What is obvious to a teacher is not obvious to students:
• It is easy to assume that students think like us.
• The challenge for teaching is figuring out how students’ ideas make sense.
• It is easy to make connections for ourselves.
• It is impossible to make connections for others.
• The challenge for teaching is figuring out how to support others in making connections.
Every wrong idea carries a grain of truth:
• It is easier to see mistakes than to see what students do right.
• It is easier to learn if we can see what we are doing right.
• The challenge for teaching is figuring out how to build on students’ mathematical ideas.
First I thought that a Teacher must be right in all things.
Then I imagined that my teacher was wrong in many things.
Then I realized what was right and what was wrong.
What was wrong was to remain in either of the first two states.
What was right was to convey this to everyone.
From “The Wisdom if the Idiots”
How do you think this quote relates to teaching and learning?