The determinants influencing bilingual instruction in Chinese higher education: a complex network analysis

Abstract

The primary objective of this research was to investigate the determinants influencing bilingual instruction at the tertiary level in the Chinese educational context. A complex network analysis was adopted for this study. Twenty-one factors were first identified using the Delphi method, a qualitative research method. A complex network was then designed for analysis of the factors. The results indicate that the network is a scale-free network with certain key factors. The findings further reveal that the subject language feature and bilingual instruction models have more connections with other factors, and thus they are the most significant factors to ensure the effective implementation of bilingual instruction. The findings of this research may provide implications for bilingual education.

Introduction

Bilingual education, which involves the integration of language and content, can be traced back more than two millennia (Coyle et al. 2010). In the Chinese context, its origins date to 1897 when the first Western missionary established a bilingual school in Shanghai. However, this endeavor encountered interruptions during periods of conflict and turmoil. In 2001, the Ministry of Education of the People’s Republic of China initiated the promotion of bilingual instruction in universities as a means of fostering economic development. Universities in China have since embraced bilingual instruction, utilizing both English and Mandarin as mediums of instruction for non-language courses. The primary objective of this approach is to facilitate content learning through language integration, enabling students to master subject knowledge, attain language proficiency, and enhance cognitive abilities (Coyle 2007). The central focus of the research in this domain revolves around the effective implementation of bilingual instruction.

Since 2001, our engagement in the implementation and research of bilingual instruction at the tertiary level has exposed us to the considerable complexity of the factors influencing comprehensible input within this educational framework. These factors include teaching materials, bilingual instruction module, bilingual instruction model, teaching method, teachers and students’ English proficiency, bilingual instruction concept, subject language feature, etc. Among these factors, some exhibit interdependence, while others hold substantial significance, and certain factors are deemed essential. The varying degrees of importance attributed to these factors are contingent upon the specific roles they play in the implementation of bilingual instruction. We were determined to validate the significant factors. However, it is noteworthy that the field has thus far lacked a comprehensive and effective methodological approach to support the argument.

In this study, we have taken an innovative approach by applying complex network analysis to the field of bilingual instruction. Complex network analysis has been used in studies across various disciplines since 2000.The disciplines include science and social science such as technology, computing, neural networks, transportation, aviation, trade, economics, finance, and social connections (Barrat et al. 2004; Peng 2011; Lu et al. 2013; Saleh et al. 2018; Stephenson et al. 2017). Complex network analysis allows this research to depict relations among these factors and to analyze the determinants influencing bilingual instruction with interdisciplinary perspectives, which contributes to the theory and methodological approaches in bilingual education.

This research endeavors to investigate the determinants that contribute to the improvement of bilingual instruction effectiveness. It involves a complex network analysis of the interactions among various factors and aims to discern whether certain factors significantly impact the enhancement of bilingual instruction effectiveness.

Specifically, the study addresses the three key research questions as follows:

• 1. Does the network representing the factors exhibit a scale-free topology?

• 2. Which nodes within the network hold the higher centrality?

• 3. What are the features of the significant nodes in the network?

Theoretical framework

The theoretical framework of this study is grounded in the works of pertinent literature that include comprehensible input hypothesis (Krashen 1985), common underlying proficiency (CUP) (Cummins 1979) and cognitive academic language proficiency (CALP) (Cummins 1979), bilingual instruction models (Baker 2011), subject language feature (Cheng 2011), These theoretical underpinnings collectively provide a theoretical foundation for the examination of the factors contributing to bilingual instruction effectiveness.

Comprehensible Input Hypothesis

Krashen’s Comprehensible Input Hypothesis posits that language learners make progress when they comprehend language input that is slightly more advanced than their current level, represented as “i + 1”. Here, “i” is learners’ current language level and “+1” represents language that is slightly more advanced than the learners’ current level and extra-linguistic knowledge. The extra-linguistic knowledge includes learners’ understanding of the world, subjects, and situations. The “+1” signifies the acquisition of new knowledge relating to a particular subject or language that learners should be prepared to grasp. Ellis (1997) similarly contends that comprehensible input is integral to the success of bilingual instruction across various teaching models.

In the context of China, bilingual education at the tertiary level typically employs Mandarin and English as the instructional languages. Two situations may impede comprehensibility within the instructional language. First, when the English language demands for comprehending specific subjects exceed students’ English proficiency, and second, when the cognitive requirements for understanding subject-specific content surpass students’ cognitive capacity. If bilingual instructors consistently rely on English or incorporate only minimal use of the mother tongue as the instructional language without compromising the content knowledge, the instructional language may advance to levels of i + 2, i + 3 or even i + 4, rending it incomprehensible and thus undermining teaching effectiveness. Hence, employing a comprehensible instructional medium in bilingual subject instruction facilitates the acquisition of both language and content knowledge.

Additionally, bilingual learners’ cognitive academic language proficiency plays a pivotal role in determining the extent to which the instruction language is comprehensible. This phenomenon can be elucidated by invoking the concepts of common underlying proficiency and cognitive academic language proficiency.

Common underlying proficiency and cognitive academic language proficiency

Both Common Underlying Proficiency (CUP) and Cognitive Academic Language Proficiency (CALP) are the basis for learners to comprehend languages and extra-linguistic knowledge. Cummins (1981) postulates the existence of a Common Underlying Proficiency (CUP) as the foundational framework upon which both a language learner’s first and second languages are constructed within the cognitive architecture. Furthermore, CUP extends to encompass Cognitive Academic Language Proficiency (CALP), which serves as the cognitive academic performance in both languages (Cummins 2000, 2001). According to the CUP theory, both linguistic skills and logical reasoning abilities are developed in one’s mother tongue as a base, which can be transferred to the learners’ foreign language, provided that the input is rendered sufficiently comprehensible. This holds particular relevance within the domain of bilingual subject instruction, where Chinese students, in preparation for bilingual instruction in English, require the cultivation and enhancement of their CALP within their native language. It is imperative that students possess a substantial CALP in both their native language and the target language to comprehend the subject matter effectively. Building on this premise, it becomes essential to examine various bilingual instruction models.

Bilingual instruction models

Bilingual instruction, when implemented through various instruction models, may offer varying degrees of comprehensibility to learners with different levels of CALP in their native language and foreign languages.

According to existing literature, there are primarily three bilingual instruction models: transitional, maintenance, and enrichment. The transitional model involves the temporary use of the child’s first language (L1) as the medium of instruction until they achieve fluency in the second language (L2) (Ambert and Melendez 1985; Baker 2011; Fishman and Lovas 1970). Maintenance programs are designed for students to receive instruction in two languages, enabling them to acquire proficiency in and maintain both languages (Baker 2011; Fishman 1976; Gonzālez and Lezama 1974; Spolsky 1989). Enrichment programs, on the other hand, offer foreign-language instruction to non-native speakers (Ambert and Melendez, 1985). These models are typically implemented at the elementary school level.

In China, bilingual instruction at the tertiary level mainly adopts three distinct models, each characterized by variations in the proportion of the instructional language and the use of teaching materials (Zheng and Dai 2013). Model 1, designated as level 1, employs Mandarin as the primary instructional language with 5 to 10% of the content delivered in English. For courses delivered in Model 1, understanding the content delivered in English can be challenging for students, leading to the potential deficiency of comprehensible input. Thus, teachers predominantly use the native language for better comprehension. Simultaneously, they may integrate the foreign language to guide students toward mastering the target language. Model 2, referred to as level 2, balances the instruction equally between English and Chinese, with each language comprising 50% of the instructional content. In model 2, teachers seamlessly blend Chinese and English, using them interchangeably and treating them equally important, which helps students express subject matter in English in the context of studying content. Model 3, or level 3, employs English as the primary instructional language, supplemented with 5 to 10% of the content delivered in Chinese. In Model 3, subject-specific language can be effectively explained with synonymous words even if students lack a full grasp of its meaning, grammar, and function, facilitating the acquisition of content-related language skills in the context of studying the subject.

The selection of the appropriate model is one of the critical factors influencing the bilingual instruction effectiveness in that it affects the learners’ comprehension of the instruction. Cheng (2011) indicates that the subject language feature serves as a guiding principle for selecting the most suitable model.

Subject language feature

In the context of bilingual instruction, particularly regarding language skills and content knowledge, a distinction is made between content-obligatory language and content-compatible language (Genesee 1987; Met 1994; Snow 1987). The term “subject language feature” pertains to the extent of content-obligatory vocabulary coverage within subject-specific texts (Cheng 2011). The higher the coverage rate, the greater the cognitive aptitude required to comprehend the content. Consequently, a higher level of proficiency in the instructional language is necessary to grasp the subject matter.

Content-obligatory language encompasses vocabulary and expressions that are essential for conveying the core meaning of the subject matter. In the context of bilingual subject instruction, content-obligatory language includes subject-specific terminology, concepts, and definitions, all of which are indispensable for students to master the discipline’s content. This specialized language is frequently used within specific scientific disciplines and is rarely employed in non-scientific contexts. Wildsmith-Cromarty (2018) has noted that translating complex terms and concepts into the students’ native language represents an effective approach to rendering the content accessible to learners. However, it is important to acknowledge that numerous English content-obligatory terms lack suitable Chinese equivalents, making code-switching impractical in bilingual instruction. The subject language feature directly influences the selection of appropriate bilingual instruction models.

Content-compatible language (Met 1994) refers to the language that learners acquire through the study of content knowledge. This language is not essential for a comprehensive understanding of the subject content. Using the synonymous words, the learners can understand the content without knowing the meaning of the content-compatible language, grammar and language function. This language component plays a vital role in enhancing learners’ overall language proficiency. Empirical corpus research has demonstrated that content-obligatory language typically constitutes around 5% of the vocabulary found in general academic literature, whereas content-compatible language accounts for approximately 9% (Nation 2001). It is worth noting that these coverage rates vary significantly across different academic disciplines (Nation 2001). Consequently, the coverage rate serves as a key indicator of the subject language feature, and these features are utilized in the selection of appropriate bilingual instruction models.

Taken together, this theoretical framework demonstrates that learning occurs from comprehensible bilingual instruction input. The comprehensible input depends on the learners’ CALP and bilingual instruction model to make sure the instructor’s input is appropriate for learners’ level. The model selection depends on the subject language feature which is determined by the presence of content-obligatory and content-compatible language in the subject. Bilingual instruction prioritizes the delivery of content in a language comprehensible to learners, thus ensuring its effectiveness. However, there are various factors that contribute to the comprehensible input in language.

Thus, this research aimed to examine the determinants that influence the effectiveness of bilingual instruction, particularly focusing on the provision of comprehensible input, within the tertiary education setting in the Chinese context.

Research methodology

In this section, we will begin by presenting the instruments utilized in this study, followed by an overview of the Delphi process, and concluding with an explanation of the complex network model we developed.

Instruments

In this study, we adopted complex network method and Delphi technique to comprehensively analyze and assess the various factors influencing the effectiveness of bilingual instruction.

The complex network

The complex network method can be used to analyze the complex relationships among individuals in real-world contexts. In our study, we adopted this method as the primary approach to examine interactions among the factors influencing bilingual instruction effectiveness and to identify the determinants impacting its efficacy. The complex network model which is the key of complex network method is a topological model composed of the components that may interact with each other. Nodes represent different components, and edges, connections, or lines symbolize the interactions between the nodes (Bar-Yam 2002; Santo and Cohen 2011).

We built a complex network model to represent the components, i.e. the factors influencing bilingual instruction effectiveness (FIBIE), where nodes represent factors and edges represent the interactions between the factors. This complex network model is depicted by a graph (as illustrated in Fig. 1). Within this model, we conducted calculations pertaining to degree, degree distribution, degree strength, and clustering coefficients as observation indices for these factors, such as the identification of the determinants influencing bilingual instruction effectiveness.

Fig. 1: The graph of the directed network model of FIBIE.

A graph or network structure visually represents the complex network.

The Delphi technique

The Delphi process is a consensus-based methodology designed to assess the degree of agreement among experts regarding a specific issue (Vernon, 2009). We employed Delphi technique to identify the factors as the nodes in the complex network model. It operates as an iterative procedure, involving multiple rounds of communication with the aim of refining expert opinions on the subject matter and striving towards a mutually acceptable level of consensus. In this study, a modified Delphi process involved an initial role description and an exhaustive inventory of potential factors. These were then presented to an expert panel for evaluation and consideration across four iterative rounds.

Delphi process

In this section, we detail Delphi process employed in this study, which involved the categorization of topics in bilingual instruction, expert invitation, pre-Delphi meeting process, and a four-round modified Delphi process aiming at attaining expert consensus regarding the factors within the complex network model matrix. The process proceeded as follows:

Categorization of topics in bilingual instruction

First, we performed keyword searches to retrieve bilingual instruction-related papers published in China between 2001 and 2023 from the existing resources of the China Integrated Knowledge Resources Database (https://kns.cnki.net/). A total of 28,773 papers were identified, and further statistical analysis revealed 21 categories of related topics. They are as follows:

• 1. Conceptualization of bilingual instruction

• 2. Implementation of bilingual instruction at the tertiary level

• 3. Bilingual instruction modules

• 4. Curriculum design for bilingual instruction

• 5. Subject language feature

• 6. Sentence complexity

• 7. Subject content within bilingual instruction

• 8. Development of teaching materials

• 9. Models for bilingual instruction

• 10. Teaching methodologies employed in bilingual instruction

• 11. Evaluation of English proficiency among instructors

• 12. Teacher training initiatives

• 13. Prior subject knowledge of instructors

• 14. Assessment of how learners’ English proficiency influences the efficacy of bilingual instruction

• 15. Evaluation of students’ Chinese language proficiency

• 16. The bilingual instructional environment

• 17. Challenges and issues arising from bilingual instruction

• 18. Challenges posed by bilingual instructional practices

• 19. Difficulties encountered in the context of bilingual instruction

• 20. Evaluation methodologies for assessing bilingual instruction

• 21. Attitudes towards bilingual instruction

Expert invitation

In January, 2023, we formed a panel of twenty experienced bilingual instruction experts, each affiliated with renowned universities. Among these experts, sixteen were professors, while two were associate professors, and the remaining two were lecturers. Each of these experts held a doctorate in a relevant discipline, and collectively possessed a minimum of six years of experience in delivering bilingual instruction to undergraduate students. Their areas of bilingual instruction included diverse subjects, such as physics, mathematics, international law, civil engineering, Java programming, transportation management, marketing, and economics. These experts had been actively involved in both implementing and researching bilingual instruction at the tertiary level. Furthermore, they affirmed their commitment to complying with ethical clearance procedures.

Pre-Delphi meeting

Before the Delphi process, we held an online meeting to serve four key purposes:

• 1. Clarification of research questions: We ensured a shared understanding of the research questions.

• 2. Objective and method explanation: We provided an in-depth explanation of the objectives and methods of the study.

• 3. Principles and role descriptions: We outlined the guiding principles and clarified the participants’ roles.

• 4. Matrix factor selection: We achieved consensus on integrating the twenty-one topics outlined in the preceding section into the matrix of our complex network model. Matrix is a set of elements arranged in rows and columns to form a rectangular array. These twenty-one topics are the elements, i.e. the factors in the matrix to be used for the calculations and analysis (see Table 4). Additionally, we explored the possibility of introducing new factors to the matrix. However, we discerned certain factors to be necessary while designating others as critical.

Four Delphi rounds

In this stage, we distributed scoring sheets to each participant via email to ensure anonymity. Participants were given a two-week timeframe to rate each factor identified in the matrix using an 8-point Likert scale. The ratings focused on the perceived importance of these factors in influencing bilingual instruction effectiveness. Following the collection of expert ratings in four rounds, we proceeded to explore the key factors, using the data derived from the matrix. The analytical approach encompassed the calculation of degree, degree distribution, degree strength, and clustering coefficient (refer to Section 3.3).

Through this comprehensive process, we aimed to distill expert insights and achieve a consensus on the pivotal factors that contribute to the bilingual teaching effectiveness.

Round 1 accomplished three primary objectives:

• 1. Factor selection for subsequent Rounds: During this round, the participants engaged in the evaluation of factors, deliberating on which ones to exclude in the ensuing rounds and which to retain for Round 2.

• 2. Direct retention of key factors for round 3: It suggests that specific important factors identified in the first round would be advanced directly to the third round because those factors were deemed directly relevant and integral to bilingual instruction effectiveness. The factors scoring a mean rating of 6.0 or higher (a total of eleven factors) would be automatically kept in Round 3.

• 3. Identification of new influencing factors: Participants were encouraged to contribute new factors that they believed exerted an influence on bilingual instruction effectiveness. A total of seven new factors were introduced, including class size, students’ motivation, students’ learning strategies, students’ self-esteem, students’ self-confidence, teachers’ reputation, and students’ acceptance of English culture.

In Round 1, participants rated the factors, assigning scores based on the degree of importance these factors attributed to bilingual instruction effectiveness. Factors scoring between 3.0 and 5.0 (three factors in total) were included in Round 2, while those with a mean score between 1.0 and 2.0 (seven factors) were excluded from subsequent rounds. A comprehensive overview of the outcomes of Round 1, including the retention and exclusion decisions, can be found in Table 1. The results from Round 1 were disseminated to the participants before they embarked on the rating process in Round 2.

Table 1 The scoring results of round 1.

The scores of the factors in Round 2 were shared with the participants (reported in Table 2).

Table 2 The scoring results of round 2.

During Round 3, the participants identified a total of twelve factors and received the corresponding results (reported in Table 3).

Table 3 The scoring results of round 3.

Prior to Round 4, we conducted an online meeting to determine the factors to be included in the network model matrix. During this session, the participants collectively reached a consensus, confirming that the matrix should include the twelve factors identified.

In Round 4, numerical values were assigned to these twelve factors on an 8-point Likert scale within the matrix (see Table 4). The matrix was a specific interconnection pattern, with each factor appearing both in the left-column cell and the top-row cell of the matrix. The bilingual instruction effectiveness was the core node in the first cell.

Table 4 Mean Values of Each Factor in Twenty Matrices.

Each participant set the matrix cells with numerical values that reflected the strength of interaction between the factors. For instance, the subject language feature (SLF) was deemed to significantly influence bilingual instruction effectiveness (BIE), resulting in a value of 7.45 assigned to the interaction between SLF and BIE. Conversely, SLF had no influence on itself, yielding a value of zero for the interaction between SLF and SLF.

The mean values for each factor across the twenty matrices collected from twenty participants are presented in Table 4, while Table 5 contains a list of acronyms corresponding to the factors listed in Table 4.

Table 5 List of acronyms and abbreviations.

A complex network model

We designed a directed complex network model of the factors with a central node (core node) and twelve surrounding nodes, aiming at understanding the factors that influence bilingual instruction effectiveness. The central node is bilingual instruction effectiveness (BIE), and the surrounding nodes are the twelve factors identified by Delphi technique in Table 4. The model is represented by

$${\rm{G}}=({\rm{V}},{\rm{E}},{\rm{W}})$$

Where G represents the graph forming the network, V signifies the collection of 12 nodes (vertices, points), E stands for the total number of edges (links, lines), and W is the weightiness, indicating the nodal degree strength correlation (Iyanaga et al. 1977). Each quantitative weighted link in the model is characterized by an impact degree, signifying the direction assigned to each link.

A link is a line or an edge connecting two nodes. The link shows the connectivity between a pair of nodes. Links represent whether there exists a direct connection between any pair of nodes, shedding light on the presence or absence of relationships between them. The direction indicates the impact degree of the interaction between two nodes (Fletcher et al.1991).

The network model we have introduced in this section provides a systematic approach for examining the intricate web of FIBIE. Through the use of nodes and links, this model facilitates the visualization and analysis of relationships and interactions among these factors.

A directed network graph

Graphs are frequently depicted visually in the form of diagrams, with dots representing nodes and lines symbolizing the links that connect these nodes. We constructed a graph by running UCINET software with the mean values of the nodes (refer to Fig. 1) to visualize the directed network representing FIBIE. Within the graph, the direction of the arrows signifies the presence of interaction between the nodes. For example, the arrow direction of the node representing previous subject knowledge points to the node representing teaching method, which depicts that the previous subject knowledge affects the teaching method.

Degree and degree distribution

The degree is used to detect if there are key nodes in the network. The degree is the number of the node’s direct interactive connections with other nodes in the network, reflecting the range of a node’s direct impact. The nodes with a high level of degree are key nodes. The degree includes out-degree and in-degree. The out-degree is the number of links a node has with others, and the in-degree is the number of links other nodes have with the node.

The higher value of out-degree or in-degree indicates a wider range of the node’s direct impact (Zhong et al. 2016). These values are computed by Eq. (1) and Eq. (2).

$${\,k}_{i}^{{out}}=\mathop{\sum }\limits_{j=1}^{n}{d}_{{ij}}$$

(1)

$${\,k}_{i}^{{in}}=\mathop{\sum }\limits_{j=1}^{n}{d}_{{ji}}$$

(2)

Where if node i has an influence on node j, a link from i to j is built, and d_ij = 1. Otherwise, no link is built, and d_ij = 0. The out-degree ${{k}}_{i}^{{out}}$ of node i is the sum of d_ij, and the in-degree ${{k}}_{i}^{{in}}$ of node i is the sum of d_ji. The degree can also be applied to the analysis of the fundamental property of the network model of FIBIE.

The degree distribution decides if the network is a free-scale network. A free-scale network represents that there must be significant nodes in the network. The degree distribution characterizes the distribution of node degrees within the network model. The network has a degree distribution that can fit a power-law distribution described in Eq. (3), where r is the power-law index, k is the degree of nodes and P(k) is the probability of the node strength (Geng et al. 2014). If the value of r is between 2 and 3, it implies a scale-free network (Barabasi and Albert 1999). Furthermore, the log-log coordinate figure of the power-law distribution would show a linear trend.

$${\rm{p}}\left(k\right)={K}^{-r}$$

(3)

The salient characteristic of a scale-free network is that the majority of the nodes have very few direct interactive connections with other nodes, contrasting with a minority of nodes that possess numerous connections. The minority of the nodes (factors) in a scale-free network plays a leading role influencing bilingual instruction effectiveness.

To validate this observation, we applied the cumulative degree distribution as a means to describe the degree distribution of the nodes. This analysis yielded evidence confirming the existence of significant factors influencing bilingual instruction effectiveness.

Degree strength

Degree strength, i.e. nodal strength, also referred to as nodal centrality, serves as a metric for quantifying a node’s centrality within the network. It positions a given node relative to others within the network structure (Ducruet et al. 2010). Nodal strength offers insights into a node’s significance within the network, taking into account both its interactions and its impact on bilingual instruction effectiveness. A higher nodal strength value corresponds to greater influence; in essence, nodes with higher nodal strength values are identified as key nodes. This metric is formally defined by Eq. (4) as outlined by Freeman (1978).

$$\,{S}_{i}=\mathop{\sum}\nolimits _{j\in {N}_{i}}{w}_{{ij}}$$

(4)

Where ${S}_{i}$ denotes the strength of node i, and ${w}_{{ij}}$ is the total weighted amount between node i and node j in the network model. It determines the significant factors influencing bilingual instruction effectiveness.

The clustering coefficient

The clustering coefficient is the ratio of the number of actual edges ei (links) between the adjacencies of node i to its neighbors. It stands for the connectivity between the nodes. See Eq. (5), where$\,{k}_{i}$ represents the degree of node i, which is the number of links related to node i (Barrat et al. 2004). The smaller the value is, the greater the importance of the nodes to the central node, or vice versa.

$${{\rm{C}}}_{{\rm{i}}}=2{{\rm{e}}}_{{\rm{i}}}/{{\rm{k}}}_{{\rm{i}}}({{\rm{k}}}_{{\rm{i}}}-1)$$

(5)

Take node 1, i.e. BIM for an example.

$${{\rm{k}}}_{1}=11,{{\rm{e}}}_{1}=35$$

$${{\rm{C}}}_{1}=2\times 35/(11\times (11-1))=0.64$$

The value of this node 1 is 0.64. If this value were the smallest, it would be the critical node, thus a significant factor. The application of the clustering coefficient is to support the findings reported by degree strength.

Results

Degree distribution of network structure

The degree distribution of network structure proves that the network model is a scale-free network. The approximate straight line shown in the log-log coordinate figure (see Fig. 2) demonstrates that the network model of FIBIE follows power-law distribution. As explained in “Degree and degree distribution”, r is the power-law index, k is the degree of nodes and P(k) is the probability of the node strength (Geng. et al. 2014). The value for r is calculated by MATLAB. MATLAB is a multi-paradigm numerical computing environment and proprietary programming language allowing matrix manipulations (Stormy 2019).

Fig. 2: Cumulative degree distribution of network model of FIBIE.

The cumulative degree distribution demonstrates that the network model of factors influencing bilingual instruction effectiveness follows power-law distribution.

The value for ‘r’, which is calculated as 2.2, falls within the range of 2 to 3. This observation substantiates that the network model is a scale-free network. In this context, a scale-free network implies that a small subset of nodes (factors) maintains numerous connections with other nodes (factors), while the majority of nodes (factors) exhibit only a limited number of connections. This scale-free network highlights the presence of noteworthy factors within the network. Moreover, we conducted an analysis of nodal degree strength and the clustering coefficient to further validate the significance of these factors.

The nodal degree strength

The values of out-degree strength of nodes depict that the subject language feature and bilingual instruction model hold the higher centrality. Table 6 reports the out-degree strength value of each node. The values of out-degree strength of nodes are calculated by UCINET. It is software for the analysis of social network data in which data are stored, shown and described by a format of matrix. Since both teachers’ English proficiency and students’ Chinese proficiency are prerequisites for the performance of bilingual instruction, the values of the two nodes are not compared with those of others; However, they are still considered the essential factors in the research. In addition to the value of teachers’ English proficiency, the subject language feature (57.6) is of the greatest value compared to those of other nodes. The subject content (51.95) ranks second. The value of the bilingual instruction model (45.62) is notably higher in the group of nodes with values between 21.1 and 57.6. This value implies BIM is more important for effectiveness.

Table 6 Out-degree strength of nodes.

A model graph represents the values in Table 6 (see Fig. 3), where the more significant the value, the larger the size of the node. The size of the subject language feature is larger than those of others, which is evidence that the subject language feature is a key factor. Both the size of the subject content and that of the BIM node are comparatively large. The sizes show the interactive connections between and among the nodes. The more edges a node has, the more interactions a node has with others. The thinner the edge is between the two nodes, the weaker the interaction between the two nodes, or vice versa. Whether an edge is thin or wide or not, all the edges have interactions with the central effectiveness node. To confirm the results of out-degree strength and model graph of nodes, we calculated the clustering coefficient of nodes as follows.

Fig. 3: Out-degree strength of network model of FIBIE.

A model graph represents the values in Table 2, where the more significant the value, the larger the size of the node.

The clustering coefficient of nodes

The clustering coefficient of nodes proves that both the subject language feature and bilingual instruction model are critical to bilingual instruction effectiveness. The values of the clustering coefficient of nodes are calculated by UCINET. As the clustering coefficient shows, the smaller the value is, the more influential the node is to the central node. The value of BIM is 0.64, and that of the subject language feature is 0.65 (reported in Table 7).

The value of the clustering coefficient determined the size of the node (demonstrated in Fig. 4). The smaller the value is, the larger the size of the node. Both subject language feature (SLF) and bilingual instruction model (BIM) have smaller values than those of others. The two nodes (SLF and BIM) have more connections with other nodes. The two larger-sized nodes establish the connections among other nodes. This shows that the two nodes play a key role in the network model of FIBIE. From the findings of out-degree strength and clustering coefficient, we validate that subject language feature (SLF) and bilingual instruction model (BIM) are the key factors in Table 7.

Fig. 4: The clustering coefficient of the network model of FIBIE.

The smaller the value is, the larger the size of the node.

Table 7 The clustering coefficient of nodes.

Discussion

The study explored the determinants influencing bilingual instruction, aiming at providing theoretical guiding principles for bilingual instructors and researchers at tertiary level and introducing the complex network analysis to the bilingual educational domain. The findings from the complex network analysis yield valuable insights into the complexities of the studied domain.

Interpretation of Findings

Research question 1 aimed to examine whether the network representing the factors exhibits a scale-free topology. Our research reveals a clear demonstration of a scale-free topology within the network, indicating the presence of significant factors. This initial snapshot of the findings aligns with earlier studies. Bilingual instructors have engaged in diverse forms of bilingual teaching, followed by a series of studies focusing on bilingual teaching concepts (Luo and Wang 2004), textbooks (Dai 2003; Sun 2003), teacher training (Xing 2005; Fan 2023), bilingual instruction models (Cheng 2011; Li 2018), teaching methods (Chen 2004; Li 2005; Chen et al. 2022), curriculum design and factors enhancing teaching quality (Cheng 2011; Li et al. 2023; Fan 2023). Han and Yu (2007) conducted an investigation into the impact of students’ prior proficiency in English on the efficacy of bilingual instruction. Their findings revealed that students do not get significant benefits from bilingual instruction unless they have achieved a certain proficiency threshold in English. Their contributions have been exemplary in promoting bilingual education.

However, as bilingual teaching advances, two primary concerns arise. Firstly, certain courses such as physics, chemistry, mathematics, biology, medicine, mechanics, and finance, etc. pose challenges due to extensive content-obligatory vocabulary, hindering comprehensive input, particularly when English remains the primary instructional language. Secondly, educators acknowledge the existence of key factors amidst the various factors influencing bilingual instruction effectiveness, yet they lack a clear methodology to discern it. The significance of the scale-free network lies in its ability to illuminate bilingual instructors about the presence of pivotal elements among the factors investigated in previous studies, thus validating their hypotheses.

Research questions 2 and 3 sought to identify nodes with higher centrality within the network and explore their features. The application of the degree strength highlighted the significance of subject language feature and bilingual instruction model as the factors with elevated centrality in the network. The findings are in line with our previous study. Cheng (2011) delved into the interplay between subject language feature and bilingual instruction models. This empirical investigation elucidates the significance of subject language feature and bilingual instruction models. The results revealed that Model 3 exhibits greater adaptability when applied to courses characterized by a substantial presence of content-compatible language, with a coverage rate exceeding 15.32%. Conversely, Model 1 proves more effective for courses abundant in content-obligatory language, with a coverage rate surpassing 10.45%. Model 2, on the other hand, emerges as the preferred choice for subjects where the coverage rate of content-compatible language hovers around 10.89% and content-obligatory language stands at approximately 8.04%.

To further verify the nature of significant nodes, the examination of the clustering coefficient validated the pivotal role of the subject language feature and bilingual instruction model as determinants influencing bilingual instruction effectiveness.

Implications

The complex network analysis clearly illustrates the existence of the determinants, providing major implications for bilingual instruction across three key aspects within the theoretical framework.

The first aspect concerned the coverage rate of content-obligatory and content-compatible words and the selection of appropriate bilingual instruction model. There exist courses where the subject language feature exerts considerable dominance, manifesting in a content-obligatory word coverage rate exceeding 10.45%. In such cases, students lacking prior knowledge and adequate English proficiency encounter challenges comprehending the content. Furthermore, the instructors find it arduous to provide comprehensible input language, even in the native tongue with the teaching methods. Students encounter difficulties in transferring subject-specific terminology, concepts, definitions, and content from their native language to English. The teaching efficacy suffers when instructors persist in delivering the subject matter in English or resort to code-switching. Under these circumstances, it is recommended to employ Model 1, utilizing the native language as the medium of instruction to facilitate students’ comprehension of the content knowledge.

Cummins (2007) emphasizes that students’ native language should not be viewed as an impediment to fostering proficiency in the second language. Rather, when the native language is leveraged as a cognitive and linguistic resource through bilingual instructional strategies, it can serve as a stepping stone to scaffold more advanced performance in the second language.

In accordance with the Common Underlying Proficiency (CUP) framework (Cummins 1979), it is important to acknowledge that both language and logical thinking skills are initially developed in the native language, serving as the foundational basis. Consequently, a higher level of proficiency in the native language can potentially facilitate the development of greater proficiency in the target language. According to the subject language feature, educators make informed decisions regarding the selection of different bilingual instruction models, with the goal of providing Krashen’s comprehensible input. This approach enables students to attain mastery of subject knowledge, enhance language competence, and improve cognitive abilities. It is evident that both the subject language features and the chosen bilingual instruction models play pivotal roles in realizing the bilingual instruction. Subject language feature also influences the selection of teaching materials.

The second aspect concerned teaching materials. Teaching materials, particularly textbooks, assume a pivotal role in the realm of education (Elliott and Woodward 1990). They serve as instrumental tools for enhancing bilingual instruction effectiveness. Research indicates that a substantial proportion of classroom instruction, ranging from more than 70% (Tyson and Woodward 1989) to as high as 90% (Suarėz 2001), is derived directly from textbooks. Furthermore, textbooks contribute significantly to structuring students’ homework, accounting for approximately 90% of assignments (Jackson 1981). In the learning process, textbooks function as indispensable resources for both students and educators, offering explanations and exercises to students while providing teachers with valuable instructional guides (Van Steenbrugge et al. 2013). It is important to note that instructional materials not only augment the intrinsic complexity of core information but also influence the cognitive activities required of students through their presentation (Sweller 1994).

In the context of bilingual instruction at the tertiary level in China, subject content presented in English aligns with the curriculum syllabuses across various disciplines, and encompasses subject language filled with subject-specific terminology, content-obligatory language, content-compatible language, and syntactic structures. When the coverage rate of content-obligatory vocabulary within authentic versions proves excessively high, rendering the content challenging for students with limited CALP to comprehend, bilingual instructors judiciously opt for the development of simplified textbooks. In doing so, they ensure that subject content remains uncompromised. Alternatively, instructors may choose to compile elaborated texts that provide further clarification and reinforcement of subject material. Consequently, the selection of teaching materials by bilingual instructors is intrinsically tied to the subject language feature.

The third aspect concerned bilingual instruction teaching module (BITM). BITM, in essence, denotes the structural framework of bilingual instruction courses. At the tertiary level, the curriculum encompasses foundational, elective, and compulsory courses across all academic disciplines, predominantly conducted in Mandarin. However, certain courses within this curriculum are specifically designed to be delivered in English, either as standalone subjects or along with the students’ English language learning journey. The development of the students’ English language proficiency is foundational before taking bilingual instruction courses.

Nonetheless, in many Chinese universities, bilingual instruction courses are often initiated by the instructors who voluntarily choose to instruct in English without the systematic design of subject-specific curricula. These instructors may opt for English-medium instruction, even in courses with a substantial prevalence of content-obligatory vocabulary, such as mathematics, physics, mechanics, maritime law, marine engineering, finance, and others. This practice persists and occurs before students have completed their English language requirements. Additionally, some universities employ evaluation mechanisms for bilingual instruction. For instance, when employing Model 3, instructors are assigned a threefold teaching workload, and a similar doubling of the workload applies to Model 2. Instructors may adopt these models without adequate consideration of students’ CALP and the subject language feature. Potentially, the instructors compromise either the subject content or comprehensive input (Wu and Yan 2010; Cheng 2007).

To address these challenges, the establishment of a structured bilingual instruction course framework becomes imperative. This framework entails a three-year bilingual instruction teaching module encompassing foundational, elective, and compulsory courses. It delineates the courses to be taught, the timing of their delivery, the pedagogical approaches employed, rationale behind course selection, the venues for course delivery, and the intended beneficiaries. This structured module unfolds as a systematic, progressive teaching and learning process meticulously designed to optimize the bilingual instruction effectiveness.

Conclusion

This study has identified two pivotal determinants, subject language feature (SLF) and bilingual instruction model (BIM), employing a complex network analysis. The comprehensive research process, addressing key questions about network topology, centrality, and features of significant nodes, has produced some helpful findings. The findings suggest a scale-free structure in the network, identifying key factors through degree analysis. The examination of degree distribution confirms the presence of central factors, and the subsequent analysis sheds light on intricate relationships and heightened connections among them. The degree strength highlights the significance of subject language feature and bilingual instruction models. The calculation of the clustering coefficient further validates the pivotal role of the subject language feature and bilingual instruction model in bilingual instruction effectiveness.

The determinants should be helpful for both teachers and researchers working on bilingual instruction and may have some pedagogical implications. For teachers, the findings show clearly the need for them to provide comprehensive input, particularly in situations where students exhibit varying levels of CALP and where the bilingual courses have different coverage rates of content-compatible and content-obligatory language. The teachers should select the most appropriate bilingual instruction model, considering both students’ CALP and the subject language feature.

Moreover, the study acknowledges the significance of teaching materials in structuring classroom instruction and shaping cognitive activities. In instances where subject content involves an excessive number of content-obligatory words, it is imperative to adapt textbooks without compromising the core content. Failure to do so may result in increased workload for teachers (Baetens Beardsmore 2009) and a substantial cognitive burden for students. The teachers’ decisions regarding teaching materials are intricately tied to subject language features, ensuring comprehensibility for students with varying CALP levels.

Additionally, Subject language feature serves as the foundational principle underpinning the establishment of a systematic and scientifically designed Bilingual Instruction Teaching Module (BITM). BITM represents a methodical blueprint, distinct from mere subjective considerations of “I can teach in English” or “I want to teach in English.” It operates as a structured framework, guiding both teachers and students on their ascent towards the ultimate goal of attaining proficiency in subject language and content knowledge. Furthermore, SLF significantly informs the selection of specific teaching methods. Notably, the cognitive demands of a subject course can dynamically vary throughout its entirety (Cummins 2007). In such instances, the development of diverse teaching methods or strategies becomes not only necessary but also highly beneficial. The aforementioned points emphasize the pedagogical implications for bilingual instruction at the tertiary level, underscoring the importance of providing comprehensible input to foster the integration of language and content.

Regarding implications for researchers, the findings should encourage more researchers to do research in the educational area with cross-disciplined methods such as Delphi technique, complex network analysis and mathematical calculation method.

Despite the promising results, the study has potential limitations. We invited the participants from prominent universities, which may not be representative of all bilingual instructors from different institutions. In addition, the bilingual courses that the participants taught involved diverse disciplines. If the method was used on a single discipline, such as medical science, the guiding principle may be subject to change. Hence, future research should conduct a replication study to validate the results with different groups of participants for the generalizability of the findings and test the reliability of our proposed determinants as principles for bilingual instruction in special disciplines and particular areas.