ryang
  • Member for 7 years, 10 months
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Is there a virtue to learning how to compute by hand?
52 votes

I couldn't agree more with @Steve's comment. The following response is written with elementary-to-high-school mathematics in mind. A lack of a decent number sense really does encumber making sense of ...

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Difficulty in explaining sample space
7 votes

The (correct) sample space depends on how the probability problem has been framed: The set of letters in “$MISSISSIPPI$” is indeed $S_1=\{M,I,S,P\}.$ In a probability experiment with sample space $...

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Questions about proofs
6 votes

Comparing the RHS of (1) and (2) one deduces that $(a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)^2$. First question: Is this considered an acceptable proof at a post-secondary level? It's perfectly valid to ...

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Are ‘constant difference’ and ‘common difference’ synonymous?
4 votes

There is a constant difference between A's and B's ages. Here, the value of interest is constant as the input, time, varies. There is a common difference between successive terms of sequence S. Here, ...

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Unique candidate that fails
4 votes

Given the equation $$\lvert2x\rvert=x-1,$$ rewriting the left-hand side as $\pm2x$ results in the unique solution set $\{-1,\frac13\},$ which nonetheless fails to satisfy the equation. In other words, ...

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Analyzing an answer to the following problem: Give meaning to $\frac{4}{5} + \frac{2}{3}$
4 votes

The student was conflating the sum $$\frac45+\frac23$$ and the weighted average (where the weights account for group-size differences) $$\left(\frac{\color{#00F}5}{\color{#180}{5+3}}\right)\frac45+\...

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How to explain loss of significance in numerical analysis?
2 votes

In statistics, business and science, I keep hearing about how precision = consistency = low variability = closeness of the data points = reproducibility & repeatability. In numerical analysis, ...

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Standard word for a formula that is always true
2 votes

Expanding my comment into an answer: So you want the umbrella term for a predicate (propositional function), like the triangle or Cauchy–Schwarz inequality, that's always true, but not necessarily so ...

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How to explain Monty Hall problem when they just don't get it
2 votes

How about encapsulating the entirety of the explanation in a tree diagram, which is visual, accessible, and relevant to any Intro Probability classroom? We drew this today while going over the Monty ...

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Clearest verb phrases for operations
2 votes

"The function $h$ raises $2$ to the $x$, where $x$ is the input" and "The function $h$ raises $2$ to the $x$th power, where $x$ is the input" both ape the structure of $f$ and $g$ ...

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Average Cost to Velocity Analogy
1 votes

These two averages are of different types. Given the position function $s(t) = t^2+50$, what is the average velocity after 10 seconds? $\frac{(10^2+50)-(0^2+50)}{10} = 10$. The average velocity ...

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How to read chained equalities out loud?
1 votes

I fully agree with the self-accepted Answer, and am adding an orthogonal point: in mathematics, $$p \Leftrightarrow q \Leftrightarrow r$$ is commonly understood as $$(p \Leftrightarrow q) \;\text{ and ...

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How many zeros do we need to add to get a nonzero value?
1 votes

✔ explaining by contrapositive Adding up any number of zeros gives zero; so, it is impossible to obtain a nonzero value by adding up just zeros. explaining by deriving contradiction Let $c$ be a ...

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Getting students to actually read definitions
1 votes

I’ve been able to inculcate students with the awareness that definitions are not just legal agreements—which they basically are—or boring fine print, by persistently demonstrating҂ using definitions ...

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At what grade/age levels do students in Florida/USA stop using mixed fractions?
1 votes

In parts of the UK and Commonwealth countries, mixed numbers (aka mixed fractions) are commonly used till about 16 years old. So, mark schemes typically specify $5\frac14$ instead of $\frac{21}4.$ For ...

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The word "numeral", is it being taught and does the word exist for it in your language?
1 votes

In Mandarin Chinese, numeral: 数字 number: 号码

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simple statistics (binomial) terminology
1 votes

You might point out that the $3$-trial experiment has $8$ possible outcomes and $256$ possible events, which are subsets of the sample space; whereas each trial has $2$ possible outcomes, which can be ...

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Which works better for learning 6 * 7 = 42: saying "six sevens are forty-two", or "six times seven equals forty-two"?
1 votes

Not a proper acceptable answer, just an expansion of my original comment: A literal/direct/mechanistic recitation probably involves a lighter cognitive load than a quirkier sentence-translated ...

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Rhombuses, kites etc
1 votes

The observation that a rhombus's diagonals bisect its internal angles gives rise to an efficient method to find an angle bisector. Here, a British national-exam question hints this method to the ...

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Definition of the term, equation
0 votes

As pointed out by @AmyB and @DanielRCollins, an equation is simply a statement that two expressions are equal. @Adam remarks that the equation-identity distinction doesn't seem useful; on the contrary,...

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Should I avoid writing: $ 11:40 - 15 \text{ min} = 11:25$, and what are alternatives to this way of writing?
0 votes

It is as cromulent (thanks, MatthewDaly!) to write $$11.40\text{ a.m.} \color{#00F}- 15\text{ min} = 11.25\text{ a.m.}$$ as it is to write $$(4,3) \color{#00F}-\begin{pmatrix}1 \cr1\end{pmatrix}=...

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Examples of vocabulary that have different meanings in Mathematics compared to "everyday" English
0 votes

In ordinary speech, the adjective random describes something that occurs without a definite pattern or predictability. In mathematics, its meaning is, in a sense, inverted: random/stochastic processes ...

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