New answers tagged algebra
6
votes
Special topics for introductory probability
One example of elementary probability is the so-called Birthday problem which asks for the probability that in a room of $n$ people two will share the same birthday. Sometimes formulated as a paradox ...
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1
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Special topics for introductory probability
[Additional to previous answer--can't edit, sorry.]
dt688:
I would be very wary about being too difficult or particular, when teaching in a corporate environment. I.e. if GMers are your target ...
2
votes
Special topics for introductory probability
I would look ar some of the basic six sigma literature and at doe. It is connected to all kinds of factory snd other process improvement. Very clear business connection.
I would eschew the Bayesian ...
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5
votes
Special topics for introductory probability
Bertrand's Paradox is an old saw. The point is that trying to randomize an experiment is tricky since there can be different points of view.
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0
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Special topics for introductory probability
I would suggest geometric probability and applications in stereometry!
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10
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Accepted
Special topics for introductory probability
A classic application of Bayes' Theorem is in medical testing, and the difference/conversion between "what is the probability I test positive, given I have the condition" vs. "what is ...
6
votes
Special topics for introductory probability
You might already be aware of this one, given how famous it is, but the first thing that comes to my mind is the Monty Hall Problem. It doesn't require any fancy mathematical machinery, just a basic ...
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2
votes
How to justify teaching students to rationalize denominators?
When we work with numbers of the form $a+b\sqrt{2}$ (with $a$ and $b$ rational), it is useful to rationalize. For example, to determine that the set of numbers of that form is closed under division. ...
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0
votes
Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
Maybe a bit of a lateral solution compared to the other answer here, but given you're meeting online, have you considered using emojis to represent your unknowns? This can help keep things tangible.
$...
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0
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Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
Without math, you can ask what is left 8f you take one apple from 2 apples. Write down algebraic expressions for one apple and two apples, and abbreviate apples by a. So she may know how to compute 2a-...
0
votes
Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
Have you tried to use the balance metaphor to solve the equation?
To solve the equation $3x=9$ using the balance metaphor, you can imagine a scale with two sides in balance. On one side of the scale, ...
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1
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Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
I'm not a teacher, so maybe I don't get your advanced teaching techniques, but why isn't anyone explaining what 3x means in reality? When I have 3 apples, I can show 3 apples. Why aren't you breaking ...
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1
vote
Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
Following up on Daniel R. Collins' suggestion,
teach the student a step-by-step way to solve and check problems.
For problems that are given to her in the terse algebraic format (like "3x = 9&...
- 3,148
4
votes
Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
A thing that I do in my low-level college courses is to spend a beat with each new example/exercise to inspect the statement and make sure we all agree with what we're looking at. "What ...
- 24.4k
7
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Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
Unfortunately I do not have experience in your (the OP’s) role, but at one time I was in the shoes of your student.
When I encountered rudimentary algebra for the first time I was completely lost and ...
- 171
0
votes
Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
I think you need to work on muscle memory, more than concepts. You have given her the concepts before, but clearly it wasn't sufficient. No problem with repeating the "why" also, while ...
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14
votes
Accepted
Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
From very limited experience: have you tried writing $$3 \times x$$ (or using one of the various stars, dots, etc.)?
It might be that it’s not obvious that there is a multiplication here: you say that ...
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5
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Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
tl;dr– You might just work out whatever algebraic manipulations the student suggests, showing them the results of their ideas until they get a hang of it.
Show them how the math would work out.
It ...
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7
votes
Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
This is a classical case of having learnt algebraic manipulation without meaning. The first thing to try is to build up algebra again from the foundations. You already tried using (virtual) concrete ...
- 6,751
10
votes
Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)
If it were me, I'd try building on what you mentioned here:
Use word problems. Even when she's just written down an equation where she knows that, e.g., $3x$ represents $3$ chocolates of unknown cost,...
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3
votes
Is there a standard convention for interpreting ambiguous absolute value expressions?
As I was looking at your expression, something just seemed typographically off, and then I realized that it was the missing padding around the bars that you see when mathematics is well-typeset. This ...
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2
votes
How does one explain that transformations 'inside' a function operate in the opposite direction than intuition suggests?
I think the best way to think about this is that is to use the concept "as if". For an example, for $f(x+2)$, it is like $f(x)$, but as if $x$ were two values ahead. That's why the graph ...
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7
votes
Is there a standard convention for interpreting ambiguous absolute value expressions?
I don't know about standards, but I read these things using a left to right, greedy algorithm. More specifically, the bars are like parentheses but you don't automatically know if they are opening or ...
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7
votes
Is there a standard convention for interpreting ambiguous absolute value expressions?
If I want to have nested absolute-value expressions, I would use different sizes
$$
\big|x + 2|x + 3|x + 4\big|,
$$
with variations possible
$$
\bigg|x + 2|x + 3|x + 4\bigg|.
$$
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1
vote
Intuition for order of operations in compound transformations
Is there a good intuitive explanation for how to think about the order of steps when constructing these compound transformations?
Here's a stab at what it would mean to obey the order of operations. ...
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