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1 vote

How does one explain that transformations 'inside' a function operate in the opposite direction than intuition suggests?

I think the best way to think of this is not to try to somehow create yet another arbitrary rule, but instead to invite more examination of just what both the graph of a function is, what a ...
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1 vote

How does one explain that transformations 'inside' a function operate in the opposite direction than intuition suggests?

Here is a more general framework which explains (mathematically at least) what is going on. This would need to be adapted into age appropriate lessons if it were to be used. The basic idea is ...
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7 votes

How can you elicit the $\log x = \log \cdot x$ error?

Writing from a software engineer's point of view, it's a fact that mathematics uses a notation that's highly ambiguous. If you don't know that $log$ is used to denote some logarithm function, then ...
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8 votes

How can you elicit the $\log x = \log \cdot x$ error?

Ask the student to critique this work: Solve for $x$: $\sqrt{x} = 3$ Easy: $x = \frac{3}{\sqrt{\phantom{x}}}$. I have tried this a small number of times, and it has worked so far. The students ...
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1 vote

How can you elicit the $\log x = \log \cdot x$ error?

Function concept and various types of symbols and terms (e.g. log) are new to the students. It is not uncommon for weaker ones to struggle. The solution is not some secret aha revelation, not some ...
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