NB. I was honored to write the foreword to Peg Smith and Miriam Sherin’s fantastic new book The Five Practices in Practice, reprinted here with permission. Smith & Stein’s original book, 5 Practices for Orchestrating Productive Mathematics Discussion, was transformative for me professionally, but also personally, as I narrate in kind of oblique second-person fashion below. (Suffice to say: I am very much one of the two teacher types I describe.) Smith and Sherin’s follow-up book contextualizes those five practices in some extremely useful ways.
Why did you become a math teacher?
Perhaps you loved math. Perhaps you were good at math, good, at least at the thing you called math then. Friends and family would come to you for help with their homework or studying and you prided yourself not just on explaining the how of math’s operations but also the why and the when, helping others see the purpose and application behind the math.
Helping other people understand and love the math you understood and loved — perhaps that sounded like a good way to spend a few decades.
Or perhaps you loved kids. Perhaps even at a young age you were an effective caregiver, and you knew how to care for more than just another person’s tangible needs. You listened, and you made people feel listened to. You had an eye for a person’s value and power. You understood where people were in their lives and you understood how the right kind of question or observation could propel them to where they were going to be.
Spending a few decades helping people feel heard, helping them unleash and use their tremendous capacity — perhaps you thought that was a worthwhile way to spend what you thought would be the hours between 7AM and 4PM every day.
Or perhaps you loved both math and kids. It’s possible of course that neither of the two previous exemplar teachers will speak fully to the path that brought you to math teaching, although one of them speaks fully to mine. Yet, in my work with math teachers, I find they often draw their professional energy from one source or the other, from math’s ideas or its people.
It took me several frustrated years of math teaching — and years of work with other teachers – to realize that each of those energy sources is vital. Neither source is renewable without the other.
If you draw your energy only from mathematics, your students can become abstractions, and interchangeable. You can convince yourself it’s possible to influence what they know without care for who they are, that it’s possible to treat their knowledge as deficient and in need of fixing without risking negative consequences for their identity. But students know better. Most of them know what it feels like when the adult in the room positions herself as all-knowing and the students in the room as all-unknowing. A teacher’s love and understanding of mathematics won’t help when students have decided their teacher cares less about them than about numbers and variables, bar models and graphs, precise definitions and deductive arguments.
If you draw your energy only from students, then the day’s mathematics can become interchangeable with any other day’s. Some days it may feel like an act of care to skip students past mathematics they find frustrating, or to skip mathematics altogether some days. But the math you skip one day is foundational for the math another day or another year. Students will have to pay down their frustration later, only then with compound interest. Your love and care for students cannot protect them from the frustration that is often fundamental to learning.
I could tell you that the only solution to this problem of practice is to develop a love of students and a love of mathematics. I could relate any number of maxims and slogans that testify to that truth. I could perhaps convince some of you to believe me.
But the maxim I hold most closely right now is that we act ourselves into belief more often than we believe our way into action. So I encourage you more than anything right now to adopt a series of productive actions that can reshape your beliefs.
Here are five such actions: anticipate, monitor, select, sequence, and connect.
Those actions, initially proposed by Smith and Stein in 2011 and ably illustrated here with classroom videos, teacher testimony, and student work samples, can convert a teacher’s love for math into a love for students and vice versa, to act her way into a belief that math and students both matter.
For teachers who are motivated by a love of students, those five practices invite the teacher to learn more mathematics. The more math teachers know, the easier it is for them to find value in the ways their students think. Their mathematical knowledge enables them to monitor that thinking less for correctness and more for interest. Would presenting this student’s thinking provoke an interesting conversation with the class, whether the circled answer is correct or not? A teacher’s mathematical knowledge enables her to connect one student’s interesting idea to another’s. Her math knowledge helps her connect student thinking together and illustrate for the students the enormous value in their ideas.
For the teachers like me who are motivated by a love of mathematics, teachers who want students to love mathematics as well, those five practices give them a rationale for understanding their students as people. Students are not a blank screen onto which teachers can project and trace out their own knowledge. Meaning is made by the student. It isn’t transferred by the teacher. The more teachers love and want to protect interesting mathematical ideas, the more they should want to know the meaning students are making of those ideas. Those five practices have helped me connect student ideas to canonical mathematical ideas, helping students see the value of both.
Neither a love of students nor a love of mathematics can sustain the work of math education on its own. We work with “math students,” a composite of their mathematical ideas and their identities as people. The five practices for orchestrating productive mathematical discussions, and these ideas for putting those practices into practice, offer the actions that can develop and sustain the belief that both math and students matter.
You might think your path into teaching emanated from a love of mathematics, or from a love of students. But it’s the same path. It’s a wider path than you might have thought, one that offers passage to more people and more ideas than you originally thought possible. This book will help you and your students learn to walk it.
Kris LindebladMay 1, 2019 - 5:02 am -
You are singing my song, but your version is Andrea Bocelli while mine is more ,we’ll I won’t insult anyone. I will use this blog, with your permission, with my mentees. I love the connection to 5 Practices.
Dan MeyerMay 1, 2019 - 10:20 am -
Great! Happy it’ll be useful for you.
KariseMay 1, 2019 - 7:18 am -
Thank you for this post! It is the end of the semester and my students and I are tired. This post is the “cup of coffee” I needed to give me the energy to serve and honor my students and the mathematics they are learning until the end of the semester.
Dan MeyerMay 1, 2019 - 10:21 am -
Happy to offer some professional caffeine. Your work matters so much to students.
dennis deetsMay 2, 2019 - 6:08 am -
i think i have shared this at some time, but i might as well do it again. the paper is hard to get through in places, but …
and of course Shulman never gets old
anyway, thank you always for your hard work and oddly for being the voice or reason in math education :)
KarlMay 3, 2019 - 10:13 am -
Dan, long-time reader, first-time commenter :-) . There is a lot I could write here, but I will keep it brief. I feel the need to say what an inspiration this blog has been for me. I started reading this blog in 2008 as a college dropout working a shipping & receiving job. I felt strange reading a math education blog with no intention of teaching mathematics, but I found the conversation engaging. I wanted to change the way I viewed the world.
I went back to college and started pursuing a degree in mathematics. At the time, I didn’t tell anyone that I was doing so, because I was embarrassed to start my journey by taking remedial classes. After two semesters at a community college, I had yet to earn a college-level credit. Your blog felt aspirational; it was like seeing a window of where I would be in the future. It made me read my textbooks for meaning rather than answers. Several years later, I’m working as a data analyst with an Applied Mathematics degree under my belt. I have always stayed on the sidelines of the comments section but I want you to know that this has been a truly life-changing place for me.
Dan MeyerMay 3, 2019 - 10:27 am -
That’s the nicest thing anyone’s ever said about all the yammering that goes on at this website. Thanks for that, Karl, and congrats on your career. You’re making all your teachers — online and offline — proud.
JasonPMay 3, 2019 - 4:50 pm -
Many thanks for your writing, Dan. As an English teacher, I find it inspiring, and cross-disciplinary applicable.
Sarah PanucciMay 10, 2019 - 6:41 pm -
I’m just starting to get into blogging and following blogs and I have to say that personally I really connected with everything you said. I love mathematics and how it all fits together, but I also really enjoy my high school students. They are all hilarious in their own ways, different, challenging, and exciting and the puzzle I try to figure out every day is how to try to make math accessible to them all. Thank you for your continued enthusiasm and strategies to try to make figuring out the puzzle seem possible. :)
Tiffany WardMay 16, 2019 - 12:31 pm -
This one’s a real rollercoaster ride!
Mike GMay 17, 2019 - 10:38 am -
Great blog. I love Tiffany’s comment above.
2 small thoughts:
1. Praise phone calls to parents is a particularly powerful (and accidentally alliterative) way to show students you care about them as individuals. A bank shot of sorts.
The technique is also well suited for teachers who are less comfortable with the logistics of “listening” to students during normal school hours, b/c of the trade-offs.
2. Middle and high school teachers often think of a college professor who had such pure love of subject, and that love inspired all the students. That’s the mental model of what you describe.
A key difference is college students chose to take the class, and middle and high school kids are assigned. This lack of agency increases the need for relationship building.
Christa AmezcuaMay 21, 2019 - 10:53 am -
I’m a teacher completely because the first reason.
It’s not that I don’t love kids, but my “interpersonal intelligence” is the least developed. It’s hard for me to show that love. No one would come to me for advice, I would probably make a joke and that one would cry… Unless the advice is about how to tackle a math problem! That’s what I do best.
So, actually, teaching and math is the only way in which I can connect to people.
Dan MeyerMay 21, 2019 - 11:28 am -
Teaching needs all sorts! I’m glad you’re in it. I’m also glad that love and empathy aren’t qualities endowed in us at birth at fixed, unchanging levels. They’re qualities we can and should develop, just like math knowledge for folks who don’t know math!
M SheffnerJune 22, 2019 - 9:53 pm -
What Tiffany said. I don’t teach maths, or middle school. I don’t even teach English-speakers, so difficulties are compounded when it comes to getting them to talk about what THEY are seeing and thinking and feeling about those “180 unappetizing” (but oh-so-pedagically-sound) morsels I’m serving up endlessly.
Benjamin LiuFebruary 13, 2020 - 8:23 pm -
Dear Dan, thanks for your excellent sharing ! I’m a Chinese math teacher right now , and I’ve learned so much from your sharing. Would you mind my translating some of your articles into Chinese and posting them on my WeChat public account and my blog ? Just for sharing your brand-new and advanced teaching thoughts. Of course , there will be the original links below the translations.
Again , thanks for your sharing !
Dan MeyerFebruary 13, 2020 - 9:26 pm -
I’d be honored.
Benjamin LiuFebruary 14, 2020 - 5:46 am -
Thanks you for allowing me to translate some of your blog contentsï¼ï¼ï¼