If you want to move beyond endless drudgery, you have to have technology (or slaves, servants, or a spouse) to free you from the otherwise all-consuming task of survival. Technology is the least-objectionable way of generating free time, in my opinion. People have a limited mental capacity, so we can't just keep adding on new skills. So irelevant subjects like Latin, square roots by hand, etc. have to go.
Today, it's nice to be able to add small numbers, and larger numbers in a pinch, but the specific mental tricks and habits needed to get the right answer consistently when adding lots of numbers are just not helpful. Calculus classes are focused on drill, computation of integrals and derivatives, etc. While there are some conceptual questions, functions as tables and graphs instead of just formulae. These computations could be done much more easily in Mathematica or with a numerical solver. Calculus classes should focus on modeling and numerical algorithms (e.g. estimating areas using triangles and rectangles). Calculus classes could be more focused on modelling and use of the computer to approximate things (e.g. use of Euler's method in the movie Hidden Figures) : teach how to design, analyze, and run mathematical models on a computer. Furthermore, writing the word "lim" in front of everything but not defining a limit is a silly pretense to rigor, just teach it like Newton did.
If you are worried that your child will suffer by not learning to solve a polynomial by hand integrate, etc., I would suggest worrying more about not learning how to skin a rabbit, or how to start a stalled car.
Even assuming hand computation, most of the problems could have been done using the AM-GM inequality the whole time or are just elementary problems obfuscated with integral symbols, probably so it is easier for the professors and TAs to grade.
Today, it's nice to be able to add small numbers, and larger numbers in a pinch, but the specific mental tricks and habits needed to get the right answer consistently when adding lots of numbers are just not helpful. Calculus classes are focused on drill, computation of integrals and derivatives, etc. While there are some conceptual questions, functions as tables and graphs instead of just formulae. These computations could be done much more easily in Mathematica or with a numerical solver. Calculus classes should focus on modeling and numerical algorithms (e.g. estimating areas using triangles and rectangles). Calculus classes could be more focused on modelling and use of the computer to approximate things (e.g. use of Euler's method in the movie Hidden Figures) : teach how to design, analyze, and run mathematical models on a computer. Furthermore, writing the word "lim" in front of everything but not defining a limit is a silly pretense to rigor, just teach it like Newton did.
If you are worried that your child will suffer by not learning to solve a polynomial by hand integrate, etc., I would suggest worrying more about not learning how to skin a rabbit, or how to start a stalled car.
Even assuming hand computation, most of the problems could have been done using the AM-GM inequality the whole time or are just elementary problems obfuscated with integral symbols, probably so it is easier for the professors and TAs to grade.
