Numerous active learning strategies can effectively enhance student engagement, yet not every strategy is indispensable for every class. Therefore, it’s crucial to provide options while devising our lesson plans. Revisiting the Complex Number topic, its objectives encompass describing the components of complex numbers, applying algebraic simplification with imaginary numbers, and utilizing these techniques within the context of complex numbers. To achieve these objectives, employing active learning strategies involves providing students with immediate feedback and facilitating teaching methods through a series of activities.
Tailoring multiple active learning techniques to correspond with each objective of the topic can significantly bolster student engagement. For instance, to encourage early class engagement and leverage students’ prior knowledge of the topic from their high school education, prompting students to review the planned notes a day prior to class can be effective. Introducing real-world applications of complex numbers can broaden their understanding of the topic. To aid in understanding complex number concepts, a brief in-class discussion on complex number formats could be beneficial. Understanding how imaginary numbers are produced, especially converting radicals to imaginary numbers, stands as a crucial aspect. Encouraging students to plot points on the complex plane helps them visualize the location of complex numbers. Implementing techniques for complex number operations involves promoting peer instruction, engaging students in group discussions about instructor-designed questions, and encouraging them to present unresolved questions from their discussions.
The section focusing on the power of ‘i’ is relatively challenging compared to other content in this area. Thus, peer discussions and instruction play a vital role in helping students grasp exponentiation techniques in the complex number system.
During discussions on ‘i’ exponentiation, students might face challenges in selecting methods to decompose the power of ‘i’ for simpler exponentiations. The diversity in complex number formats might discourage further exploration, leading to detachment. Implementing the think-pair-share approach can be beneficial. It involves pairs discussing related questions, sharing opinions with the class, and synthesizing their answers to draw conclusions. Utilizing role play, students can delve deeper into the study of complex number exponentiation, especially when discussing the properties of ‘i’ to the fourth power. Providing opportunities for students to understand the nuances of computing processes and how different powers lead to the same endpoint can enhance comprehension.
While employing classroom design strategies to improve engagement in this exponential context is suitable, it might be time-consuming for undergraduate precalculus classes. Hence, utilizing polling methods could be beneficial. Employing online software tools or traditional methods such as raising hands can still effectively increase engagement among students studying this topic.
