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89 votes

Why is learning mathematics compulsory?

Questions like this, or variants (from students, the notorious "when will I use this in real life") seem to be pretty common, and I'm always a little surprised, because the unstated premise - that ...
Henry Towsner's user avatar
56 votes

What skills do algebra teachers wish their students had mastered before taking algebra?

Automaticity on basic arithmetic. That is, the ability to carry out basic arithmetic effortlessly without conscious thought. Automaticity goes beyond capability, proficiency, and even fluency. Simply ...
Justin Skycak's user avatar
54 votes
Accepted

How rigorous should high school calculus be?

Not very rigorously at all, but that doesn't (and shouldn't) mean just memorizing calculations. (I should add that I'm basing this on my experience teaching calculus to non-major college students, ...
Henry Towsner's user avatar
47 votes

Response to Students Who Say "This Is Not Important"

"Lately, my students keep telling me why what we are learning is not important. They ask me when will we use this in the real world?" There's a quick reply to this that I think people won't ...
Nullius in Verba's user avatar
46 votes

How do I show students the Beauty of Mathematics?

Imagine you are put in jail. You are forced to paint a painting every day for 10 years. You have no choice in the subject: one month you paint dogs, another month you paint horses, another month ...
Steven Gubkin's user avatar
44 votes
Accepted

Are there science-backed effective teaching strategies?

In terms of controlled experiments, then, yes. Note that most are opposite or orthogonal to virtually all pedagogical norms in math education. Active recall. "Put away all your notes and ...
BravoMath's user avatar
  • 564
43 votes

Response to Students Who Say "This Is Not Important"

Math is just as useless as almost any other subject As a math tutor, I've thought about this a lot over the last 15 years or so. Aside from tutoring, I don't use my math education in "the real ...
Todd Wilcox's user avatar
43 votes

Student asked me if it is necessary to simplify fractions at the end of answering a question. I'm not sure how to respond

The short answer to your question is: everyone is right. I agree with people here that in many contexts, $0.75$ or $\frac{3}{4}$ would be a more desirable answer than $\frac{45}{60}$. I also agree ...
Vaekor's user avatar
  • 630
42 votes

What value is there in requiring students to answer word problems in complete sentences?

Yes, there is mathematical pedagogical value in the usage of complete sentences - but this does not only refer to "answers" and not only to "word problems", but to all parts of the ...
Jochen Glueck's user avatar
40 votes

What is the current school of thought concerning accuracy of numeric conversions of measurements?

The product of two numbers should be given with as many significant digits as the least precise of the numbers multiplied (see https://www.nku.edu/~intsci/sci110/worksheets/...
Acccumulation's user avatar
38 votes

What value is there in requiring students to answer word problems in complete sentences?

I do think there is value in expecting students to give answers in correct English. It will certainly help when they start to face longer and less structured questions. However, the example you give ...
Especially Lime's user avatar
37 votes
Accepted

How do I show students the Beauty of Mathematics?

To expand on my comment, I found that high school kids like watching YouTube videos. (I mean, they don't have to do any work right? Just sit and listen.) These are a few of my go to channels to pull ...
ruferd's user avatar
  • 2,099
37 votes
Accepted

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

In the U.S. Common Core standards, functions are supposed to be introduced in the 8th grade, i.e., around age 13-14. So arguably age 15 is a year or two behind where they ought to be. The standard for ...
Daniel R. Collins's user avatar
36 votes
Accepted

When writing log, do you indicate the base, even when 10?

And a computer scientist thinks that $\log=\log_2$. I am using $\log$ for the natural logarithm by default in all my courses though I clearly state that in the beginning of each course (I teach at the ...
fedja's user avatar
  • 3,939
36 votes
Accepted

Why not think of derivatives as fractions?

If you have a function $f(x,y)$ where $x=x(t)$ and $y=y(t)$ are themselves functions of a parameter $t,$ and you blindly cancel out differentials, then you can get to incorrect statements like $$\...
Justin Skycak's user avatar
36 votes
Accepted

To 17 year olds, how can I explain that two numbers with arbitrarily small difference are equal?

I'd recommend to play a little game with them. You choose a number $a.$ They choose a number $b$ that they think will satisfy $|a-b| < \epsilon \,\,\, \forall \epsilon > 0.$ You try to state a ...
Justin Skycak's user avatar
35 votes
Accepted

Explaining Sigma-Notation

I've experienced positive results by first having students spend some time writing out sums in full (or using ellipsis notation if there are many terms). That way, it gets annoying to spend so much ...
Justin Skycak's user avatar
33 votes

Difference between high school and college calculus courses

Assuming we're talking about mostly US students, most American high schools teach calculus in a way that's very focused on the AP test. The pressure to get students through that with an adequate ...
Henry Towsner's user avatar
33 votes

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

I would say the standard implementations of the Rational Root Theorem (make a huge list for the sake of making the huge list) indeed feel like a complete waste of time. However, the theorem can ...
Chris Cunningham's user avatar
32 votes

Why do we teach complex numbers?

We owe students a presentation of the Fundamental Theorem of Algebra -- that every nonconstant polynomial has a root; or, equivalently, the marvelous fact that every polynomial of nth degree has ...
Daniel R. Collins's user avatar
32 votes
Accepted

How does one tutor an A-level student past the derivative paradox?

There is no royal road to geometry. - Euclid Nor calculus. The essence of calculus thinking is really the limit concept. One needs to wrap one's mind around that. Formally: it's the core technique ...
Daniel R. Collins's user avatar
32 votes

When did math start to be a hated subject in schools and universities?

Here are a few reasons: (1) math is a subject that students are required to take every year, (2) once you fall behind, it is hard to catch up again because of the way that mathematical knowledge is ...
KCd's user avatar
  • 3,536
31 votes

How does one tutor an A-level student past the derivative paradox?

I teach calculus at a community college in the U.S. (2 year college, from which many students transfer to a university). I explain limits from about day two in an informal way ("h gets infinitely ...
Sue VanHattum's user avatar
  • 21.1k
31 votes

Applications of High School Geometry

Every time I'm doing carpentry/DIY remodeling on my house, I use so much high school geometry that it makes me chuckle. I've had instances where I need to cut angles to make pieces parallel and used ...
Aeryk's user avatar
  • 8,019

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