Integrating Multimodal Learning into a Personal Learning Theory on Mathematics: An Enriched and Humanistic Perspective
Introduction
I have developed a personal theory of learning for mathematics that is based on a nuanced understanding of knowledge (Dahl, 2018). For me, knowledge combines facts and a web of understanding that connects theoretical principles with practical applications ( Lowrie & Jorgensen, 2016). On the other hand, learning is the process through which we acquire, synthesize, and apply knowledge using our cognitive, emotional, and sensory faculties (Dahl, 2018; Rittle‐Johnson, 2017).
My learning theory is informed by constructivist and multimodal learning frameworks, which suggest that effective learning involves more than traditional teaching methods (Malhotra et al., 2022). To truly understand a subject, we must engage with it on multiple levels, using different learning styles, such as visual, auditory, and hands-on engagement (Mayer & Fiorella, 2021; Nasir et al., 2021). This approach cultivates a setting that nurtures meaningful learning and enables us to unlock our utmost potential (Malhotra et al., 2022; Zajda & Zajda, 2021).
Core Components of My Personal Learning Theory
In a Calculus 3 lecture, I demonstrated how real-world applications acquire and process knowledge by explaining the design of a rollercoaster using calculus principles and facilitating the lesson with a computer program called Mathematica (Schad et al., 2021; Abell & Braselton, 2021), which not only engaged my students and enhanced their understanding of each concept (Delgado, 2021) but also served as an exemplary instance of how learners actively construct knowledge through engagement with real-world problems (Malhotra et al., 2022). Thus, by applying mathematical theories to practical examples like rollercoaster design, students can experience firsthand how knowledge is synthesized and applied; this method effectively narrows the divide between theoretical concepts and real-world applications, transforming learning into an active, problem-solving endeavor (Nasir et al., 2021).
Active Learning and Cognitive Engagement in the Classroom
Furthermore, using Mathematica to explore Discrete Mathematics is an excellent example of how people can learn actively through collaboration (Abell & Braselton, 2021; Delgado, 2021). The course has evolved over the years and now focuses more on computer science principles than when I took it. In one of the lessons, we cover basic computer science and graph theory NP-complete methodologies, using this tool to visualize and interpret each graph construction as a class (Abell & Braselton, 2021; Azcona et al., 2019). Thus, this approach emphasizes that knowledge is processed interactively, with learners actively constructing understanding through exploration and dialogue (Malhotra et al., 2022). Therefore, the cognitive process involves absorbing and applying information to solve complex problems using technological tools that enhance conceptual visualization and interpretation (Guo et al., 2020).
Supportive Learning Environments
In addition, incorporating storytelling and MyMathLab in teaching mathematics demonstrates the emotional and cognitive dimensions of learning (Maguire et al., 2017). This method leverages Mayer’s Principles of Multimedia Learning, emphasizing that knowledge is processed more deeply when emotional engagement accompanies cognitive efforts (Mayer & Fiorella, 2021). The narratives provide context, making abstract concepts relatable and accessible, while MyMathLab offers a platform for practical application (Warren et al., 2021). Showcasing the diverse nature of learning environments in fostering comprehension and retention (Adams et al., 2019; Biwer et al., 2020).
Developing Mathematical Intuition with Hands-on and Visual Activities
Moreover, as I teach my math courses, I face my students, incorporate many colors to emphasize the step process and project my lecture on the screen using my pad and pen (Mayer & Fiorella, 2021). Once we do three to four problems together, I break them into groups, have them solve the problems as a group, and present their results to the class, leading to class discussions (Theobald et al., 2020). Students experience the kinesthetic and visual dimensions of learning mathematics through manipulatives and interactive simulations (Abrahamson & Sánchez-García, 2016). This approach underlines the idea that knowledge is not merely received through listening or reading but also through doing and observing (Abrahamson & Sánchez-García, 2016; Theobald et al., 2020). Engaging with the material hands-on enhances the intuitive grasp of mathematical principles, illustrating how knowledge is processed and internalized through multimodal experiences (Malhotra et al., 2022).
Reflective Practices and Metacognition in the Math Classroom
I recall a college algebra class I taught a few semesters ago where I introduced polynomial equations. The lesson initially confuses many students. So, instead of moving forward with the planned lecture, I encourage the students to reflect on why they find the material challenging (Ayers et al., 2020). As a discussion, they responded to questions like, “What part of the polynomial equations is most confusing to you?” and “How does this challenge relate to your previous knowledge of algebra?” The conversation led to project-based projects as we tackled polynomial equations (Guo et al., 2020). In the end, each group presented what they had learned and how it answered the questions they had asked at the beginning of the class. Thus, this reflective exercise, in response to challenges with material in math classes, displays the metacognitive aspect of learning (De Backer et al., 2015; Mayer & Fiorella, 2021). It emphasizes that learning is about acquiring knowledge and understanding one’s cognitive processes. Thus, reflective practices enable learners to assess their understanding, identify gaps, and adjust their strategies, highlighting a self-regulated approach to knowledge acquisition and processing (Hooshyar et al., 2020; Mayer & Fiorella, 2021).
Reflections on Humanism and Learning
Building upon the foundational elements of my Personal Learning Theory, exploring the profound philosophical themes that further shape this perspective is essential (Wilkinson, 2015). Reflecting on works such as “Blade Runner 2049” and engaging with the philosophical underpinnings of humanism enriches our understanding of the learning process, highlighting the essential role of consciousness, personal development, and the human soul in education (Like Stores of Old, 2018).
The philosophical themes explored in “Blade Runner 2049” profoundly reflect on the essence of being human, the nature of consciousness, and the impact of these fundamental aspects on learning and personal development (Like Stores of Old, 2018; Hauser, 2021).
Multimodal Learning offers a comprehensive framework that accommodates and celebrates the complexity of human learning processes (Antonenko, 2015; Malhotra et al., 2022). This approach aligns with Mayer’s Multimedia Learning Principles, emphasizing the importance of using multiple sensory modalities and cognitive processes in learning (Mayer & Fiorella, 2021). Thus, by engaging visual, auditory, and kinesthetic channels, along with cognitive processes such as selecting, organizing, and integrating information, Multimodal Learning caters to diverse learning styles and enhances comprehension and retention of knowledge (Massaro, 2012; Mayer & Fiorella, 2021).
Testing the Theoretical Framework
The Tutor, Advisor, Professor (TAP) Support Program at Lone Star College was inspired by Georgia State University’s innovative methods of eliminating the achievement gap students enrolled in online courses, particularly in challenging first-year courses like College Algebra, English, and EDUC 1300 (Arnold, 2023; Gumbel, 2020; Kurzweil & Wu, 2015). Thus, to test Multimodal Learning’s effectiveness, we will compare students who use TAP resources against those who do not in online college algebra courses (Arnold, 2023; Wilkinson, 2015). This research will analyze five years of academic performance and retention rates, utilizing Kirkpatrick’s 4 Levels of Learning for evaluation with scaled Google Forms questions (Piskurich, 2015). Responses will be assessed for satisfaction, understanding, application, and impact trends (Arnold, 2023; Park-Gaghan et al., 2022; Piskurich, 2015). Furthermore, statistical and ANOVA analyses will examine engagement with different support modalities, thereby providing comprehensive evidence of Multimodal Learning in a virtual environment (Rouder et al., 2016; Adams et al., 2019; Massaro, 2012; Park-Gaghan et al., 2023; Ruona & Lynham, 2004). However, quantitatively measuring subjective aspects like emotional and intellectual growth is a potential challenge (Adams et al., 2019; Massaro, 2012; Park-Gaghan et al., 2023; Ruona & Lynham, 2004).
Personal Insights
This theory articulates a comprehensive view of what knowledge and learning entail within mathematics education, asserting that knowledge is both a product and a process—acquired through active engagement, processed through diverse sensory and cognitive experiences, and enriched through reflection (Theobald et al., 2020). Furthermore, it advocates for educational practices that acknowledge the complex, interactive nature of learning, emphasizing the need for environments that support multimodal engagement, foster emotional connections, and encourage reflective thinking (Ayers et al., 2020; Malhotra et al., 2022). Hence, through this lens, we see learning as a journey of discovery, where knowledge is accumulated, lived, and experienced, leading to a deeper, more intuitive understanding of mathematics and enriched by an awareness of our human essence and the transformative power of learning on the soul (Becker, 2010; Ezebuilo, 2020a; Ezebuilo, 2020b; Schewe, 1978; Warren et al., 2021).
Conclusion
In conclusion, integrating these diverse perspectives highlights the profound impact of the soul on learning, emphasizing that learning is a deeply personal, spiritual, and existential process intricately linked to our essence as human beings and the eternal journey of the soul (Like Stores of Old, 2018; Ezebuilo, 2020a; Ezebuilo, 2020b; Hauser, 2021). Thus, this reflection provides a comprehensive view of the soul’s role in learning, aligning with philosophical and theological insights and enriching our understanding of learning as a complex, deeply personal, and spiritually significant process (Like Stores of Old, 2018; Ruona & Lynham, 2004; Schad et al., 2021).
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