Great article. We definitely need both. I wonder if we might extend this thought to ‘we need to love math, students and TEACHING?’ Feel like I have seen those that love math & students but it often isn’t powerful enough without a good understanding of pedagogy? Of course it is easier to acquire this swiftly if you love the math and the kids :)
"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. " -DMeyer.
Such a powerful point -- great teachers need to cultivate a love of the subject and love of math. And what I particularly appreciate about this point is the sense of time. We start something -- a project or even our life's work -- for one reason. And over time, it grows and morphs and other reasons come into play. Recognizing that we're all on trajectories would help us swat away alot of those "gotcha!" arguments that seem to happen so frequently.
But I digress: I also wanted to underscore the point that I quoted from Dan's intro: Meaning is made by the learners. We're not just dumping information into their brains. I'd love to hear thoughts from others about how AI tutors support that insight. I think many of us worry that much of the "tutoring" that is going on treats students' minds like one of those old "paint by numbers" exercises.
Or perhaps we should be okay with that? Because bridging the love for the student and love for the subject may be the exquisitely most human part of teaching?
> Or perhaps we should be okay with that? Because bridging the love for the student and love for the subject may be the exquisitely most human part of teaching?
I think this tweet & the responses offer about the most perfect rendering of the work teachers do that computers cannot. (And won't ever I don't think.) The teacher starts the year with social capital invested in them by the state licensing board, the school that hired them, etc, and then develops more throughout the year, throughout their interactions with students. And then the teacher gives that capital away lavishly on students who perhaps have very little of it.
What do you think of “love of learning” as a motivation? I’m not a teacher but seriously considered it. Me, I love that “aha” moment when something clicks and want to help others feel it too. Is that a sustainable energy source for teaching? (I still debate if adjunct professor is something I should try as a “retirement career.”)
Hi Brian, I'm unlikely to discourage anyone from taking up teaching. Love of learning ... what? ... is my question, though. There is a love of learning the discipline, of an understanding about math for example. And then there is the love of learning about yourself, learning that some of the ways you THOUGHT you were limited as a learner were in fact illusory. I think great teachers are motivated by the "love of learning," yes, but in this very expansive way.
I wonder if it’s helpful to have a definition of teaching, or the definition of a teacher. It might be that because of the fuzziness of this situation, that we are forever backing our heads against the different versions, and what passes for teaching. One problem I have thought present is that pedagogy is not regarded As a separate endeavor to pursue, whether artfully or scientifically. It is this lack of regard that I believe renders teaching the second class citizen the world over, second to the subject matter.
Really thought provoking. Writing and literature are my things rather than math, and I certainly started with a love (or rather fascination) with reading and writing, but once I started teaching I became hugely interested in the "problem" of teaching, how to best help students learn the skills, attitudes, knowledge and habits of of mind that help them engage in what I call a "shared inquiry into the subject at hand," or in other words, the course. Teaching then became a continuous experiment with real-life stakes where students could be collaborators in the experiment. That experiment is ultimately what I'm most fascinated by, but the fascination with the underlying subjects seems to be necessary fuel as well.
Right. We all start somewhere, on some default heading, and then the heading changes. Certainly we've both seen people whose love of their discipline intensifies, rather than broadens, through teaching, with negative consequences for the students who lack the kind of dedication and reverence the teacher increasingly expects. I like your description of students as collaborators as a contrast.
That collaboration came after years of thinking my job was to tell them how to do stuff in a very prescriptive way and it dawning on me that I wasn't allowing them to have the kinds of struggles that would allow them to learn. As I evolved toward more of a "I think this stuff is fascinating for these reasons, what do you all think" approach, everything started to fall into place. The experiment continues.
Hi Dan! When you get back from Spring Break, can you tell us more about how this book is different from the original. I would have preferred that you were more transparent about the original 5 Practices in your letter to us.
I love this article and it fits perfectly with some teacher reflection I am leading this spring. The second link to the Smith and Stein information took me to the same page for the book you wrote the forward to. I would appreciate getting the correct link and seeing the resources you mentioned if possible.
Thanks for always sending your thoughtful articles that often seems to land in my inbox on the perfect day with a message I need to hear!
Great article. We definitely need both. I wonder if we might extend this thought to ‘we need to love math, students and TEACHING?’ Feel like I have seen those that love math & students but it often isn’t powerful enough without a good understanding of pedagogy? Of course it is easier to acquire this swiftly if you love the math and the kids :)
"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. " -DMeyer.
Such a powerful point -- great teachers need to cultivate a love of the subject and love of math. And what I particularly appreciate about this point is the sense of time. We start something -- a project or even our life's work -- for one reason. And over time, it grows and morphs and other reasons come into play. Recognizing that we're all on trajectories would help us swat away alot of those "gotcha!" arguments that seem to happen so frequently.
But I digress: I also wanted to underscore the point that I quoted from Dan's intro: Meaning is made by the learners. We're not just dumping information into their brains. I'd love to hear thoughts from others about how AI tutors support that insight. I think many of us worry that much of the "tutoring" that is going on treats students' minds like one of those old "paint by numbers" exercises.
Or perhaps we should be okay with that? Because bridging the love for the student and love for the subject may be the exquisitely most human part of teaching?
> Or perhaps we should be okay with that? Because bridging the love for the student and love for the subject may be the exquisitely most human part of teaching?
I think this tweet & the responses offer about the most perfect rendering of the work teachers do that computers cannot. (And won't ever I don't think.) The teacher starts the year with social capital invested in them by the state licensing board, the school that hired them, etc, and then develops more throughout the year, throughout their interactions with students. And then the teacher gives that capital away lavishly on students who perhaps have very little of it.
https://twitter.com/jennalaib/status/1774831021277557087
For those who have eyes to see IMO.
What do you think of “love of learning” as a motivation? I’m not a teacher but seriously considered it. Me, I love that “aha” moment when something clicks and want to help others feel it too. Is that a sustainable energy source for teaching? (I still debate if adjunct professor is something I should try as a “retirement career.”)
Hi Brian, I'm unlikely to discourage anyone from taking up teaching. Love of learning ... what? ... is my question, though. There is a love of learning the discipline, of an understanding about math for example. And then there is the love of learning about yourself, learning that some of the ways you THOUGHT you were limited as a learner were in fact illusory. I think great teachers are motivated by the "love of learning," yes, but in this very expansive way.
I love this book! I did my PhD with it! Thank you for remembering it to me!
I wonder if it’s helpful to have a definition of teaching, or the definition of a teacher. It might be that because of the fuzziness of this situation, that we are forever backing our heads against the different versions, and what passes for teaching. One problem I have thought present is that pedagogy is not regarded As a separate endeavor to pursue, whether artfully or scientifically. It is this lack of regard that I believe renders teaching the second class citizen the world over, second to the subject matter.
Really thought provoking. Writing and literature are my things rather than math, and I certainly started with a love (or rather fascination) with reading and writing, but once I started teaching I became hugely interested in the "problem" of teaching, how to best help students learn the skills, attitudes, knowledge and habits of of mind that help them engage in what I call a "shared inquiry into the subject at hand," or in other words, the course. Teaching then became a continuous experiment with real-life stakes where students could be collaborators in the experiment. That experiment is ultimately what I'm most fascinated by, but the fascination with the underlying subjects seems to be necessary fuel as well.
Right. We all start somewhere, on some default heading, and then the heading changes. Certainly we've both seen people whose love of their discipline intensifies, rather than broadens, through teaching, with negative consequences for the students who lack the kind of dedication and reverence the teacher increasingly expects. I like your description of students as collaborators as a contrast.
That collaboration came after years of thinking my job was to tell them how to do stuff in a very prescriptive way and it dawning on me that I wasn't allowing them to have the kinds of struggles that would allow them to learn. As I evolved toward more of a "I think this stuff is fascinating for these reasons, what do you all think" approach, everything started to fall into place. The experiment continues.
Hi Dan! When you get back from Spring Break, can you tell us more about how this book is different from the original. I would have preferred that you were more transparent about the original 5 Practices in your letter to us.
I love this article and it fits perfectly with some teacher reflection I am leading this spring. The second link to the Smith and Stein information took me to the same page for the book you wrote the forward to. I would appreciate getting the correct link and seeing the resources you mentioned if possible.
Thanks for always sending your thoughtful articles that often seems to land in my inbox on the perfect day with a message I need to hear!
Thanks for the feedback and for checking me on the link, Linda. I have updated it in the post and I'll add it here:
https://www.nctm.org/Store/Products/5-Practices-for-Orchestrating-Productive-Mathematics-Discussions,-2nd-edition-(Download)/
Thanks!