Application of Whiteboard Animation in Engineering Mathematics Education Based on YouTube OpenCourseWare ^†

Abstract

With advancements in digital technology, OpenCourseWare (OCW) has become a crucial tool for enhancing learning outcomes. Therefore, the innovative application of whiteboard animation in engineering mathematics education was explored, utilizing YouTube as a platform as a free digital learning resource. More than 300 animated teaching materials and implemented interactive mechanisms were developed to improve students’ study effectiveness and self-directed learning abilities. Pre-tests and post-tests were conducted in “Engineering Mathematics I” and “Engineering Mathematics II” to assess the educational effectiveness of whiteboard animation. The results presented significant improvements in students’ performance. The average scores of Engineering Mathematics I and II increased from 64.37 and 63.73 in the pre-test to 87.03 and 92.39 in the post-test. Whiteboard animation effectively enhanced the learning experience in engineering mathematics, improving students’ comprehension and motivation. Such results provide a reference for the development of digital education technologies in engineering.

1. Introduction

The evolving landscape of science, technology, engineering, and mathematics (STEM) education is fundamentally reshaped by integrating digital tools, pedagogical innovation, and emerging technologies aligned with the Fourth Industrial Revolution [1]. As global educational ecosystems transition toward sustainable and technology-enhanced frameworks, the imperatives of student engagement, retention, and self-directed learning in STEM disciplines have become important in scholarly discourse and policy reforms.

Industry 4.0, characterized by automation, cyber–physical systems, and data-driven technologies, demands a reevaluation of traditional STEM curricula [1]. Its pervasive influence necessitates industry applications and new technologies for students to acquire technical knowledge and develop adaptive problem-solving thinking. Aâboubou [2] emphasized the role of technology-driven curricula in fostering student retention and engagement, which are critical in the high-attrition domains of engineering and mathematics.

COVID-19 catalyzed an accelerated transition to online and hybrid learning models. In Malaysia, Pang et al. [3] explored how software tools and social-networking platforms enhanced mathematical learning in post-pandemic education and highlighted the role of digital literacy and remote collaboration. Similar challenges and adaptations were studied in Ukraine. Shunevych [4] analyzed the viability of Massive Open Online Courses (MOOCs) in agrarian universities, raising broader questions about the sustainability and scalability of open-access learning resources.

In digital instruction, Semerikov et al. [5] provided a historical overview of computer-assisted mathematics education for engineering students in the United States between 1965 and 1989. The evolution from early experimentation to present-day mainstream adoption is marked by increasing interactivity, personalization, and visualization. Joksimoski et al. [6] explored the digitalization of mathematics learning in higher education, noting opportunities for innovation and challenges in faculty training and curriculum design. Complementing these developments, Godoy Simões and Ribeiro [7] advocated sustainable and forward-looking models of engineering education that prepare future professionals for the demands of the electrified, automated world.

Whiteboard animation is one of the most effective modalities for delivering visual and engaging content. Türkay [8] provided early empirical evidence demonstrating the effectiveness of visual and engaging content in enhancing knowledge retention and learner satisfaction, particularly in complex subjects such as advanced physics. In mathematics and engineering education, these results were used to explore pedagogical and cognitive dimensions. For instance, Patete and Marquez [9] demonstrated how online animation tools served as valuable supplements for instruction during the pandemic. Schneider et al. [10] investigated whether whiteboard animations’ procedural and narrative style influenced student outcomes, revealing nuanced interactions between content format and learner engagement.

Suwardika et al. [11] proposed an integrated framework by combining flipped classrooms with whiteboard animations and printed modules to enhance self-regulation, communication, and critical thinking. Their implementation results suggested that thoughtfully embedded visual aids significantly contributed to holistic cognitive development. Krieglstein et al. [12] emphasized the importance of visual design strategies, such as the timing and style of hand-drawn insertions, to mediate attention and improve information processing. These strategies were reflected in teacher-oriented evaluations, such as Kleftodimos [13], who analyzed student reactions and educators’ experiences on creating animated instructional content.

Advancements in synchronous and asynchronous learning technologies have also transformed mathematics education in engineering education. Jin [14] examined online interactive face-to-face learning models and concluded that these formats effectively replicated but surpassed traditional classroom dynamics. Terekhova and Zubova [15] emphasized the necessity of tailored information and communication technology (ICT) when teaching higher mathematics at technical universities’ disciplines that rely on cumulative knowledge and structured practice. Kutluca et al. [16] studied how integrating interactive whiteboards into mathematics teaching promoted sustainable learning behaviors, reshaping the teacher’s role from content-deliverer to learning facilitator.

A recurring theme across contemporary research indicated self-directed learning (SDL) as a pedagogical goal. In mathematics education, SDL empowers learners to take ownership of their learning process, set goals, monitor progress, and adjust strategies in-dependently [17]. Tang et al. [18] demonstrated that self-selected STEM projects, especially those with real-world applications, significantly enhanced student autonomy and motivation. These results were substantiated by Lin and Chen [19], who developed and validated a mathematics-specific SDL scale to evaluate learners’ readiness and attitudes toward independent study.

Zhu et al. [20] linked SDL strategies with student satisfaction in online engineering programs, showing that learners who actively managed their study behaviors tended to report more positive outcomes. Mercado [21] further reinforced these findings through a systematic review. The established SDL correlates with academic achievement and nurtures lifelong learning skills, which are essential in rapidly evolving STEM professions. Voon et al. [22] supported these trends through conducting a literature review of engineering mathematics pedagogy, identifying SDL as a key solution to the persistent challenge of low student engagement.

Technological tools were used to foster self-direction. Wiggins and van der Hoff [23] analyzed the use of online homework systems to promote reflective learning practices and formative feedback. Magas [24] constructed and evaluated SDL materials for mathematics, documenting measurable improvements in academic performance among STEM students.

The synergies between digital platforms, visual learning aids, and self-directed strategies show a transformative potential for mathematics education. Each component, such as interactive systems, whiteboard animations, or adaptive assessment tools, empowers learners with holistic imperative integration. This emerging paradigm challenges institutions to adopt new technologies and cultivate educational environments that are learner-centered, evidence-based, and dynamically responsive to student needs.

The result of the literature review in this study provides a robust conceptual and empirical foundation for exploring innovative strategies in mathematics education, particularly those leveraging whiteboard animation and self-directed learning frameworks. Extended reality and interactive systems were adopted in the context of engineering mathematics based on the previous research results and the principles of designing future-ready learning environments.

2. Research Purpose

In this study, more than 300 whiteboard animation videos were created, focusing on engineering mathematics. These animations have been systematically organized into a structured list and published on YouTube. Each video description contains hyperlinks that allow learners to access other related instructional videos. The videos show step-by-step blackboard solutions, evaluate self-learning outcomes, practice symbolic computation software, and access advanced learning videos for deeper understanding. These videos represent the culmination of the author’s teaching and research achievements for six years, supported by the Ministry of Education-funded projects. The continuous efforts offer students a wide array of learning materials. The motivations and objectives of this research include the following.

• Relevance of engineering mathematics in national examinations

According to the “Examination Archive” provided by Taiwan’s Ministry of Examination, engineering mathematics is a core subject in numerous civil service and professional licensing examinations. For instance, in 2023, engineering mathematics was tested across six examinations, spanning eleven categories and subjects. Problems from these examinations were incorporated into its whiteboard animation explanations to enhance practical relevance.

• Bilingual whiteboard animations

The whiteboard animations are presented in Chinese and English to attract learners whose native language is not Chinese and address language barriers, aligning with the global trend of multilingual learning. The bilingual design also resonates with Taiwan’s ongoing educational development strategies on internationalization.

• Whiteboard animation’s visual and engaging nature

Many students perceive engineering mathematics as abstract, complex, and unengaging. By transforming difficult concepts into visual narratives through whiteboard animation, the developed materials help learners better grasp fundamental ideas and engage more effectively with the content within a limited period.

• Continuous enhancement of instructional effectiveness

Whiteboard animation enhances course appeal, increases interactivity, and fosters greater student participation, which is crucial in professional training for engineering disciplines. The curriculum innovation project contributes to constructing a diversified set of instructional materials in engineering mathematics.

• Increasing students’ learning motivation

A growing body of research suggests that well-designed whiteboard animations boost student interest by making learning more appealing and enjoyable. This fosters stronger intrinsic motivation to engage and master the material.

Digital technologies enable synchronous in-person classes and asynchronous open-access learning modules. Incorporating whiteboard animation materials encourages students and cultivates consistent self-directed learning habits, thereby supporting long-term academic development and engagement.

3. Methodology

The development of whiteboard animation materials begins with appropriate authoring software. After a comprehensive evaluation, we selected VideoScribe v3.14 to produce animation-based instructional content. We previously assessed five similar animation platforms before ultimately adopting the current software. Proficiency in using the selected tool is essential to ensure the quality and consistency of the produced materials.

In designing each whiteboard animation, the following critical components are required: (1) collecting relevant instructional content, storyboard scripting, character design, visual aesthetics, and music selection, (2) animating output format, editing and correction of audiovisual artifacts, (3) optimizing video duration, and integration of symbolic computation commands using Mathematica (Version 14.3), (4) presenting in bi-lingual languages presentation (Chinese and English), (5) recommending related advanced learning videos, and (6) premiere scheduling upon uploading to YouTube. Since 1 August 2023, a daily publication strategy has been adopted to enhance production quality and maintain consistency, releasing one new whiteboard animation each day. This scheduled publication continues as part of the ongoing dissemination effort.

A central pedagogical philosophy in this study is to provide students with opportunities for self-directed learning in engineering mathematics. Each animation uploaded to the YouTube platform includes a description section with detailed learning guidance to facilitate this goal. Alternative methods for solving the same problem are introduced to encourage students to learn strategies using the symbolic computation software Mathematica. In particular, the basic functionalities of Mathematica are available online for free without creating an account. The key to use this tool lies in mastering its command syntax, which is supported by linked content, which enables learners to look at the same example from multiple perspectives.

In April 2025, the YouTube channel had 4310 subscribers. Analysis of channel analytics revealed the following viewer characteristics.

• Age distribution: 55.1% of viewers were between 18 and 24 years old, while 26.3% were aged 35 and above.
• Gender: 81.5% of viewers were male, and 18.5% were female.
• Subscription rate: 9.3% of viewers were subscribed to the channel.
• Geography: 88.7% of viewers were from Taiwan, and 1.8% were from Hong Kong.
• Access pathways: 27.1% of viewers accessed the videos through the “Playlist” feature, while 26.3% came from “External Sources.”
• Device usage: 60.5% of learners accessed the materials via desktop computers, while 33.0% used mobile phones.
• Operating systems: 57.0% of learners used the Windows operating system, and 22.0% used Android devices to access the instructional content.

These analytics present the channel’s reach and information on learner behavior, preferences, and platform usability. The information is used for future enhancements in the instructional design of whiteboard animation materials.

Moodle’s online quiz system (version 3.6) was used to administer knowledge checkpoint assessments in Engineering Mathematics I and II. Ten sets of pre-and post-tests were conducted for Engineering Mathematics I, and thirteen sets were designed for Engineering Mathematics II. The average scores for Engineering Mathematics I were 64.37 (pre-test) and 87.03 (post-test), while those for Engineering Mathematics II were 63.73 (pre-test) and 92.39 (post-test) (Figure 1 and Figure 2).

To enhance students’ learning experience and support autonomous learning, the Moodle quiz settings were adjusted, including the following.

• Students were only provided with their overall test scores after completing each quiz. The detailed feedback on specific incorrect responses was not disclosed.
• The same set of questions was used in the pre-and post-tests to ensure identical levels of difficulty across assessments.
• Students were allowed to take the assessments at any point during the semester, offering greater flexibility and minimizing time constraints.
• There was no restriction on the number of attempts for the post-test, enabling students to experience the motivational benefits of gradually improving scores.
• Participation in the pre-and post-tests was voluntary. However, only the data from students who completed both assessments were included in the analysis of learning effectiveness.

Statistical analysis was conducted using p-values. The p-values were close to zero in both tests, indicating a statistically significant improvement in students’ performance from pre-test to post-test.

4. Conclusions

The effectiveness of whiteboard animation as a digital instructional strategy in engineering mathematics education was assessed on a YouTube-based OpenCourseWare platform. Students’ comprehension, motivation, and self-directed learning capabilities were enhanced by integrating visual learning tools with interactive online assessments.

Implementing whiteboard animation in Engineering Mathematics I and II enabled notable improvements in student performance. The average pre-test and post-test scores increased from 64.37 to 87.03 in Engineering Mathematics I and from 63.73 to 92.39 in Engineering Mathematics II. Statistical analysis results confirmed the significance of this improvement, with p-values close to zero. The instructional design encouraged students to take ownership of their learning by embedding learning prompts, downloadable materials, symbolic computation tutorials, and recommended video extensions in each animation’s YouTube description. Integrating the Moodle testing system supported autonomous study behaviors with flexible access and unlimited post-test attempts. The structured development and daily publication of over 300 bilingual whiteboard animation videos enabled a sustainable model that produces and disseminates open-access educational resources. The platform’s growth, evident in its subscriber count and engagement metrics, highlights its scalability and adaptability for diverse learner demographics.

Using Chinese and English in the animations enhanced accessibility and inclusivity and attracted learners from various linguistic backgrounds. The narrative-based visual delivery made abstract mathematical concepts more concrete and engaging, addressing common learning barriers in STEM education. By integrating VideoScribe, Mathematica, Moodle, and YouTube, a comprehensive ecosystem was created for digital learning. This multi-platform approach ensured effective content delivery and provided valuable analytics on learner behavior, which can inform future instructional design and research.

The results of this study confirmed that thoughtfully designed and systematically implemented whiteboard animation played a transformative role in engineering mathematics education. The positive outcomes provided a reference for further adoption and refinement of digital learning technologies in STEM education.