Saturday, October 01, 2011

Truth Tables

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!

15 comments:

1. Nice example of a bit of scaffolding making a difference.

I've got a game Ilike for this stuf... SPQR: http://mathhombre.tumblr.com/post/9468928317

2. That looks way fun! Thanks for sharing the game. I'll do that some time this week.

3. Heidicrafts10:36 PM

I really liked truth tables in college. I worked for some time for a company that makes cockpit displays for airplanes. My job was to test that the software did what it should in all conditions. Truth tables and the ability to prune out redundant cases was the main part of my job designing incident tests.

4. This comment has been removed by the author.

5. Thanks, Heidicrafts ... I relayed your example to my students about a direct application of truth tables :).

6. THis great practice...it here a typo for answers #9 or #14. Although I am not super strong with truth tables (even though I am teaching them?!?!), so I could have done it wrong.

7. Hi ER,

I believe the answer to 9 is FFTF (an AND is only true if both are true), and the answer to 14 is FFTF (the NOT gives you the opposite truth value). I totally have typos often, but I think this time it's okay .... are those the answers you got?

8. Those ARE the answers I got...and I am the queen of having typos, so I understand. I changed a couple of the answers on the bottom because not everything matched up...how I hope I did it correctly!! The students got it today to work on.

9. Hmmmm, on this particular sheet, I don't think there are mistakes. Here's what I got:
6. tfft
7. ttft
8. ttft
9. fftf
10. ffft
11. ffff
12. tftt
13. tttf (be careful because the hypothesis is the 2nd column, not the 1st
14. fftf
15. fftt
16. tftt (again hyp. is 2nd column) and ttft

1. Anonymous2:51 AM

very good ms

10. Those are the same answers I got. Phew...I thought I was doing something wrong. I like how you switched up the columns, it threw my kids for a loop, but they got it after a second look. Some classes had GREAT discussion amongst the students while they were working on it. You do have an a that is FTTT, did you just added that to throw the kids off? Did you tell the students that each column could be used more than once?
Again, THANKS for sharing. I have made quite a few worksheets for both Pre-Alg and Geometry modeled off your's. Also today I tried to use my time wisely, those "pockets" of time. You are definitely an inspiration and I learn something from EVERYTHING you post.

11. Thanks, ER! I'm glad the sheets are being useful. I'm loving the answer banks instead of "joke sheets" because I CAN have duplicate answers, and I don't have to adjust. The kids also like the instant feedback on their knowledge.

12. So here I am now, preparing to teach truth tables to a group of homeschooling elementary kids and Google led me back to you. :) This is just an overview of truth tables with them.

-- Heidicrafts

13. Heidi! Hope your year is going well. I'm actually not teaching geometry this year (for the first time in a long time).

Shireen

14. For interactive lessons on truth tables, see https://weblogic.a2hosted.com/Logic/index.html?2.3.0.html