F-LE A.1.a Use of "Prove" in standards

[jtravis08]

RE: a. Prove that linear functions grow by equal differences over equal intervals…
My question is in two parts…
1) When a standard like this one says “prove,” what specifically do you mean?

2) How do you think this standard might be assessed from a student perspective?

[Bill McCallum]

A good working definition is that “prove” means provide a logical argument appropriate to the grade level. Exactly what “appropriate” means is up for discussion and adjustment as achievement improves. But the fundamental requirement is that the argument be faithful to the mathematics. One might define a linear function to be a function of the form $f(x) = b + mx$ and then adopt a fairly straightforward algebraic proof: over an interval of length $d$, $f(x)$ grows by the constant amount $f(x+d) – f(x) = b + m(x+d) – (b +mx) = md$.

As for assessment, I would expect it to be difficult, but not impossible, to assess this standard with a summative, machine-graded assessment. The ideal would be in-class observation by knowledgeable teachers.

[Author]

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