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

The study addresses how to effectively implement bilingual instruction (primarily Mandarin–English) in Chinese higher education by identifying which factors most strongly influence comprehensible input and overall instructional effectiveness. Motivated by policy promotion of bilingual instruction since 2001 and the observed complexity and interdependence among factors (e.g., teaching materials, models, methods, language proficiencies, subject language features), the authors seek a comprehensive analytic approach. The research questions are: (1) Does the factor network exhibit a scale-free topology? (2) Which nodes hold higher centrality? (3) What are the features of the significant nodes? The study’s significance lies in introducing complex network analysis to model and evaluate inter-factor relationships, providing evidence-based guidance for selecting instructional models and designing courses to ensure comprehensible input and improved outcomes.

The theoretical framework integrates: (1) Krashen’s Comprehensible Input Hypothesis (i+1), emphasizing that input must match learners’ linguistic and cognitive levels to be comprehensible; (2) Cummins’s Common Underlying Proficiency (CUP) and Cognitive Academic Language Proficiency (CALP), positing transfer of cognitive-academic skills across L1 and L2 and the need for strong CALP in both languages to learn content; (3) Bilingual instruction models—transitional, maintenance, and enrichment, adapted in Chinese universities as three models varying in proportions of Mandarin/English (Model 1: mostly Mandarin with 5–10% English; Model 2: ~50/50; Model 3: mostly English with 5–10% Mandarin)—which affect comprehensibility; and (4) Subject language feature (SLF), distinguishing content-obligatory vs. content-compatible language and using coverage rates of obligatory terminology as a guide to model selection and material design. Together, these perspectives suggest that effectiveness depends on fitting the model and materials to learners’ CALP and the linguistic demands of the subject to ensure comprehensible input.

Design: Mixed qualitative–quantitative approach using a modified Delphi technique to identify factors and a directed, weighted complex network model to analyze their interrelations. Data sources and topic scoping: Keyword searches of Chinese literature (2001–2023) in CNKI identified 28,773 papers and 21 topical categories related to bilingual instruction. Expert panel: 20 experts (16 professors, 2 associate professors, 2 lecturers) from renowned universities; all with doctorates and ≥6 years’ experience teaching bilingual courses across disciplines (e.g., physics, mathematics, law, engineering, programming, management, economics). Ethical compliance affirmed. Delphi procedure: Pre-Delphi meeting aligned research questions, methods, and roles, and mapped 21 topics into a factor matrix. Four anonymous rating rounds (8-point Likert scale) via email.

• Round 1: Rated 21 factors; factors scoring ≥6.0 (11 items) advanced directly to Round 3; mid-scoring (3.0–5.0) moved to Round 2; low-scoring (1.0–2.0) excluded. Seven new factors proposed: class size, students’ motivation, learning strategies, self-esteem, self-confidence, teachers’ reputation, students’ acceptance of English culture.
• Round 2: Ten factors rated; low-scoring excluded; culture, curriculum designs, students’ motivation, and learning strategies retained.
• Round 3: Fifteen factors rated; twelve selected for the network model (see below).
• Round 4: For the final 12 factors, each expert completed a square matrix (8-point Likert) of directed influence strengths among all pairs, including BIE (bilingual instruction effectiveness) as the central outcome. Twenty matrices were collected; mean cell values computed (Table 4). Final factors included (with acronyms): BIE (central node), SLF (subject language feature), SCO (sentence complexity), SC (subject content), PSK (previous subject knowledge), BIM (bilingual instruction model), TM (teaching method), TMA (teaching materials), BITM (bilingual instruction teaching module), SCP (students’ Chinese proficiency), SEP (students’ English proficiency), TEP (teachers’ English proficiency), SM (students’ motivation). Network modeling and metrics: A directed, weighted network G=(V,E,W) was constructed with nodes as factors and edge weights as mean influence scores. Analyses performed using UCINET (for degree, strength, clustering coefficient) and MATLAB (for power-law fitting). Metrics:
• Degree and cumulative degree distribution (to test scale-free property; power-law p(k)∝k^{-r}).
• Degree strength/centrality S_i = Σ_j w_{ij} (out-strength) to identify influential nodes.
• Clustering coefficient C_i = 2e_i/[k_i(k_i−1)] to assess local connectivity; smaller values indicate more influential nodes toward the central node, used to corroborate strength findings. Visualization: Directed network graph and node-size mappings produced from UCINET outputs to illustrate connectivity, edge thickness, and centrality patterns.

• The factor network is scale-free: The cumulative degree distribution follows a power-law with r = 2.2 (within 2–3), indicating a scale-free topology with a few highly connected nodes and many sparsely connected nodes.
• Central determinants: Subject language feature (SLF) and bilingual instruction model (BIM) have the highest centrality/importance.
• Out-degree strength (selected values): SLF = 57.6 (highest), Subject content (SC) = 51.95, BIM = 45.62, Students’ English proficiency (SEP) = 41.45, Teaching materials (TMA) = 38.7, Previous subject knowledge (PSK) = 36.7, Syntactic complexity (SCO) = 31.85, Teachers’ English proficiency (TEP) = 31.15, Students’ motivation (SM) = 26.0, BITM = 22.8, Students’ Chinese proficiency (SCP) = 22.05, Teaching method (TM) = 21.1. Teachers’ and students’ proficiencies are considered prerequisites and were not directly compared in ranking, but their strengths are reported.
• Clustering coefficients (smaller = more influential): BIM = 0.64, SLF = 0.65 (lowest two values), confirming their critical roles. Other nodes: SC = 0.79, TMA = 0.80, TM = 0.81, PSK = 0.81, SEP = 0.82, TEP = 0.84, SCO = 0.85, SCP = 0.85, BITM = 0.89.
• Network visuals corroborate that SLF and BIM have more connections with other factors and are larger in node-size mappings, evidencing their pivotal status.

The findings address the research questions by: (1) confirming a scale-free topology, implying the presence of a few dominant determinants; (2) identifying nodes with higher centrality—particularly SLF and BIM—as key levers for effectiveness; and (3) characterizing these nodes as highly connected influencers that structure interactions among other factors. Significance: SLF, reflecting the coverage of content-obligatory vs. content-compatible language within disciplines, directly guides the choice of bilingual instruction model to ensure comprehensible input aligned with learners’ CALP. This impacts teaching material selection (e.g., simplified or elaborated texts when obligatory vocabulary coverage is high) and the structuring of a Bilingual Instruction Teaching Module (BITM) to sequence courses and methods appropriately. Practically, for subjects with high content-obligatory demand (e.g., >10.45% coverage), Model 1 (mostly Mandarin) is recommended to maintain comprehensibility until learners’ proficiencies and prior knowledge suffice. The results underscore the need for data-driven model selection, careful textbook design, and programmatic BITM planning to balance content mastery and language development.

Using Delphi-informed factor selection and complex network analysis, the study demonstrates that the ecosystem of factors influencing bilingual instruction effectiveness in Chinese higher education is scale-free. Subject language feature (SLF) and bilingual instruction model (BIM) emerge as pivotal determinants, validated through degree distribution, out-degree strength, and clustering coefficients. Pedagogically, aligning instruction models with SLF and learners’ CALP, judiciously adapting teaching materials, and establishing a structured BITM are essential to ensure comprehensible input and integrated content-language learning. Methodologically, the work illustrates the value of cross-disciplinary analytical tools (Delphi, network analysis) for educational research and decision-making. Future research should replicate with broader and discipline-specific samples to test generalizability and refine guidance for specialized fields.

• Expert sample drawn from prominent universities may not represent the full diversity of institutions or teaching contexts.
• Participants taught across diverse disciplines; determinants and their weights may vary by discipline. Applying the method within a single discipline (e.g., medical science) could yield different guiding principles.
• Findings require replication with different participant groups to assess generalizability and to test the reliability of identified determinants across specific disciplines and regions.