Tuesday, December 13, 2016


     Emily doesn't really like math.  She'll tell you that right to your face if you ask her.  Not in a confrontational or disrespectful way; that's not her nature.  But with a scrunched up half- frown and shoulder shrug, and a nearly imperceptible shake of the head, she'll say, quietly, almost apologetically, "No, not really."
     I watch her walk into class every day.  She's tall for a fifth grader, but when she folds herself in at her desk in the back of the room she shrinks down to about half her size, like she's trying to disappear.
     Emily's very quiet.  She never interrupts.  She won't raise her hand.  If you call on her she'll respond, but in a whisper you can hardly hear.  She doesn't cause any trouble.  She follows directions.  Her journal is always turned to the right page.  She always has a pencil and an eraser.  She turns her homework in on time.   If you didn't know any better, if you were just a casual observer, you'd think she knows what she's doing because she looks like she knows what she's doing.  She's one of those under the radar kids.
     I watch her at her desk, elbows flat, head down, pencil up and moving.  She appears to be working away.  What's she doing?  She's managed to get by, doing just well enough to keep one step ahead of the basic skills program.  But if you sit down next to her and really, but I mean really try to get at what it is she actually knows, if you look at her work and try to ask her some questions about it, you'll find that her understanding is very superficial.  She's doing her best to remember and follow some rules she's been told.  She's memorized some things, but they're all fragmented.  They don't cohere.  She studies for the tests, and does her best to hold the pieces together, but when the tests are over the pieces fall back apart.  She doesn't really understand. And despite her best attempts to hide,  I know that she knows she doesn't really understand.  I think it bothers her, which is why she says she doesn't really like math anyway.
     I have to be careful.  I can't poke around too much or she'll shrink down even further, away to a place I might not be able to reach.  It doesn't take much for me to imagine what math experiences she's had to make her feel this way.  I know it's not too late to undo them.
     Justin Lanier, in his brilliant, moving Ignite talk The Space Around the Bar, says the following:

"Students Will Be Able To (And Will Never Want To Again.)  This is how we can write our lesson objectives if we don't pay attention to how kids feel about math." 

Rich and I agree.   Rich and I are trying to create a classroom where it's OK to be wrong; where you can ask and answer questions that you yourself have generated and that serve an intellectual need; where you can solve problems in ways that make sense to you, even if it's not the way they want you to do it in the teacher's manual; where tasks have low barriers to entry and high ceilings and open middles and three acts; where you can move around the room and work them out on big whiteboards; where you can collaborate with your classmates, play games, talk, argue, and laugh. We're trying to create that kind of a classroom.  We don't always succeed, but we're trying.
     Emily's my measuring stick, my benchmark, my litmus test.  Whenever Rich and I  re-work a lesson, or I get an idea for a task or an activity, I ask myself: What will Emily think?  How's she going to react?  I want her approval.  If I can get her approval I know I'm onto something.  The skills and the content are the easy part.  If we can create the conditions in class where she feels it's OK to just be herself, to feel safe and secure enough stand up and stretch out to her full height, I know true learning will occur.
     When class is ending,  I'll find her and ask, "Well, what did you think?"  She doesn't give much away.  It doesn't always go as well as we thought it would.  But sometimes I get a guarded, "Well, that was OK."  I'll do a little fist pump, and she'll maybe even smile.  Baby steps.  Lesson objective: met.


  1. Many responses, with only loose connections between them.
    (1) I wonder what is really going on with the kids in the middle, the "kind of understand" or sometimes get it kids. It is much easier for me to understand the ones who get it (at least a certain level of mastery) and the ones that don't understand at all. Perhaps this is because that's how I feel about my own understanding in math: there are quantum levels of understanding.

    (2) I often say things like "it doesn't matter so much to me whether they learn the particular math concepts, I want their math experience to be a sandbox for broader learning." In particular: power of reasoning over power of authority, sense of what it means to really understand something (see (1)), freedom to explore, habits of notice and wonder, productive collaboration.

    However, I wonder if I consistently practice this? I'm sure teachers facing standardized assessments feel constantly pushed in one direction. Even without that, though, the temptation is still very strong to get through material.

    (3) It always breaks my heart to hear about people like Emily who dislike and fear math, who are made to feel intellectually weak and small by their experience of it. Particularly because I love it so much and it has been such a big part of my life.

    (4) I'm concerned about how difficult it appears to be to change Emily's attitude and bring her out of her shell. Your teaching practice sounds awesome, your mindsets and attitudes are wonderful. Isn't that enough?

    1. Thanks Joshua for your comments. I'm right with you on point #2. It often feels to me like the sandbox classroom model and the one where we plow through material, ready or not, in order to get ready for tests, standardized and otherwise, are in a state of near constant tension. There are times when I feel the pressure and backslide, and get frustrated with students who don't seem to be getting it, and I know they can hear it in my voice. Then I feel really bad about how I've reacted. It's hard not to let it get to you, especially for teachers whose evaluations hinge on standardized test scores.
      As for changing Emily's attitude, it takes time. I know this from my own experience as a learner with severe math anxiety. This goes to your point #3. It took a while for her to get this way and it will take time for the damage to be undone. And who knows what her math teacher will be like next year, or in the years after that. It's sadly ironic because it's math teachers who cause students to feel that way! Talk about subverting your own subject!

  2. Sometimes I don't want a post to end and this is one of those posts. I think we all have or know an "Emily" in our math world. Thanks for refocusing our lesson objectives.
    Beautiful bud. Well done!

  3. Thank you Joe for calling our attention to refocus on the Emily's of the world.

    1. Thank you Josh for taking the time to read and respond!

  4. These are the type that are afraid to ask why in a group and may write down answers but not the work to be able to analyze it or verbalize the process. These types I like to check in with purposefully.

    But yeah I like how you wonder how your somewhat disengaged student can grapple with a task that hooks his or her interest and has like you said a low floor and high ceiling.

    1. I'm glad you mentioned the group work, because these kids can hide in a group pretty easily. They can get overwhelmed by the more outspoken and vocal students, and are happy to hang back. We want kids to work together and collaborate, but this is something we really need to be aware of. I like your idea of purposeful check-ins.