We want every learner in our care to be able to say

**I can attend to precision.**

But what if I can’t attend to precision yet? What if I need help? How might we make a pathway for success?

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Level 4:

I can distinguish between necessary and sufficient conditions for definitions, conjectures, and conclusions.

Level 3:

I can attend to precision.

Level 2:

I can communicate my reasoning using proper mathematical vocabulary and symbols, and I can express my solution with units.

Level 1:

I can write in complete mathematical sentences using equality and inequality signs appropriately and consistently.

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How many times have you seen a misused equals sign? Or mathematical statements that are fragments?

A student was writing the equation of a tangent line to linearize a curve at the point (2,-4).

He had written

y+4=3(x-2)

And then he wrote:

He absolutely knows what he means: y=-4+3(x-2).

But that’s not what he wrote.

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Which student responses show attention to precision for the domain and range of y=(x-3)2+4? Are there others that you and your students would accept?

How often do our students notice that we model **attend to precision**? How often to our students notice when we don’t model **attend to precision**?

**Attend to precision** isn’t just about numerical precision. **Attend to precision** is also about the language that we use to communicate mathematically: the distance between a point and a line isn’t just “straight” – it’s the length of the segment that is perpendicular from the point to the line. (How many times have you told your Euclidean geometry students “all lines are straight”?)

But it’s also about learning to communicate mathematically together – and not just expecting students to read and record the correct vocabulary from a textbook.

[Cross posted on Experiments in Learning by Doing]