paw88789
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6 answers
13 votes
474 views
Unique steps leading to a non-unique answer
6 votes

To find a basis for the row space of a matrix, perform elementary row operations to get to reduced row-echelon form. The nonzero rows of the row-reduced matrix are a basis for the row space of the ...

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5 answers
8 votes
553 views
How long would it take to teach proper limit calculations?
6 votes

It might be enough to show an example or two of what can go wrong with the logic of the first solution: $\lim_{x\to\infty} \frac{e^x}{x^2}=\frac{\infty}{\infty^2}=\frac{1}{\infty}=0$ But of course ...

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

I read the left-hand side as 11 minutes and 40 seconds minus 15 minutes. (Analogous to 11.4 - 15). So I expected the right-hand side to be negative. I would not write this, especially as a teacher. I ...

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20 answers
44 votes
13k views
How to explain that winning the lottery is not a 50/50 distribution?
5 votes

Ask him whether the probability of winning is the same if you bought 1000 tickets rather than one ticket. Or, imagine a lottery with 100 tickets, of which only one was a winner. If 100 different ...

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5 answers
10 votes
340 views
Drumming up interest in journal-problem-solving and competition prep
5 votes

Our MAA section (North Central) has an annual team math competition for undergraduates. It has proven more attractive to the students than the Putnams (which we haven't tried for many years). The ...

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4 answers
8 votes
256 views
Should school syllabus include chapters partially?
4 votes

My sense is that often authors are encouraged (required?) by publishers to make books very 'complete'. This means the book has all the topics that any instructor would be likely to want for a subject. ...

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1 answers
8 votes
173 views
Multiplying two decimals using (camouflaged) binary representation
3 votes

I am someone (in a country), and I teach it in certain (college) classes. In a discrete math class I teach it and then use the fact that if you multiply $n\times 1$ with this method (halving $n$ ...

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3 answers
7 votes
787 views
A good antonym for reducing/simplifying equivalent fractions
3 votes

How about : rescaling the fraction. This could refer to going in either direction.

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4 answers
7 votes
1k views
Acceptability of creative questions in assessments
2 votes

A compromise approach could be to give a problem (with parts), as you might on a guided worksheet. Such as: A function $f$ has domain $(2,4)$. We define $g$ by $g(x) = f(x-2)$. a) Is $g(3)$ ...

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7 answers
5 votes
374 views
Category mistakes regarding symbols and their impact on math (mis) understanding. ( Object symbol/ sentence symbol confusion)
2 votes

Another example of this sort of issue: I have often seen students write things like $\frac84$ when they mean $4\mid 8$ (i.e., $4$ divides $8$.) It takes a while (for some) to see that the former has ...

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3 answers
4 votes
212 views
Analogy for multiplying modulo N
2 votes

How about this: I made $\$12$ per hour for $7$ hours. I then bought as many books as I could for $\$$15 each. How much money did I have left? This would illustrate $7\cdot 12\equiv ? \pmod {15}$.

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9 answers
11 votes
518 views
Simple examples that violate group axioms
2 votes

In the game of Set, https://www.setgame.com/set, you can define a binary operation on the cards by Card1 * Card2 gives the card that completes the 'set'. (In the case that the two cards are equal, ...

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7 answers
23 votes
4k views
Repeated addition: standard notation?
2 votes

I would like to suggest a (English) language based approach: "I went to the store three times." (Should be totally clear). "Three times I went to the store." (Still clear). "I went to the store ...

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2 answers
12 votes
424 views
What are your opinions of a flipped classroom at the secondary level?
2 votes

While it may be true that sometimes 'backwards' flipping might be effective, sometimes it might rather be preferable to provide some of the low level content in a video watched beforehand. This would ...

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