ﬂat on a table. Each card has a single-digit number on one side and one of two colors (blue or green) on the other side. Consider the following statement: 1
ﬂat on a table. Each card has a single-digit number on one side and one of two colors (blue or green) on the other side. Consider the following statement: If a card shows an even number on one face, then its opposite face is blue. 1
ﬂat on a table. Each card has a single-digit number on one side and one of two colors (blue or green) on the other side. Consider the following statement: If a card shows an even number on one face, then its opposite face is blue. Which cards must you turn over in order to test the truth of this statement without turning over any unnecessary cards? 1
ofﬁcer in a bar looking for underage drinkers. The rule is: If a person is drinking beer, then that person must be over 21. You see four people: Which people do you need to check to make sure the rule is being followed? 2
task in psychology experiments, only 10% of people selected the right answer. • When the task was reframed in the underage drinking context, 75% of people got the right answer. 3
task in psychology experiments, only 10% of people selected the right answer. • When the task was reframed in the underage drinking context, 75% of people got the right answer. • Psychologists: When given abstract tasks, the brain cuts corners and we act irrationally. 3
task in psychology experiments, only 10% of people selected the right answer. • When the task was reframed in the underage drinking context, 75% of people got the right answer. • Psychologists: When given abstract tasks, the brain cuts corners and we act irrationally. • Underscores why we need mathematical frameworks to support our thinking. 3
As you explore, keep a record of the process: Explore Blink • Where is the mathematics? • Rules, conjectures, proofs, generalizations? • Record all mathematical ideas and questions. Meta-Process • Record any mathematical moves you or your peers make. • If possible: What is the motivation behind those moves? Our objective is to become consciously aware of the questions we ask and moves we make while doing mathematics. 4
As you explore, keep a record of the process: Explore Blink • Where is the mathematics? • Rules, conjectures, proofs, generalizations? • Record all mathematical ideas and questions. Meta-Process • Record any mathematical moves you or your peers make. • If possible: What is the motivation behind those moves? Ponder: How do your moves look in other mathematical contexts? 7
about the process of doing mathematics: • The ideas generated in Part 1 • Your own experiences doing mathematics for fun/research • The behaviors you’ve seen in your students The goal is to produce a visual representation for the process of mathematical inquiry. 10