A student does this. How would you respond? (Multiple ideas welcome!) pic.twitter.com/SzWzuFfQmn
— Michael Fenton (@mjfenton) June 10, 2016
Lots of responses to this great tweet. I wanted to understand the themes in what people were replying, so I went through everything and tried to summarize it here.
Response #1: Check Your Work, Start a Conversation
tell them to plug back in and defend their answer. Start a dialogue about the role of factoring in the solution. Why do it at all?
— Eric Fleming (@dailyvalueomath) June 10, 2016
I'd ask them to verify their answer and see what they get, then use that moment of cog-dissonance to develop 0-prod prop
— Daniel Schneider (@MathyMcMatherso) June 10, 2016
Response #2: Just Check Your Work (No Conversation Mentioned in Tweet)
@Thalesdisciple Remind them to check their proposed answer by plugging it back into the original problem and see if it works.
— Dan Hagon (@axiomsofchoice) June 10, 2016
maybe try to have them plug in their solutions and see if they work.
— Kathy H (@kathyhen_) June 10, 2016
@mpershan Have them plug in to check… but plug in factored form, not original problem.
— Samuel Otten (@ottensam) June 10, 2016
Response #3: Explain the Zero Product Property
@mpershan The reason we factor is that there's a special rule when the product is zero
There's no rule for product of 2.— Christopher J. Burke (@mrburkemath) June 10, 2016
I'd talk about why there is no one-product property, or two-product, only a zero product
— Brian Miller (@TheMillerMath) June 10, 2016
Students can then realize just because two factors * to 2 doesn't imply either factor could be 2. Only works if product = 0.
— Tim Brzezinski (@TimBrzezinski) June 10, 2016
Response #4: Thinking About How to Teach the ZPP Unit
When I teach ZPP I start with a game. Ab=1. If you guess a and b you win $20. I would remind them of this activity. A=sqrt(91)/e
— Thomas Totushek NBCT (@TheMathProphet) June 10, 2016
https://twitter.com/philliphsquared/status/741394601399967744
possibly turn it into a systems of eqs prob. I'd also rethink how I taught the ZPP
— Amanda Sinner (@avsinner) June 10, 2016
https://twitter.com/bowenkerins/status/741281577687240704
Response #5: Switch to a Graphical Context
https://twitter.com/EulersNephew/status/741315075223363584
"Why aren't both of the blue points on the parabola?" pic.twitter.com/zVsC62myZU
— Christopher Danielson (@Trianglemancsd) June 10, 2016
Love this mistake. I would put it on @Desmos, then add the equation set equal to zero, discuss.
— Julie (@jreulbach) June 10, 2016
Response #6: Ask for Explanations
https://twitter.com/ProfNoodlearms/status/741276100953706496
maybe an algebraic proof… ask what math "rule" allows for line 3??
Or go there with the language and vocabulary+— Madelyne Bettis (@Mrs_Bettis) June 10, 2016
Response #7: Run a New Activity with the Whole Class
https://twitter.com/geometrywiz/status/741329839488000002
I’m sure I didn’t capture everyone’s response, and I don’t know what any of this means. But there you go.