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.
— Chris 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 (@dynamic_math) 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
my team dvlpd lesson investigating this; Ss concluded easier if = 0 even tho cld b solvd; 1st yr ever taught truly conceptually
— Phillip H-H (@philliphsquared) June 10, 2016
possibly turn it into a systems of eqs prob. I'd also rethink how I taught the ZPP
— Amanda Sinner (@avsinner) June 10, 2016
Response #5: Switch to a Graphical Context
Look at a graphical representation of the original equation. https://t.co/H0QY8c0HSt
— Chris Bolognese (@EulersNephew) June 10, 2016
"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
@Thalesdisciple ASK why line three follows from line two. Wait for response.
Each step has a meaning. The stu is missing that.
— TJ Hitchman (@ProfNoodlearms) June 10, 2016
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
A my favorite no? Present it to the class for ideas.
— Teresa (Teri) Ryan (@geometrywiz) June 10, 2016
I’m sure I didn’t capture everyone’s response, and I don’t know what any of this means. But there you go.