88
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 ...
- 11.6k
53
votes
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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, ...
- 11.6k
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 ...
- 24.3k
45
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 ...
- 459
44
votes
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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 ...
- 564
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 ...
- 630
41
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 ...
- 1,695
40
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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/...
- 1,440
39
votes
How do I nicely tell my coworkers that they are NOT mathematicians?
I do not know if there is an accepted definition of what a mathematician is. There are teachers of mathematics and professors of mathematics, for example, and most people agree that people of the ...
- 2,992
38
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 ...
- 576
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 ...
- 2,061
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 ...
- 24.3k
37
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 ...
- 459
37
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 ...
- 6,191
36
votes
Should I be teaching point-slope formula to high school algebra students?
As someone who teaches calculus to college students, I expect my students to have seen point-slope form. We just start using it (because it's the right way to talk about tangent lines and ...
- 11.6k
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 ...
- 3,599
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
$$\...
- 6,191
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 ...
- 6,191
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 ...
- 11.6k
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 ...
- 21.2k
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 ...
- 3,258
30
votes
Accepted
How to convince my student that this is an Identity : $\sec^2x-\tan^2x=1$?
An identity always holds for some values of the free variables. Sometimes the allowed values are all real numbers, sometimes something else. In this case the identity holds whenever $\sec x$ and $\tan ...
- 3,720
30
votes
Why is absolute value difficult?
(My answer is just a guess and not based on any formal research.)
I suspect the absolute value function may be difficult to understand because it involves "negative numbers that aren't negative." ...
- 10.8k
30
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 ...
- 24.3k
30
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 ...
- 20.1k
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