Calculus Methods and Linear Regression Comparison

Multiplying two ten-digit numbers is considered a basic arithmetic fact.

The computation of an intricate definite integral falls under the category of complicated and profound mathematical facts.

Linear regression is a topic that wobbles uneasily between mathematics and philosophy.

The trace of Frobenius on a modular form of conductor 2377 is a simple and shallow mathematical fact.

Basic identities like $sin(2x) = 2 sin x cos x$ are more conceptually challenging than $1 + 2 = 3$.

Arithmetic mistakes are carefully screened off in textbooks.

Calculus methods are similar to linear regression in that they require a lot of creativity and intuition.

It is dangerous to use calculus methods and linear regression inattentively.

Making arithmetic mistakes when solving calculus problems under time pressure is common.

Arriving at a result like a jug of water weighing $-4$ grams is considered acceptable in a calculus exam.

Performing an integral or linear regression is a task that requires human guidance to ensure the result makes sense.

Math courses should train students to be fast and efficient calculators like Microsoft Excel.

Reformists argue that classical algorithms should be removed from the classroom to encourage students to discover mathematical properties on their own.

The author supports the idea of completely eliminating classical algorithms from mathematics education.

The author suggests that extracting square roots by hand is a necessary skill for students to learn in the modern world.

According to the author, it is important for students to master long division using pen and paper.

Overemphasizing algorithms and precise computations in education may lead to students who excel in tests but lack a deep understanding of mathematics.

The risk of emphasizing 'getting the answer right' in mathematics education is that students may become proficient at testing but lack fundamental mathematical knowledge.