For my final project of all of grad school, I decided to do an exploration of derivatives. I never felt comfortable tutoring calculus, so I did not take the time to re-learn it like I did with other forms of math. I felt like my mathematical content knowledge took a complete nose dive at the end of pre-calculus. After this week-long exploration I feel like it is way more of a slow descent into cluelessness instead of falling straight off a cliff. That's something.
Here it is: eight total video of my time figuring out derivatives and the earliest parts of calculus. I took AP Calculus in high school, as well as Calc I in college. In Calc I, I taught my table members how to do the problems. They all got A's and I got a B in the class. There is some kind of lesson there, but I am not sure what it is. I have some memories from the courses, but I really took the time to dig in here and gain relational understanding.
Link, in case of error above: Derivatives Exploration
References
Coad, M. (2012). Mathematics for the international student: Mathematical studies Sl for use with Ib Diploma Programme (Third). Haese Mathematics.
Khan Academy. (n.d.). Derivative as a concept (video). Khan Academy. Retrieved April 27, 2023, from https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-1/v/derivative-as-a-concept
Khan Academy. (n.d.). Differentiability and continuity (video). Khan Academy. Retrieved May 1, 2023, from https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-4/v/differentiability
Khan Academy. (n.d.). Finding tangent line equations using the formal definition of a limit (article). Khan Academy. Retrieved May 1, 2023, from https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-2/a/finding-tangent-line-equations
Khan Academy. (n.d.). Formal and alternate form of the derivative (video). Khan Academy. Retrieved May 2, 2023, from https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-2/v/alternate-form-of-the-derivative
Khan Academy. (n.d.). Formal definition of the derivative as a limit (video). Khan Academy. Retrieved May 2, 2023, from https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-2/v/calculus-derivatives-1-new-hd-version
Khan Academy. (n.d.). Justifying the power rule (article). Khan Academy. Retrieved May 3, 2023, from https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-5/a/justifying-the-power-rule
Khan Academy. (n.d.). Power rule (video) | applying the Power Rule. Khan Academy. Retrieved May 3, 2023, from https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-5/v/power-rule
Khan Academy. (n.d.). Power rule (with rewriting the expression) (video). Khan Academy. Retrieved May 3, 2023, from https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-5/v/power-rule-with-rewriting
Khan Academy. (n.d.). Secant lines & average rate of change (video). Khan Academy. Retrieved April 27, 2023, from https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-1/v/secant-lines-and-average-rate-of-change
Khan Academy. (n.d.). The fundamental theorem of calculus and Accumulation Functions (video). Khan Academy. Retrieved May 4, 2023, from https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-4/v/fundamental-theorem-of-calculus
Khan Academy. (n.d.). Worked example: Derivative as a limit (video). Khan Academy. Retrieved May 2, 2023, from https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-2/v/formal-and-alternate-form-of-the-derivative-for-ln-x
Khan Academy. (n.d.). Worked example: Derivative from Limit Expression (video). Khan Academy. Retrieved May 2, 2023, from https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-2/v/formal-and-alternate-form-of-the-derivative-example-1
Larson, R. E., Hostetler, R. P., & Edwards, B. H. (1997). Limits and an Introduction to Calculus. In C. B. Hoag (Ed.), Precalculus with Limits: A Graphing Approach (Second Teacher's Annotated Edition, pp. 865–914). essay, Houghton Mifflin.
Skemp, R. R. (1978). Relational understanding and instrumental understanding. The Arithmetic Teacher, 26(3), 9–15. https://doi.org/10.5951/at.26.3.0009
Comments