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Conditional Statements & Instructional Adjustments

I wrote recently about A-S-N-T-F.

I also wrote recently about what happens when students don’t recognize that a statement and its converse are different. We explicitly worked on conditional statements after that lesson.

So we defined converse/inverse/contrapositive/biconditional using symbolic logic, and then students decided which was which for a given conditional statement: If a shape has four sides, then the shape is a rectangle.

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What happens when you change which statement is the conditional statement?

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Again, students figured out which was which using the “new” conditional.

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We formatively assessed their progress on conditional statements:

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And then we were ready to start thinking about the truth value of the statements.

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Or maybe we weren’t ready actually ready, but we started thinking about the truth value anyway.

I never click on the student results for a Quick Poll in front of the students for the first time. My projector remote is an extension of my hand (except when I’ve carelessly laid it down and can’t find it), and so while students are working, I freeze the screen to look at the results and decide whether to make an instructional adjustment and if so, what instructional adjustment to make before I show the results to the students. Sometimes (as is the case in the contrapositive QP above), I have time to go talk to students who have answered incorrectly to clear up misconceptions while other students are still working. Sometimes (as is the case with this question), I deselect “Show Correct Answer” before displaying the results to students.

A student usually asks, “So who is correct?”

To which I reply, “So who is correct?”

I asked students to find someone in the room at a different table who answered differently. Convince them you are correct. Then let them convince you they are correct. (Practice construct a viable argument and critique the reasoning of others.) Then send in your answer again.

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Sometimes the responses change to 100% correct. Sometimes they don’t. And so I have to decide my next instructional adjustment. Do we have time to try this again? Or is the clock ticking more quickly?

My decision this time was to have a student come draw her counterexample.

What do we mean when we say two angles are supplementary?

Does that counterexample convince those who say the statement is true?

What if we are evaluating whether this statement is A-S-N?

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And so the journey continues, grateful for technology that gives every student in my classroom a voice – from the quietest to the loudest – so that I can make more informed decisions for when to make instructional adjustments.

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Posted by on November 29, 2014 in Angles & Triangles, Geometry

 

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