Black and brown and completely different in different ways.
One of the other Algebra 1 teachers at my school teaches graphing of inequalities this way:
"Make the inequality so that the variable appears on the left. Then graph according to which way the 'arrow' points."
True, this procedural method allows some students to get the correct answer more consistently. But I don't like it because understanding the meaning of the inequality is lost. How do you really know what the variable is greater/less than? And what the hell: an inequality sign is NOT an 'arrow.'
This method of teaching graphing of inequalities is So. Very. Grating. To. My. Soul. The beauty of knowing what those math symbols mean is gone. There is no thinking involved - it's all robotic work.
This is the same teacher with whom I got into a little spat with on Friday - in front of my students no less - with the way I give grades. I allow homework redos and extra credit assignments, but I don't allow test re-takes for a better grade. She allows test re-takes, but no homework redos and no extra credit assignments.
She thinks my way of grading is too easy.
I think the way she teaches is not accurate, nor rigorous enough.
That evens us out, right?
I, frankly, don't give a damn what kind of grades my students get. My priority is to have them think critically - and grades are not necessarily a good measure of how well students can think.
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