Last year when I introduced the unit on logic I quickly realized that students were experiencing a ton of vocabulary with no context, and there was no way they would be able to "mind their p's and q's" just working with the textbook definitions. I tried to backpedal but we'd already reached the "we're never going to need to know this" and "this isn't math" frustration level so it was only marginally successful.
This year I did things differently. As students walked in I asked them to write a couple true sentences that fit the form "If ______, then _______." Then we got started with this worksheet:
It went much better than last year's introduction, but I need to rewrite the questions on the second page since I ended up doing most of those with the class (there were too many questions to answer individually). Even so, they realized that a) and d) were always true, which translates to "if a conditional statement is true, so is the contrapositive." And most quickly saw the repeated structure once I explained exactly what I was talking about. Best of all, only one student asked why we were studying sentences in math; she asked it genuinely and was happy with the answer I gave about precise definitions and careful explanations. When reading the journal entries about this class period there were students who said this was fun! Such a difference from last year!
After we went over the general form for a) through d) I gave them the names (conditional, converse, inverse, contrapositive). Vocabulary goes over so much better when they already have a context to apply it to. The next class we talked about biconditional statements and I used some of the examples that students had made up, which is always more fun than creating my own.
On a slightly less successful note, we're still struggling with counterexamples. At the beginning of the year we did an activity I call "True, False, Fix" (a simplification of Prove or Disprove and Salvage if Possible from PROMYS) where students read a statement, decide if it's true or false and fix the false ones. They keep wanting to fix when I ask for a counterexample. We've quizzed on it twice and I hand it back with "counterexample?" and re-explain, but they still keep fixing and explaining without providing examples. I hate to mark off for accurate statements, but they aren't answering the question I asked.
So, advice on re-wording the 2nd page of the activity? And/or how to convince my students that counterexamples are actually examples that prove the statement is false? Thanks!