Introduction
The selected lesson to complete the course activities and the final project is an introduction to calculus. The lesson is taught in higher education (undergraduate level), and it entails teaching students how to find the exact derivative of functions from their formula without utilizing graphical methods. The rules learned can use used to calculate derivatives of almost all functions one will encounter in mathematics. An undergraduate curriculum was chosen because as the world changes, technology is advancing unlimitedly, leading to complex challenges in politics, business, and the environment. Higher education prepares students to resolve these challenges effectively (Krause, 2022). This paper provides a rationale for choosing the aforementioned lesson and analyzes its components and technologies applied to achieve success in learning. In addition, it recommends an evidence-based instructional strategy that can be used to deliver the lesson effectively.
The Rationale for Selected Lesson
The rationale for choosing the introduction to calculus lesson is that it teaches individuals how to determine a quantity’s rate of change. In the wake of technological advancement, climate variation, and the adoption of automation, differential calculus can be employed to determine the rate of change to predict future events (Tarasov, 2020). The class concepts offer a framework for molding systems that involve change and deducing future expectations from such models.
Components of the Lesson
The components of the introduction to calculus lesson include estimating derivatives of polynomials, interpreting and comparing curve slopes at different points, and applying the acquired knowledge in studying rates of change in real-world situations. The first module of the class introduces the phenomenon by teaching the various techniques used in differential calculus (Hashemi et al., 2020). The subsequent section of the lesson involves features and applications of derivatives. The instructor familiarizes students with the first and second-degree function derivatives. Sign diagrams are utilized in developing systematic curve sketching protocols. Additionally, individuals are taught to find derivatives of complex functions that emerge from simple ones. The product rule, chain rule, quotient rule, and data on the correct derivative to resolve complicated optimization problems are introduced in this module.
Another module of the lesson is the introduction to integral calculus; it considers tangent line slopes are areas under curves, building the fundamental theorem of calculus. Students explore how areas under velocity curves can determine displacement and approximation limits to estimate the formula for the areas under parabolas and circles. Moreover, definite integrals and Riemann sums are employed in capturing particular regions under curves (Hashemi et al., 2020). Lastly, instructors use this module to teach indefinite integrals, substitution as a method of integration, and reflectional and rotational symmetry. Differential calculus can be applied in evaluating the rate of change of atmospheric carbon (IV) oxide using polynomial differentiation. Subsequently, students will predict future CO2 levels based on current trends, thus informing the climate’s corresponding impact.
Technologies that Promote Lesson Success
A technology that can be incorporated into the lesson to enhance its success is the SimCalc software, which fosters visualization in the instruction process and fulfills both symbolization and generalization requests. SimCalc enables students to interact with calculus concepts and create tools utilized in studying change (Tatar et al., 2020). The digital environment enables students to create and organize content in such a way that students can intuitively work on critical facts embedded in the estimation of integrals and derivatives. Consequently, this builds their confidence when sharing results with others in the class. Additionally, they might develop mathematical theorems that explain the qualitative relationship between derivatives and their functions. As a result, this creates an ideal lesson where learners can think and produce conjectures, support conclusions, and challenge hypotheses.
Another technology that can be incorporated into the calculus lesson is a computer algebra system (CAS), such as Mathematica and Maple. The digital tool can be integrated with portable computing devices to allow symbolic and graphical computation (Bognar et al., 2018). Learning institutions can acquire site licenses for Mathematica to ensure students access it on their local machines. According to research, a CAS-oriented calculus lesson has a significant positive impact on students’ spatial visualization skills. Therefore, one implication of using CAS technology is improving spatial visualization skills through training using necessary content. In addition, using the software allows learners to construct solids, curves, and lines on the screen in 3D. Consequently, enhancing spatial visualization ability promotes calculus success.
Researched Instructional Strategies for Lesson Delivery
An evidence-based instructional strategy that can effectively support the delivery of the lesson is the use of visual representations. The practice is gaining popularity in mathematics education and involves establishing, analyzing, and reflecting images and pictures (David et al., 2020). In the introduction to calculus lesson, diagrams can be used to visualize, for instance, definite integral concepts to solve problems. Instructors can recommend using a high percentage of imaginative images and algebraic expressions for students with high visualization skills. Conjoining these two properties results in successful problem-solving. On the other hand, they should advise learners with low visualization ability to utilize memory images to resolve issues effectively. The visualization strategy will help students articulate representations to produce other prototypes that promote solving problems.
Conclusion
To conclude, undergraduate education offers a holistic experience to explore one’s individuality, skill, and perseverance, thus regarded as a transformation from potential to realization. Introduction to Calculus is a mathematics lesson taught at the undergraduate level. It examines change rates of curves and slopes; it involves the study of functions’ rates of change concerning their variables by using differentials and derivatives. Through the use of SimCalc and CAS technologies, instructors can enhance learning and comprehension of the lesson by using visual representations.
References
Bognar, L., Fáncsikné, É., Horvath, P., Joos, A., Nagy, B., & Strauber, G. (2018). Improved learning environment for calculus courses. Journal of Applied Technical and Educational Sciences, 8(4), 35-43.
David, E., Hah Roh, K., & Sellers, M. (2020). Teaching the representations of concepts in Calculus: The case of the Intermediate Value Theorem. PRIMUS, 30(2), 191-210.
Krause, K. (2022). Vectors of change in higher education curricula. Journal of Curriculum Studies, 54(1), 38-52.
Hashemi, N., Kashefi, H., & Abu, M. (2020). The Emphasis on Generalization Strategies in Teaching Integral: Calculus Lesson Plans. Sains Humanika, 12(3), 35-43.
Tarasov, V. (2020). Mathematical economics: application of fractional calculus. Mathematics, 8(5), 660.
Tatar, D., Roschelle, J., & Hegedus, S. (2020). SimCalc: Democratizing access to advanced mathematics (1992–present). In Historical instructional design cases (pp. 283-314). Routledge.