Fractions have always been hard for me.

That was a partial truth.

Math has always been hard for me. I'm not saying those dreaded words, "I'm bad at math." I am saying that it was the subject that tripped me up more often than any other in school, from elementary all the way through college where I took as few math classes as I could get away with. In high school I did summer school because I spent freshman year in a (fairly unhelpful) remedial math class and needed to get through to Algebra 2 for most college applications. Or something, I don't remember exactly. I just remember going from the pool, where I was a pool aid, to my high school to sit in a room and do geometry on a computer. Woo, checking boxes!

Because of all this, I've never been as comfortable teaching math as I am any other subject. I love reading and writing, I enjoy science and history, but it took me a long time to not get squeamish around teaching math. To not feel like I was bad at it. Whereas I feel incredibly at ease going off book, so to speak, for a reading lesson, I have a tendency to play it safer in math. Not necessarily, "What's the book say? Ok, let's do exactly that then do pg. 53 #s 2-26 Even Only to practice," but not going big and crazy with confidence either.

Many things are changing when it comes to my math instruction. One, I've become very good friends with Megan Schmidt, who for years has been a very patient recipient of and replier to long DMs written minutes after the end of a particularly frustrating math lesson. She introduced me to the concept of Math Talks, which was something I think I probably knew about, and was one of those Teaching Strategies that, as soon as she said it, made my brain go, "Ohhhhhhh, that make total sense. I should do that." But, because of my mental training and process of untraining, I had a harder time going from, "Ohhh, that makes total sense," to, "This is how this would look in my room." Instead it was, "How would this look in my classroom?" Which is not a question I ask often.

When I go to conferences I always find at least one interesting looking math instruction session. Take responsibility for your learning and all that, right? Don't practice your strengths, no matter how fun and gratifying that is. Arnold Schwarzenegger hated his legs when he was a body builder. So he did ridiculous leg days. So I look for math sessions. The best math session I ever attended at a conference was the last one I went to, just last weekend. It was run by Matt Vaudrey, who is one half of Classroom Chef. His session was all about math talks and being comfortable and getting the kids to dig deeper into math conversations. It was fantastic enough that not only did I buy myself and my student teacher a copy of the Classroom Chef book, but I also got a hug. Hugs are important. I have a million ideas from Matt's session that I can't wait to start dropping on my kids.

But asking for help in a DM is easy. It's private. Getting ideas in a session at a conference is easy, you're in a sea of people, a face in the crowd. Asking for help in a big public way about something you think you should know is harder. I think. Probably. Honestly, not for me, and I don't say that to toot my own horn, but to be honest about having very little ego about being embarrassed when I don't know something. Or at all. It's a confidence thing plus a genuine belief that my ego has before and will again get in the way of my learning, so I push it aside and ignore it. Honestly, there's no way to not sound like a jerk after those last few sentences, so let's move along quickly and hope you forget about them. *smokebomb*

ANYWAY, I was teaching my kids about fractions (see, it all comes back around, I have a point). And it's pretty easy (now) to illustrate and explain why adding and subtracting fractions works how they do. Even multiplying fractions makes sense in my head. But dividing fractions- I got no ideas. I know

*how*to do it. Flip the second fraction and multiple. Great. But how is that helpful. I spend all year preaching at my kids that learning isn't magic. I tell them, specifically, "You cannot say, 'I know this is right because it's right.' You might as well say, 'Because magic!' It's not magic. WHY does this work?" They hear it in science, they hear it in language arts, they hear it in math. Not up until dividing fractions. Through dividing fractions. Before, for years, I would say, "This is the trick for dividing fractions, it's real simple." And they'd be able to do it. But they wouldn't know WHY. And, in my classroom, with my current teaching philosophy, WHY is paramount.

The problem is, it's real hard to teach WHY if I don't know WHY. And I had

*No Freaking Idea*why flipping the whatever and doing the thing made the stuff.

So I did what we all do when we don't know- I googled it. And google FAILED ME. It's not that I struck out, there's a million pages about why flipping the whatsit and doing the stuffs makes tada, but none of it made sense in my head. Most of the time I'm a "I will figure this out on my own, go away" kind of guy. but with stuff like this I'm a "Pretty please won't someone hold my hand and speak in slow, measured tones" person.

And this is where the goddess known as Kate Nowak enters our narrative. I took the the Twitterz for help.

Many very nice people responded, but Kate "Dr Feelgood" Nowak had the thing that's easily understood. She broke it down for me step-by-step, holding my hand and spending just a ridiculous amount of time explaining exactly why the whositwhat getting flipped allows the jillywack to get all up in the shnizzle. For a whole, long, step-by-step-by-step thread. And in the end I got it!MATH HELP PLEASE!— Doug Robertson (@TheWeirdTeacher) February 13, 2017

I understand HOW to divide fractions (flip second fraction and multiply). WHY does that work? #mtbos (I googled, no help)

I was able to make four math videos for my kids starring Sophie (my math-centric monster), allowing me to blend the lesson and giving Student Teacher Veronica and I the freedom to mix and help.@TheWeirdTeacher Start with unit fractions... Can you draw a picture that represents 4 divided by 1/3?— Kate Nowak (@k8nowak) February 13, 2017

Here's the thing- I felt like I shouldn't be needing to ask for help with this. I'm in my 11th year of teaching. My second year in fifth grade. I should know by now how dividing fractions works. I'm going to put my teacher chin right out there in public for everyone to see and say, "I don't know how to do something"? That's asking for a swing, isn't it? At least a little. It's inviting DM groups across the EduTwitters to Copy+Paste the link into their thread, "Funny guy knows how to make with the jokes, but not with the teachie teaching."

Now, no one did that. Not in public. Probably not in private, but if they did, eh, whatever. We constantly preach modeling behavior. I was modeling total frustration and confusion and asking for help. I was utterly thankful for the help I got.

And this is where I assume, which I've heard has a Pinocchio in Funland effect on people, what other people think. And that's not totally fair, but it helps me make the point of all of this, and I think I'm at least a little right. The public nature of twitter makes it harder for us to ask serious pedagogical questions about things we think we should already know. I'm not talking about, "Oh, new Google toy, what's this do?" "How do you use Spheros in your classroom?" "What's a cool new project I can do to teach the life cycle of a basket full of puppies?" I'm talking about, "Why does creating a reciprocal fraction result in the quotient?" "Seriously, what's the deal with all these commas? How do you know where they go?" "What happens inside a cocoon has never made sense to me and I have to teach it. Help!" As grown professional educators it kinds feels like we should have those answers. Maybe not the best way to teach them, but at least the WHY.

Do we get scared of asking in public what we'd be ok asking in private? And how does this build out? Can we follow the ripples? You're scared to ask why dividing fractions work the way they do in public, are you really going to ask why DeVos crying "School Choice" is bad if you've never spent the time thinking about that system? If we can't ask the simple WHY questions, how much less likely are we to ask the hard WHY questions? I mean, if we're sweating the heat we might get from other teachers for not knowing some pedagogical peccadillo...

I leave open the very real chance that I'm totally wrong about this. Maybe it's in my head and I'm projecting. Maybe we're all good with admitting to not knowing, no matter what the thing not known is. But maybe we all know we need more leg day, and we're hoping everyone is too distracted by our awesome biceps to notice.

If you like this post and the other posts on this blog you should know I’ve written two books about teaching- He’s the Weird Teacher and THE Teaching Text (You’re Welcome). I’ve also written one novel- The Unforgiving Road. You should check them out, I’m even better in longform. I’m also on the tweets @TheWeirdTeacher.

I don't teach flip and multiply to divide fractions

ReplyDeleteA much easier strategy to understand and remember is to get common denominators(just like add and subtract) and divide the numerators.

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ReplyDeleteI’m am elementary educator too; this is my 25th year. I’ve struggled with math my whole life. I knew I wasn’t very good at math with my fifth grade teacher told me so! I made it my life‘s passion to prove him wrong and went back and visited him after I graduated summa cum lauda. When I started teaching there was no Internet. I looked for help for my mentors, but I never felt anyone truly heard me. I really like what you did by reaching out for help like this. I’m no longer in the classroom, I’m a librarian now, but I could see myself doing the exact same thing. Well done! Do you model for your students that vulnerability and that sense that you don’t know all the answers and that you’re willing to look for help when you need it. To me that’s the greatest lesson in mathematical thinking you could ever have!

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