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Logic Session #5: The Jabberwock and the Converser

The Jabberwock and the Converser

’Twas brillig, and the slithy toves

Did gyre and gimble in the wabe

So begins Dodgson/Carroll’s poem Jabberwocky.  I read it aloud without introduction as the students colored their own Jabberwock puppets.  The coloring focused students’ attention, as they were, as usual, excited about the impending puppet use.  They commented on the poem:

  • “That doesn’t make sense.” (L)
  • “Is it a boy?” (J, about the illustration, which looks like a girl but is called “he” in the poem)
  • “How old is the story?” (C, thinking that it’s pretty old since it starts with “’twas”)
  • “Well, it makes a little sense… It was in Alice in Wonderland.  A lot of that doesn’t make sense.” (M)

Everyone was then focused enough to attack some statements on the board.  These statements were all conditional or categorical.  The children added a few of their own, and came up with responses appropriate to D’s creation, The Backwardser.  They tried to categorize the Backwardser as Knight, Liar, or Normal.  Then they revisited their debate about how to categorize the Blender, who gives a compound sentence comprised of a statement and its negation.  Some attempted to find explanations for, or loopholes in, sentences such as “I love you and I don’t love you,” and “This pencil is yellow and it is not yellow,” while others considered them to be lies.  They did not reach a consensus, although the latter opinion prevails at this point.

I then introduced Waggy (the fox puppet) in a pair of high-top purple sequined sneakers.  The kids read the statements on the board to him, and tried to guess his role.

  • Baseball is a type of sport.
  • Thunder is a type of storm.
  • If it rains, then I get wet.
  • If there’s a fire, then there is smoke.  (Interestingly I had accidentally written the converse of this statement first, and the kids demanded that I switch it to this.)

Waggy gave the converse of each statement, for instance, “If there’s smoke, then there’s a fire.”

The kids called him a Switcher, and a few other things.  They described this manipulation as “taking the end and putting it at the beginning.”    I called him The Converser, a label the kids found pretty lame because many were unfamiliar with Converse sneakers, and the rest realized that they weren’t “real” Converses.  I asked the kids to predict Waggy’s response to a few more statements, which they did with glee:

  • If I am a human, then I am mortal.
  • If you are a sailor, then you are a good swimmer.

I did not even have to ask for the truth value of each statement and its converse; the kids were calling them out.  They were also coming up with their own statements for Waggy until everyone was shouting over each other.  It was time to refocus, so I moved the group to the floor on the other side of the room and got out my Bobble Head Doll.  This activity quickly relaxed and focused the group, so M and V then finally got their turns to play roles with the puppets.

M played a Negator and had fun negating such student-produced statements as “You are not a fox,” and “Mia is not wearing blue pants.”

V chose a sock puppet with pom-poms.  “You are made out of a sock,” said someone.

“I am made out of a sock and bally things,” said V/sock.

“V has 3 legs,” said someone else.

“V has 1 leg,” replied V/sock.

“Poor V,” consoled S, as class time ended with a bit of uncertainty over the sock’s role as V was determined to prove that a Negator does not have to be a Normal.  He and a few others clustered around me as I straightened the room after class.  V posited that a Negator could be a type of Liar if the statements were numerical.  He demonstrated example after example of untruthful statements in response to numerical falsehoods, and identified them as both lies and negations. For instance, I said “1 + 1 = 3.”  He responded “1 + 1 = 5.”  I was afraid that I had burst his bubble when I finally asked, “Are your responses true negations, or are they fancy wordplay?”

“Well, they are fancy wordplay,” admitted V, but he was not deflated.  He (and the others who were listening) left with the intention of developing a justification for the conjecture that fancy wordplay might be a type of negation that allows a lie to be negated by another lie.

Once again, the kids have given me something to think about between sessions.

Rodi

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