My 10th grade geometry students keep trickling in to take their logic retests, and many of them still had a hard time remembering the laws of inference to use in logic proofs. They would confuse the following two:
p --> q
(Law of Detachment)
p --> q
(Law of Contrapositive Inference)
I tried 2 or 3 or 1000 different ways of explaining it, and nothing stuck. I thought I hit gold with the following:
If the Dog is a Terrier, then the CHihuahua likes MENTos.
The Dog is a Terrier. (I thought this would help them connect it to detachment).
If the CON is a TRAitor, then I POSsibly like TV.
I hate TV. (for contrapositive inference).
So that helped some kids, but wasn't the raving success I thought it would be. Then just the other day, we were going over problems in tutoring, and I was circling things to make a point, and saw this:
Do you see it? The Detachment scribbles look like "D", and the Contrapositive scribbles look like "C". Well. They thought that was SO cool, and then they started accusing me, "why didn't you just show us this in the FIRST PLACE!". Like I was secretly storing away the "good stuff" and doing things the "hard way" until they finally wore me down to giving up the goods. Is this on ALL their minds: teachers always do things the hard way and hold back on us. Phwueey. I told them I just thought of it, and there was nothing to prevent them from figuring things out on their own and stop bothering me kid. .... They also passed their retests with flying colors.