She teaches logic to full classes “95% of whom actively don’t want to be there.” So she has to sell the course. [That’s pretty standard.]
Her course is half formal logic/half informal critical thinking. Venn diagrams, propositional logic.
Games motivate because they try strategies and they don’t work, so they see the need to improve their thinking.
Divide students into groups of 3 or 4 to play the games. More than 4 and you get free riders.
She says she uses clickers and peer review in class, but won’t be talking about it today. [I want to hear her techniques here.]
Students who are really really struggling don’t like groups, because they are embarrassed at their lack of ability.
20-30 minutes a game. Doesn’t replace anything—just supplements.
Be really really explicit about what the point of the game and how it relates to the other material.
Sixty four squares
Good in the first session of class.
Draw a 8 by 8 grid on the board (number the columns, letter the rows.)
Goal: Find the secret square in as few questions as possible. Asking only yes/no questions.
The groups have to come up with a sequence of questions to ask that will get the answer quickest.
Worst strategy: Guess individual squares.
Best strategy: binary search—get it in 6 questions.
Tell the students to play out the strategies on their own.
After the small groups ask “Is there anyone who can get it in 3 questions?”
Have them play out the strategy—don’t have them explain it.
Two groups will succeed at six. Ask what those two strategies they came up with have in common. Now we have an abstract solution.
Connect to the curriculum.
Variation: Now devise a strategy in which each yes/no question is either a conjunction or a disjuction.
How do you ask “Is the square B6” as a conjunction? As a disjunction?
[put a distracting pattern in the square, so they ask questions like “is it inside the smiley face or outside.” When you give the solution, point out that you have to abstract from the stuff that isn’t relevant.]
Also a daily puzzle at the NYT.
Cards with 4 variables: color, shape, shading and number of symbols.
A set is three cards where each feature either matches on all three cards or are all different on all three cards.
Objective: Identify as many 3-card sets as possible.
Connect to the curriculum
· Use venn diagrams to identify three random properties.
· Talk about stipulative definitions.
· Identify three random cards and have them identify categorical propositions. (No red card is solid, etc.)
Playing the game doesn’t directly relate to any lesson.
Problem: Two people in the room were red-green color blind.
Solution: write the names of the colors.
Andrew Mills: can you teach conditional reasoning asking students to fill in sets.
Other questions: How many sets can start with this card.
Fun thing to do: given 12 cards on the table, prove there are no sets there.
Wason selection task
Which cards to you turn over to verify a rule, like if a card has a circle on one side it is yellow on the other. If the person is drinking, then they are over 21.
Connect to the curriculum
Symbolize and use truth tables. The relevant line you need for the truth table is T → F. Have them note that the same line for the contrapositive claim.
Circle → Yellow ~Yellow → ~Circle.
T T T F T F
T F F T F F
F T T F T T
F T F T T T
Do at least a few weeks on truth tables before you introduce this.
So the Wason selection task is an add-on at the end of the truth table section, not a way to teach it.
Mills: This helps calm logic anxiety because you can talk about how people get the Wason task in the alcohol context and not others.