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Hi Kim,
Thanks for writing. It’s great to hear CH8 resonated with you. I wonder how many kids we lose because they don’t see the connections and relationships?
I have every confidence you’ll continue to grow as you teach. I hope you’ll keep me posted!
Thanks again,
Tracy
Hi Linda,
I’m so sorry it’s taken me so long to reply! I missed your comment somehow. Thank you so much, and I’m glad you enjoyed the session!
All my best,
Tracy
Lindsey,
I love this question so much. I actually loved it enough to put it on twitter and see what kind of thoughts we might get over a few days. Check it out: https://twitter.com/TracyZager/status/908363750775906304
There’s a lot of interesting input there.
So, where do I stand? Hmm. I see the danger of over-identifying a student with an idea, as Michael described with Kat’s idea. I’ve gone too far down that road myself.
I also share your concern about how to be respectful when disagreeing. Absolutely. But I don’t think I share the worry about disagreeing with a person vs. an idea.
In our society, we have a massive problem, which is that people don’t know how to disagree amicably. I find myself suspicious of the idea that the solution to that problem is to somehow stop disagreeing with people, and instead disagree with their disembodied ideas. It feels like avoiding a problem, rather than solving it. To me, dissociating the idea from the person feels like sweeping something important under the rug, rather than dealing with it directly. And it impinges on ownership, too.
I think we have to teach students how to disagree with one another fully–even passionately–and still respect each other. Still be friends. Still go play at recess. I actually want explicit instruction in that.
When I think about our kids arriving in adult society, they’ll need to be able to disagree with other people. If you’re writing an academic paper and you disagree, you cite the name. And then you see each other at conferences and are professional and have a respectful discussion. If you’re running for office or trying to legislate, you say, “I agree with my opponent that it’s important to….but I disagree with my opponent about how to…” And then, at the end of the debate or floor session, you shake hands. Maybe even get a beer together.
I think I’d rather talk about why we assume disagreeing with a person is insulting, or personal? What’s there to unpack?
When you get to CH 12, on page 333, there’s a quote about this from Ian Stewart that I love so much. He makes the case that disagreeing and arguing are part of math, and that’s a good thing. Take a peek. The internal logic of math makes disagreements resolvable, which is refreshing, and good practice. I mean, in the rest of life, lots of disagreements are about opinions, where there’s no real evidence who is “right.” Much harder.
For example, my husband and I disagree on a lot of music. He likes these white hair bands from the 80s. I was a teenager in the 80s. Hated those bands then, hate those bands now. I spent those years listening to Prince instead! Still do. And yet we’re married. Whoever’s doing the dishes gets to pick the music. We don’t need to agree or come to consensus on everything. In fact, our different outlooks and opinions add some spice. What we do need to do, though, is disagree respectfully and not tear each other down.
In those scenarios you describe, i.e., “Are you disagreeing with Mabel?” the kids were totally able to handle disagreement without taking it personally. I think Soledad described what that feels like really well in the risk-taking chapter. I want that for kids.
And I even wonder if there’s a gender component? In my experience, girls have a harder time disagreeing because they are afraid of being threatening or seeming like they’re attacking. Think about, “No offense, but…” or “Sorry, but…” or “I could be totally wrong, but…” or “I’m not sure, but…” There are exceptions, of course, but most girls don’t feel entitled to state what they think without disclaimers and qualifiers that soften the message. They want to be “nice” about it. Women do this all the time in the workplace. We’re boxed in by it. I want my own daughters to be able to say, “I disagree with you and here’s why.” Not yelling, not attacking, not insulting, but disagreeing, with reasons. And eye contact. Person to person. That’s not an ad hominem attack. It’s just a disagreement. I don’t think it’s something to fear.
I also want my daughters to be able to hear a counter-argument and say, “You’ve laid out a good argument. I think I might be changing my mind.” I am trying to teach them how to revise their thinking, publicly, and acknowledge a good reason when they hear one.
In such a politically polarized country, I think we need more explicit instruction about how to disagree both with our neighbors AND with the more general ideas they espouse, and still have our kids play together. I have to think that’s possible. I mean, if that’s not possible, we’re screwed.
tl;dr: I think disagreeing with one another is fine, but, as always, the real issue is HOW. How do we disagree respectfully? How do we teach that?
Thanks for the great question and sorry for the rambling answer! I’m obviously still thinking!
Amie, I’m so glad you didn’t take a walk before posting! I freaking love this. Thanks for calling out the crap in the article and finding the good stuff!
T
I’m definitely in the latter camp. Words learned without need don’t stick well anyway. I like this little ignite from Dan Meyer about creating the need for the vocabulary before teaching the words: https://www.youtube.com/watch?v=PIHQH005dJ4
Hi Licia,
Great question. I would not consider the equation a representation in this case. Jen was looking for some kind of schematic, diagram, or picture to represent the situation. It could be abstract and didn’t need to involve stick figures–if a student had made a line that was 2 feet tall and then showed that three of those lengths was 6 feet, that would have been a representation too. Students who wrote the equation but couldn’t figure out how to draw something that showed how their equation matched the scenario were exactly the students Jen wanted to find and nudge. They were able to plug numbers into an equation, but not really describe what that three meant. She wants them to be able to do both.
Tracy
Ann Elise,
I’m so glad you’re here! You’ve clearly forgiven me for being the worst mentor in the world. Ha! I hope you understand why I was so busy during the blogging initiative–that was the final push to finish this giant book and I was flat-out.
Anyway, I’m glad we can learn together here and now. I can’t wait to hear how your work with your math methods class goes. Chrissy Newell used Becoming the Math Teacher You Wish You’d Had with her preservice teachers and learned a lot. Maybe you two could chat and let me listen in?
Tracy
Oh my goodness, Lori, I am so sorry. Dr. Buss sounds like an absolute monster. Horrible.
It feels good, though, to prove him wrong, doesn’t it? I had a teacher tell my mother, “Tracy has no aptitude for science, whatsoever.” I sent her a letter when I won a National Science Foundation Graduate Research Fellowship to study at MIT. Screw her!
I think you’re amazingly brave for sticking it out and becoming the anti-Dr. Buss. Thank you.
And your first paragraph! Holy cow! So true for so many! That calculation that you made–that you should not worry about those two because they were only -2 points–that’s so smart and reveals how wrong the system was!
Tracy
Catherine,
I think we all have to work on moving away from the procedural way we were taught. It’s hard work, but I believe in us! Thank you for sharing your story and learning. We’re in this together.
Tracy
I’m so glad you’re here, Kenny! And I hope we can talk more at CMC-S this year. Kindergarten is a fascinating world and I have a ton to learn from you.
Thanks for sharing your story.
Tracy
Jeff,
This is an amazing reflection on your journey thus far, and where you’re headed. Thank you for sharing it all.
Tracy
