Students rehearse and learn their parts in a play where the
characters' statments can only be interpreted if you think logically
about them. By playing the roles of the people making the statements,
students explore the logical possibilities of the statements that they
make. Students will appreciate and enjoy the power of logical
deduction.
Explain that the class is going to perform a play about people
called Brights, who always tell the truth and people called Braves,
who always lie. Everyone in the play is either a Bright or a
Brave, and either always tells the truth or always
lies. When we
start out, however, not even the people in the play will know which
kind of person they are.
Distribute scripts, assign parts and have students begin
rehearsing.
When students rehearse, help them to recite their lines
accurately and not leave out any details. Sometimes a particular
twist of wording is essential. Embellishments must be added with
caution. Students can add them, but only after they can analyze them
to be sure the changes don't alter whether people are Brights or
Braves.
Have students perform parts of the play for one another so that
they can discuss and analyze them together.
Help students see that in each interaction there are only four
possible cases--both students are Brights, both students are Braves,
the first is a Bright and the second is a Brave, or vice-versa.
Students can then try out the assumptions one at a time. For example,
begin by saying, "OK, let's imagine we are both Brights..." Then
examine
the content of each statement--was that true? Could a Bright have
said that? Sometimes it is useful to make a chart or table of the
possibilities.
It make take quite a few days for the students to catch on to ways
to find out who the Brights and Braves are. Give them time, and try
to assist them in structuring their thinking if they become
frustrated.
It's not uncommon for students to lose solutions as fast as they
find them. Help students to make tables, write down statements or use
other tricks to remember how they figured something out. Logical
structures are often intricate and hard to hold in our minds all at
once. Encourage students by assuring them that it gets easier with
practice. If you discover an answer and then lose it again, it will
be much easier to discover the second time.
We often think of people who lie as being bad people. We may
expect them to be rude, unfriendly, or disobedient. This is not the
case at Unusual School, however. Make sure that students realize that
they can only draw conclusions about
whether people are Brights or Braves based on statements that
are made and not any other part of their behavior.
When the need arises, help the students make the distinction
between a true statement and a false statement that allows us to
conclude something that we know to be true. Braves do not give bad
information or try deliberately to mislead you. Braves give direct
answers to the questions they were asked, and the statement that they
use to answer the question is always false. For instance, if you know
that someone is a Brave and that person points to someone else and
says, "She's a Bright," you can conclude that the person she has
pointed to person is a Brave. This is an example of how true
conclusions can be drawn from a Brave's false statement.
Sometimes when students are trying to help one another understand
how they drew a conclusion they can be frustrated when another student
doesn't follow their chain of reasoning. Help students realize that
"argue" has a special meaning in mathematics. They are not arguing
about opinions like we often do in discussions and conversations.
They are presenting logical arguments that are either true, false, or
inconclusive, based on the logic of the statements. When someone does
not accept your conclusions, it is either because they have found a
flaw in your in your reasoning, or because they are having trouble
following it. This happens often when mathematicians present logical
arguments to one another, and there is nothing wrong with not
understanding--even though the person presenting may find it
frustrating at the moment. Sometimes the person who does not
understand needs to have it explained in a different way, and
sometimes they just need time to think about it.
Discussing the logic puzzles embedded in the play is inseparable from
the preparation for the play, because the students will need to talk
to one another, ask questions and explain their interpretations of
what is happening. Unlike other activities where discussion debriefs
and reviews what students have learned, the performance of the play is
the culmination and celebration of the fruits of all the
discussion that went into its preparation.
The following suggestions for discussion will help students extend
some of the logical deductive skills that they developed by performing
the play, and also think about and gain insights into their own
thinking and problem solving process.
Did you think at first that you would be able to figure out what
was going on in the play? How did you start to get ideas for how to
figure it out? Did you have one strategy that worked better than
others. Which conversation was the one that you figured out first?
Was that the easiest one?
Can you think of questions that Terry could have asked to make the
job much easier?
Invent some other conversations that Terry could have with
students that would reveal whether they were Brights or Braves. Add
them to the play for future performances.
Each of Terry's conversations was with two other people. Invent
some conversations that Terry could have had with three people that
would have revealed their identity.
An adaptation of a famous puzzle in logic to Unusual School would
have Terry lost in the hall, and not knowing if any of the passersby
were Brights or Braves. What is one question that Terry
could ask to
anyone to find out whether to go to the right or to the left to find
the cafeteria?
The play would be quite a bit more complicated if the students
names were not pinned on their clothing. How would you change the
script so that another thing that Terry has to find out from all of
the Brights and Braves is what their names are? Try not to make it
too easy, or to provide any more information than you need to.
Perform the play for a different group of students. As a group,
plan ahead of time how to talk over the play afterwards with the
audience. Simply telling them who's who at the end of the play will
not be satisfying for them, they will want to be sure, and to do this
they will have to figure things out for themselves. Have the members
of the class plan how they will help their audience understand the
play. After performing the play and helping their audience understand
it, have them think about the other students' experience and compare
it with their own.
Did the other students experience some of the same frustrations
that they did?
What strategies did the other students find most useful for
understanding the play?
Did all of their plans for helping the other students
understand work? What would they do differently another time?
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