Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

Most Popular

more tags
1500 questions
24
votes
10 answers

Is 'estimating' still considered a valuable skill?

I was with a 2nd year high school class, preparing for our (US) state's standardized test. I asked the class how they would solve this, and they flipped through the sheets to find $$V=\frac{1}{3}\pi r^2h$$ (To be clear, there is a 'formula' page…
JTP - Apologise to Monica
  • 9,770
  • 43
  • 70
24
votes
2 answers

Separating the roles of "teacher" and "assessor"

Teachers at the university level (at least what I've seen in the US) are responsible for both teaching students the material for a course, and assessing the students' understanding of the course material. This seems to encourage the creation of…
Mike Pierce
  • 4,845
  • 1
  • 20
  • 56
24
votes
6 answers

What is the proper way to ask a "find the domain" question?

A function is not really a function unless it's defined everywhere on its domain. So consider these three questions: Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be the square root function $f(x) = \sqrt{x}$. What is its domain? Let $f: [0, \infty)…
Paul Castle
  • 351
  • 1
  • 6
24
votes
10 answers

Why would you teach Calculus before teaching Real Analysis?

Let's assume our students are actual aspiring mathematicians. Why would we introduce our students to Calculus rather than Real Analysis? After all, "Calculus is a subset of Real Analysis". He will have to learn everything that he had already learned…
ClassicEndingMusic
  • 348
  • 3
  • 4
24
votes
17 answers

Examples of Mathematical Slang

Unless you have taught highschool algebra in Iran, you could not make sense of the phrase: Elephant and Teacup Identity! This is what teachers use to refer to the following identities: $ (a+b)(a^2-ab+b^2)=a^3+b^3$ and $ (a-b)(a^2+ab+b^2)=a^3-b^3$…
Amir Asghari
  • 4,428
  • 17
  • 40
24
votes
4 answers

How to Teach Adults Elementary Concepts

I've recently taken on the task of helping out in my school's Math Center. The courses I assist in range from Algebra to Calculus. While I'm younger (in my 20's), most of the students at the school are 40+. The first students I worked with were…
charliefox2
  • 351
  • 3
  • 7
24
votes
3 answers

How to teach perseverance?

I have found that when I give problems that require multiple steps or ideas to solve, students often give up quickly and come to office hours begging for hints. Sometimes I break up such problems into steps, with hints for each step; this enables…
Mike Shulman
  • 6,560
  • 21
  • 53
23
votes
4 answers

"Calculators are so twentieth century."

Even though I studied maths, I became familiar with programming in my junior year at university. I'm indebted to the professor who encouraged me in that pursuit, as it provided me with an avenue not just for problem solving but for exploration that…
Andrew
  • 1,776
  • 10
  • 22
23
votes
5 answers

Natural, rich, calculus questions

We have the good fortune of having "lab sections" here at my college. I'm interested in conducting some activities in the spirit of this talk. However, even in my stash of inquiry-based learning resources I can't easily find a large number of…
Jon Bannon
  • 6,173
  • 19
  • 44
23
votes
8 answers

Should we teach trigonometric substitution?

This is the question that was not asked here. Also related is this question, but both presuppose that it will be taught and ask about how best to do it. My question here is, suppose we are designing a calculus curriculum; should we include…
Mike Shulman
  • 6,560
  • 21
  • 53
23
votes
0 answers

What are some good simple examples that getting the right result is not enough?

When I want to point out to my students that getting the right result is not enough, I like to show them the example: $$\frac{16}{64} = \frac{1\hskip-.1cm- \hskip-.4cm{6}}{-\hskip-.2cm{6}\,4} = \frac14.$$ This example works well in some of my…
user11235
  • 1,280
  • 7
  • 19
23
votes
9 answers

Is it good to have solutions of homework published?

At a course at the university, the students have to do homeworks every week which will be graded and discussed in exercise groups. Is it a good idea to put "official" solutions of the homework on the homepage (or give it to the students in some…
Markus Klein
  • 9,438
  • 3
  • 41
  • 96
23
votes
2 answers

Is Knuth's suggestion on teaching calculus a good idea?

Note: I myself am not a math educator, though I plan to be one someday. In this letter, Donald Knuth suggests an alternate way of teaching calculus, based on big-O (introduced via a related big-A notation). He says "it would be a pleasure for both…
Akiva Weinberger
  • 331
  • 1
  • 5
23
votes
9 answers

Any tips in explaining the central limit theorem in statistics?

Many of my students don't have a mathematical background, and are not comfortable with concepts such as limits, random variables and distributions. Is there any intuitive way of explaining why the means of a random variable will form a normal…
Kenji
  • 333
  • 2
  • 8
23
votes
3 answers

Mathematic reasoning in nonEnglish/non Western languages

I am teaching in an Eastern Asian environment (precisely, teaching Mathematics using English in Korea, with Asian students) and I figured out that my reasoning is a lot based on my language proficiency in English and latin languages. As a latin…
Taladris
  • 1,433
  • 7
  • 18
1 2 3
…
99 100