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## If sin(x)/cos(x) = 3/5, then 1/cos(x) = 1/5.

The submitter asks: What would you write as feedback here? What would actually help this kid?

I ask: What’s the role of written feedback, more generally?

(Thanks again, Tina!)

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## Trig Identities Unteach Functions

Hypothesis: Proving trig identities unteaches functions.

After all, thinking of these as functions really just gets in the way, so all of our sensible students just treat these functions like variables.

(Thanks, Tina!)

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## “How do we get kids to stop and think when the cognitive load is higher?”

Tina reflects:

“Kids seem to forget their skills when the level is increased. They revert back to intuition like “subtract numerators, subtract denominators” when faced with trig functions, but as soon as I ask “how do you subtract fractions?” they immediately recall “common denominators.” How do we get them to stop and think when the cognitive load is higher?”

That’s a great question.

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## cos[arctan(5/7)]…

What’s up with this cool work?

via Tina

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## Slope of two parallel lines

Tina says: “Two students have done this so far. Not a mistake, but still curious what these kids are thinking:”

She’s talking about the 4/6 thingy. Any ideas, people?

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## Infinity!

The question asked for the range of the function SQRT(x).  What are your thoughts about the way the student answered the question. What does it show about what this particular student knows.*

In the past, I’ve publicly kvetched about how the only questions that we grapple with on this blog are about the particularities, rather than the generalities, of student work. This is a time when I think that the most interesting questions are accessed through thinking about what this particular kid was thinking. I’d also be interested in hearing how you think this represents a trend in students’ thinking, in general.

Thanks to Tina for the submission!

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## Constants and Exponents

Open thread. Go wild!

(Thanks to Pam for the submission.)

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## Completing the Square, II

Matt submits the above, and Matt writes, “I think it’s especially interesting that this student left the mistake on the board even though she had found the correct solutions by graphing in Desmos.  I’m not really sure if she did half of forty, or sqrt 4 and then stuck a zero on it (she wasn’t sure either).”

I vote for “half of 40.” You?

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## Completing the Square

What do you notice in this student’s work?

Thanks to Matt Owen for the mistake.