mathematics, school-level mathematics, mathematics education pedagogy, teaching methods, and school-based teaching practicum experience (see Table 1 for detailed information). The 19 items on the scale for OTL in tertiary-level mathematics were further classified into three groups based on classifications proposed in a previous study: advanced university mathematics, advanced secondary mathematics, and fundamental mathematics (Wang & Tang, 2013). Items classified as advanced university mathematics mainly referred to courses that had precursors or were taught in Year 3 or Year 4 in Mainland China.

Table 1. Basic information regarding the study’s dependent variables.

Scale	Variable	Item Example	Number of Items	Scale Reliability
Tertiary-level mathematics	Advanced secondary mathematics	Number theory Axiomatic geometry Probability	5	.85
	Fundamental mathematics	Mathematics logic Differential equations Calculus	7	.90
	Advanced university mathematics	Abstract algebraReal analysisNon-Euclidean geometry	7	.82
School-level mathematics	Basic school-level mathematics	Numbers Geometry Measurement	4	.90
	Advanced mathematics thinking	Calculus Functions and equations	3	.92
Mathematics Education Pedagogy	Foundation	Foundation of mathematics Development of mathematical ability and thinking	3	.67
	Instruction	Mathematics instruction Developing teaching plans	5	.83
Teaching Methods	Lecturing	Listen to s lecture	1
	Class participating	Discuss in class Make a presentation in class Group study in class	4	.75
	Research-based learning	Read research papers about mathematics Analyze videos of mathematics instruction	4	.85
	Problem-solving	Solve mathematics problem with ICT Write mathematics proofs	4	.78
School-Based Teaching Practicum	Connecting theories with practice	Observe models of the teaching strategies you learned on your course.	7	.87
	Reinforcement of university goals	Use the ideas and thoughts you learned on your course and discuss your teaching.	6	.64
	Feedback quality	Use feedback from your internship instructor to improve your teaching methods.	5	.91

OTL in school-level mathematics in TEDS-M was assessed using seven items referring to typical mathematics content areas, such as numbers or calculus, at the school level. According to the classification suggested by Wang and Tang (2013), in the present study, these seven items were further classified into two subgroups. The first subgroup was labelled basic school-level mathematics topics, mainly including items such as numbers, measurement, and geometry, which are taught at the junior secondary school level in Mainland China. The second subgroup was labelled advanced mathematics thinking and included calculus, functions, and equations, which are mainly taught at the senior secondary school level in Mainland China.

In TEDS-M, OTL in mathematics pedagogy was investigated through a few items related to domains such as the foundations of mathematics instruction, the development of mathematics ability and thinking, the instructional applications of mathematics, and the development of mathematics teaching plans. We selected seven items for this study, which we further classified into two subgroups: foundation and instruction. In addition, teaching methods related to mathematics pedagogy were further investigated in TEDS-M. In total, we used 13 items in this study, which referred to four types of teaching methods: lecturing, class participation, research-based learning, and problem solving. Lecturing (1 item) referred to listening to lectures, class participation referred to participating in activities such as group discussions and presentations, research-based learning referred to activities such as reading mathematics education research reports or analysing teaching cases, and problem-solving referred to writing proofs or using multiple strategies to solve problems.

OTL in school-based teaching practicum referred to experiences in schools where preservice teachers completed their teaching practicums. In this study, we included three aspects of teaching practicums in schools: connecting theories with practice, reinforcement of university goals, and feedback quality.

Items used in the first three scales required each preservice mathematics teacher to indicate whether they had OTL for a specific topic (with ‘yes’ coded as 1 and ‘no’ coded as 0) during their preservice teaching training periods. However, items used in the last two scales required the participants to indicate on a four-point scale the frequency of a specific activity (never = 1, rarely = 2, occasionally = 3, and often = 4) or their agreement with a statement (do not agree = 1, somewhat disagree = 2, somewhat agree = 3, and agree = 4). In total, we used 67 items from the original TEDS-M instruments and further modified them according to the teaching tradition and reality in Mainland China. The internal consistency of each subgroup of each scale was estimated using Cronbach’s alpha reliability coefficient, which ranged from .64 to .92.

3.2.4. Scaling and data analysis

The data analysis comprised the following steps: First, the open-response items for MCK, MPCK, and noticing were coded according to the coding rubrics of the coding manual developed for TEDS-M and TEDS-FU. Four trained postgraduate students in mathematics education worked as independent raters and first coded 80 of the questionnaires together. Good Cohen’s kappa values were obtained (k > 0.78 and K _average = 0.86). For all the open-response items, items without answers or with incorrect answers were scored as 0, and correct answers were scored as 1. After the completion of coding, the relative item difficulties for a one-parameter (Rasch model) item response theory (IRT) model were calculated separately for MCK, MPCK, P_PID, and M_PID. Items with extreme difficulty were excluded from the final analysis because they did not substantially contribute to the measurement of the relevant construct (Bond & Fox, 2007).

Thereafter, we estimated the internal consistency of the remaining items for each of the four constructs related to professional competencies using Cronbach’s alpha reliability coefficients, which ranged from .78 to .86. After this, a multigroup graded response model was applied to the four components of professional competence. The calibration of the a-parameters (item discriminations) and b-parameters (item difficulties) was conducted on the basis of two preservice mathematics teacher groups (concurrent calibration). Thus, the item parameters were constrained to be equal across all groups, ensuring the same metrics for the groups. Then, the person parameters (maximum likelihood estimates) were computed by transforming the person parameters of the four constructs into a scale with an average score of 500 and a standard deviation of 100.

Then, a series of T-tests were performed separately to examine differences in various aspects of OTL and the four components of professional competence between preservice teachers trained in different types of institutes in Mainland China. Finally, simple correlation and multiple regression analyses were conducted to explore the associations between OTL and each aspect of the four competence components.

4. Results

4.1. Descriptive analysis

The overall OTL reported by preservice mathematics teachers attending the two levels of universities are presented in Table 2, which shows that for OTL in tertiary mathematics, the mean proportions reported by the participants ranged from 0.77 to 0.92, indicating that they had quite adequate OTL in university mathematics. However, clear differences existed between national-level and provincial/local-level normal universities in terms of the learning of university mathematics. National-level normal universities emphasize advanced-level mathematics; in contrast, provincial/local-level normal universities emphasize foundation-level mathematics.

Table 2. Basic statistics for the study variables (mean, standard deviation, and t-test results).

	National-level normal university		Provincial/local-level normal university
	Mean	SE	Mean	SE	$\mathit{t}$	$\mathit{p}$
Tertiary-Level Mathematics
Advanced secondary mathematics	0.89	0.007	0.93	0.010	−3.77	.000
Fundamental mathematics	0.83	0.006	0.92	0.008	−7.89	.000
Advanced university mathematics	0.84	0.007	0.77	0.013	4.43	.000
School-Level Mathematics
Basic school-level mathematics	0.89	0.009	0.91	0.014	−0.97	.309
Advanced mathematics thinking	0.96	0.006	0.94	0.011	1.45	.149
Mathematics Education Pedagogy
Foundation	0.77	0.012	0.75	0.020	0.77	.440
Instruction	0.85	0.009	0.85	0.017	−0.04	.967
Teaching Methods
Lecturing	3.87	0.019	3.79	0.041	1.83	.068
Class participation	2.73	0.028	2.62	0.048	2.00	.046
Research-based learning	2.72	0.033	2.55	0.056	2.56	.011
Problem-solving	3.10	0.029	3.15	0.048	−0.84	.397
School Teaching Experience
Connecting theories with practice	2.92	0.029	2.87	0.057	0.88	.378
Reinforcement of university goals	2.95	0.020	2.87	0.042	1.64	.103
Feedback quality	3.87	0.015	3.82	0.031	1.41	.161
	Mean	SD	Mean	SD	t	p
Knowledge
MCK	526.29	91.82	424.79	83.00	12.00	.000
MPCK	511.87	98.22	466.05	97.54	4.94	.000
Noticing
M_PID	510.68	102.33	469.44	86.26	4.81	.000
P_PID	509.40	101.96	473.10	89.13	4.15	.000

For OTL in school mathematics, the mean proportions reported by the participants ranged from 0.89 to 0.96, implying that they had plenty of OTL in secondary school mathematics during initial teacher preparation. For OTL in mathematics education pedagogy, the average proportions reported by the participants ranged from 0.75 to 0.85. Relatively speaking, the proportions were slightly lower than the mean proportions for OTL in the other two mathematics-related domains. In addition, no significant differences were identified between the two levels of normal universities.

For OTL in teaching methods, as shown in Table 2, the participants reported that they frequently listened to lectures (with high means of 3.87 and 3.79) and solved problems but were less frequently involved in classroom-related activities, such as presentations and working in groups, and research-based learning. Preservice mathematics teachers attending provincial/local-level normal universities reported that they have even less of such opportunities.

For OTL in school-based teaching practicums, participants attending both levels of universities reported that the feedback they received from school supervisors largely helped them improve their understanding of the curriculum or teaching methods. Relatively speaking, the participants reported that they did not have adequate opportunities to connect the theories learned in university with school practices, and that their teaching practicums in schools did not enhance their overall understanding of what they learned in universities.

The overall preservice teachers’ MCK, MPCK, P_PID, and M_PID for participants attending the two levels of universities are presented in Table 2. The overall means of the two groups were combined and transformed into 500 test points, with a standard deviation of 100. As Table 2 indicates, participants attending provincial/local-level normal universities demonstrated much weaker performance, especially regarding MCK and MPCK, although it is interesting that their achievement in MPCK was lower than that in their MCK.

4.2. Correlation analysis

To examine how each of the subdomains of OTL was related to each aspect of preservice mathematics teachers’ professional competence, we estimated Pearson’s r based on the estimated scores for MCK, MPCK, P_PID, and M_PID and the means for each OTL subdomain. Table 3 summarizes the results.

Table 3. Correlation results for comparisons between each OTL variable and professional competence.

	Knowledge		Noticing
	MCK	MPCK	M_PID	G_PID
Tertiary-Level Mathematics
Advanced secondary mathematics	−.078	−.107**	−.049	−.034
Fundamental mathematics	−.106**	−.004	−.012	.017
Advanced university mathematics	.136***	.132***	.088*	.089*
School-Level Mathematics
Basic school-level mathematics	−.081	−.027	−.031	−.027
Advanced mathematical thinking	.091*	.055	.051	.043
Mathematics Education pedagogy
Foundation	−.055	.028	−.049	−.049
Instruction	−.112**	.018	.066	.054
Teaching Method
Listen to a lecture	.015	.060	.100*	.072
Class participation	.014	.028	.149***	.148***
Research-based learning	.030	.070	.112**	.115**
Problem-solving	.012	.023	.066	.084*
School-Based Experience
Connecting theories to practice	.018	.058	.127**	.113**
Reinforcement of university goals for practicums	−.012	−.007	.128**	.117**
Feedback quality	.007	.072	.186***	.197***

${\mathit{\hspace{0.17em}}}^{\ast }\mathit{p}<.05;{\mathit{\hspace{0.17em}}}^{\ast \ast }\mathit{p}<.01;{\mathit{\hspace{0.17em}}}^{\ast \ast \ast }\mathit{p}<.001$.

As illustrated in Table 3, the overall relationships between the 13 subdomains of OTL and the four components of teachers’ professional competence were all quite weak, suggesting that the overall relationships between OTL and preservice mathematics teachers’ professional competencies in Mainland China are also quite weak. More specifically, for OTL in tertiary-level mathematics, only OTL related to advanced university mathematics was positively associated with the four competence constructs. Extremely weak associations were identified between OTL in school-level mathematics and mathematics education pedagogy and the four competence components.

Although the relationships between OTL in teaching methods and school-based teaching practicum experience and MCK and MPCK were quite weak, the relationships between OTL in these two fields and M_PID and P_PID were relatively stronger. Such a pattern of findings may imply that more practice-related experiences, such as preservice teachers’ experiences in mathematics education pedagogy courses and school-based teaching practicums, would enhance the development of their situation-specific components of competence, such as M_PID and P_PID.

4.3. Regression analysis

To further examine the relationship between OTL and preservice mathematics teachers’ professional competencies, we conducted a series of multiple regression analyses for each of the four competence components (MCK, MPCK, M_PID, and P_PID) to determine the joint influence of all the subdomain of OTL. To identify which OTL subdomain contributed significantly to multiple correlations, we examined standardized regression coefficients (β), and Table 4 summarizes the findings.

Table 4. Multiple regression analyses for associations between OTL and professional competence.

	Knowledge		Noticing
	MCK	MPCK	M_PID	P_PID
OTL Category	$\mathit{\beta }\left(\mathit{SE}\right)$	$\mathit{\beta }\left(\mathit{SE}\right)$	$\mathit{\beta }\left(\mathit{SE}\right)$	$\mathit{\beta }\left(\mathit{SE}\right)$
Tertiary-Level Mathematics
Advanced secondary mathematics	−0.080(3.160)	−0.180***(3.000)	−0.063(3.144)	−0.057(3.153)
Fundamental nonteaching mathematics	−0.112*(3.795)	0.009(3.840)	−0.009(3.776)	0.022(3.787)
Advanced university mathematics	0.194***(2.851)	0.170***(2.886)	0.090**(2.837)	0.081(2.846)
School-Level Mathematics
Basic school-level mathematics	−0.078(2.435)	−0.024(2.464)	−0.073(2.423)	−0.067(2.430)
Advanced mathematics thinking	0.106*(3.300)	0.038(3.337)	0.051(3.281)	0.037(3.290)
Mathematics Education Pedagogy
Foundation	−0.023(1.849)	0.028(1.871)	−0.122*(1.839)	−0.124*(1.845)
Instruction	−0.110*(2.435)	−0.005(2.464)	0.078(2.423)	0.058(2.430)
Teaching Method
Lecturing	0.022(1.003)	0.048(1.015)	0.056(1.000)	0.027(1.000)
Class participation	−0.007(0.922)	−0.029(0.933)	0.104(0.918)	0.108*(0.920)
Research-based learning	0.033(0.772)	0.047(0.781)	0.012(0.768)	0.020(0.770)
Problem-solving	0.041(0.812)	0.001(0.822)	−0.024(0.808)	0.011(0.810)
School-Based Experience
Connecting theories with practice	0.014(0.823)	0.030(0.833)	0.013(0.819)	-0.007(0.821)
Reinforcement of university goals	−0.024(1.041)	−0.044(1.054)	0.061(1.036)	0.046(1.039)
Feedback quality	−0.014(1.271)	0.041(1.286)	0.146***(1.265)	0.161***(1.268)

Note: ${\mathit{\hspace{0.17em}}}^{\ast }\mathit{p}<.05;{\mathit{\hspace{0.17em}}}^{\ast \ast }\mathit{p}<.01;{\mathit{\hspace{0.17em}}}^{\ast \ast \ast }\mathit{p}<.001$.

As shown in Table 4, similar to the correlation analysis findings, the regression weights (β) indicated that only OTL in advanced university mathematics positively and significantly predicted the two knowledge components MCK and MPCK. For the other OTL-related variables, they either negatively or extremely weakly predicted MCK and MPCK. In addition, the regression weights (β) further indicated that most OTL in tertiary-level mathematics, school-level mathematics, and mathematics pedagogy did not positively or significantly predict P_PID and M_PID. Only OTL in advanced university-level mathematics, advanced mathematics thinking, and feedback quality positively and significantly predicted P_PID and M_PID. Notably, the regression analysis findings again showed that almost all OTL in teaching methods and school-based teaching practicums positively predicted P_PID and M_PID.

5. Discussion

The aim of the present study was to investigate the relationship between preservice mathematics teachers’ self-reported OTL and the cognitive and situation-specific components of their professional competence according to their attendance at four preservice teacher education universities. Notably, the participants reported that they had adequate opportunities to acquire knowledge of tertiary-level and school-level mathematics but, relatively speaking, fewer OTL for developing mathematics PCK. These findings are consistent with previous descriptions of the intended curriculum level for preservice teacher education in Mainland China. Aligning with the literature review, the results of the current study confirmed that the academically oriented teacher preparation model is still the dominant model of teacher education in Mainland China (Liao & Hu, 2017; Paine, 1990). Due to this tradition, most time or credit requirements relate to the learning of subject content knowledge, and ‘pedagogical content knowledge has not received much attention’ during the initial preparation period, as already reported by Wu and Huang (2018, p. 114).

In addition, concerning OTL in teaching methods related to mathematics education pedagogy courses, similar to previous findings, the participants in the present study reported that ‘direct lectures’ were the most frequently experienced teaching method (Blömeke, 2012; Li, Zhao et al., 2008). However, unlike the experiences of their counterparts in other contexts, the participants also reported that they had quite limited opportunities to gain experience in group discussions, presentations, and research-based learning (Blömeke, 2012). These inconsistencies may be explained by Wu et al. (2017) study, which showed that regarding the teaching of mathematics education pedagogy courses, mathematics teacher educators in China apparently face major challenges, such as a lack of appropriate teaching cases for illustrating the taught theories. In addition, preservice teachers were found to possess negative attitudes towards these courses, such as low interest and low willingness to participate in relevant classroom activities. Therefore, because of the lack of appropriate teaching cases and students’ negative attitudes towards mathematics education pedagogy courses, the dominant teaching methods are still ‘direct lectures’, with little time spent analysing teaching cases (Li, Zhao et al., 2008).

Moreover, concerning OTL in school-based teaching practicums, the preservice teachers tended to agree that their supervisors’ feedback was more helpful for their professional development than theoretical elaborations. However, they did not strongly agree that their school-based teaching practicums helped them connect theories with practice or enhanced what they had learned in university. This finding confirms the critique widely reported in the literature that general pedagogy or mathematics education pedagogy courses are more theoretical than practice oriented, meaning that preservice teachers do not see them as particularly relevant to school practice (Liao & Hu, 2017; Wu & Huang, 2018).

In terms of the relationship between the OTL and the four components of professional competence (MCK, MPCK, M_PID, and P_PID), both the correlation and regression analysis results pointed to quite weak associations between them. Therefore, it can be concluded that in teacher education in Mainland China, what preservice mathematics teachers learn at university is only weakly related to their learning outcomes, namely, their professional competence, which holds for the cognitive as well as the situation-specific skills of preservice teachers. These findings are only partially consistent with the results of previous studies. For example, in mathematics education, a few statistically significant associations have been identified in previous studies between OTL in mathematics pedagogy and preservice teachers’ knowledge components, such as MCK and MPCK (e.g. Blömeke et al., 2017; Qian & Youngs, 2016). However, for preservice teachers in other fields, such as language education, no significant or positive relationships were identified between OTL and preservice teachers’ knowledge, such as GPK and PCK (e.g. König, Bremerich-Vos et al., 2017).

The surprisingly weak relationships between OTL in various domains and Chinese preservice secondary school mathematics teachers’ professional competence can be explained as follows: To begin with, the overall educational culture in Mainland China may function as a particularly influential factor. As described previously, the knowledge expectations for teachers differ between Eastern and Western cultures (Kim & Ham, 2017). According to traditional Chinese culture, teachers should first possess a profound knowledge base (i.e. be scholars or experts in the subjects they need to teach; Hsieh et al., 2018; Leung, 2001; Paine, 1990). Therefore, mathematics teachers are primarily expected to be mathematicians with a deep, broad, and solid advanced mathematics knowledge foundation in addition to school mathematics (Kim & Ham, 2017; Li, Huang et al., 2008). Due to these cultural influences, preservice teacher education programmes in Mainland China generally ‘represent a strong orientation towards subject-matter knowledge’ (Paine, 1990, p. 55). That is, preservice mathematics teachers are required to ‘take almost all courses offered for a regular mathematics major’, and ‘educational courses are addendums’ (Hsieh et al., 2018, p. 48). Such an academically oriented teacher preparation model equips preservice mathematics teachers with a solid subject-matter knowledge base, but they receive quite ‘limited pedagogical preparation’ (Liao & Hu, 2017, p. 631) and therefore encounter great challenges in teaching practice.

In addition, a prevalent and dominant teaching culture in the Chinese context is ‘direct teaching’ (Leung, 2001, 2017). This cultural influence, whether for the teaching of advanced mathematics courses or mathematics education pedagogy-related courses, means that teacher-dominated lectures with little self-exploratory learning are the dominant mode of teaching, while written exams are the dominant mode of assessment for teacher educators in Mainland China as well (Li, Zhao et al., 2008). Therefore, although such preservice learning experiences facilitate the development of knowledge at the theoretical level, they make it difficult to equip preservice teachers with the necessary knowledge and skills to teach school mathematics (Appova & Taylor, 2019). This method of teaching may further increase the theory—practice gap that has long been criticized in teacher education research (Korthagen, 2010).

Second, the lack of coherence in teacher education programmes may function as another important influence. As is widely discussed in the teacher education literature, there is a clear disconnect or mismatch between university courses and real classroom teaching practices in China (Wu et al., 2017). University courses and the need for teaching practice in schools are not structurally connected (Canrinus et al., 2019; Richmond et al., 2019). In the current study, the participants also reported that, during their practicums in schools, they had few opportunities to connect theories with practice or reinforce what they had learned in their universities. In addition, even among university courses, there are not very strong links between them, that is, there is no strong conceptual coherence for preservice teacher education in Mainland China at present (Canrinus et al., 2019; Richmond et al., 2019). Li, Huang et al. (2008) clearly pointed out that most advanced mathematics courses aim to enhance preservice teachers’ deep understanding of mathematics itself ‘rather than immediately connecting to what they will teach in schools’ (p. 70). Therefore, the lack of conceptual coherence in teacher education has reinforced the existence of a ‘double discontinuity’ between university mathematics and school mathematics (Klein, 1932/2016). This weak coherence in teacher education programmes is likely to weaken the relationship between OTL and preservice teachers’ professional competence.

Third, the current teacher education policy in the context of Mainland China may provide a further explanation for the weak associations. Unlike the teacher education policies in many other cultures and societies, where formal teacher preparation is considered to be fully completed by the end of university-level preparation, newly graduated teachers in Mainland China are not regarded as fully qualified, but as ‘semi-finished products’ (Paine et al., 2003, p. 216). In other words, novice teachers in Mainland China are expected to continue learning and developing their knowledge and teaching skills after obtaining formal teaching positions in schools (Li, Huang et al., 2008). To accomplish this goal, there is a coherent, institutionalized, school-based teacher education programme for in-service teachers in Mainland China (Huang et al., 2014). Through well-organized school-based teacher professional development activities, such as compulsory mentoring programmes, open lessons, and exemplary lessons, in-service teachers, especially novice teachers, have opportunities to further develop their professional competencies (Li & Huang, 2018). Such policy may further weaken the relationship between OTL during preservice training periods and preservice teachers’ professional competence.

Finally, the qualifications of teacher educators in Mainland China may be another factor influencing the identified weak associations. Regarding the qualifications of teacher educators in Mainland China, previous studies have shown that quite a number of teacher educators have no experience in school teaching (Wu & Cai, 2022; Wu et al., 2017). Because of the lack of school teaching experience, teacher educators may not have the knowledge to offer OTL for preservice teachers to gain a deeper understanding of school mathematics, knowledge about students’ mathematical learning and thinking, or, more generally, the connections between the theories of mathematics pedagogy and the reality of mathematics instruction (Wu & Cai, 2022). However, despite mathematics teacher educators’ lack of practical school experience, it is mainly their responsibility within preservice teacher education in Mainland China to connect ‘collegiate mathematics to school mathematics’ and provide ‘high quality mathematics pedagogical knowledge’ (Huang et al., 2010, p. 132). Overall, based on the reports of the evaluated preservice teachers, mathematics teacher educators seem to have difficulties in offering learning opportunities to enable their students to construct connections between mathematical and didactical perspectives, as described by Wasserman et al. (2023).

However, it is worth noting that, relatively speaking, OTL related to teaching methods and teaching practice in schools was found to be more closely related to the two situation-specific skills (P_PID and M_PID). Similarly, König, Bremerich-Vos, et al. (2017) found that teaching practice experience could positively predict the lesson planning competence of preservice language teachers. This comparatively strong association between OTL in teaching methods, teaching practice, and situation-specific skills may be due to the theoretical differences between the cognitive and situated aspects of competencies. Generally speaking, situation-specific skills, such as noticing, are proximal indicators of teaching practices (Kaiser et al., 2015, 2017). That is, they are more closely related to ‘learning-from-teaching competencies’ (Santagata et al., 2018, p. 477). Therefore, such knowledge could be more strongly facilitated by preservice teachers’ experiences in practice (Kersting et al., 2010). However, more studies in this field are needed before solid conclusions can be drawn.

6. Conclusions and limitations

Researchers have widely discussed the separation or discontinuity between theoretical learning in initial teacher education and preservice teachers’ learning outcomes. However, limited empirical evidence is presently available at the secondary school level from the social and cultural context of Mainland China within East Asian culture. Focusing on mathematics education as an example, our aim in the present study was to close this gap by adapting the standardized testing instruments developed in previous studies for the TEDS research programme. The findings of the present study suggest that, generally speaking, preservice teachers in Mainland China have adequate OTL in various domains, such as tertiary level mathematics and mathematics education pedagogy. However, the associations between OTL and various aspects of preservice mathematics teachers’ professional competence, including MCK, MPCK, M_PID, and P_PID, are rather weak. We identified a relatively strong relationship between OTL in teaching methods, school teaching practicums, and the situation-specific aspects of competence (M_PID and P_PID). Such findings imply that although initial teacher preparation in Mainland China has started to emphasize practice-based knowledge in recent years (Wu & Huang, 2018), no strong relationship exists between OTL in initial teacher preparation and preservice teachers’ learning outcomes, such as knowledge and noticing skills.

Although the present study is, to date, one of the very few studies to empirically investigate the effectiveness of initial teacher preparation in Mainland China through the relationship between OTL and preservice mathematics teachers’ cognitive and situated aspects of professional competence, the limitations of the present study should be discussed. First, a relatively large number of preservice teachers participated in the study, but they were only chosen from four preservice teacher universities. Therefore, to a certain degree, the sample in this study may not be typical and representative enough to reflect the overall situation of preservice mathematics teacher education in Mainland China. Future studies could consider using a larger sample of preservice teachers chosen from a greater number of preservice teacher education universities, especially universities at the provincial and local levels. Moreover, the present study employed only paper-and-pencil tests and questionnaire surveys as the main means of data collection. Future studies could consider employing classroom observations and interviews with preservice teachers and teacher educators to collect more information about OTL and enrich the understanding of the relationship between OTL and teachers’ professional competencies. In addition, because the MCK and MPCK tests developed for TEDS-M and the noticing test developed for TEDS-FU were adapted in the present study, each participant needed approximately three hours to complete the two tests and the OTL survey. To lessen the test burden for participants, future studies could consider using shorter versions of the knowledge instruments or evaluating the participants at two different time points.

Acknowledgement

This study was supported by the National Office for Education Sciences Planning, Ministry of Education, China (Grant Number: BMA 220225).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.