Today I asked my PreCalc kids what they think of when they hear the word unit in mathematics. They joyfully answered, “ONE!”
Hoorah! “So what do you think a unit vector is?” I asked, hoping that maybe this year someone would be able to put the pieces together and give the definition to the class so I wouldn’t have to. To my delight, a couple students answered: “A vector with length one?”
As soon as they heard my approval, I saw a guy extend a fist bump to the girl behind him. They were very pleased with themselves.
Fostering an environment where kids get excited about math and cheer each other in their mathematical accomplishments is not easy work. But when you see those small victorious moments–as small as a fist bump–it just makes your heart soar as a teacher.