Math(chat)misconceptions

I missed a good #mathchat last night.  Chats are regularly scheduled twitter on-topic conversations. (Completish list; dizzying array of topics; mathchat is Thursday 8 pm (US-east) with a follow up on the same topic Monday at 3:30 pm.) You use twitters nice hashtag search feature to interact with people you may not typically follow (though it is a great place to find new follows).  Mathchat, started by Colin Graham (@colintgraham), has a wiki page where topics are voted on and chats are archived.  My current favorite way to follow is using TweetChat.

So if I missed the chat, how did I know it was a good one? There's the wiki archive, but also this time Bon Crowder (@mathfour) used Evernote to record and share the TweetChat record. Slick. It was good enough that I wanted to organize the list, which led me to figure to Tumbl it, but it turned into a blogpost when I realized the extent of the chat and that I had never blogged about mathchat before.

One thing that does not come across in this reorganized list is the conversational aspect. In Twitter you can click on a tweet and see all the previous tweets in that specific conversation.

People

• lostinrecursion must change misconception: you're either an applied person or a pure math person. Bleh
• mathheadinc  Misconception: Students below 10th grade can't be in college algebra, calculus...
• daveinstpaul Misconception: People with "math brains" learn math effortlessly.
• LinaSouid misconception: Math teachers only know/care/love math.
• LinaSouid misconception: Girls aren't good at math. Girls don't make good engineers.
• lostinrecursion must change misconception: it's ok to say "I'm so dumb at math. I'm not just not a math person." especially for kids
• delta_dc misconception: "I'm not good at math." form many of my preservice elementary teachers.
• LinaSouid A majority of elem teachers at my school hated math. Spread it to all their students like a disease.
• daveinstpaul If I have to pick just one misconception, it has to be "I'm not good at math."
• MrHonner For me, this S misconception: "I'm good at math, so it's not important to work hard to become a better writer."

Teaching

• lostinrecursion must change misconception: math is math class and homework should look like homework 
• lostinrecursion must change misconception: you really need to know algebra for the real world.
• lostinrecursion must change misconception: practice is the best way to get better. (personal experience actually is) 
• LinaSouid #mathchat misconception: Math teachers know how to solve every problem, ever!
• lostinrecursion must change misconception: you have to play the role of "teacher" to get class to work.
• TenMarks Misconception: Memorization is the only way to learn math. (I'm looking at you, multiplication tables!)
• lostinrecursion must change misconception: "they" write the problems. I just answer them. Can we tell what "they're" asking?
• @lostinrecursion must change misconception: "there are problems I need to solve. I need someone to show me how to do that." - Salman Khan!
• @lostinrecursion #mathchat must realize: math is made by humans like the ones in the classroom. So let's make math.  
•  lostinrecursion must change misconception: stick to the book or you're in trouble (aka I don't trust you)
• delta_dc Many of the misconceptions in math are result of learners trying to make sense w/o understanding. @graceachen has 2 nice posts.
• LinaSouid misconception:" With a graphing calculator I can do anything"--especially from over confident high school students.
• lostinrecursion must change misconception: you need the teacher to learn math. You need school to learn math.
• lostinrecursion must change misconception: texting in class is bad. (I'm in field theory class enjoying this much more) 
• rvdemerchant misconception: there is an old math and a new math.
• rvdemerchant old/new math? Did the old math think concept. understanding was bad? New math think procedural understanding bad? Nope
• delta_dc misconception: memorizing multiplication table will make one better at math. A lot of parents of MS kids say this.
• MrHonner I think the primary teaching misconception is "There is 1 right way to solve this problem."
• cheesemonkeysf IMHO this is also the primary TESTING misconception!
• MrHonner It is related to this misconception: "It is wrong for the teacher to admit they don't know something". 
• LinaSouid  I don't know when math teachers (20 years ago) learned that part of their job was to be socially inept
• mathheadinc Probably when they themselves were humiliated, probably at an early age. Vicious cycle

Field

• ColinTGraham For me, if it was only one chance... I would want to change the idea that mathematics is about doing calculations.
• MariaDroujkova Clear one misconceptions! math=arithmetic
• ekendriss Misconception I'd like to clear: Statistics = boring.
• MrHonner Major Math Misconception: There's only one right way to solve this problem. ColinTGraham Or: there *is* a right way....
• msnorthrup Luckily this is fading with elem tchrs RT @MrHonner the primary tchg misconception is "There's one right way to solve a problem"
• MrHonner Misconception: The most important thing is math is whether your answer is right or wrong
• MrHonner Student Misconception: "If I try something and it didn't work, I've done something wrong."
• shawn_ny That it lacks creativity.
• delta_dc Misconception - being fast at math means being good at math.
• LinaSouid misconception: You need to know how to prove something to use it and understand it.
• LinaSouid: misconception: You can't guess.
• lostinrecursion must change misconception: go with your first instinct. Your second is wrong (aka don't trust yourself)
• delta_dc Misconception - math is only worthwhile if it applies to real world.
• OoeyGooeyLady That u can "like" it but still struggle at it. I didn't need it 2 be easy. Just wanted to have chance to try!!
• LinaSouid So true. People focus on perfection. Another misconception!

Specific topics

• daveinstpaul Misconceptions: y is always a function of x. 0^0 cannot be consistently defined. √4 has two values. Everyone should take algebra.
• daveinstpaul  4 has two square roots, which are denoted √4 and -√4. By itself √4 indicates the positive square root.
• ColinTGraham By convention = accepted academic 'whatever'
• lostinrecursion must change misconception: fractions are wrong if they're not reduced.
• mathheadinc Misconception: This is not how to write a fraction (1 1/2)/4
• daveinstpaul Oh, another misconception: All polygons are convex.
• MathMatters2Me Misconception: radicals can never be left in the denominator
• MathMatters2Me Misconception: Asymptotes are lines a graph approaches but never touches
• MrHonner For purely math misconceptions, nothing beats sqrt(a^2 + b^2) = a + b.
• msnorthrup As a 5th grade teacher - the misconception that "You can't take a big number from a small number" is rampant and problematic
• daveinstpaul Misconception: When proving a trigonometric identity, you must work with one side of the equation at a time.
• MrCHRISatCSI You don't have to carry a one!

Is Google cooking the books?

Then what?

• LinaSouid Misconceptions will be resolved when math teachers are friendly, social, good role models
• ColinTGraham "friendly, social, good role models" depends very much on how people arrive at teaching mathematics...
• MariaDroujkova I am making a poster of today's #mathchat about misconceptions. So much concentrated math ed genius! You rock, #mathchat people!
• MrHonner We need to remind ALL teachers that they teach kids, not math. 

Think I'll have to at least lurk on Monday. I've been putting it on for background music during my preservice HS teacher class. (With occasional comments. Like you could resist.)

Photo credit: bfishshadow, petesimon @ Flickr