Active learning, in contrast to traditional lecturing, significantly enhances student engagement, thereby improving the effectiveness of learning outcomes. Implemented within the classroom environment, active learning encourages students to take ownership of their knowledge construction. Various active learning activities, such as projects, presentations, and peer discussions, are commonly utilized. However, not all techniques suit every lesson plan; the choice of active learning method should align with the learning objectives and outcomes of a specific topic.
Consider the case of Complex Numbers in College Algebra, where a minimum session of one and a half hours is necessary for comprehensive understanding, depending on students’ proficiency levels. The session aims to elucidate techniques for simplifying mathematical operations within the complex number system. Post-study, students should demonstrate improved calculation skills, rooted in the concept of simplification. The lecture is meticulously structured to fulfill these session goals.
The lecture is divided into four sections. The initial section introduces the concept of complex numbers, employing tools like concept mapping to showcase real-world applications. Expanding on this in the second section, additional content exploration includes how complex number solutions of polynomials find practical utility. To aid comprehension, peer discussions, such as think-pair-share and small group discussions, are recommended for understanding square roots of negative numbers, imaginary numbers, and the properties of ‘i.’
The third section delves into mathematical operations like multiplication and division, utilizing peer reviews for enhanced understanding. Further reinforcement through activities like polling assists in clarifying complex concepts like negative square roots and square roots of negative numbers.
Given the necessity for class-wide discussions, a traditional classroom setting is deemed appropriate for this topic. However, a potential challenge arises in the final section, which contains numerous exercises on complex number operations. In a rigid classroom setup, students with diverse learning backgrounds might face difficulty completing these exercises within the allotted class time, leading to unfinished homework or unresolved questions. To address this, a flexible classroom design encourages student collaboration, forming study groups post-class, and fostering a supportive environment among students and the instructor, positively influencing the learning experience.
