Study on design and practice of PBL teaching model based on STEM education concept

Abstract

As a new concept of engineering education around the world, STEM (Science, Technology, Engineering, and Mathematics) education has become the focus in academic circles. However, there are many realistic puzzles on how to realize the Chinese teaching of STEM education. This study proposes a new design of teaching model, namely the Problem-Based Learning (PBL) teaching model based on the concept of STEM education (hereinafter referred to as the PBLbSTEM), that is, the design of talent training objectives focusing on technological innovation literacy, engineering humanities literacy and data intelligence literacy; the design of scientific programming focusing on inquiry -practice -communication; the design of multi-dimensional evaluation based on evidence-based practice; and the design of environmental protection promoting the integration of industry and academia, as well as professional and general education. After three rounds of teaching practice in the Discrete Mathematics course, it is proved that this model can improve students’ learning engagement, enhance students’ above three literacy, enhance students’ learning experience and teaching satisfaction, and promote the deep integration of industry and academic research, which can provide reference for the teaching reform of first-class undergraduate education and the cultivation of innovative talents of engineering science and technology in colleges and universities.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-18485-x.

Introduction

The world is currently in an important period of a new round of technological and industrial revolution, that is, the age of artificial intelligence (AI) has arrived¹. The leading role of technological innovation in society is becoming increasingly important, and the demand for innovative talents in the whole society is growing day by day. In the report to the 20th National Congress of the Communist Party of China (CPC), education is an important component of national strategy, emphasizing the deep integration of education, technology, and talent to achieve the goal of building an education powerhouse by 2035. Under this great background, the rise of STEM education that advocates interdisciplinary integration and emphasizes the cultivation of innovative spirit and practical ability has attracted the attention of domestic experts. STEM courses have also sprung up like mushrooms in China, with the aim of cultivating more innovative talents. In recent years, the scale of training STEM professionals in Chinese universities has shown a significant growth trend. From 2015 to 2022, the number of STEM majors in Chinese universities has significantly increased. The number of graduate students has increased from 1.011 to 2.221 million, an increase of up to 120%; The number of undergraduate students has increased from 7.795 to 10.3 million, an increase of 32%; At the vocational stage, the number increased from 5.657 million to 9.893 million, a growth of 75%². This significant growth trend not only reflects the increasing emphasis on STEM disciplines in China’s higher education system, but also demonstrates the growing demand for scientific and technological innovation talents in the country, which highlight the importance of adapting education to societal and technological changes.

AI has assumed an increasingly pivotal role in STEM education. However, a comprehensive review that captures the current landscape and research trends in this domain remains conspicuously absent^3–5. The landscape of education is continually evolving, adapting to the changing needs of society and the advancements in technology and knowledge. In recent decades, Science, Technology, Engineering, and Mathematics (STEM) education has emerged as a pivotal element in this transformation⁶. The STEM education involves the systematic cultivation of composite talents throughout the entire chain from basic education to higher education⁷. Its core is to cultivate high-level talents with innovative and problem-solving abilities through systematic scientific education and practical training. What’s more, the STEM education emphasizes the organic integration of knowledge, pays much attention on basic quality of creative talents such as innovative and creative, problem-solving, communication and cooperation ability. The cultivated talents can quickly adapt to the core abilities of problem-solving, critical thinking, and communication and cooperation in the era of artificial intelligence. Therefore, emerging information technologies represented by AI are redefining the mission and value of higher education. The cultivation of STEM discipline innovative talents in colleges and universities that meet the requirements of the development of the times is the guarantee to improve China’s talent team and the talent support to enhance China’s voice in the field of scientific and technological innovation in the world. Moreover, the arrival of the artificial intelligence era may trigger layout adjustments and transformation upgrades in related industries. Faced with the new situation, STEM education, which shoulders the responsibility of cultivating innovative talents, is increasingly prominent in its role and status. However, currently STEM education in China still faces challenges such as incomplete curriculum system, unreasonable evaluation mechanism, overall low level of teaching staff, and relatively weak STEM literacy among students. To deeply integrate STEM education with artificial intelligence technology and turn “Crisis” into “Turning Point“^5,8–10.

Problem-based Learning (PBL) is a problem oriented teaching model, which is applied to identify and address problems in a given scenario for knowledge enhancement and better understanding^11–13, which is designed to direct students’ thinking, problem-solving and intellectual skills^14,15. More specifically, PBL starts with a problem that needs to be solved, through teacher inspiration, learner engagement in problems, and learner independent exploration and collaboration to solve problems. This enables students to develop problem-solving skills and the ability for self-directed learning, which has strong targeting for cultivating skilled and applied talents. Additionally, PBL teaching model focuses on real-world issues and incorporates Sternberg’s constructivist learning theory, Dewey’s pragmatic educational theory and Bruner’s discovery learning theory educational ideas^16–18. From the perspective of learning essence and theoretical foundation, PBL inherits the characteristics of STEM education and has become the most important learning model for cultivating students’ interdisciplinary literacy. And it has a significant effect on improving students’ self-efficacy, creativity, and adaptability in SETM subject autonomous learning¹⁹.

The Quality Report of Engineering Education in China (https://www.gov.cn/xinwen/2014−11/13/content_2778139. htm) showed that the number and scale of engineering students in ordinary universities in China have ranked first in the world. In recent years, the effective implementation of a series of plans to improve the quality of higher engineering education, such as the Engineering Education Certification, New Engineering Program, Outstanding Engineer Education and Training Program, Artificial Intelligence Innovation Action Plan,National Action Plan for Cultivating Digital Talents and Project on Cultivation of Qiu Chengtong’s Mathematics Science, has profoundly promoted people’s re understanding of the goals, connotations, and models of engineering talent cultivation. STEM education, as a new concept that influences global engineering education, has gradually become a hot topic of research for domestic scholars. However, how to achieve the Chinese design of STEM education in higher education, Chinese scholars have focused more on theoretical exploration and less on empirical research, resulting in many confusion and blind spots in the guidance of theory in the practical process. Recently, the China Education Development Strategy Society released the “STEM (Science, Technology, Engineering, and Mathematics) Education 2035 Action Plan”, which states that Chinese design of STEM will take six major action measures, namely, establishing a new mechanism for cultivating and connecting scientific and technological talents, building a high-quality STEM curriculum and project system, conducting STEM education evaluation, innovate STEM teacher training models and promote evidence-based practice in STEM teacher education, digital construction of STEM education, and leading the transformation of learning methods and strengthening the educational value of STEM education. Another study found that after four years of university study, the critical thinking and academic skills of Chinese STEM university students did not increase but decreased, with the worst performance among the four countries of China, the United States, Russia and India²⁰.

However, the application of STEM education in college mathematics courses still faces problems such as insufficient cognition and vague goal positioning, which affects its effectiveness. Discrete mathematics, as an important foundational course in computer science and mathematics, has the advantage of promoting abstract thinking, logical reasoning, and algorithm design abilities. However, current teaching mainly focuses on theoretical lectures and formula derivation, with insufficient practical application, making it difficult to stimulate students’ interest in learning and creative thinking. PBL is a problem oriented and student-centered teaching model that promotes students’ self-directed learning and practice through task design, enhancing their creative thinking and problem-solving abilities. Combining STEM education with the PBL model can help students deepen their understanding of abstract theories in discrete mathematics, enhance their practical abilities and interdisciplinary literacy, and provide a new path for curriculum reform. Whereas, this study is based on the PBL teaching model of STEM education concept, taking the foundational course of Discrete Mathematics in universities as an example for teaching practice design, and conducting empirical analysis on teaching effectiveness. The aim is to to explore new paths for cultivating technological innovation talents.

Theoretical framework

STEM education core concept

STEM education, originated from the United States, is a conceptual movement aimed at cultivating students’ technological innovation literacy and characterized by subject integration. It cultivates students’ ability to apply interdisciplinary knowledge to solve real-world problems in the four “meta disciplines” of STEM, as well as related interdisciplinary fields. The National Research Council of the United States has pointed out that the core concepts of undergraduate STEM education reform are interdisciplinary integration, evidence-based teaching and active learning¹⁹.

Specifically speaking, first interdisciplinary integration thinking is an important prerequisite for STEM education, of which the integrated courses are divided into three levels, namely multidisciplinary, interdisciplinary and trans-disciplinary²¹. Where, how to strike a balance between broken disciplines and establish new curriculum structures poses new challenges for front-line teachers and policy makers²². In response to these challenges, teachers need to sort out and structurally integrate the interdisciplinary knowledge required for students to solve a project problem, pay attention to the systematic connection of knowledge between disciplines at each stage, and maintain balanced coverage and overlapping cross cutting of each block of knowledge, helping students creatively solve problems. Second, the evaluation practice of evidence-based teaching is an important guarantee for STEM education. It includes three layers of evidence-based research: first the design of teaching content should be based on evidence of “project problems”, second the selection of teaching methods should be conducive to students exploring evidence-based reasoning, and third the evaluation method of teaching should reflect the developmental evaluation of the entire learning process. Third, the favorable environment for active learning is an important driving force for STEM education. Its curriculum based on the characteristics of interdisciplinary integration and evidence-based teaching embodies the concepts of “student-centered” and “practice centered”. It is a teaching practice based on constructivism and cognitive science theory, which creates a favorable environment for students’ autonomous learning²³.

In a word, the interdisciplinary integration thinking, evaluation practice of evidence- based teaching and active learning based on constructivism and cognitive science, are the core of STEM education philosophy. The choice of teaching model is particularly important for how to transform these three key points through functional design of teaching activities to enhance students’ technological innovation literacy and other higher-order abilities.

The PBLbSTEM teaching model.

Different from teaching methods and strategies, the teaching model is is a learning environment system that achieves different teaching goals or learning outcomes. A complete teaching model consists of teaching objectives, procedures for achieving teaching objectives, principles of learning responses, and social support systems for learning to occur. It should highlight features such as evidence- based teaching, integration with curriculum objectives, and application of information technology²⁴. PBL is a student-centered project-based learning teaching model that solves the problem of how to learn²⁵which focuses on real-world issues and incorporates constructivist learning theory, pragmatic education theory and discovery learning theory educational philosophy. Savery²⁶ defined PBL as “a learner centered approach in teaching or curriculum that allows learners to conduct research, integrate knowledge and theory, and practice, applying learned knowledge and skills to develop a feasible and reasonable solution to a specific problem or a proposed problem. The four elements of PBL teaching are content, activities, context and outcomes. From the perspective of learning essence and theoretical foundation, PBL inherits the characteristics of STEM education and has become the most important learning model for cultivating students’ interdisciplinary literacy^{24,27]– [28}. It has a significant effect on improving students’ self-efficacy, creativity, and adaptability in SETM subject autonomous learning.

The PBLbSTEM teaching model adopts the PBL learning method, fully utilizing the advantages of interdisciplinary integration, evidence-based teaching and active learning in STEM education. It enables students to integrate interdisciplinary knowledge and skills such as science, technology, engineering, and mathematics, carry out learning activities such as scientific exploration, engineering practice, and communication reinforcement, and further develop core competencies such as STEM, technological innovation literacy, engineering humanities literacy and data intelligence literacy. Moreover, the teaching model is based on project design, constructed through the integration of interdisciplinary knowledge, leading students to explore methods of problem verification, summarize answers, innovate cognition, and enhance higher-order thinking abilities. Meanwhile, the PBLbSTEM is not only a systematic teaching system that encompasses content and objectives, processes and methods, but also a dynamic, developing, and verifiable complete teaching process. Interdisciplinary exploration and interactive practices both inside and outside the classroom demonstrate the infinite possibilities of dynamic development in teaching; The close interaction and continuous exploration of problems between teachers and students in teaching demonstrate the harmonious development of collaborative innovation in teaching; The visualization of learning outcomes throughout the entire process and the measurability of students’ innovative abilities reveal the effectiveness of evidence-based teaching.

From the perspective of teaching model, the PBLbSTEM has five major features, namely inquiry-based, practical, collaborative, comprehensive and evidence-based. Meta analysis of STEM integrated curriculum research shows that PBL is currently the learning model with the largest number of STEM integrated courses²⁹.

Methodology

Design concept

The PBL teaching design based on STEM education philosophy is a teaching model that aims to promote students’ autonomous learning and ability improvement, which emphasize students’ “innovative learning” and teachers’ “innovative teaching”. To be specific, the former is can effectively promote the improvement of students’ higher-order thinking abilities after increasing course investment through the situational learning, PBL and inquiry-based learning; the latter is encourages teachers to reform their teaching behavior to stimulate learning participation through the interdisciplinary curriculum reconstruction, integration of industry and academia, and multidimensional evidence-based evaluation, whose ultimate goal is to cultivate engineering and technological talents with higher innovation and entrepreneurship abilities and cross-border integration capabilities. The effective implementation of both depends on the effective integration of teaching and learning curriculum ecology. More broadly, the effective implementation of both depends on the effective integration of teaching and learning curriculum ecology.

Design objects

Under the background of the data intelligence age, Discrete Mathematics, as the core theoretical foundation of many cutting-edge technologies, is crucial for cultivating innovative talents who can meet the needs of the times through innovative teaching. Moreover, as a key bridge connecting data and algorithms, it provides indispensable theoretical support for many fields and is the core foundation of cutting-edge technologies such as AI and big data. In the education of engineering majors in universities, it is a fundamental course in computer science, information science, mathematics, and other disciplines. It is of great significance for cultivating students’ logical thinking, abstract thinking, and algorithm design abilities.

In terms of the distribution of content in Discrete Mathematics course, it can be roughly divided into five major sections: Mathematical Logic, Set Theory, Combinatorial Analysis, Algebraic Structure and Graph Theory. Based on Rosen’s classic textbook, the logical relationships and dependencies between the various parts of the course are shown in Fig. 1, with the expected teaching duration of each module indicated in parentheses. The Mathematical Logic section covers propositional logic and predicate logic, dedicated to exploring how to abstract real-world problems into mathematical logical forms and conduct rigorous derivations; The set theory section includes three major parts, namely sets, binary relations and functions. It systematically explains the basic operating laws of sets, the operational properties of binary relations, and the characteristics of functions. Binary relations are rooted in the concept of sets, while functions, as a special type of binary relation, delve into the concept of mapping; The Combinatorial Analysis section focuses on solving counting problems and enumerating counting objects, starting from basic techniques, emphasizing the use of analytical methods to solve technical problems, and conducting in-depth algorithm analysis; The Algebraic Structure section is based on the operational properties of elements and related axioms and basic definitions, constructing a mathematical framework and providing a detailed introduction to basic concepts, properties, and several typical algebraic systems; The Graph Theory section starts from the basic concepts of graphs and explores special types of graphs such as Euler graphs, Hamilton graphs, plane graphs and trees, and extends the important applications of graphs on this basis. These five major sections are both relatively independent and interrelated, forming an organic whole that lays a clear and challenging path for students’ learning journey.

Fig. 1.

The dependencies between modules in Discrete Mathematics course.

The Discrete Mathematics course not only focuses on cultivating students’ mathematical literacy, that is, deepening their understanding and construction ability of mathematical arguments, but also strives to enhance students’ core abilities such as mathematical abstract thinking, computational thinking, logical reasoning, and causal reasoning. As the only way to advanced courses in mathematical science and computer science, discrete mathematics has laid a solid mathematical foundation for many courses in computer science and AI, provided accurate model description tools and rigorous theoretical analysis methods for the application of computers, the Internet and AI, and laid a solid foundation for the subsequent study of data structure, algorithm analysis and design, artificial intelligence, machine learning and career development. For example, Graph Theory is a mathematical branch that studies graphs and their properties, characteristics, and patterns of change. A graph consists of Vertex and Edge, which can be used to represent various complex relationships and network structures. In AI, graph theory is widely used in fields such as pattern recognition, recommendation systems, network analysis and path planning.

To verify the effectiveness of the PBLbSTEM, this study takes the Discrete Mathematics teaching of the engineering major mathematics foundation course at Jiangxi University of Water Resources and Electric Power as the starting point, aiming to explore the innovative practice project of the “AI Path Planning System” carried out after the completion of the Graphic Theory chapter. This work has carried out three rounds of teaching practice from September to November 2022, 2023 and 2024. A total of 1775 students from 7 engineering majors studied this course at our school. The course adopts a hybrid teaching model of online (MOOC or Tencent Meeting) and offline, with a total of 48 class hours. Interdisciplinary knowledge is integrated into online teaching, while theoretical teaching is implemented offline, and student teams are guided and assisted in real engineering project design practice. The teaching team consists of three teachers, covering multiple disciplines and professional fields, with rich experience in PBL model teaching and innovation and entrepreneurship work. The course also invites multiple industry experts and graduate assistants to participate in teaching work.

Design path

This study takes the AI innovative practice project, namely AI Path Planning System, as an example to further elaborate on the design path of PBLbSTEM. It is designed with interdisciplinary integration, evidence-based teaching, and active learning as the main themes based on Discrete Mathematics course^30–32as shown in Fig. 2. And in particular, it aims to cultivate technological innovation, engineering humanities and data intelligence literacy as its teaching objectives; it focuses on the engineering research practice carried out by students in designing and developing an AI innovation project as its teaching content; it is a teaching process consisting of four stages: course preparation, scientific exploration, engineering practice, and communication reinforcement; it adopts a multidimensional evidence-based system of multi-party participation, coexistence of multiple forms, and mutual growth of teaching and learning as the teaching evaluation; it is a teaching model that promotes the integration of industry and academia, as well as the integration of professional and general education, as the teaching guarantee.

Fig. 2.

The design path of PBLbSTEM.

The design of talent training objectives focusing on the three literacy

By clearly defining the course objectives to avoid the concentration and dispersion of the course, PBLbSTEM focuses on cultivating students’ technological innovation literacy, engineering humanities literacy and data intelligence literacy. Among them, the first literacy focuses on cultivating higher-order thinking abilities such as analysis, evaluation and creation, which highlightes the transformation from general engineering literacy to that of innovation^33–35. The engineering humanities literacy pays more attention to cultivating the supe cultivating a mindset of understanding goodness, experiencing freedom, transcending and critical thinking, with a goal of improving students’ academic adaptability^36,37. The data intelligence literacy is a comprehensive ability possessed in the digital age, including digital information literacy, data literacy, information literacy and technological literacy^38–41. It not only focuses on digital technology operation ability, but also needs to master the ability to acquire, process and comprehensively apply information.

The design of scientific programming focusing on inquiry-practice-communication

The PBLbSTEM takes projects as the carrier of course teaching, design as the process of course teaching, and the creative application of interdisciplinary knowledge and skills as the purpose of course teaching⁴². Taking the general AI course “Artificial Intelligence Innovation Project Design” as an example, the teaching content covers unified knowledge sections such as artificial intelligence, product prototype design, industrial design, and innovation and entrepreneurship, as well as cross-disciplinary knowledge areas involved in different projects. The teaching procedure design includes four steps: course preparation, scientific inquiry, engineering practice, and communication reinforcement. Course preparation mainly involves setting course goals, teaching methods, project team formation, and team building to create a good learning atmosphere. Scientific inquiry is completed through industrial research and field visits, covering three learning stages: problem identification, collaborative exploration, and solution formulation. Engineering practice includes two practical processes: design and construction, and testing and improvement. Communication reinforcement is carried out through student startup project roadshows and cross-disciplinary and cross-border teaching guidance from the teaching team, helping students to structurally reflect on their learning. The above four steps are rooted in the real world, creating a favorable environment for inquiry-based learning, problem-based learning, and cooperative learning, effectively stimulating students’ psychological motivation for self-directed learning.

The design of multi-dimensional evaluation based on evidence-based practice

The characteristics of evidence-based practice based on PBLbSTEM teaching model determines the implementation of a multidimensional evaluation system that involves multi-subject participation⁴³coexists in multiple forms⁴⁴ and the learning benefits of teaching^45–47. The learning outcomes of students include design plans, physical installations, video displays, software systems, development reports, roadshow reports and question answering situations. These pieces of evidence reflect the entire process of project practice and can effectively monitor the actual effectiveness of teaching and learning. By establishing an evaluation system for students’ abilities and course satisfaction, it provides information for teachers to understand course effectiveness and improvement goals, and promotes the common growth of teachers and students.

The design of environmental protection promoting the industry-university integration

The PBLbSTEM is based on the practical needs of talent cultivation, scientific research and educational management, which establishes a dialogue mechanism between education and industry. On the one hand it collaborates with industry associations and enterprises to build STEM teaching and training bases, student innovation project design platforms, which develop course project pools, making cutting-edge industry achievements valuable teaching resources, increasing students’ opportunities for engineering practice and technical experience, and improving their ability to design innovative projects. Moreover, combined with Challenge Cup, Internet+, and other competitions, it achieves collaborative education between schools and society, helps students establish resonance between the learning world and the work world, builds a teaching ecology that integrates industry and academia. Additionally, it integrates majors and general education, which provide environmental protection for the localization practice of STEM education through innovative integration of internal campus resources and social resources, and inviting industry investment and financing experts to carry out entrepreneurial landing and investment incubation of course achievements. The research made the following basic assumptions for the PBLbSTEM: the first being able to significantly stimulate students’ curriculum engagement; the second being able to effectively enhance students’ three major qualities; the third being able to significantly improve course satisfaction.

Where it needs to be declared that all methods mentioned above were performed in accordance with relevant guidelines and regulations.

Results and discussion

Course implementation process

The AI Path Planning System is based on the structured reorganization of interdisciplinary knowledge of science, technology, engineering and mathematics required to guide students in completing an AI innovation practice project. The teaching content covers unified knowledge modules such as artificial intelligence, system prototype design, algorithm design (such as Dijkstra’s algorithm), innovation and entrepreneurship, as well as interdisciplinary knowledge fields involved in different projects. The teaching program includes four steps, namely course preparation, scientific exploration, engineering practice and communication reinforcement. The implementation of the course usually lasts until the third semester, ensuring that students have sufficient time to participate in the entire process of course project design. In the course preparation phase, 2 class hours of online teaching will be conducted to explain the talent cultivation objectives, teaching method requirements, and related teaching resources. And offline time was used to complete team building and quality development, totaling 4 class hours. Personality testing, product manager self recommendation, and other methods are adopted to quickly form teams, expand outdoor skills to enhance team cohesion, and encourage students to actively adapt and cooperate with teaching model reforms.

In the scientific exploration phase, there are 3 class hours of online learning and 5 class hours of offline research practice. After class practice includes students conducting industry visits, product research, group discussions, and completing assignments, totaling approximately 20 class hours. This section is divided into three parts: the firs is identifying problems. Teachers use case normals to teach a brief history of the application and development of world AI technology in map navigation, as well as industry research and learning. Offline, they organize students to experience AI products and ask questions to stimulate students’ thinking; The second is collaborative exploration. Teachers organize students to visit AI map companies offline to understand AI projects and engineering research and development processes, allowing students to explore future solutions for combining their own disciplines with AI technology in real scenarios, write an AI product experience report, and determine topics of interest based on the project pool resources provided by industry association enterprises; The third is the formulation of the plan, where the teacher explains the development process of the engineering project, sets up an evaluation form to guide the team to complete the conceptual research and development design of the product based on collaborative exploration, and conducts team research and sharing reports. The teacher should ensure that each team receives at least 2–4 communication and coaching sessions during this stage.

In the engineering practice phase, there are 4 h of online learning, 8 h of offline design practice classes, 2 h of post class product video production guidance, and 8 h of teacher project guidance. Students need to invest more than 30 h in pre - and post class learning. This step includes: (1) Design and construction. Firstly, the teacher responsible for software development explains the AI algorithm, guides the group to discuss development, reports the algorithm flowchart, and makes a technical roadmap report; Secondly, the teacher in charge of product prototype design will explain the embedded system design process, guide the team to integrate AI products, and prepare an evaluation form to systematically benchmark and evaluate the products, in order to improve the plan. This section includes the analysis and construction of mathematical models, as well as the engineering practice process of embedding and integrating AI products. (2) Testing and improvement, with the teacher responsible for system design teaching AI product functions and industrial design specifications, the teaching assistant team providing post class guidance on video production techniques for product demonstrations, the group conducting system design and testing optimization, and completing stage summaries through product prototype interaction design reports.

In the communication strengthening session, there are 2 class hours of online learning, 4 class hours of offline reporting, and approximately 15 class hours of post class AI product innovation and entrepreneurship incubation research and practice. In this stage, students will learn online about the project roadshow and product innovation and entrepreneurship incubation taught by teachers, understand the policies, funds, competitions and other resources for further sustainable development of this project, and carry out product innovation and entrepreneurship incubation practices. Finally, they will conduct a project roadshow and receive feedback and guidance from an expert review panel composed of AI industry associations, AI investment and financing experts or corporate executives, and teachers. Improve the project based on suggestions and share learning gains and reflections within the team. After the course is completed, excellent projects will be selected to continue cultivating and incubating in the “AI Student Innovation Studio”. Combined with school funding support, competition participation, science and technology innovation research guarantee, science and technology innovation honors and other incentive and guarantee mechanisms, it will promote the transformation and improvement of teaching achievements. The team reported and shared four times, including project topic selection report, product algorithm and technical roadmap report, product prototype and interaction design report. As a note, all three are process evaluations, accounting for 35%, daily attendance accounts for 15%, and AI product innovation incubation project roadshow (final evaluation accounts for 50%). The evaluation subjects include three categories: experts, peers, and individuals. After the course ended, the selected students participated in self-evaluation of course satisfaction and ability development, as well as in-depth interviews with learning summaries.

Teaching verification design

Research design

In order to better understand the PBLbSTEM, this work designed an application effect evaluation questionnaire. In addition to basic information, the questionnaire is divided into three parts: the first part is an assessment of learning engagement, including post class engagement time and deep learning; The second part is the assessment of ability development (namely the three literacy mentioned above); The third part is the evaluation of satisfaction, including learning experience and teaching implementation satisfaction. Except for the topic of “project participation” in the first part of the learning engagement assessment, other parts of the questionnaire use the Likert Psychological Response Scale and are scored on a scale of 5–7 based on the problem situation.

The initial draft questionnaire first randomly invited 100 selected course students for pre-questionnaire testing, and selected 25 students for testing interviews to revise and optimize the questionnaire’s wording. Next, the Alpha reliability coefficient method was used to test the reliability of the questionnaire. The Cronbach’s alpha coefficient for 60 items was 0.984, and the Alpha reliability coefficients for each sub dimension exceeded 0.942, indicating high reliability and internal consistency of the questionnaire. Meanwhile, factor analysis showed that the KMO values for each sub dimension were all greater than 0.7, and the Bartlett sphericity test was at the 0.01 level. The factor loadings of each dimension are all greater than 0.6, and the cumulative contribution rates of variance are all greater than 70%. The questionnaire has good validity and can reflect the overall effect of the course well.

Data collection and analysis

In November 2024, the teaching team conducted a questionnaire survey on 1000 students from our school who participated in the course selection in the past three rounds through Wechat Mini Program (namely Laibao). A total of 892 students from 5 engineering colleges and 7 engineering majors submitted questionnaires, accounting for 50.3% of the course selection population. Among them, there were 761 males (85.3%) and 84 females (14.7%). In addition to the survey questionnaire, the course also conducted course summaries and in-depth interviews with 45-planned/42-valid students to comprehensively understand the effectiveness of the course implementation. The comparative results show that the introduction of the new model can apparently stimulate students’ course engagement, effectively improve their three major competencies, and significantly improve course satisfaction. Where it needs to be declared that the participants provided their written informed consent to participate in this study. The research hypothesis is validated as follows:

The level of student engagement in learning has significantly increased

This study verifies the efficiency of student course participation from two aspects, namely time investment in after-school learning and deep learning. All students participated in group inquiry learning after class, with 71.9% of students participating in 4 ~ 6 times or more group discussions after class. Among them, 11% participated in up to 9 spontaneous group discussions after class, as shown in Fig. 3. The algorithm design stage and product molding design stage, which are the two stages of scientific exploration and engineering practice, are the most time-consuming stages for discussion, as shown in Fig. 4. 65.7% of students stated that they will continue to improve their incubation projects and participate in scientific and technological innovation competitions, research projects, or social practices after the course ends, as shown in Fig. 5.

Fig. 3.

The number of group discussions after class.

Fig. 4.

Distribution of post class group discussion time stages.

Fig. 5.

Follow up ideas for the project after the course ends (multiple choice).

Interdisciplinary and self-directed learning are the main features of the PBLbSTEM, which reflects the depth of students’ learning. The research results show that 91.2% of students believe that the frequency of “interdisciplinary learning combined AI with their own profession to solve problems” in the course is “slightly more”, “frequently” or even “very frequently”, while 89.1% of students believe that the frequency of “comparing, judging, analyzing and evaluating solutions to problems”, “not adhering to ready-made practices, independently thinking and innovating to solve problems”, and “reflecting and absorbing experience” in the course is “slightly more”, “frequently” or even “very frequently”; 91.2% of students believe that they tend to focus more on themselves in the course and often engage in self-directed exploration and learning with problem objectives; 91.4% of students often actively participate in group discussions, share learning skills, and actively seek advice from teachers. For example, ZMV (male) said that “this teaching method is great; my teacher provides us with a platform and direction, allowing us to explore everything on our own; without a doubt, this learning method is memorable and also promotes rapid growth”. It can be seen that the PBLbSTEM teaching model effectively increases students’ learning engagement, promotes deep learning and inquiry learning.

The students’ abilities have significantly improved. Table 1 reflects the evaluation status of students’ three major literacy indicators before and after the course. In terms of innovation literacy, students believe that the abilities that have made “good progress” and “great progress” include the following abilities. “Innovation consciousness, innovative thinking, and innovative practical ability”, “problem analysis and solving ability”, “interdisciplinary application ability” and “technology and tool use ability” and “product design and development capability” are above 87%, 87%, 83% and 80% respectively. In terms of engineering humanities literacy, students believe that the abilities that have made “good progress” and “great progress” include the following abilities. Both “sense of social responsibility” and “self reflection ability” are over 88%; And the “investigation and research ability”, “project management and communication cooperation ability” and “self-learning and lifelong learning ability"are over 83%. WKH, a student from the School of Electrical Engineering, described his progress in interdisciplinary skills and project communication management, as follows. “AI innovation project management is a field I have never been involved in before. I have found that the value of this course is higher than I imagined, and learning through practice is more efficient than simply studying from books. In terms of digital literacy, 92.4% of students believe that the course has “increased their understanding of their profession and the real-world application of Discrete Mathematics”, and 89.2% of students “increased AI projects interesting”. More than 92.8% of students believe that they have a better understanding of the practical significance of technological innovation, and over 93.4% of students believe that the curriculum will prevent them from easily giving up when facing academic difficulties in the future.

Table 1.

Student innovation development indicators.

Indicators for the development of students’ innovation ability	Frequency (Percentage)
	No progress	Less progress	General progress	Good progress	Great progress
Application of multi-discipline knowledge	0 (0.0%)	66 (7.4%)	83 (9.3%)	541 (60.7%)	202 (22.6%)
Analysis and solution of problems	0 (0.0%)	71 (8.0%)	40 (4.5%)	538 (60.6%)	243 (27.2%)
Product design and development	0 (0.0%)	89 (10.0)	88 (9.9%)	517 (58.0%)	198 (22.2%)
Innovative consciousness, thinking and practice	0 (0.0%)	38 (4.3%)	73 (8.3%)	534 (60.0%)	247 (27.7%)
Self-reflection	0 (0.0%)	41 (4.6%)	61 (6.8%)	529 (59.3%)	261 (29.3%)

High student learning experience and teaching satisfaction. The students’ satisfaction with the implementation of PBLbSTEM teaching model, including teaching situation, teacher support, group cooperation, enterprise visits, team building expansion and learning environment, reached over 95%. MXX (male) said that “the course provides us with a rapid growth process. The most rare thing about learning AI projects and their development and production is that this course truly allows us to witness the growth of products in our hands in a very short period of time. Although it is not a very mature project, every step of its growth has been hand crafted and polished by our members. So, although it’s not an excellent work, it’s a perfect experience”. LLW (female) emphasized that “through this course, I have gained a group of like-minded friends. Walking on campus, we are all ordinary, but meeting each other makes us realize that we can also be innovative and creative. For the overall experience of the course, the memories are very pleasant, but the process is also very rushed, constantly in a cycle of discussion modification discussion”.

Conclusion

This study proposes a PBL teaching model design based on the STEM education concept, which focuses on the talent cultivation objectives of technological innovation literacy, engineering humanities literacy and, data intelligence literacy. What’s more, it focuses on the scientific programming of exploration→practice→ communication, multi dimensional and multi-level evaluation design under evidence-based practice, and promoting the design of environmental protection for the integration of industry and academia, as well as the integration of majors and mathematics. The teaching practice has shown that the application of PBL teaching model based on STEM education concept in Discrete Mathematics course is feasible and effective. It helps to improve students’ learning engagement, enhance the above three literacy, as well as increase their learning experience and teaching satisfaction. The new model also promotes the deep integration of industry, academia and research, and can provide reference and inspiration for the reform of first-class undergraduate education and the cultivation of engineering technology innovation talents in Chinese universities.

Looking forward, with the rapid development of AI technology, the role of Discrete Mathematics course in cultivating students’ innovative thinking and ability to solve complex problems will become more prominent. Through continuous teaching reform and content optimization, we are committed to guiding students to deeply understand the core concepts and methods of discrete mathematics, and paving a broad path for their future research and career development. At the same time, we will actively explore the integration of discrete mathematics and cutting-edge technology, striving to achieve more significant results in cultivating high-quality talents and promoting technological innovation, and contribute our wisdom and strength to the progress and development of society.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Zuhan Liu: Conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing—original draft preparation, writing—review and editing, visualization, supervision, project administration, funding acquisition.

Funding

This work was supported by the program of graduate education and teaching reform of Nanchang Institute of Technology (NGYJG-2023-002) and institute-level educational reform project (2022XGJG07).

Data availability

The datasets used and/or analysed during the current study available from the corresponding author Zuhan Liu on reasonable request via e-mail lzh512@nit.edu.cn.

Declarations

Competing interests

The authors declare no competing interests.

Ethics statement

The studies involving human participants were reviewed and approved by School of Information Engineering, Jiangxi University of Water Resources and Electric Power Ethics Committee. The participants provided their written informed consent to participate in this study. All methods were performed in accordance with relevant guidelines and regulations.