2.1. Co-Production and Collaboration

To clarify the definition of co-production, we follow McMullin’s framework, which defines it as the collective involvement of teachers, community elders, educational institutions, and policy intermediaries working together to generate public value through shared practices ⁵. While collaboration often refers to coordinated actions among peers or organizations with similar power and expertise, co-production extends further by involving diverse stakeholders, including citizens or community actors, in shaping both the processes and outcomes of public services or knowledge production ⁶.

We emphasize that this distinction is particularly salient in indigenous educational contexts, where cultural and epistemic participation from community members is integral to teaching and learning. In such settings, coproduction reflects a more inclusive and distributed form of engagement that acknowledges the role of community knowledge holders.

2.2. Knowledge Building in Indigenous Teacher Development

This study adopts a knowledge-building perspective of co-production, emphasizing the importance of co-creating knowledge between formal educators and local knowledge holders, such as tribal elders, as a core mechanism for professional development. Knowledge building is particularly vital for indigenous teachers in rural contexts, where the transmission and integration of indigenous languages, cultural practices, and community-based wisdom are essential for both educational equity and cultural sustainability. As Hill et al. ⁸ have noted, collaborative knowledge generation enhances both teacher learning and community engagement.

In this study, we define knowledge construction as the process by which indigenous teachers engage in meaning-making and interpretive practices through interactions with institutional and community actors. It is considered an emergent outcome of co-productive behaviors, especially in environments where professional development is embedded within relational community-based practices.

2.3. Network Theory and Epistemic Structures

Traditional approaches in social network analysis have largely relied on one-mode network structures, often focusing on interactions among actors without accounting for the relational dynamics between actors and events, such as professional development activities or roles ^11,12. This limitation narrows our capacity to capture complex role-based or institutional relationships, especially in multilevel educational governance settings ¹³. To address this gap, the current study integrates a two-mode network analysis, enabling a more accurate representation of the relational structure between indigenous teachers and their professional growth activities.

Moreover, while ENA has become a powerful tool in learning sciences—particularly for modeling knowledge construction and collaborative discourse ^14,15,16—its application to education policy and governance research remains scarce. As Elmoazen et al. ¹³ note in a systematic review, most ENA studies center on STEM education or online learning environments, with limited application to public policy, teacher agencies, or network governance ^17,18.

2.4. Rationale for Network-Based Methodology

Building on this conceptual foundation, we clarify the rationale for applying network theory and methods to the study of co-production. Co-production processes are inherently relational and involve complex patterns of interaction among actors, such as teachers, community members, and policy intermediaries. Network analysis enables us to systematically map and quantify these ties, uncover structural patterns, and identify influential nodes.

In particular, ENA provides a powerful tool for capturing both social and conceptual co-occurrence patterns in discourse, offering insights into how knowledge is constructed and distributed across professional development networks. By combining two-mode network modeling with ENA, this study tracked the relational architecture of co-production and highlighted the cognitive and discursive elements of knowledge construction in indigenous teacher-learning environments.

3.1. Data

This study employed a survey-based data collection method conducted through teacher-training workshops specifically arranged for indigenous language educators. These workshops, which were officially mandated for professional development, provided a practical context for administering and collecting responses. The survey period was from June 2023 to June 2024, during which we targeted certified indigenous language teachers across three rural counties in Taiwan. We purposefully selected Nantou, Miaoli, and Hsinchu counties as research sites because of their high indigenous population densities, particularly among the Atayal and Bunun groups, which ensured strong ethnic representativeness. These counties also reflect a balanced regional distribution spanning Taiwan’s central and northern mountainous areas, which are known for their concentration of rural indigenous communities. Importantly, all three counties have established indigenous education centers (IECs) that function as local intermediaries responsible for implementing indigenous language policies, organizing teacher-training programs, and facilitating community engagement. Thus, their inclusion offers a policy-relevant lens for examining how co-production and professional development unfold in localized and culturally embedded settings.

A total of 85 valid responses were collected. The distribution of the participants is summarized in Table 1. Among them, 36.5% were from Nantou County (\(n=31\)), 15.3% were from Miaoli County (\(n=13\)), and 48.2% were from Hsinchu County (\(n=41\)). The cumulative percentage reached 100%, indicating complete coverage of the valid sample pool.

3.2. Instrument

To investigate indigenous teachers’ professional development networks and co-production behaviors, this study designed a two-part questionnaire based on existing literature and policy contexts.

A network questionnaire was developed to examine professional interaction networks among educators. This design was informed by foundational frameworks in educational research, including those of Greany and Higham ¹⁹, who analyzed system leadership through school network structures, and Thompson ²⁰, who conceptualized governance networks in education. To identify key relational patterns, the primary item in the network questionnaire asked respondents, “Whom do you most frequently consult regarding indigenous language or culture-related teaching matters?” to identify the distinct contributions of government agencies (such as IECs and county education bureaus), schools, community-based actors (such as principals, school leaders, and tribal elders), and other supporting institutions (such as universities and NGOs).

These items were carefully reviewed and revised with reference to the operational objectives of Taiwan’s IECs, ensuring alignment with local policy mechanisms and teacher role expectations. This co-design process aimed to reflect the actual governance environment in which indigenous teachers engage, including both formal and informal channels of knowledge exchange. Each of these actors plays a specific role—policy coordination, cultural knowledge transmission, and capacity building—in supporting professional growth and enacting co-production mechanisms.

The participants were allowed to select multiple options across three categories: government agencies, schools and communities, and other institutions. The options were derived based on the governance structure and policy guidelines of IECs in Taiwan, and each selection was binary-coded (\(1=\) selected, \(0=\) not selected).

The full set of node options and selection frequencies is presented in Table 2.

The design of the questionnaire’s co-production component was fundamentally informed by McMullin’s typology of public value creation, which distinguishes three modes of civic engagement: individual, group, and collective co-production ⁵. This framework was adapted to the educational context of indigenous language teachers in Taiwan and further contextualized using policy guidelines issued by IECs. Individual co-production refers to personal initiatives undertaken by teachers to enhance their professional capacity, such as attending workshops or seeking educational resources independently. A sample item is, “I attend indigenous education professional development workshops.” Second, group co-production captures collaborative efforts among peers, including community building and the co-design of learning materials. A representative item is “I initiate or join teacher communities focused on indigenous education.” Finally, collective co-production involves broader system-level actions such as advocating for policy improvements or participating in community-based implementation. An example item includes: “I propose better teaching strategies to indigenous language promotion officers or the indigenous education center.” The survey instrument employed a three-point Likert-type scale (\(1=\) never, \(2=\) occasionally, and \(3=\) frequently) to measure the frequency of participants’ engagement in co-production behaviors. Based on the cumulative scores, participants were classified into three levels according to McMullin’s co-production typology. This distinction helps differentiate between the operationalization of behavioral frequency (through survey measurement) and the analytical categorization of actors into co-production levels used in the interpretation of network structures.

To evaluate the internal consistency of the co-production scale, Cronbach’s alpha was calculated across the 12 items representing the individual, group, and collective dimensions. The resulting coefficient was \(\alpha=0.92\), indicating excellent internal reliability. This value exceeds the commonly recommended threshold of 0.80, as suggested by Tavakol and Dennick for reliable use in social science research instruments ²¹.

Descriptive statistics for each item on the co-production scale are presented in Table 3. The items were grouped into three categories:col1_\(x =\) individual-level co-production behaviors, col2_\(x =\) group-level behaviors, and col3_\(x=\) collective-level behaviors.

All items were answered by 85 participants with no missing values. The mean scores ranged from 1.95 to 2.67, with standard deviations generally below 0.80, indicating moderate dispersion. The skewness and kurtosis values were within acceptable bounds, suggesting that the data distribution did not violate the normality assumptions substantially.

To further analyze engagement patterns, the summed scores for each participant across the 12 items were calculated and used to classify participants into three distinct levels of co-production. The classification logic was hierarchical: participants with a total score above 27 (\(\ge~9\) points from each level) were classified as Level 3 (high-level co-production), those who scored highly in the first two levels but not collective were coded as Level 2, and others were assigned to Level 1 (low-level co-production).

Consequently, 43 participants were identified as Level 3, 9 as Level 2, and 33 as Level 1. Mean total scores differed significantly across levels, with Level 3 averaging 32.21 and Level 1 averaging 21.91. An independent samples \(t\)-test confirmed a statistically significant difference between the two groups (\(t(74)=-12.93\), \(p<.001\)), demonstrating the validity of this tiered classification strategy in capturing behavioral variation across co-production intensities.

3.3. Methodology

We used the ENA Web Tool available at https://www.epistemicanalytics.org/ to conduct our analysis ^1,11. This platform provides an interactive environment for performing ENA, enabling researchers to model, visualize, and compare patterns of connections in coded discourse data. This tool supports the construction of network models that represent the co-occurrence of concepts over time and facilitates the application of statistical and dimensionality reduction techniques, such as singular value decomposition (SVD) and mean rotation, to reveal meaningful differences between groups or conditions.

More specifically, ENA constructs a high-dimensional vector space where each unit of analysis (\(\mu\)) is associated with a normalized co-occurrence vector \(\textrm{N}\mu\). Through SVD, ENA rotates this high-dimensional space into a reduced coordinate system that retains the maximum variance in the data while minimizing dimensionality. Each unit \(\mu\) is then represented as a point \(\textrm{P}\mu\) in this transformed space, capturing its underlying knowledge structure or semantic signature ¹⁵.

Initially, data from all 85 participants were used to construct a weighted two-mode network representing the connections between teachers and the actors or institutions they consulted frequently. Each edge in the network was binary (\(1=\) selected, \(0=\) not selected) because only the presence or absence of a connection was recorded.

In addition to the visual comparison of networks, ENA points can be analyzed statistically. For example, we may test whether the patterns of association in one condition are significantly different from those in another. To demonstrate both parametric and nonparametric approaches to this question, the following examples use a Student’s \(t\)-test and a Mann-Whitney U test to test for differences between different conditions. For more details on the differences between the parametric and nonparametric tests, see Kurkela et al. ²².

4.1. Professional Development Networks of Indigenous Teachers in Rural Areas

Figure 1 presents an ENA projection of professional development networks among indigenous language teachers in rural regions. In this network visualization, each node represents a key actor or institutional role involved in teachers’ learning and co-productive engagement, while the red connecting lines (edges) reflect the strength of the co-occurrence between actors, measured through normalized adjacency vectors. The thickness of these lines indicates the weighted frequency and intensity of co-production ties. Among the identified connections, the link between Community Language Staff and Tribal Elders (E–L) emerged as the most prominent, with a normalized weight of 0.10, highlighting this dyad as the most significant link in the network. This suggests that indigenous teachers rely heavily on the cultural and linguistic knowledge passed on by Tribal Elders, often mediated by Community Language Staff, underscoring the centrality of localized cultural expertise in rural indigenous professional development. Other strong ties included connections between Indigenous Education Center Directors and School Leadership (D–F) and between School Leadership and Tribal Elders (F–L), both with weights of 0.08, reflecting the bridging role of formal educational institutions in supporting traditional knowledge systems. Moderate associations such as those between Other Indigenous Teachers and Tribal Elders (J–L), Community Language Staff and School Leadership (E–F), and School Leadership and Principals (F–G), each with a weight of 0.05, further demonstrate the layered, multilevel structure of support that indigenous teachers navigate. However, the dominant E–L connection underscores the indispensable role of older knowledge systems and community language brokers in sustaining culturally grounded professional development.

These patterns revealed a strong reliance on locally embedded figures, particularly school-based personnel (F: Directors of Academic Affairs, E: Indigenous Language Promoters) and traditional knowledge holders (L: Tribal Elders). The connection between E and L (0.10) was the most prominent, suggesting that informal intergenerational mentorship played a critical role in the transmission of indigenous cultural and linguistic knowledge.

Moreover, the D–F–L triangle highlighted an integrated support system between the Indigenous Education Center, Formal School Leadership, and the Community. This resonates with the notion that network-based governance structures, as discussed by Thompson ²⁰, facilitate horizontal collaboration between institutional and non-institutional actors, which is necessary in decentralized or underserved educational contexts.

Network visualization revealed notable co-occurrence patterns among actors such as Indigenous Education Center Directors, School Leaders, and Tribal Elders. Although this structure may reflect important institutional and cultural linkages, further qualitative research is required to confirm how trust and mediation function. However, these preliminary patterns suggest that indigenous teacher development may be influenced by both formal structures and community-based relationships.

4.2. Knowledge Construction Differences Among Teachers with Varying Co-Production Behaviors

To investigate how co-production behaviors influence the structure of knowledge construction, participants were categorized into three groups based on their levels of co-production engagement: Level 1 (low involvement), Level 2 (moderate involvement), and Level 3 (high involvement). Levels 1 and 3 represent the contrasting ends of the co-production spectrum, and the comparison follows a maximum contrast approach. Fig. 2 presents the composite ENA model, where each dot represents an individual teacher, and the lines represent the co-occurrence relationships between key actors.

The overlapping yet structurally differentiated clusters suggest that teachers at different co-production levels construct knowledge using distinct social strategies and epistemic associations.

To explore the most contrasting patterns, we compared Level 1 (individual) and Level 3 (collective) co-production groups. Fig. 3 shows the ENA networks. The red network (left) corresponds to Level 1, whereas the purple network (right) corresponds to Level 3. Visual inspection revealed that Level 3 participants formed denser and more distributed connections, particularly among school-based actors (F: Academic Directors, G: Principals, E: Language Promoters) and traditional knowledge holders (L: Elders).

Statistical analyses further supported these observations. A two-sample \(t\)-test, assuming unequal variances, was conducted to examine group differences along the ENA projection axes (Table 4).

The significant difference along the \(Y\)-axis indicated that the Level 3 participants exhibited more integrated and distributed epistemic structures, suggesting a higher degree of cross-boundary collaboration and knowledge exchange. This finding supported the proposition that teachers who actively engage in collective co-production develop richer and more interconnected professional knowledge networks.

These findings emphasize that engagement in collective co-production not only expands the scope of participation but also shapes the structure and diversity of professional knowledge construction. Active collaboration with both institutional actors and community elders appears to facilitate a more robust epistemic ecosystem for rural indigenous teachers.

Although the primary comparative analysis focused on Level 1 (individual co-production) and Level 3 (collective co-production), we also examined Level 2 (group co-production) participants. The statistical results showed that Level 2 did not differ significantly from either Level 1 or 3 in terms of epistemic structure along the primary ENA dimensions. This suggested that group-level co-production might represent a transitional or hybrid engagement form that incorporates elements of both individual and collective practices. Teachers in Level 2 typically collaborated within institutional contexts (e.g., among teaching peers or school-based projects) but did not consistently extend their engagement to include broader community actors, such as tribal elders or policy intermediaries. Thus, while Level 2 behaviors demonstrated moderate co-occurrence patterns, they lacked the boundary-crossing intensity observed in Level 3 or the isolated patterns of Level 1. This interpretation aligned with the ENA visualizations (Fig. 2), where Level 2 (blue nodes) occupied an intermediary position, further supporting its role as a bridging category.

5.1. Decentralized, Community-Centric Professional Networks

The first key finding highlights that indigenous teachers in rural areas tend to rely heavily on school-based personnel (e.g., directors of academic affairs, principals) and community elders for professional learning. Nodes such as F (school leadership), L (tribal elders), and E (language promotion staff) emerged as the most central and frequently co-occurring actors. This suggests that indigenous teacher development is not exclusively facilitated by formal institutions but is often co-constructed through hybrid spaces, blending policy-driven roles with traditional, community-based knowledge sources.

This pattern supports the perspective of network governance in public services ²⁰ and relational co-production ^8,23, which argue that effective service delivery, particularly in culturally sensitive domains, requires horizontal coordination among multiple actors. The prominence of elders and community institutions in these networks emphasizes the importance of local knowledge sovereignty, echoing the findings of Hill et al. ⁸ that indigenous learning environments benefit from inclusive and epistemologically pluralistic systems.

5.2. Co-Production as Driver of Epistemic Diversity

The second major contribution lies in the demonstration that co-production behavior levels are closely tied to teachers’ epistemic network structures. Participants who engaged more actively in collective co-production (Level 3) displayed more complex, distributed, and semantically integrated networks than those who engaged primarily in individual-level actions (Level 1). While visual and statistical comparisons along the ENA \(X\)-axis showed no significant differences, the \(Y\)-axis revealed a meaningful distinction (\(p<0.001\), Cohen’s \(d=0.71\)), underscoring a qualitative shift in knowledge construction patterns associated with group collaboration and systemic engagement.

These findings align with Shaffer’s theory of epistemic frame development ¹⁴, which posits that professional competence is not merely the accumulation of content but also the development of structured ways of seeing and acting in a domain. Teachers who operate within collective co-production settings appear to construct knowledge not just through personal expertise but also through socially negotiated understanding, a key feature of distributed cognition.

These results are partially consistent with McMullin’s typology ²⁴ of co-production, suggesting that individual, group, and collective levels may be associated with differences in behavioral patterns as well as epistemic structures. While the Level 3 group showed broader access to relational and knowledge nodes, such differences should be interpreted cautiously, given the limited inferential scope of the current dataset.