1 Introduction

In the current society, the field of education is undergoing a profound transformation, with traditional offline classes gradually integrating with digital online education. The wide application of digital technology has made online education more accessible, and as of June 2020, the number of Chinese online education users has reached 380 million, accounting for approximately 40.5% of the total internet user population [1]. During the COVID-19 pandemic that swept across the globe in 2020, the learning environment for Chinese students shifted from schools to homes [2], highlighting the popularity and widespread nature of digital learning in Chinese households. Preschool children have also had increased exposure to educational games in the home environment, and this integration of home and school education has demonstrated significant improvements in preschool children' learning outcomes [3, 4]. Therefore, research on educational games for preschool children has become increasingly prominent [5].

Educational game research involves multiple disciplines such as education, psychology, and computer science [6], educational games hold tremendous potential in enhancing student engagement and learning outcomes [3, 4]. The effectiveness of educational games has been widely studied in the academic community, with research indicating that well-designed educational games can enhance learners' hands-on ability, problem-solving skills, creativity, and teamwork ability. Game design should be based on effective educational principles, such as problem-solving, self-directed learning, and task-oriented learning, which integrate educational objectives into the gameplay, thereby enhancing engagement and challenge [7]. As an innovative form of digital online education, educational games hold potential significant impacts on preschool children's education for enlightenment. These games integrate audio, video, and interactive elements to provide preschool children with an interactive and enjoyable learning experience that can foster the development of cognitive, language, and thinking abilities. Furthermore, educational games create an atmosphere of family-based interactivity, allowing parents to participate in the games with their children, promoting positive family interactions [2].

To maximize the effectiveness of preschool children's enlightenment educational games, game design is crucial. This requires designers to accurately identify and grasp the key factors that affect game design during the development process. The primary contribution of this study is the systematic examination of key factors in the design of preschool children's enlightenment educational games through decision analysis methods, guiding the creation of both enjoyable and effective enlightenment educational games and ultimately enhancing preschool children's learning interests and improving their outcomes. From a theoretical perspective, this study utilizes decision analysis methods to propose key factors for the design of preschool children's enlightenment educational games, offering more comprehensive and in-depth theoretical support for educational game design. Practically, the study's findings provide targeted design guidance for designers, significantly impacting the deeper application and development of educational games in the preschool education sector.

The remaining part of this paper is organized as follows: Section 2 reviews relevant research. Section 3 introduces decision analysis methods, including the application of SET analysis method to identify gaps in development opportunities, constructing an interactive system design model for educational games aimed at preschool children's enlightenment using Analytic Hierarchy Process and identifying key factors in game design by calculating the weight values of various factors, and the utilization of Fuzzy Comprehensive Evaluation method to verify the reasonableness of the proposed scheme. Section 4 presents the research results. Section 5 offers corresponding discussions on the research. Section 6 summarizes the study and outlines future directions.

2 Related work

Through a literature review, this paper elaborates on the significance of educational games and their application in early childhood or preschool education. It explores the advancements and limitations of current research in the design of educational games for preschoolers' enlightenment, thereby determining the direction of this study.

2.1 Educational games and the development of preschool children

The positive impact of educational games on the development of preschool children: Cognitively, games can foster the development of children's language, mathematical logic, and spatial cognition abilities [8]. Emotionally, the interactive elements and storyline designs in games aid in cultivating children's emotional management skills, self-awareness, and empathy [9]. Socially, through multiplayer online games or collaborative game tasks, children can establish connections with peers, learning to respect others, follow rules, and resolve conflicts through interactions [10].

The importance of combining game design elements with child development theories: Child development theories offer game designers a profound understanding of children's cognitive, emotional, and social skill development. They guide designers in integrating appropriate challenges, stimuli, and interaction methods into game designs. Piaget's Cognitive Development Theory [11] highlights those preschool children are in the preoperational stage, characterized by concrete and intuitive thinking. In game design, vibrant colors, lively animations, and intuitive user interfaces can effectively capture children's attention and enhance their learning. Erik Erikson's Psychosocial Development Theory [12] underscores the significance of social interaction in children's emotional and social development. Games should incorporate elements of both cooperation and competition, stimulating a sense of belonging and achievement while fostering social skills. Extensive explorations have been made in this domain. Some studies [13, 14] concentrate on leveraging game design elements to advance specific skill development in children, such as language proficiency, mathematical thinking, or creativity. These investigations often employ experimental methods, comparing the impact of various game designs on children's learning outcomes. Other studies [15,16,17] focus on translating child development theories into pragmatic game design principles and practical guidelines, aiming to provide educational game developers with frameworks that ensure both enjoyability and educational value in their creations.

2.2 Key factors and theoretical frameworks for educational games design

A review of key factors in educational game design, particularly for preschool children: In the field of educational game design for preschool children, there are numerous intertwined key factors. Firstly, the age-appropriateness and engaging nature of game content are crucial [18]. Preschool children have limited cognitive abilities and attention spans, so the game content must be simple and straightforward, while being engaging enough to capture their attention. Secondly, interactivity and feedback mechanisms are central elements in game design [19]. Children learn new knowledge through interaction with the game, and immediate feedback can enhance their motivation and sense of achievement. Thirdly, achieving educational goals is a non-negligible aspect, games must effectively impart knowledge and skills [20]. Fourthly, the intuitiveness and ease of use of the game interface are also important [21]. Preschool children have limited understanding of complex operations, so the game interface must be intuitive and clear for quick mastery. Lastly, visual and auditory elements such as color, sound effects, and animations have proven to play a significant role in attracting children's attention and enhancing their interest in learning [22]. However, given these numerous factors, which ones take precedence?

Exploring existing theoretical frameworks and models for educational game design and their limitations in practice: Various theoretical frameworks and models have emerged in the field of educational game design, offering designers diverse perspectives and methodological guidance. For instance, behavioral learning theory underscores shaping learners' behavior through reward and punishment mechanisms, employing elements like points and badges in game design to motivate children in completing learning tasks [23]. Cognitive learning theory focuses on the progression of learners' internal psychological processes and cognitive structures, emphasizing the nurturing of children's thinking patterns and problem-solving abilities in game design [24]. Constructivist learning theory highlights learners' active construction of knowledge and its contextual nature, emphasizing the creation of authentic scenarios, opportunities for interactive collaboration, and spaces for independent exploration within game design [25]. Nonetheless, there are certain limitations to the application of these theoretical frameworks and models in practice: Firstly, integrating different theoretical frameworks poses a challenge, as a singular framework may not comprehensively explain and guide the intricate and multifaceted processes of educational game design. Secondly, the disconnect between theoretical frameworks and practical implementation is a noteworthy concern. Sometimes, theoretical guidance may be overly abstract or idealized, rendering it challenging to directly implement in practical game design projects.

2.3 Current situation and challenges of digital enlightenment educational applications in the Chinese market

Describing the current situation of digital enlightenment educational applications for preschool children in the Chinese market: Currently, the Chinese market witnesses a booming trend in digital enlightenment educational applications for preschool children. These applications primarily fall into categories such as cognitive enlightenment, language learning, artistic cultivation, and comprehensive skill enhancement, with representative ones listed in Table 1. However, these applications still encounter numerous challenges in addressing the educational needs of preschool children [17]. Firstly, there is often a mismatch between game content and educational objectives, where some applications overly emphasize entertainment at the expense of educational value, resulting in minimal tangible learning outcomes for children during play. Secondly, many applications lack targeted approaches, failing to tailor learning content to children's age, cognitive level, and interests. Furthermore, some applications are not user-friendly in terms of their interfaces and usability, posing difficulties for both children and parents. It is precisely based on the challenges faced by existing digital enlightenment educational applications in meeting the educational needs of preschool children, as well as the shortcomings in game design, that this study identifies an opportunity to refine game design by extracting key factors from enlightenment educational game design, ultimately aiming to enhance learning outcomes.

Table 1 Overview of existing digital enlightenment educational applications in the Chinese market [26]
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Based on the research review, this study posits that there is still a lack of the methods capable of swiftly extracting the key factors for designing preschool children's educational games for enlightenment, which can be directly applied to practical game design projects. This would assist designers in promptly recognizing significant design factors and responding effectively in their design practices, ultimately leading to efficient game designs that elevate preschool children's learning interests and enhance their learning outcomes. The next section will elaborate on the approaches, presenting how they can be used to identify gaps and opportunities in developing preschool children’s educational games for enlightenment, to construct an interactive system design model for such games, to highlight the key factors for design practice, and to evaluate practical solutions.

3 Methods

This section introduces the decision analysis methods employed in this study. SET analysis method is used to deeply examine the impact of social, economic, and technological factors on the educational games market, thereby revealing potential gaps in development opportunities; Analytic Hierarchy Process is applied to construct an interactive system design model for enlightenment educational games and to calculate the relative importance among various factors; and Fuzzy Comprehensive Evaluation method assesses the rationality of the design proposals. The application of these decision analysis methods provides strong theoretical support and practical guidance for the design of preschool children educational games for enlightenment. When employing relevant methods for the study, Zhu Yan, as the lead researcher, actively participated in and oversaw the entire process of interviewing and researching.

3.1 SET analysis method

SET analysis method was introduced by Jonathan Cagan and Craig M. Vogel in 2002 [27]. It is a method used in the new product development process to analyze market opportunity gaps. It can be used to evaluate the balance between social, economic, and environmental factors. The goal of this method is to help decision-makers comprehensively understand various factors, thereby better understanding potential impacts, opportunities, and challenges, and making more informed decisions. SET analysis method can be regarded as a specific application of decision analysis methods.

This study aims to use SET analysis method to identify opportunities and gaps in developing preschool children's educational games for enlightenment. Analyzing the SET elements faced by the preschool children's educational games for enlightenment and understanding the characteristics of existing products and technologies in the market can help identify gaps in new product development opportunity gaps.

  1. 1.

    Data collection: data collection was primarily carried out through focus group discussions. To ensure comprehensiveness and representativeness of the data, we carefully selected 70 parents of preschool children and 20 system designers as participants from districts with abundant educational resources in Shanghai, such as Minhang and Xuhui. Each focus group consisted of 7 parents of preschool children or 5 system designers. This group size ensured that every participant had an opportunity to speak and allowed for in-depth discussions, while enabling researchers and research assistants to effectively manage the interview process. Table 2 presents demographic information of the interviewees and survey participants, along with the duration and frequency of the dialogues. For the parents of preschool children, the interviews were led by Zhu Yan and Zhang Yuexia, along with two research assistants, between June and August 2021. The interviews were conducted in various locations, including community centers, libraries, and online platforms, to facilitate participants' free expression of views and sharing of experiences. As for the system designers, interviews were conducted by Zhu Yan, Zhou Rui, and two other research assistants between June and September 2021. Considering the nature of the designers' work, some interviews took place in design firms or via online meetings.

  2. 2.

    Data recording and transcription: all interviews were rigorously transcribed. During the interviews, high-quality audio recording devices were used to ensure the completeness and clarity of the audio. Immediately following each interview, research assistants commenced the transcription process, converting the audio into verbatim text. This crucial step preserved the integrity and finer nuances of the raw data, thereby facilitating subsequent data analysis.

  3. 3.

    Data analysis and preparation: following transcription, research assistants Chen Jiawei and Yue Yisheng undertook data analysis from October to December 2021. Initially, they reviewed all transcripts to obtain a comprehensive understanding of the data. Subsequently, they employed qualitative data analysis software to assist with data coding and categorization. The data was systematically organized and labeled based on themes, viewpoints, and emotions, enabling in-depth analysis and comparison. Throughout the analytical process, specific emphasis was placed on examining divergences and areas of agreement in opinions among different cohorts, namely parents of preschool children and system designers, along with their varying perspectives on SET elements and demands for smart curricula. To resolve points of contention, we periodically organized discussion sessions and invited interview participants, striving for deeper insights and consensus. These deliberations were also documented and integrated into the data analysis. Ultimately, we comprehensively compiled, summarized, and analyzed the collected information, culminating in a concise summation of the SET elements.

Table 2 Demographic information of interviewees and survey participants, as well as the duration and frequency of their dialogues
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3.2 Analytic Hierarchy Process

Analytic Hierarchy Process, initially proposed by Thomas L. Saaty [28] in 1971, is a decision-making support tool designed to handle multi-level structural problems. It systematically organizes complex judgment processes by converting intuitive cognition into distinct hierarchical elements, enabling quantitative calculations, comparisons, and analyses of these elements. This approach results in a ranked importance of factors, aiding in the development of strategic plans. Analytic Hierarchy Process offers a systematic and structured approach for decision-making in complex situations, enabling decision-makers to better understand and evaluate the relationships among various factors.

This study aims to utilize the Analytic Hierarchy Process in constructing an interactive system design model for enlightenment educational games. Through user research to understand the needs and expectations of preschool children's enlightenment education, including interviews, surveys, and interactions with target user groups such as parents, teachers, and preschool children, initial information was obtained, and initial criteria and factor layers were summarized.

Tables 3, 4, and 5 present the demographic information of the various user groups participating in the survey. Considering the distinct characteristics and needs of parents, teachers, and preschool children, moderate arrangements were made in terms of group size, conversation duration, and frequency. Each group of parents consisted of 5-7 individuals, with each parent's conversation lasting 60 minutes. Interviews with parents were conducted every two weeks. For teachers, each group comprised 4-6 individuals, and each teacher's dialogue lasted for 45 minutes. Teacher interviews also took place every two weeks. As for preschool children, groups of 3-5 kids participated, with each child engaging in a 30-minute conversation. Interviews with the children were held weekly. This arrangement ensured that participants could provide valuable information adequately without being overly fatigued. The entire research process spanned three months.

Table 3 Demographic information of the parents participating in the survey
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Table 4 Demographic information of the teachers participating in the survey
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Table 5 Demographic information of the preschool children participating in the survey
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During the parents' interviews, two distinct viewpoints emerged: one placing emphasis on subject knowledge and exam skills, and the other prioritizing the cultivation of interests and creativity. To address these differences of opinion, we adopted the following coping strategies: conducting an in-depth inquiry into parents' educational philosophies and expectations, organizing group discussions aimed at identifying commonalities, encouraging frank expression through anonymous feedback, and conducting a comprehensive analysis of opinions to strike a balance between academic disciplines and creativity.

We convened system designers, professors of industrial design, and experts in children's games to jointly discuss using the Delphi method. They employed interview guides, questionnaires, and expert discussion materials to comprehensively understand the needs of early childhood education. To ensure the effectiveness of these tools, we carefully designed and refined them through literature research, professional consultation, and small-scale pilot testing. After multiple rounds of discussions, the expert team reached a consensus and used this as a foundation to construct a hierarchical model, guaranteeing the model's rationality and practicality. Finally, the model's validity was verified through rigorous testing and evaluation.

Based on the established interactive system design model, Zhu Yan and Zhang Yuexia were responsible for developing the expert evaluation form. Experts were invited to assess pairwise comparisons and assign scores for each indicator at the criterion and factor layers. The importance levels were scaled from 1 to 9, with specific meanings as shown in Table 6 [29]. In Table 6, the indicators i and j are utilized, denoting the rows and columns of the judgment matrix, respectively. More precisely, i represents the row index, while j corresponds to the column index. A total of 22 experts were invited to participate in the scoring process, encompassing 10 system designers, 7 professors specialized in industrial design, and 5 professionals in the field of children's game coaching. This diverse assemblage of experts ensures a comprehensive and multifaceted approach to the study. Under the direction of Zhu Yan and Zhang Yuexia, aided by a research assistant, the experts were systematically organized in March 2022 to conduct evaluations within designated timeframes, thereby ensuring timely and efficient assessments. Upon completion of the evaluation forms, the compilation and analysis of data were entrusted to Zhou Rui, alongside two dedicated research assistants. The judgment matrices and weight values of each layer of indicators are obtained through expert scoring.

Table 6 Value scale of judgment matrix index importance level
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Due to the variability, randomness, and diversity in each expert's perception, it is necessary to validate the reasonableness of the judgment matrices and weights. When applying Analytic Hierarchy Process to compute the characteristic vectors of judgment matrices, it is relatively easier to perform accurate calculations for second and third-order matrices. However, as the order of matrices increases, the computational difficulty also escalates. The hierarchical model of interactive system design encompasses numerous indicators, making precise calculations challenging. Therefore, the square root approximation method has been adopted.

Calculate the weights using the square root method:

$${\varpi }_{i}\text{=}\sqrt[n]{{\sum }_{i=1}^{n}{a}_{ij}}$$
(1)

Normalize the weight vector:

$${\omega }_{i}=\frac{{\varpi }_{i}}{{\sum }_{i=1}^{n}{\varpi }_{i}}$$
(2)

Calculate the maximum eigenvalue and CI value:

$${\lambda }_{max}=\frac{1}{n}{\sum }_{i=1}^{n}\frac{{\left(A\omega \right)}_{i}}{{\omega }_{i}}$$
(3)
$$CI=\frac{{\lambda }_{max}-n}{n-1}$$
(4)

In the equation, n represents the order of the matrix, and A is the judgment matrix

To calculate the CR (Consistency Ratio) based on the CI (Consistency Index) and RI (Random Index) values and determine if the consistency is acceptable or not:

$$CR=\frac{CI}{RI}$$
(5)

RI is a random consistency index of the same order as A. It is derived by repeatedly calculating the eigenvalues of randomly generated judgment matrices over 500 times and then taking the arithmetic mean. The specific values can be determined by referring to a table. Table 7 lists the values of the average random consistency index for orders 1 to 12.

Table 7 Average random consistency index
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3.3 Fuzzy Comprehensive Evaluation method

Fuzzy Comprehensive Evaluation method, first proposed by Lotfi A. Zadeh in 1965 [30, 31]. It serves as a decision-support tool for handling information uncertainty and fuzziness, which enables decision-makers to consider the fuzzy relationships among different factors. Through fuzzy logical operations within fuzzy set theory, it facilitates comprehensive evaluations of various factors. In this method, the concept of fuzzy mathematics is employed to express uncertainty, fuzzy sets are used to describe fuzzy relationships, and fuzzy logical operators are utilized for comprehensive evaluations. This approach confers distinct advantages when addressing decision-making problems that are characterized by fuzziness and uncertainty.

This study aims to employ the Fuzzy Comprehensive Evaluation method for assessing the design proposal. Firstly, the factor (index) set of the evaluated target and the evaluation criteria universe are determined. Then, a membership matrix is obtained by conducting fuzzy evaluations for individual factors. After that, fuzzy synthesis is performed on the weight vector group of each factor (index) to obtain the result of fuzzy comprehensive evaluation. Fuzzy comprehensive evaluation can be divided into first-level and multi-level evaluations. This article adopts a multi-level fuzzy evaluation approach. Through multi-level fuzzy evaluations, the membership degrees of the hierarchical classification universe at each level are obtained. It is particularly suitable for evaluating indicators with multiple factors, ensuring reliable evaluation results.

  1. 1.

    Determine the factor set: let the factor set be \(Z=\left\{{A}_{1},{A}_{2},\dots ,{A}_{n}\right\}\), where \({A}_{i}\), \(i=\text{1,2},\dots ,n\) represents the i-th criteria layer, and \(n\) is the number of criteria layers. Each criteria layer \({A}_{i}\) contains several factors, forming a subset of factors \({\mu }_{i}={B}_{i1}, {B}_{i2},\dots ,{B}_{im}\), where \(im\) represents the number of factors under the i-th criteria layer.

  2. 2.

    Determine the comment set: the comment set is set as \(\xi =\{{\xi }_{1},{\xi }_{2},\dots ,{\xi }_{p}\}\), representing \(p\) different evaluation levels (such as excellent, good, qualified, unqualified, etc.), and the specific value of \(p\) is determined according to actual needs. The comment vector is \(\alpha ={[{\alpha }_{1},{\alpha }_{2},\dots ,{\alpha }_{p}]}^{T}\), where \({\alpha }_{j}, j=\text{1,2},\dots ,p\) corresponds to the score of the j-th level. 34 experts were invited to evaluate the system, including 15 system designers, 7 design professionals and students, and 12 system users.

  3. 3.

    Determine the fuzzy comprehensive evaluation matrix: for each criteria layer \({A}_{i}\), there is a corresponding fuzzy evaluation matrix \({M}_{i}\). The number of rows and columns of the matrix \({M}_{i}\) is determined by the number of factors in the factor subset \({\mu }_{i}\) and the number of levels in the comment set \(\xi\), respectively. The elements of the matrix \({M}_{i}\) represent the membership degrees of each factor at different comment levels.

  4. 4.

    Calculate the evaluation vector of the criteria layer: let the weight vector of the criteria layer \({A}_{i}\) be \({\omega }_{i}={\omega }_{i1}{,\omega }_{i2},\dots {,\omega }_{im}\), then the evaluation vector \({T}_{i}\) of the criteria layer can be obtained through the fuzzy synthesis of \({\omega }_{i}\) and \({M}_{i}\): \({T}_{i}={\upomega }_{i}\times {M}_{i}\). The fuzzy synthesis operation here can be weighted average, maximum, and minimum operations, etc., specifically selected according to actual needs.

  5. 5.

    Establish a fuzzy comprehensive evaluation model for overall indicators: the fuzzy comprehensive evaluation model for overall indicators consists of evaluation vectors for all criteria layers, i.e., \(T=[{T}_{1}, {T}_{2}, ..., {T}_{n}]\). Here, \(T\) is a two-dimension matrix whose number of rows and columns are determined by the number of criteria layers and the number of levels in the comment set, respectively.

  6. 6.

    Calculate the comprehensive evaluation vector and score: let the weight vector of the criteria layers be \(\Omega =[{\omega }_{1}, {\omega }_{2}, ..., {\omega }_{n}]\), \({\omega }_{i}\) here refers to the weight of the criteria layer \({A}_{i}\) in the overall evaluation, which is different from the factor weight mentioned earlier, then the comprehensive evaluation vector \(W\) can be obtained through the fuzzy synthesis of \(\Omega\) and \(T\): \(W=\Omega \times T\). The final score \(Y\) is calculated by taking the dot product of \(W\) and the comment vector \(\alpha\): \(Y=W\bullet \alpha\). The dot product operation here refers to multiplying corresponding elements and then summing them up.

4 Results

According to the methods introduced in section 3, this paper reveals the potential development gaps in preschool children's educational games for enlightenment, has constructed an interactive system design model, and identified key factors in the design process based on this model. It proposes specific design practice schemes and carries out scheme verification.

4.1 Identifying development opportunity gaps based on SET analysis method

Table 8 presents a summary of the SET elements according to the methods described in Section 3.1. Based on the analysis of the SET elements mentioned above, the product development opportunity gaps for preschool children's educational games for enlightenment are summarized as follows:

Table 8 Analysis of SET elements in preschool children's initial education
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At the societal level, there is a market need for more personalized learning support tools to meet the diverse needs of children at different ages and stages of development. Developing interactive platforms for families can help parents better understand and support their children's educational needs. This includes designing more digital early childhood education content. On the economic front, as disposable incomes of families increase, parents are more willing to invest in their children's education, creating commercial opportunities for the development of high-quality early childhood education products. However, it should be noted that designing a game solely for learning purposes differs from creating a game intended for sale. The former aims to enhance learning outcomes, while the latter places greater emphasis on market demands and entertainment preferences. This difference can influence the priorities in game design. For instance, an excessive emphasis on extrinsic motivations like rewards may undermine learning effectiveness. Therefore, it is crucial to strike a balance between education and entertainment in the design of preschool children's educational games for enlightenment, striving to meet both learning objectives and market demands. The market for personalized education and training services is rapidly expanding, with online education courses complementing traditional offline kindergarten education. Games, as tools for children's enlightenment education, offer high market value. On the technological side, big data analytics tools can be employed to monitor and assess children's learning progress, aiding in the customization of graded educational content. Technological innovation contributes to the creation of more creative and educational multimedia content, enhancing the user experience and educational effectiveness of products.

4.2 Building an interactive system design model for preschool children's educational games for enlightenment based on Analytic Hierarchy Process

Based on the methods outlined in Section 3.2, the interactive system design model illustrated in Fig. 1 has been ultimately established.

Fig.1
figure 1

Interactive system design model

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The judgment matrices and weight values of each layer of indicators obtained according to the methods in Section 3.2 are shown in Tables 12, 13, 14, 15, 16 and 17 in the Appendix .

We have verified the rationality of each judgment matrix and its corresponding weights. Usually, if CR is less than or equal to 0.1, the judgment matrix is considered consistent, and the weights are reliable. If CR is greater than 0.1, it is necessary to revise or review the judgment matrix to improve consistency. As shown in Table 9, the relative consistency indices (CR) for various levels of indicators are all less than 0.1, indicating that the consistency tests for all judgment matrices have passed. Finally, the comprehensive weights for each factor are calculated, as shown in Table 10.

Table 9 Consistency test results of judgment matrix
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Table 10 Integrated weight of individual factors
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From the analysis of the data in Table Appendix 12, it is evident that in descending order of importance, the criteria layer includes user experience, educational content, technical performance, security, and sustainability. This indicates that user experience holds the highest importance throughout the system design process. It directly impacts the acceptance, engagement, and learning effectiveness of the early childhood education system. Technical performance holds a certain level of importance in system design. It not only affects the stable operation of the system but also directly influences user experience and educational quality. While security is ranked lower in terms of weight, its importance lies in providing a safe online learning environment for children. Although sustainability ranks lower in terms of weight, it plays an irreplaceable role in safeguarding the long-term health and user satisfaction of the application.

Starting from the criteria layer, it is further broken down into more specific indicators at the factor layers, as is evident from Table 10. According to the table, interface design (weight: 0.5342), operational convenience (weight: 0.2073), and visual effects (weight: 0.1575) are of high importance in user experience. Interactivity (weight: 0.3602), appropriateness (weight: 0.3118), and purposefulness (weight: 0.1878) carry significant weight in educational content. Data processing capability (weight: 0.4576) and device performance requirements (weight: 0.2543) are crucial aspects of technical performance. Promotional content control (weight: 0.5334) and age-appropriateness control (weight: 0.2756) significantly impact safety. Content updates (weight: 0.4864) and fault tolerance (weight: 0.3431) are key considerations in terms of sustainability.

4.3 The practice of interactive system design for preschool children's educational games for enlightenment

The proposal of the games interactive system design solution in this paper is an iterative process because interactive systems involve various complex factors. It is not practical to solve all the issues at once in practice. Instead, it is necessary to identify and prioritize the factors that have a more significant impact on the overall system and address problems in incremental steps.

After calculating the weights of factors based on the Analytic Hierarchy Process method, the top 9 key factors in the priority ranking are selected for focused design. Following an in-depth review and analysis of relevant literature, the study proposes specific solutions closely related to the design of children's educational games for enlightenment, as shown in Table 11. These solutions are centered around the core objective of guiding children through direct perception, personal experience, and hands-on operation for enlightenment learning. Each design solution is carefully crafted based on scientific theories of children's learning and previous research findings, ensuring both theoretical depth and practical applicability in the design and practice of children's educational games for enlightenment.

Table 11 Design solutions under weight analysis of interactive system design model
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The game's operational logic structure depicted in Fig. 2 details the overall process of the interactive system and the execution of specific game tasks. It guides subsequent visual design and programming development by defining jump conditions between game nodes and cyclic execution paths. The interactive system is supported by operating systems above Android 4.4, developed using H5+JS technology. It boasts rapid packaging speed, high efficiency, minimal memory usage for the application, fast loading times, and convenient cross-platform compatibility. Users log in and enter the game lobby, sending their user ID. The system reads user information to retrieve relevant data Users are provided with multiple learning pathways, Initially, users can enjoy a free trial of a certain number of games to complete the learning process. If users wish to continue their learning, they can subscribe to corresponding premium packages. Subscribers gain access to new interactive games and earn stars upon completion. After completing an interactive game, the system returns to the lobby and sends the interaction results. When users accumulate a certain number of stars, they can unlock advanced courses. Advanced courses encompass comprehensive learning of five major modules: logical reasoning, observation, memory, general knowledge, artistic creativity, and physical coordination. Users earn stars of various types and quantities as they progress. The system encourages daily participation through the provision of five daily tasks. Both trial and premium users can participate and earn stars upon task completion. The lobby sends the results to the server.

Fig. 2
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Game operation logic diagram

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Figure 3 is the startup loading page. As shown in Figs. 4, 5, 6, and 7, based on the educational needs for the development of learning abilities in five domains for preschool children: science, language, social skills, arts, and health, the interactive course content is divided into five major modules: logical reasoning, observation, memory, general knowledge, and artistic creativity.

Fig. 3
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Startup loading page

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Fig. 4
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Five major modules of course content

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Fig. 5
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Three varying levels of difficulty

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Fig. 6
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Immediate grading

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Fig. 7
figure 7

Lightweight interactive game

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It allows for setting different difficulty levels based on the child's age or learning performance, ranging from easy, medium, to difficult in three progressive modes. The system assesses the child's performance during use and provides a score assessment, enabling parents to gain insights into the child's strengths and weaknesses, enhancing the system's purpose and guidance during use.

After multiple uses by children, the system can learn relevant data and intelligently recommend more suitable personalized course content. The system creates a positive user experience through lightweight interactive settings, engaging interactive content, and heartwarming interactive stories, allowing children to learn during fragmented periods of time.

4.4 Using Fuzzy Comprehensive Evaluation method to verify the design scheme

Using the methods described in Section 3.3, the scores from 34 experts were obtained. Different values are assigned to the evaluation levels in the evaluation set, resulting in an evaluation vector \(\alpha ={\left[\text{90,80,60,50}\right]}^{\text{T}}\), The scores are categorized as follows: excellent (90 or above), good (80-90), qualified (60-80), and unqualified (below 60).

As stated in Section 4.2, the criteria layer consists of five elements. According to the methods outlined in Section 3.3, the criteria layer includes education content denoted as \({\text{m}}_{1}\), user experience denoted as \({\text{m}}_{2}\), technical performance denoted as \({\text{m}}_{3}\), security denoted as \({\text{m}}_{4}\), and sustainability denoted as \({\text{m}}_{5}\).

$${\text{m}}_{1}\text{=}\left[\begin{array}{cccc}\text{0.6176}& \text{0.1765}& \text{0.2059}& \text{0.0000}\\ \text{0.2941}& \text{0.5000}& \text{0.2059}& \text{0.0000}\\ \text{0.5882}& \text{0.2647}& \text{0.1471}& \text{0.0000}\\ \text{0.7059}& \text{0.1765}& \text{0.1176}& \text{0.0000}\end{array}\right]$$
$${\text{m}}_{2}\text{=}\left[\begin{array}{cccc}\text{0.5000}& \text{0.3824}& \text{0.1176}& \text{0.0000}\\ \text{0.5882}& \text{0.3235}& \text{0.0882}& \text{0.0000}\\ \text{0.5882}& \text{0.3529}& \text{0.0588}& \text{0.0000}\\ \text{0.4706}& \text{0.2941}& \text{0.2353}& \text{0.0000}\end{array}\right]$$
$${\text{m}}_{3}\text{=}\left[\begin{array}{cccc}\text{0.3824}& \text{0.5000}& \text{0.1176}& \text{0.0000}\\ \text{0.2941}& \text{0.4412}& \text{0.2647}& \text{0.0000}\\ \text{0.2353}& \text{0.5588}& \text{0.2059}& \text{0.0000}\\ \text{0.4412}& \text{0.5588}& \text{0.0000}& \text{0.0000}\end{array}\right]$$
$${\text{m}}_{4}\text{=}\left[\begin{array}{cccc}\text{0.4706}& \text{0.4706}& \text{0.0588}& \text{0.0000}\\ \text{0.4118}& \text{0.4706}& \text{0.1176}& \text{0.0000}\\ \text{0.6471}& \text{0.2941}& \text{0.0588}& \text{0.0000}\end{array}\right]$$
$${\text{m}}_{5}\text{=}\left[\begin{array}{cccc}\text{0.4412}& \text{0.5000}& \text{0.0588}& \text{0.0000}\\ \text{0.3529}& \text{0.4706}& \text{0.1471}& \text{0.0294}\\ \text{0.3824}& \text{0.5882}& \text{0.0294}& \text{0.0000}\end{array}\right]$$

The numerical values for the weight calculations from Table 9 and Appendix Tables 13, 14, 15, 16, and 17 are as follows:

Criteria layer weight vectors

$${\omega }_{1}=\left(\text{0.3602 0.3118 0.1878 0.1402}\right), {\omega }_{2}=\left(\text{0.5342 0.2073 0.1575 0.1009}\right), {\omega }_{2}=\left(\text{0.1089 0.4576 0.1792 0.2543}\right), {\omega }_{4}=\left(\text{0.5334 0.2756 0.1909}\right), {\omega }_{5}=\left(\text{0.4864 0.3431 0.1705}\right)$$

These weight vectors ω are calculated by their respective criteria layer fuzzy evaluation matrices \({\text{m}}\), and the criteria layer evaluation vectors \({\text{t}}\) are obtained. The evaluation vectors for each criteria layer index can be determined through the solution.

$$\begin{array}{c}{t}_{1}={\omega }_{1}\times {m}_{1}=\left(\begin{array}{ccc}\text{0.5236}& \text{0.2939}& \begin{array}{cc}\text{0.1825}& \text{0.0000}\end{array}\end{array}\right)\\ {t}_{2}={\omega }_{2}\times {m}_{2}=\left(\begin{array}{ccc}\text{0.5292}& \text{0.3566}& \begin{array}{cc}\text{0.1141}& \text{0.0000}\end{array}\end{array}\right)\\ \begin{array}{c}{t}_{3}={\omega }_{3}\times {m}_{3}=\left(\begin{array}{ccc}\text{0.3306}& \text{0.4986}& \begin{array}{cc}\text{0.1708}& \text{0.0000}\end{array}\end{array}\right)\\ {t}_{4}={\omega }_{4}\times {m}_{4}=\left(\begin{array}{ccc}\text{0.4880}& \text{0.4369}& \begin{array}{cc}\text{0.075}{0}& \text{0.0000}\end{array}\end{array}\right)\\ {t}_{5}={\omega }_{5}\times {m}_{5}=\left(\begin{array}{ccc}\text{0.4009}& \text{0.5050}& \begin{array}{cc}\text{0.0841}& \text{0.0000}\end{array}\end{array}\right)\end{array}\end{array}$$

establish a fuzzy comprehensive evaluation model for overall indicators:

$$T=\left[\begin{array}{c}{t}_{1}\\ {t}_{2}\\ \begin{array}{c}{t}_{3}\\ {t}_{4}\\ {t}_{5}\end{array}\end{array}\right]=\left[\begin{array}{c}\begin{array}{ccc}\text{0.5236}& \text{0.2939}& \begin{array}{cc}\text{0.1825}& \text{0.0000}\end{array}\end{array}\\ \begin{array}{ccc}\text{0.5292}& \text{0.3566}& \begin{array}{cc}\text{0.1141}& \text{0.0000}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{ccc}\text{0.3306}& \text{0.4986}& \begin{array}{cc}\text{0.170}{8}& \text{0.0000}\end{array}\end{array}\\ \begin{array}{ccc}\text{0.4880}& \text{0.4369}& \begin{array}{cc}\text{0.075}{0}& \text{0.0000}\end{array}\end{array}\\ \begin{array}{ccc}\text{0.4009}& \text{0.5050}& \begin{array}{cc}\text{0.0841}& \text{0.0101}\end{array}\end{array}\end{array}\end{array}\right]$$

From \(\omega =\left(\text{0.2902 0.4041 0.1643 0.0882 0.0545}\right)\), the comprehensive evaluation vector \({\text{W}}\) for the game interactive system can be established:

$$W=\omega \times T=\left(\text{0.4850 0.3774 0.1383 0.0006}\right)$$

Finally, the rating for the system in the design practice is calculated:

$$Y=W\cdot \alpha =82.17$$

The assessment level domain comprises four grades: excellent, good, qualified, and unqualified. Therefore, the evaluation level domain can be expressed as\(\xi =\left\{{\xi }_{1},{\xi }_{2},{\xi }_{3},{\xi }_{4}\right\}\), the corresponding score ranges are defined as follows: \(\left\{\left[\left.\text{90,100}\right]\right.\text{,}\left[\left.\text{80,90}\right)\right.\text{,}\left[\left.\text{60,80}\right)\right.\text{,}\left[\left.\text{0,60}\right)\right.\right\}\). By integrating triangular and trapezoidal distributions, an enhanced triangular-trapezoidal distribution is employed to represent the distribution status and membership degrees more precisely. The membership functions for each grade are defined using this triangular-trapezoidal distribution as follows:

$$\text{Excellent }{\upxi }_{1}:\text{f}\left({\text{x}}_{4}\right)=\left\{\begin{array}{cc}0,& x\le 80\\ \frac{x-80}{10}& 80<x\le 90\\ 1,& x>90\end{array}\right.$$
$$\text{Good }{\upxi }_{2}:\text{f}\left({\text{x}}_{3}\right)=\left\{\begin{array}{cc}\frac{x-60}{20},& 60<x\le 80\\ \frac{90-x}{10},& 80<x\le 90\\ 0,& x\le 60,x>90\end{array}\right.$$
$$\text{Qualified }{\upxi }_{3}:\text{f}\left({\text{x}}_{2}\right)=\left\{\begin{array}{cc}\frac{x-50}{10},& 50<x\le 60\\ \frac{80-x}{20},& 60<x\le 80\\ 0,& x\le 50,x>80\end{array}\right.$$
$$\text{Unqualified }{\upxi }_{4}:\text{ f}\left({\text{x}}_{1}\right)=\left\{\begin{array}{cc}1,& x\le 50\\ \frac{60-x}{10},& 50<x\le 60\\ 0,& x>60\end{array}\right.$$

In these expressions, f(xk) represents the membership degree of a given state quantity with respect to the four assessment levels; x denotes the state quantity score; and xk (k=1, 2, 3, 4) represents the fuzzy boundary interval corresponding to each assessment level. For generality, we assign x1=50, x2=60, x3=80, x4=90. \(W=\omega \times T=\left(\text{0.4850 0.3774 0.1383 0.0006}\right)\)

The result indicates that the degree of excellent is 48.50%, the degree of good is 37.74%, the degree of qualified is 13.83%, and the degree of unqualified is 0.06%. Furthermore, \(Y=W\alpha =82.17\) The result falls within the range \(\left[\left.\text{80,90}\right)\right.\), suggesting that the overall assessment level of the design practice program is good. This indicates that the design possesses a reasonable degree of quality, meeting the enlightenment educational needs of preschool children, although there remains room for further refinement and enhancement.

5 Discussion

This study delves into the key factors of preschool children's educational games design. By comparing them with existing theoretical frameworks and models in the field of educational games design, we find that although previous research has yielded substantial results, our study still demonstrates a certain degree of innovation when compared to them.

Firstly, in terms of key factors, previous studies [18,19,20,21,22] have encompassed various aspects such as age-appropriateness of game content, entertainment, interactivity, feedback mechanisms, achievement of educational goals, and the intuitiveness and usability of the game interface. However, they have not provided a definitive conclusion on the relative importance of these factors. Through analysis, our study further clarifies which factors occupy a significant position in the design of educational games for preschool children, providing designers with more concrete guidance.

Secondly, regarding the application of theoretical frameworks and models, although predecessors have proposed various educational games design models based on different learning theories [34,35,36], in practical applications, these models tend to be overly theoretical, making it difficult to directly apply them in the complex and ever-changing practice of educational games design. Additionally, these models typically lack a clear and systematic method to refine and integrate the key factors for educational games design. This study is dedicated to proposing a practical approach for identifying and refining such factors, aiming to assist designers in making effective decisions within complex design environments. It is hoped that this approach can bridge the gap between theory and practice in previous studies.

Thirdly, as times evolve and user needs change, the key factors in educational games design may also undergo transformations. The approach proposed in this study can be repeatedly used by other researchers to continuously refine potential new key factors, facilitating iteration and optimization. This facilitates the continuous development of research in educational games design, leading to the creation of educational games that better align with user needs and educational objectives.

There are some limitations to this study. For instance, the focus primarily lies on extracting key factors for game design, with relatively less exploration on how to specifically apply these factors to the practical game design process. Additionally, there are certain constraints in terms of sample size and study duration. Future research could consider expanding the sample size to enhance the generalizability of the findings and extending the study timeframe to gain a more comprehensive understanding of the long-term effects of the proposed design solutions.

6 Conclusion and future works

This study systematically investigated the key factors (such as educational content, user experience, technical performance, and security) in preschool children's educational games for enlightenment through decision analysis methods. This research not only identified the core points (such as the setting of game content, feedback mechanisms, and user-friendliness of the interface) in the design process but also constructed a comprehensive and in-depth theoretical framework, injecting new theoretical support into the field of educational games design. Meanwhile, this study provides targeted guidance for designers, enabling them to develop both interesting and effective enlightenment educational games. This not only enhances preschool children's interest in learning but also improves their learning effectiveness, thus confirming the practical application value of the research results. Overall, this study not only enriches the knowledge system of educational games design at the theoretical level but also makes a substantial contribution to the application and development of educational games in the field of preschool education from a practical perspective.

Despite notable achievements in the realm of preschool children's educational games design, numerous avenues remain unexplored. Future investigations can branch out in the following directions:

Expanding application scenarios is our first consideration. While this study predominantly focuses on designing educational games for preschool children, the applicability of such games extends far beyond this demographic. Future research endeavors could apply our methods to game design targeting different age groups or educational domains, thereby validating its versatility and efficacy.

Second, we must consider incorporating new technological elements. The integration of emerging technologies like Augmented Reality, Virtual Reality, and Artificial Intelligence in educational games is gaining momentum. Future studies could delve into how these advancements can be seamlessly amalgamated with the identified key factors, elevating both the quality and impact of educational games.

Finally, it is crucial to assess the long-term impact. Ascertaining the enduring effects of educational games is paramount. Future research endeavors could involve comprehensive long-term tracking and evaluation to understand the lasting implications of preschool children’s educational games on children's cognitive, emotional, and social skill development.