Acccumulation
  • Member for 4 years, 2 months
  • Last seen more than a month ago
What is the current school of thought concerning accuracy of numeric conversions of measurements?
40 votes

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/...

View answer
Why don’t American school textbooks recognize negative numbers as whole numbers?
20 votes

I don't think that "textbooks" decided this, usage did. The term "integer" covers positive and negative, so it would be redundant for whole numbers to refer to that category. And ...

View answer
What is the point of teaching variance?
8 votes

The variance is calculated directly, while the SD is calculated in terms of the variance. The variance is additive for independent variables. The effect of sample size is a lot easier to explain using ...

View answer
"Real world" examples of implicit functions
6 votes

For circular motion, you have x2+y2 = r2, so except for at the ends, each x has two y solutions, and vice versa. Harmonic motion is in some sense analogous to circular motion. For instance, for Hooke'...

View answer
How do you explain concavity of a polynomial without any calculus?
4 votes

You might want to discuss the etymology. There's "con", which means "with", and shows up in other words such as "converse" and "context", and "cave", ...

View answer
What math courses should I take in order to become a secondary math educator?
4 votes

If you want to teach high school math, then of course you'll need to know high school math. And if you want to get a teaching credential, you'll need to take whatever courses your state says are ...

View answer
Teaching congruent triangles non-rigorously
Accepted answer
4 votes

The main points are that knowing a length restricts you to a circle, and knowing an angle restricts you to a ray. So for SSS, you can draw one side, then for each endpoint draw a circle for the ...

View answer
Why is there a disconnect in the usage of "domain" between high school and higher mathematics, and where does it come from?
3 votes

At the secondary level, students tend to think of "real numbers" as being literal: any number that isn't in the real number system isn't a "real number", and any time you're given ...

View answer
Can we skip Newton's Method?
3 votes

Reasons to study Newton's method: -It's an application of derivatives -It is a good example of numerical methods -It can help strengthen understanding of relationship between derivative and tangent ...

View answer
How to convince students of the implication truth values?
3 votes

You could say it means "Whenever P is true, Q is true". So "If it rains, I will bring an umbrella" means "Every time it rains, I bring an umbrella". It's not possible to disprove this statement by ...

View answer
How should I teach logarithms to high school students?
2 votes

Slide rules are a good tactile method of exploring logs. You can use them to calculate the $log_ba$ and $b^a$, and $a\cdot b$. They also visually illustrate the properties of logs, such as $\log(xy)=\...

View answer
Helping students who make no effort to figure things out for themselves
2 votes

Your students are in high school, which means that there are limits to how much responsibility you can expect them to take for their learning. And you're already most of the way through this year, so ...

View answer
Tips for choosing coordinates of three points such that the coordinates of the orthocenter are integers
2 votes

The coordinates will be rational numbers, so you just have to pick arbitrary points, then scale by the LCD. This quora question has several answers for what the formula for the orthocenter is; I haven'...

View answer
Can we define length and perpendicularity not via an inner product?
1 votes

In general, manifolds have not a norm, but a metric, which is a function that takes two points as input and gives their distance as output. A space with addition/subtraction and a norm has a metric (...

View answer
Does this property of subtraction and division have a name?
1 votes

I don't know if this word is used specifically to describe this phenomenon, but the term "complement" is used in general to refer to two things that combine to make some third thing, so this ...

View answer
What is the best way to intuitively explain the relationship between the derivative and the integral?
1 votes

If you want more clearly "undoing" operations, define "stacking" as the following: Take some $\Delta x$. Chop the curve into rectangles of width $\Delta x$ and height $f(x)$. (There's some leeway as ...

View answer
Why do inequalities flip signs?
1 votes

Which would you rather I give you: 10 cookies or 8 cookies? Okay, now which would you rather have me take away: 10 cookies, or 8 cookies? Adding 10 gives you a larger number than adding 8, but ...

View answer
Student converted $\sqrt{x^2}$ and ended up with just $x$ instead of $|x|$
1 votes

Other answers have concentrated on the base, but the problem can also be ascribed to the exponents. $(x^m)^n=x^{mn}$ is true for any base, as long as m and n are integers. This follows simply from the ...

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

Jordan Curve Theorem: If you have a closed curve, there is an "inside" and "outside", and those are defined globally (two points are on different sides if every path between them crosses the curve at ...

View answer
How to help students understand/remember that $x^2 = a$ has two solutions?
0 votes

The square root symbol $\sqrt {\cdot}$ means "the principal square root". For positive numbers, it's understood that it means the positive square root. But your students clearly haven't advanced ...

View answer
Interesting but very easy epsilon-delta problems?
-2 votes

You are making this WAAAAAY too complicated. One simplification is you should be centering around the value you're taking the limit at. So in this case, if you define d = x-4, then x = 4+d and 3x2 = 3(...

View answer
Cognitive traps in very early set theory
-3 votes

what are the cognitive traps that a teacher should be aware of when teaching union, intersection, and subtraction in sets? That's your job to figure out. You should be giving your students exercises ...

View answer