Description: (aka the blurb)
Being a mathematics student is about critical thinking, justification and using tools of past experiences to solve new problems. Students who approach every topic as a series of steps to memorize are not learning math. In this session we will explore how to replace some popular tricks with teaching for understanding.
Increase participant understanding of the detrimental nature of teaching tricks. Help participants to differentiate between tricks that shortcut understanding and mnemonic devices that help us remember definitions. Examine popular tricks to show how they limit students’ ability to problem solve and provide alternatives for teaching topics so students don’t revert to tricks. Provide ideas for engaging students in conversations to assess their understanding of tricks that they rely on.
Focus on Math
When students reference a trick as the reason or explanation for their work they are not precisely stating the mathematics (SMP6). This becomes a more serious problem when students need to take the inverse of their operation; how does one un-FOIL? The alternative to tricks is getting students to solve a number of similar problems, then generalize the procedures and shortcuts they notice (SMP8). When students discover their own shortcuts, and prove them, they demonstrate understanding.