Most Popular
1500 questions
11
votes
5 answers
Pedagogical considerations behind current order of presentation of trigonometry
A pre-calculus book (Precalculus ed 1 By Miller and Gerken), presents trigonometry in the following order:
1- Angles
2- Trigonometric functions defined on the unit circle
3- Right triangle trigonometry
4- Trigonometric functions of any angle
I do…
Maesumi
- 1,380
- 9
- 19
11
votes
1 answer
Diagram of Methods to Solve Differential Equations
I am currently trying to build a flow chart to visualize all tests there are to tell whether an ordinary differential equation is solvable and how to solve it. This is for tutoring purposes.
The inspiration for this project comes from another…
DLohmann
- 113
- 1
- 5
11
votes
4 answers
How to stay interested in less-tangible math
I've graduated high school and I am joining college soon. The problem with me is that I'm not finding less tangible math interesting at all.
Some people find abstract math to be very beautiful, and I'm exactly the polar opposite. I am turned off by…
phi-man
- 127
- 3
11
votes
7 answers
Introducing bounds
I've noticed that my students (primarily first-year students taking their first college math course) have a lot of trouble with inequalities. Not the math, the purpose: they seem to have a preconception that math is supposed to be about finding…
Henry Towsner
- 11,601
- 1
- 36
- 63
11
votes
8 answers
Different Kinds of Variables
Students sometimes ask whether the $x$ in the expression
$$2x$$ the same kind of thing as the $x$ in the equation
$$2x = 4.$$
In the expression $2x, \;x$ can be any real value.
However, in the equation $2x = 4, \;x$ can only be the value or values…
Frasch
- 227
- 1
- 5
11
votes
3 answers
What topics could be covered in a course on fractals?
I'd like to propose a class on fractals to my department in the next few years.
One issue is that there seems to be no consensus on what a fractal is (see the wikipedia talk page on fractals, for instance). The following are all things that I would…
Brian Rushton
- 11,680
- 14
- 67
- 137
11
votes
4 answers
Why are university algebra courses often harder than the corresponding high school courses?
Someone I know recently took an online intermediate algebra course to prepare for college algebra.
Thus course had 70+ sections, each with 10-30 poblems, beginning with set-builder notation and going on to associative/distributive/commutative laws,…
Brian Rushton
- 11,680
- 14
- 67
- 137
11
votes
4 answers
What are easy examples from daily life of constrained optimization?
A standard example of motivating constrained optimization are examples where the setup is described in a lot of lines, e.g., when you own a company and the company is making some products out of resources and are mixed in a certain ratio, etc.
Are…
Markus Klein
- 9,438
- 3
- 41
- 96
11
votes
4 answers
Notation for change of basis matrix
As far as I can tell, it's only a slight exaggeration to say that every text has a different notation for a change of basis matrix from (say) $\mathcal{B}$ to $\mathcal{C}$. That's not even to talk about the "standard" matrix for representation,…
kcrisman
- 5,980
- 20
- 42
11
votes
4 answers
Favorite datasets to use when teaching statistics
There are so many datasets available that it seems difficult to sort through them all and identify the best ones to use when teaching an introduction to statistics class. What are your favorite datasets to use when teaching statistics?
I want the…
eternalGoldenBraid
- 975
- 5
- 10
11
votes
3 answers
Are there any negative consequences in applying operations/functions to a whole equality?
Some of my students solve equations not by applying the same operations on the left and right sides of an equation, but by applying the operation to the whole equality. For example, they may write something like this:
$\sqrt{x-1} =…
Taladris
- 1,433
- 7
- 18
11
votes
4 answers
Multiple students writing $y\frac{d}{dx}$ rather than $\frac{d}{dx}y$ -- why?
I'm currently teaching a couple of courses that have a calculus prerequisite, and within the last week I've had two students make notational mistakes that amount to writing $y\frac{d}{dx}$ rather than $\frac{d}{dx}y$ (although in terms of different…
user507
11
votes
9 answers
How to help students understand/remember that $x^2 = a$ has two solutions?
I teach math in university, in France. This semester I have first-year bachelor students. I am becoming increasingly annoyed that they cannot remember the simple fact that $x^2 = a$ has two solutions for positive $a$, $x = \sqrt{a}$ and $x =…
user1362
11
votes
5 answers
Intuition for the mean for elementary school kids
I was teaching elementary school kids (aged 10) about the mean. The intuition I gave them is roughly as follows:
You are trying to find a value such that the sum of all the distances from the mean for the values above the mean is the same as the…
Simd
- 311
- 1
- 6
11
votes
3 answers
Third Grade Question -- This makes no sense to me
Third grade grandchild had this for homework. Can someone explain the intent here?
user10216038
- 396
- 2
- 8