Learning from past mistakes – mat 271 Amanda Whitt Asheville-Buncombe Technical Community College

Struggles ALGEBRA SKILLS! 𝑥+2 𝑥+1 =2 Application Problems (word problems) Understanding and applying definitions. Struggle to memorize “shortcuts” Confidence

Why Make or Use the Project? Review exams, labs, and graded assignments that have feedback. Helps students realize they need to continuously review material!

Project Overview Project 1 Project 2 Topics: Limits Derivatives Take previously asked questions (or similar questions). Answer every question with the most common, incorrect answer given by the students. Project 1 Project 2 Topics: Limits Derivatives Product Rule, Quotient Rule, Chain Rule Logarithmic Differentiation Implicit Differentiation Related Rates Topics: Analyzing graph of functions Increasing, decreasing, concavity, minimums, maximums, etc… l’Hospital’s Rule Rolle's Theorem, Mean Value Theorem Optimization Riemann Sums Definite, Indefinite Integrals Fundamental Theorem of Calculus Integration by substitution

The Project True or False: If lim 𝑥→6 [𝑓 𝑥 𝑔 𝑥 ] exists, then the limit must be 𝑓 6 𝑔 6 . True. Since we know the limit exists, then we use direct substitution to evaluate the limit. Use the definition of the derivative to find 𝑓′(4), where 𝑓 𝑥 = 𝑥 2 −3𝑥+4. 𝑓 ′ 𝑥 =2𝑥−3 𝑓 ′ 4 =2 4 −3= 5

Problem 1 True or False: 𝑓 𝑥 = 𝑥 2 −3𝑥+40 𝑥−8 and 𝑔 𝑥 =𝑥+5 are equivalent functions.   Explain your answer. Forget about domain Get lost in notation lim 𝑥→8 𝑥 2 −3𝑥+40 𝑥−8 = lim 𝑥→8 𝑥+5

Problem 2 True or False: If 𝑦= 𝑒 2 , then 𝑦 ′ =2𝑒. Explain your answer. Students don’t think about the problem, just go through the motions. Still not sure about the number 𝑒

Problem 3 True or False: If 𝑓 𝑥 = 𝑥 6 − 𝑥 4 5 , then 𝑓 (31) =0. Explain your answer. Lack of algebra skills Lost in notation

Problem 4 Find 𝑓′ in terms of 𝑔′. 𝑓 𝑥 = 𝑥 2 𝑔 𝑥 Not sure about what is being asked Not comfortable with derivative rules

Problem 5 Find the local and absolute extreme values of the function on the given interval. 𝑓 𝑥 = 𝑥 3 −6 𝑥 2 +9𝑥+2, [2,4] Understand interval notation Forget to check the endpoints for extreme values

Problem 6 Differentiate with respect to x. ℎ 𝑥 = sin x x Students rely on Power Rule too much! Applying definitions.

Problem 7 Find the general indefinite integral. (Use C for the constant of integration.) 3 𝑥 2 +𝑥+ 4 𝑥 2 +1 𝑑𝑥 Forget about the constant “c” Do not recognize trigonometric integrals

Results Realize common mistakes and how to correct them Learn from past mistakes Build confidence Review material Helps the instructor enforce critical thinking questions for the students

Contact Me! amandarwhitt@abtech.edu