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63 votes

Why is it possible to teach real numbers before even rigorously defining them?

answered Nov 2, 2019 at 5:07

27 votes

How to respond to “solve this equation” in a basic algebra class

algebra textbooks

answered Apr 8, 2017 at 12:57

22 votes

Given a 3 4 5 triangle, how do you know that it is a right triangle?

geometry visual-proof

answered Oct 28, 2015 at 13:08

18 votes

Accepted

Is there a more telling name for "Calculus 2"?

calculus curriculum terminology

answered Aug 9, 2019 at 2:10

18 votes

How to explain that the sums of numerators over sums of denominators isn't the same as the mean of ratios?

undergraduate-education students-mistakes statistics

answered Sep 27, 2019 at 23:31

14 votes

Why do we teach even and odd functions?

undergraduate-education functions precalculus

answered Sep 11, 2017 at 23:36

12 votes

A parabolic arc is not semicircular. But students think so

undergraduate-education calculus geometry students-mistakes

answered Feb 9, 2015 at 16:53

12 votes

Why do we teach the Rational Root Theorem? (high school algebra 2)

secondary-education technology-in-education solving-polynomials rational-numbers roots

answered Feb 23, 2021 at 20:15

11 votes

Why the fear of polynomial long division?

undergraduate-education mathematical-pedagogy algebra

answered Oct 27, 2021 at 13:03

11 votes

Accepted

Should $\varphi$ be monotone in the integration by substitution?

textbooks students-mistakes integration teaching

answered Aug 11, 2015 at 20:04

10 votes

How do you explain why perpendicular lines have negative reciprocated slopes?

undergraduate-education secondary-education analytic-geometry

answered Oct 1, 2015 at 1:26

10 votes

Why would you teach Calculus before teaching Real Analysis?

calculus mathematical-analysis

answered Feb 25, 2016 at 19:10

10 votes

Ideas for explaining 4D and higher dimensions

undergraduate-education geometry

answered Apr 6, 2020 at 0:39

9 votes

Why should or shouldn't we teach functions to 15 year olds?

secondary-education functions definitions

answered Apr 19, 2021 at 17:19

9 votes

I want a "true" proof by contradiction of an implication P => Q

proofs logic

answered Oct 9, 2021 at 1:02

9 votes

Why are induction proofs so challenging for students?

undergraduate-education proofs induction

answered Nov 19, 2015 at 4:57

9 votes

How to make students comfortable with the use of axiom of choice in analysis

mathematical-analysis

answered Apr 11, 2019 at 20:07

9 votes

How can I explain why numerical integration is easy, but symbolic integration is hard?

integration

answered May 29, 2019 at 1:21

9 votes

In what curricula are "rectangles" defined so as to exclude squares?

geometry curriculum definitions preschool-education culture

answered Mar 6, 2018 at 17:40

8 votes

Applications of MVT for Integrals, suitable for calculus 1

undergraduate-education calculus

answered May 2, 2016 at 21:11

8 votes

How to solve the problem of Wolfram Alpha?

technology-in-education student-motivation assessment

answered May 19, 2016 at 13:07

8 votes

How does one explain that transformations 'inside' a function operate in the opposite direction than intuition suggests?

algebra

answered Oct 22, 2014 at 19:47

8 votes

An intuitive explanation of l'Hôpital's rule for ∞/∞

calculus limits

answered Nov 26, 2019 at 5:02

8 votes

Fear of 3-dimensions

undergraduate-education

answered Feb 9, 2020 at 3:41

7 votes

Does anyone use the cubic formula these days?

algebra history

answered Sep 28, 2019 at 18:46

7 votes

How should I answer questions about the purpose of learning math?

student-motivation

answered Nov 19, 2020 at 1:36

7 votes

What's the Deal with Inverse Cotangent?

undergraduate-education trigonometry

answered Feb 22 at 1:48

7 votes

Why does the widespread erroneous definition of "irrational number" persist without being taught?

students-mistakes rational-numbers arithmetic

answered Jul 11, 2016 at 20:28

7 votes

Easy examples of correspondence between global and local, as preparation for Gauss's theorem and Stokes's theorem

examples vector-calculus

answered Sep 3, 2019 at 1:31

7 votes

Why do you need to distinguish between apparently identical objects in probability?

probability teacher-development

answered Sep 6, 2019 at 17:14

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131 Answers

Why is it possible to teach real numbers before even rigorously defining them?

How to respond to “solve this equation” in a basic algebra class

Given a 3 4 5 triangle, how do you know that it is a right triangle?

Is there a more telling name for "Calculus 2"?

How to explain that the sums of numerators over sums of denominators isn't the same as the mean of ratios?

Why do we teach even and odd functions?

A parabolic arc is not semicircular. But students think so

Why do we teach the Rational Root Theorem? (high school algebra 2)

Why the fear of polynomial long division?

Should $\varphi$ be monotone in the integration by substitution?

How do you explain why perpendicular lines have negative reciprocated slopes?

Why would you teach Calculus before teaching Real Analysis?

Ideas for explaining 4D and higher dimensions

Why should or shouldn't we teach functions to 15 year olds?

I want a "true" proof by contradiction of an implication P => Q

Why are induction proofs so challenging for students?

How to make students comfortable with the use of axiom of choice in analysis

How can I explain why numerical integration is easy, but symbolic integration is hard?

In what curricula are "rectangles" defined so as to exclude squares?

Applications of MVT for Integrals, suitable for calculus 1

How to solve the problem of Wolfram Alpha?

How does one explain that transformations 'inside' a function operate in the opposite direction than intuition suggests?

An intuitive explanation of l'Hôpital's rule for ∞/∞

Fear of 3-dimensions

Does anyone use the cubic formula these days?

How should I answer questions about the purpose of learning math?

What's the Deal with Inverse Cotangent?

Why does the widespread erroneous definition of "irrational number" persist without being taught?

Easy examples of correspondence between global and local, as preparation for Gauss's theorem and Stokes's theorem

Why do you need to distinguish between apparently identical objects in probability?