We're well into our journey of logic in geometry, and we just started truth tables. In the past, I walked them through the 5 basics (conjunction, disjunction, conditional, biconditional, and double negation). We make up funny statements and see how things work. Then IN THE PAST I have immediately stepped into building a large truth table such as: (p or q) --> (~p and q) or some such thing. Shockingly, it was too fast of a leap into the deep end.
I had tried various things such as cutting out each column on pretty paper and moving things around, or working examples with them, or whatever. Not completely successfully. And then this year, I think I got it (after my 10th or 11th year teaching the topic!).
This year, right at the end of class for the basics, I set up a 3 column truth table, where I gave them weird columns for the 1st 2, and I gave them various "T"s and "F"s for the first 2 columns. Then I had them think about what the new action was on the 3rd column.
Example (of 3 column headers):
1st column: (p -->q)
2nd column: ~r and w
3rd column: (p-->q) OR (~r and w)
At first they were all, "what?", but I kept silent and eventually would dole out little clues if they were stuck (like boxing in one color the 1st column header and that same thing in same color in the 3rd column). They FINALLY got, "oh! you're just "ORing" 2 things. Voila! They went to the appropriate basic table and filled in appropriately.
Here's a piece of their homework for that night:
Then, when I started class the next day, we did a "fill in 2 columns" one, and they were okay. THEN I just started truth tables, and it seemed more successful than before. Woot!