Interpreting institute culture dynamics of technology adoption: a downscaling dynamic model

Abstract

This study proposed a dynamic model of organizational technology adoption within a school institute culture. We described an implementation of a nonhomogeneous hidden Markov model based on a downscaling scheme that can project the cultural factors of the institute onto a teacher’s implementation behavior. To reveal the dynamics of cultural evolution, we modeled the interactions within the institute’s organization by incorporating extra dependencies and downscaling variables into the underlying process of cultural change. We applied an analysis scheme to the nine-semester e-textbook usage of a primary school and gain insight into teachers’ technology adoption from a cultural perspective. We identified three states that represented the collective adoption contexts to examine how exogenous variables influence both the organization-scale context dynamics and the individual-scale implementation changes. The results showed that the effect of exogenous variables, especially external factors, varied between contexts and scales. The school’s norm was shown to affect organizational adoption culture. Teachers were sensitive to the adopted context, as they are inclined to adjust their usage to meet preexisting norms. Interventions such as seminars initiated by the teachers’ community were observed to cause a more long-term effect on the movement of the culture to an active context. Moreover, our research provided evidence that an organization can achieve more efficacy from teachers’ involvement in a high degree of cooperation in in-class experiences.

Appendices

Appendix A

Model definition

The transition of institute culture

We model the transition between culture states as a Markov chain to capture the collective adoption dynamics. The transition matrix is defined as follows:

$${Q}_{d, {s}_{t-1}\to {s}_{t}}=0\left(\begin{array}{ccc}\begin{array}{cc}\begin{array}{c}\begin{array}{c}{q}_{d,1\to 1}\\ {q}_{d,2\to 1}\end{array}\\ \begin{array}{c}\vdots \\ 0\end{array}\end{array}& \begin{array}{c}\begin{array}{c}{q}_{d,1\to 2}\\ {q}_{d,2\to 2}\end{array}\\ \begin{array}{c}\vdots \\ 0\end{array}\end{array}\end{array}& \begin{array}{cc}\begin{array}{c}\begin{array}{c}0\\ {q}_{d,2\to 3}\end{array}\\ \begin{array}{c}\vdots \\ 0\end{array}\end{array}& \begin{array}{c}\begin{array}{c}\cdots \\ \dots \end{array}\\ \begin{array}{c}\ddots \\ \dots \end{array}\end{array}\end{array}& \begin{array}{cc}\begin{array}{c}\begin{array}{c}0\\ 0\end{array}\\ \begin{array}{c}\vdots \\ {q}_{d, K\to K-1}\end{array}\end{array}& \begin{array}{c}\begin{array}{c}0\\ 0\end{array}\\ \begin{array}{c}\vdots \\ {q}_{d, K\to K}\end{array}\end{array}\end{array}\end{array}\right)$$

(1)

${q}_{d,k\to k\mathrm{^{\prime}}}$ is the transition probability from state $k$ to state $k\mathrm{^{\prime}}$ for teacher group $d$. Since most collective changes are gradual rather than severe fluctuant (Bayerl et al., 2016), we only allow a transition to move to an adjacent state based on the parsimony restriction suggested by Netzer et al. (2008) and Singh et al. (2011).

The transitions between the states are defined as an ordered logistic function, where a movement to a discrete context of culture occurs if the collective propensity for transition passes a threshold level, which indicates the change cost within a specific norm. The transition probabilities can be written as:

$$\begin{gathered} q_{{d,{\text{s}} \to {\text{s}} - 1}} = \Phi \left( {\mu_{sl}^{d} - \beta_{s} R_{dt} } \right), \hfill \\ q_{{d,{\text{s}} \to {\text{s}}}} = \Phi \left( {\mu_{sh}^{d} - \beta_{s} R_{dt} } \right) - \Phi \left( {\mu_{sl}^{d} - \beta_{s} R_{dt} } \right), \hfill \\ q_{{d,{\text{s}} \to {\text{s}} + 1}} = 1 - \Phi \left( {\mu_{sh}^{d} - \beta_{s} R_{dt} } \right), \hfill \\ \forall s \in \left\{ {1, 2, \ldots ,K} \right\} \hfill \\ \end{gathered}$$

(2)

where, $\Phi \left(.\right)$ is the binary logit function. ${\mu }_{sl}^{d}$ and ${\mu }_{sh}^{d}$ are the lower and the higher threshold level values for the institute culture of group $d$ in a state $s$ respectively. The collective propensity to change consists of exogenous impacts ${\beta }_{s}{R}_{dt}$. Here, ${R}_{dt}$ is a vector of time-varying covariates that represent the shared experiences and triggers gained by a group $d$ in period $t$. ${\beta }_{s}$ is a vector of parameters capturing the effect of the covariates.

Thus, we assume that the collective tendency for transition is jointly affected by the pressure of the school norm, the interventions, and the collective sharing experience. For example, if the sharing experience is highly positive (e.g., benefits are received from most teachers’ feedback) and enough interventions are posed, it is likely to shift the collective propensity for transition above the norm threshold of high bound needed for a transition to a higher state. Otherwise, the culture is likely to stay in the current state or slip to a lower state.

The teacher’s culture-dependent usage

Given the culture state $s$, the number of activities organized ${y}_{it}$ by teacher $i$ at period $t$ is defined as a zero-inflated mixture of two Poisson distributions:

$$P\left({y}_{it}|s=K,\dots \right)={\psi }_{0,it}\delta \left({y}_{it}\right)+{\psi }_{1,it}Pois\left({y}_{it}|{\lambda }_{1,si}\right)+{\psi }_{2,it}Pois\left({y}_{it}|{\lambda }_{2,si}\right)$$

(3)

where $\delta \left({y}_{it}\right)$ is the mixture component indicating no usage; $Pois\left({y}_{it}|{\lambda }_{j,si}\right)$ are two Poisson densities representing mixture components for moderate ($j=1$) and intensive ($j=2$) usage, where Poisson parameters ${\lambda }_{j,si}$ vary across the culture state $s$ and individual $i$.

Next, ${{\varvec{\psi}}}_{{\varvec{i}}{\varvec{t}}}=\left({\psi }_{0,it},{\psi }_{1,it},{\psi }_{2,it}\right)$ determine the portion of three components of usage. As the mixing weights, ${{\varvec{\psi}}}_{{\varvec{i}}{\varvec{t}}}$ vary as a function of exogenous variables that allow each teacher to pose usage in response to her propensity and influence conditioned on the culture state. Then we obtain the component weights using an ordered logit model as follows:

$$\begin{gathered} \psi_{0,it} = {\Phi }\left[ {\gamma_{1} - \left( {\rho_{0,si} + {\varvec{\rho}}_{i} W_{it} } \right)} \right] \hfill \\ \psi_{1,it} = {\Phi }\left[ {\gamma_{2} - \left( {\rho_{0,si} + {\varvec{\rho}}_{i} W_{it} } \right)} \right] - {\Phi }\left[ {\gamma_{1} - \left( {\rho_{0,si} + {\varvec{\rho}}_{i} W_{it} } \right)} \right] \hfill \\ \psi_{2,it} = 1 - {\Phi }\left[ {\gamma_{2} - \left( {\rho_{0,si} + {\varvec{\rho}}_{i} W_{it} } \right)} \right] \hfill \\ \end{gathered}$$

(4)

${\gamma }_{1}$ and ${\gamma }_{2}$ are the boundaries that determine the break points between the three components; ${W}_{it}$ are the covariates that indicate impacts at individual-scale scale; ${{\varvec{\rho}}}_{i}$ is the coefficients of individual-specific impact; ${\rho }_{0,si}$ captures the unobserved intrinsic characteristics. Thus, individual-scale impacts linearly influence teacher’s propensity, which in turn affects the mixture proportion of usage components.

Appendix B

Interview protocol

See Table 8

Table 8 Interview protocol

Appendix C

Coding scheme and examples

1. Theme: Norms and pressure
➢ Code: Institute norm
Label (selection)	Interview example
Norm change	“In the beginning, a few subject leaders and a few young teachers participated more in the training and practice. The rest of the teachers were asked to join in, but using the platform in teaching was still voluntary. Since last semester (the third semester of observation), the school has asked every teacher to create two quality lessons and share them on the platform for everyone's reference, regardless of whether they use them in their regular teaching.”
Emerging norms for entrants	“Starting from the third semester, new entrants to the school must participate in the 'e-schoolbag' (platform) skills training.”
Institutional norm	“We have always had a 'push-in' tradition, where the subject leader (or the teacher who needs to learn) can go into any classroom (with permission) to observe the lecture. (I think) I'd better be on the platform when another teacher observes my class.” (subject leader)
Pressure from leadership	“This semester (the third semester), open classes are required to incorporate digital platforms, which I think the leaders believe is a feature of our school's educational information technology.”
Pressure from group leaders	“I think that since this year (the third semester), the preparation groups have become more demanding in using the platform for lesson planning and have developed more content around it.”
Norm change	“Since this semester (the sixth semester), we did not require teachers to use the platform in their work, as we felt that most teachers had become very proficient in the previous semesters”
2. Theme: Promotion and intervention
➢Code: Seminar
Label (selection)	Interview example
Demonstration in seminars	“During the teaching and research meetings, other teachers will demonstrate, and we will follow.”
Learning by doing	“When we polished the public class, we kept some good experiences and then talked about them in the teacher seminars (to introduce the experiences).”
Before-seminar communication	“When I prepare for an open class (which is before seminars), I discuss how to use the platform to organize the class with experienced veteran teachers.”
After-seminar communication	“We have an open class (with seminars) every Tuesday or Wednesday, and the teachers of this subject come to the open class. After the open class, we will arrange a class time for communication, and while everyone is there, we will arrange some technical communication activities for the teachers.”
Principal’s request for seminars	“Teachers of the same subject are required to observe and evaluate the public lectures and to participate in the post-lecture discussions.”
➢ Code: Special event
Label (selection)	Interview example
Visits	“Public classes don't always need to be on a digital platform. It depends on the teacher and the content of the class. But nowadays, many visits are related to our platform, and we use it more frequently when people visit.”
Expectations of regional administration	“We (the school) are one of the pilot schools in the district for the "e-schoolbag," and the district education administration provides support for the purchase of electronic equipment and the purchase of applications. The regional director often comes to check on its implementation, and we need to demonstrate its effectiveness.”
School identity	“We are an 'e-schoolbag' demonstration school, and people come to observe us to see how we use technology. This is what makes our school special.”
Motivation for demonstration	“People may want to observe how we use technology. During open campus days and inter-school days, some of the more technically adept teachers will show as much of their work as possible.”
Communication with visitors	“When there is a visit, visitors will fill in the class's comments; we also often communicate with visitors about this teaching method.”
3. Theme: Support from collective experience
➢Code: Shared lesson planning experience
Label (selection)	Interview example
Teaching groups	“Our teachers in the same teaching groups will share their experiences. There are two teachers who have just graduated. They have a better mastery of technology, and we often ask them for advice.”
Communication among colleagues	“Because we now have the task of producing selected lessons, the results are to be made public (shared). When we encounter something we don’t understand, we ask other teachers for advice.”
Standards and templates	“Several other teachers and I sometimes use several of the same PPT (slides) templates specifically for learning task images.”
Standards and templates	“Previously, naming the files was a bit tricky, but now we divide them into ‘before class’, ‘in class’ and ‘after class’, which is very simple and clear.”
Vicarious experience	“I will refer to the results of lesson planning shared by other teachers and share my quality lesson planning results.”
➢Code: Shared in-class experience
Label (selection)	Interview example
Communication after lecture observation:	“We (teachers) often discuss the appropriateness of the timing and learning content of having students use tablets in the classroom.”
Learning in lecture observation:	“I learned in other teachers' classes that there are times when students need to disconnect their machines from the server so that they don't misuse the equipment and neglect listening to the lecture.”
Learning in lecture observation	“After seeing the digital lesson planning materials shared by other teachers in the sharing platform, I would often imitate how he used these materials in his classroom by watching their lessons.”
Importance of observation	“The lesson planning materials shared in the system are not different from the paper lesson plans, but organizing the activity in the class to allow students to use the materials by using the tablet is very different from the previous teaching style. This needs to be observed; otherwise, it is difficult to grasp.”
4. Theme: Perceptions in personal experience
➢Code: Individual lesson planning experience
Label (selection)	Interview example
Lesson preparation burden	“This is different from how we used to prepare lessons. We used to prepare lesson plans on paper, but now we need to use computers and tablets. Actually, we teachers move our pencils faster (referring to paper-based lesson preparation).”
Change of lesson preparation content	“(In the math class) we need to take quizzes with the class. Previously, it was enough to do it in slides, but now we need to make the questions electronic and enter them into the system in advance so that students can answer them on the tablet.”
Additional time spent	“[As an entrant], the design of my teaching content is more aligned with the platform feature. Actually, I prepared for a longer period with my subject leader during lesson planning.”
Mastery from experience	“After using the system more, I slowly got used to it, and at the same time, became much more proficient.”
➢ Code: Individual in-class experience
Label (selection)	Interview example
Timely feedback	“The most helpful thing about the system is that I can assess the students’ knowledge in class. I post a question (using the platform), and I immediately know which students got it wrong.”
Timely in-class evaluation	“I can see from the teacher’s side which students have uploaded their answers, and I will praise the students who uploaded early. The students will compete with each other to see who is doing the exercises faster.”
Increase in evaluation methods	“Some assignments now have students using their tablets to complete. If it is done well, I will give credit and post it on the ‘homework wall’ (a page to showcase assignments) for other students to see.”
Perceived ease of use	“Previously, we used tools such as WeChat to communicate with parents, which was convenient but not as effective as this system is in meeting teaching needs.”

Appendix D

The time-discounted cumulative experience variables

We define the teacher’s experience of the system’s use represented by the number of specific actions accumulated up to the previous period $t-1$. It implies that more recent participations in the system impacts propensity of collective adoption than earlier involvement. In this study, the shared lesson plans and shared in-class actions are considered the collective experience that may pose the underlying impact on institute culture. This experience can be modeled by a time-discounted cumulative experience function derived from the learning curve model (Singh et al., 2011):

$$Experience_{dt} = \mathop \sum \limits_{m = 1}^{t - 1} \delta^{{\left( {t - m - 1} \right)}} \cdot log\left( {N_{dm} + 1} \right)$$

where, ${N}_{dm}$ is the number of specific actions performed by the discipline group d in period $m$. Here, we log-transform ${N}_{dm}$ to capture the potentially diminishing effects. $\delta$ is a decay factor and is positive but less than or equal to 1. $\delta$ closer to one would indicate a lower decay in the experience's impact.

We also account for the experience at the individual scale. Accordingly, ${N}_{dm}$ is replaced as ${N}_{im}$, the number of actions performed by teachers $i$ in period $m$. The individual lesson planning experience and in-class experience are modeled as follows:

$$Experience_{it} = \mathop \sum \limits_{m = 1}^{t - 1} \alpha^{{\left( {t - m - 1} \right)}} \cdot log\left( {N_{im} + 1} \right)$$

where, ${N}_{im}$ is the number of specific actions performed by teacher i in period $m$. $\alpha$ is a decay factor and is positive but less than or equal to 1.

Before the estimations, we need identify the values of discounted factors of the decaying variables. The optimal values of discounted factors are determined by comparing the log-likelihoods of models for different values. We then choose the values (${\delta }_{plan}=0.38$, ${\delta }_{in-class}=0.41$, ${\alpha }_{plan}=0.73$, and ${d}_{in-class}=0.79$, respectively) that provide a maximum joint likelihood of estimates ranging from one-state and five-state models.