Podcast
Questions and Answers
Multiplying two ten-digit numbers is considered a basic arithmetic fact.
Multiplying two ten-digit numbers is considered a basic arithmetic fact.
False
The computation of an intricate definite integral falls under the category of complicated and profound mathematical facts.
The computation of an intricate definite integral falls under the category of complicated and profound mathematical facts.
True
Linear regression is a topic that wobbles uneasily between mathematics and philosophy.
Linear regression is a topic that wobbles uneasily between mathematics and philosophy.
False
The trace of Frobenius on a modular form of conductor 2377 is a simple and shallow mathematical fact.
The trace of Frobenius on a modular form of conductor 2377 is a simple and shallow mathematical fact.
Signup and view all the answers
Basic identities like $sin(2x) = 2 sin x cos x$ are more conceptually challenging than $1 + 2 = 3$.
Basic identities like $sin(2x) = 2 sin x cos x$ are more conceptually challenging than $1 + 2 = 3$.
Signup and view all the answers
Arithmetic mistakes are carefully screened off in textbooks.
Arithmetic mistakes are carefully screened off in textbooks.
Signup and view all the answers
Calculus methods are similar to linear regression in that they require a lot of creativity and intuition.
Calculus methods are similar to linear regression in that they require a lot of creativity and intuition.
Signup and view all the answers
It is dangerous to use calculus methods and linear regression inattentively.
It is dangerous to use calculus methods and linear regression inattentively.
Signup and view all the answers
Making arithmetic mistakes when solving calculus problems under time pressure is common.
Making arithmetic mistakes when solving calculus problems under time pressure is common.
Signup and view all the answers
Arriving at a result like a jug of water weighing $-4$ grams is considered acceptable in a calculus exam.
Arriving at a result like a jug of water weighing $-4$ grams is considered acceptable in a calculus exam.
Signup and view all the answers
Performing an integral or linear regression is a task that requires human guidance to ensure the result makes sense.
Performing an integral or linear regression is a task that requires human guidance to ensure the result makes sense.
Signup and view all the answers
Math courses should train students to be fast and efficient calculators like Microsoft Excel.
Math courses should train students to be fast and efficient calculators like Microsoft Excel.
Signup and view all the answers
Reformists argue that classical algorithms should be removed from the classroom to encourage students to discover mathematical properties on their own.
Reformists argue that classical algorithms should be removed from the classroom to encourage students to discover mathematical properties on their own.
Signup and view all the answers
The author supports the idea of completely eliminating classical algorithms from mathematics education.
The author supports the idea of completely eliminating classical algorithms from mathematics education.
Signup and view all the answers
The author suggests that extracting square roots by hand is a necessary skill for students to learn in the modern world.
The author suggests that extracting square roots by hand is a necessary skill for students to learn in the modern world.
Signup and view all the answers
According to the author, it is important for students to master long division using pen and paper.
According to the author, it is important for students to master long division using pen and paper.
Signup and view all the answers
Overemphasizing algorithms and precise computations in education may lead to students who excel in tests but lack a deep understanding of mathematics.
Overemphasizing algorithms and precise computations in education may lead to students who excel in tests but lack a deep understanding of mathematics.
Signup and view all the answers
The risk of emphasizing 'getting the answer right' in mathematics education is that students may become proficient at testing but lack fundamental mathematical knowledge.
The risk of emphasizing 'getting the answer right' in mathematics education is that students may become proficient at testing but lack fundamental mathematical knowledge.
Signup and view all the answers
