#CMCMath Opening Keynote Address – Practice Problems

This is the keynote address I gave at CMC North this weekend with my co-presenters Shira Helft, Juana de Anda, and Fawn Nguyen.

The premise:

For a long time I worried I had chosen the wrong career. Other careers seemed like they had so much in their favor — better pay, less homework, more flexibility on the timing of bathroom breaks, etc. If you followed this blog ten years ago, you witnessed that worry.

Then a conversation with some of my close friends convinced me why I — and we — never have to envy any other career:

We have the best questions.

At least for me, no other job has more interesting questions than the job of helping students learn and love to learn mathematics.

A career in teaching means freedom from boredom.

To illustrate that, I interviewed three teachers at different stages in their careers — a teacher in her first decade, her second decade, and her third decade of teaching. I asked them, “What questions are you wondering right now?” Then we each took ten minutes to share our four questions.

But our talks weren’t disconnected. An important thread connected each of them, and I elaborated on that connection at the end of the talk.


Please pitch in. Tell us all in the comments:

What question motivates you this year? What question wakes you up in the morning and energizes you throughout your day?

Featured Comments


The question that drives me is “How can I present this in a fashion that will be so interesting that they will not only want to learn it, but they will remember it next week, next month, and next year?”

Andrew Stadel:

Whether with my family (most important), the teachers I support, or students I work with:
How am I being present?

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. The question that drives me is “How can I present this in a fashion that will be so interesting that they will not only want to learn it, but they will remember it next week, next month, and next year?”

  2. Great work, everyone. Thanks for posting this, Dan.

    Whether with my family (most important), the teachers I support, or students I work with:
    How am I being present?

    • Wow our wives talk to us about the same thing clearly! It’s true. I know I can’t multitask that well. We have to make time to unplug and be present with our family friendships and relationships. I see you’ve done so when you take Twitter breaks. Good for you.

  3. Last year, it was “how can I teach Mathematics to a room of students without a common written or spoken language”.

    This year, it’s “how can we better serve students whose life experiences take them off a traditional 4 year plan and stop them from falling through the cracks”

  4. Thought provoking. Thanks for sharing, Shira, Juana, Fawn and Dan.

    My question over the 18 months was shaped by Tracy Zager’s 2015 NCTM ShadowCon ‘word clouds’.

    ‘How do we orient our students towards the creative, active and collaborative ways in which professional mathematicians like myself work? How do we help them experience mathematics as a curiosity-driven, joyful, beautiful endeavour?’

  5. The last two years it’s been these:

    In the traditional (?) classroom, explanation serves computation. What would a classroom look like if you reversed the dynamic and had computation serve explanation?

    How much of the explanatory work in Algebra II and Pre-Calculus level math can 10th and 11th graders handle?

  6. What drives me as an educator is the same reason that I loved math as a student…it feels like a puzzle to be solved.

    I wonder how to bring the passion for math that I had as a student …to other students–especially the ones that seem the most disengaged. I wonder how to bring the passion for talking about teaching math to teachers that don’t know there is a whole world out there in constant communication and collaboration.

    All of these things keep me interested and knowing that I chose the right career.

  7. My main questions for the past few years have been:
    1) How to make more authentic connections between the Math that is supposed to be taught and the questions about which students are themselves interested in learning; how to develop their mathematical curiosity and demand for rigor and justification and make formal mathematics a tool they want to use and one they feel ownership of?
    2) How do you foster students’ curiousity and authentic engagement with real mathematics, while also providing sufficient practice and “coverage” that will allow them to retain material and do well on external measures of knowledge that will be almost entirely content-based? How do I marry the world of my classroom, where I make a great deal of the rules, with the world out there, which for the most part, still really only cares about computation and procedures?

    • I agree so much with your second point! I want to teach for deep understanding, but I know that one way I’m judged is by my standardized test scores, which are not as high as other teachers who teach kids to memorize procedures.

  8. At the start of my 10th year, my question would’ve been about student engagement and how to get them excited about math. Now, after our first trimester, I have realized that is the wrong question. Engagement is there. Excitement has always been there. It is in 3 ACTs, Delete the Text, WODB, Number Talks and Math Talks. I have seen it in all grades K-6. I have heard Kinders argue their point and convince a peer. I have seen 5th graders jump out of their seat to high five a neighbor after I have reveled a hidden piece of text. I have had a second grader point out my error and rationally explain how they found that error. So, my questions has evolved. It is now, how do I create the best buy in for my peers? How do I ensure their safety with all the insecurities of trying something new? How do I spread this “disease” of excitement in Math to the teachers? And lastly, how do I contain my own excitement, knowing change takes time?

    • I love your reply! I’m only in my second year of using WODB, 3-Acts, etc. I am looking forward to the day when I have skills in this set of techniques to start proselytizing. =)

  9. I worked in a tough school in a tough neighborhood for the first couple years of my teaching career. My question during that period was ‘how can I finish my math class with no or less discipline issue and reach out the max number of students?’
    The questions for the last few years have been:
    How can I bring all students to my side to run the same marathon to the same direction around the same target because some students run to the direction of east and I run to the west!

  10. These questions are awesome and offer me exactly the lens into the evolving work of teaching I wanted.

  11. 1) How do you help kids become confident and near-automatic in their skills without ruining math?

    2) Can a classroom teacher make important contributions to our knowledge about teaching math? Or is that mostly the territory of researchers, consultants, PD people, teacher educators and everyone else?

    That second one might seem to have an obvious answer, but the longer I think work on it, the more slippery it gets.

  12. This opening keynote is fantastic on so many levels.

    While I would love to share a question that drives me this year (and probably most of my career / life), I definitely need some time to “problematize” my question for others. You gave me something to blog about, Mr. Meyer, and I encourage others in #MTBoS to do the same. Like you said, we need to get awesome at this.

  13. Great post. Look forward to watching the clip.

    My question is as an 8th grade teacher how can I teach the standards and the prior years without boring the kids who get it and approaching it differently than their last teacher?

    How can I empower my students as sources of knowledge for their peers?

  14. I love this idea of driving questions and I enjoy reading all the questions people have posted so far. Here are some of mine.

    Working with students: How can I engage a student that gets easily frustrated in such a way that they invest in the hard work of sense-making without giving up?

    Working with teachers: What experiences do teachers who resist changing their practice need in order to be open to learning for themselves?

  15. Your Keynote video and your question “How do we help people believe fewer lies?” has my brain churning and burning this morning and rethinking the significance of some old lessons and past experiences in teaching. I’m going to follow Dan Luevano’s advice and turn this into a longer blog post soon. But I feel inspired to think out loud and share some reactions in the hopes that other readers/watchers have been similarly inspired.

    I used to teach high school juniors and seniors. I’ve always grappled with the dilemma about the “right” balance between teaching the “academic math they needed to know for college math and placement exams” and the “numeracy and statistical fluency they need to know to be an empowered and numerically literate citizen”. My most urgent questions: How do I get students to make sense of statistics in the media? How do I foster in them the ability to critically question statistics? If the statistic was in an interrogation room, what questions would we use to shake it down as detectives?

    Carving out time for this meant less time for finding vertical asymptotes of trigonometric functions and other crap. It also meant taking time to bring in middle school math concepts and encouraging high school students to revisit those ideas (proportionality, percentages, ratios, graphing reading, mean/median/mode, etc) and think more deeply about them. For example: A 7th grader can understand what an unemployment rate of 5% means in some numerical sense. But a 12th grader can ask questions with a much different mind. What do we mean by employed? Who do we count in the labor force? How would a politician massage the unemployment statistic to craft the story s/he want to say? A 7th grader can reason proportionally about fairness and sharing, but a 12th grader can think more deeply about wealth inequality, tax structures, and social justice.

    So eventually my questions evolved into: How do I carve out time to revisit middle school math concepts with high school students now that they have different and more complex brains? Is this the best thing for their “math future”? Am I doing them academic harm? Do I have an ethical obligation to politicize my math classroom? Or to de-politicize is? There’s more I want to unpack in a reflective post, but your question has inspired me to rethink some old questions and bring them forward in to my current work now.

    I work a lot with elementary teachers at the moment conducting lesson inquiries. Now I’m wondering: How do we structure lessons and learning experiences for younger students so that they can become capable statistical skeptics by the time they are high school graduates? What are the question frames, textbook and lesson makeovers, tasks/investigations, and instructional strategies for elementary teachers to consider? What might their professional needs be as instructors of young people and how can I help meet those needs as a coach and collaborator?

    Sorry for the longwinded comment, but I’m hoping some other teachers and leaders might have been similarly inspired by your question and have something to say. I’m really looking forward not just to the conversations and collaboration your talk will spark, but also the thinking your specific question will create. It’s a gem. Thank you!

  16. What experiences can I provide students (or teachers) that will change their beliefs about their mathematical identity, learning and what it means to learn mathematics?

  17. My question is about students’ feelings “How do I maintain a sense of forward momentum/making progress for all of my students?” I teach heterogenous classes, and I want all of my kids to both have hope and feel accomplishment. I’ve been trying to figure out pacing this year, and naming for kids (or having them name for themselves) what they’re completing, even if we never completely finish a lesson.

    My other question is “How do I have a life and still feel good about the work that I do?” Because I’m in this teaching thing for the long haul, but feel so far from sustainability.

    • Johanna,
      Your second question has been plaguing me for years. I even taught part-time for a few years, but then I didn’t feel good about my work because I felt like people didn’t take me seriously or thought I wasn’t committed to the work.

      When I had my goals meeting yesterday, my principal added “Self-care” as my second goal, because it’s something I continue to struggle with. Maybe we can support each other. Are you on twitter? @kdhowe1

  18. How can I make changing my perspective my default position? How do I balance planning “for” with listening “to”? How is it – all of it – connected? How can I make “the unknown” an exhilarating place to be – for teachers and students? How can I listen so carefully that I truly understand another person’s thinking? How can I think so reflectively about my own thinking and share it so intentionally that other people truly understand me?

  19. Sorry if this is late:

    In my daily practice, the question that drives me is the same one as always: How can I arrange the curriculum, explain a concept, create learning activities that help my students at all ability levels better understand and engage and retain knowledge?

    At the school level, the question that drives me is a new one, one I just shrugged off in prior years: How do I engage with my colleagues to convince them that my refusal to prioritize “coverage” is valid and backed up by data? (Namely, despite covering perhaps 60% of what they do, my test scores are equivalent.) I’ve had some success, but it’s wearing.

    At the societal level, the question that drives me is again an old one: How do I convince the world that we could get much better results if we understood that most kids need more time to absorb three years of math? There’s *so much* interesting math we can do without pushing everyone past algebra 2.

    Fawn Nguyen’s presentation was very funny.

    • If we’re teaching today to develop math practices, why do our assessments still focus on skills? Standards are NOT curriculum; they are not checklists. Standards are meant to guide teachers as we assemble/create learning experiences that lead students to generalize mathematical concepts.

  20. Thanks for posting! Shira’s question resonated with me – and I wonder if this my question might be how do I get my students to appreciate questioning and also for them to be okay with knowing how to choose their questions when they too have so many to choose from.

  21. Where can I find more information about the GEMA table referenced in this presentation? It looks awesome! Thank you!

  22. The question that keeps me up at night? How do I help each individual student fall in love with their inner mathematician? How can I help them believe in themselves, and challenge themselves to push beyond their perceived barriers? How do I make the math classroom challenging for all – at the same time, without pushing to the point of shutdown.

  23. Minnie Sudarsanam

    February 20, 2017 - 8:03 pm -

    Thank you for all your comments. I appreciate all the insights into what teachers go through and what teachers think about. I will recap what I have read and add to it what I have thought about myself. I liked the conference especially because it creates an avenue of teachers meeting teachers and learning from each other as I do feel isolated from other teachers being in a classroom. I am a student teacher and have finally transitioned to teaching after doing a whole lot of observing. So the questions that go through my mind are, can I finish this credential program with all its requirements ,and how do I teach in a more interesting manner and keep my students engaged, and how do I motivate the students to try their best. We are taught during our classes that we cannot be just giving direct instruction and that we have to ask probing questions. I agree that asking the students the right questions will make them think beyond rules and rote memory to understanding concepts. However I have not been successful as yet to ask these probing questions. My students will not always answer even my “what should be done next” type of questions and I have to cold-call them to get a response. I think that the students need to trust me more so that I can ask these questions and have them answer me, and I can then lead them into deeper mathematics. I am looking forward to building that connection.
    And after that happens the question is how do we guide students to ask the right questions because only when the students questions are the right questions, can a teacher’s answer lead to more understanding. A right question from the student shows that the student is now in the correct place to receive information.
    A couple of other things. One is where does my experience working in industry come in to help students. I have put any thinking about my previous career aside because teaching is a totally different career than being an engineer but my question is do my experiences have a place in the classroom at some point in time. If so, what time is that and how do those experiences get shared. The other thing is that when I attended the African American Regional Education Alliances (AAREA) seminar, they talked about how there is a need to teach African American children.


    However in order to be successful in teaching these children, we are not to have an attitude that we are going to bring them up to the level of all students by say providing them with technology but instead we are to see their strengths and only then we will be able to reach them and teach them.

    They advised reaching out to the people in their neighborhood who know the children so that we can understand the strengths of these children. My question would then be how can this be done.

    • Hi Minnie, thanks for the note. I think this is a really excellent articulation of our task:

      However in order to be successful in teaching these children, we are not to have an attitude that we are going to bring them up to the level of all students by say providing them with technology but instead we are to see their strengths and only then we will be able to reach them and teach them.

      I’m no expert here. I’m currently participating in the Call for Collective Action through TODOS, hoping to learn more.