I'm also making connections to the Monad Burrito Fallacy:
"Joe Haskeller is trying to learn about monads. After struggling to understand them for a week, looking at examples, writing code, reading things other people have written, he finally has an “aha!” moment: everything is suddenly clear, and Joe Understands Monads!
"What has really happened, of course, is that Joe’s brain has fit all the details together into a higher-level abstraction, a metaphor which Joe can use to get an intuitive grasp of monads; let us suppose that Joe’s metaphor is that Monads are Like Burritos. Here is where Joe badly misinterprets his own thought process: “Of course!” Joe thinks. “It’s all so simple now. The key to understanding monads is that they are Like Burritos. If only I had thought of this before!”
"The problem, of course, is that if Joe HAD thought of this before, it wouldn’t have helped: the week of struggling through details was a necessary and integral part of forming Joe’s Burrito intuition, not a sad consequence of his failure to hit upon the idea sooner."
Thank you! Firstly I 100% agree with everything you just said. Secondly, you gave shape to something amorphous that I have believed for a long time about the value of education that I couldn’t put into words.
I would also add that ‘socialising’ individuals is a key value of schools, both inside and outside the classroom, as interpersonal skills are crucial for success in life and are built intensively by being with 30 of your peers in a class or 100+ in the courtyard.
Super interesting, and almost exactly what I've spent the past few months thinking about with BEAM. Thank you. :)
Let me share one place where I think I disagree, though. I was intrigued by your saying that you agree with Willingham on there being no way to teach problem solving skills (and other general skills) directly, especially when you cite Schoenfeld later, because I disagree. I also find those problem solving strategies to be silly and impossible to meaningfully teach at that level of generality. At best, you can point some of them out after students have used them in the course of their work.
However, I *do* work to directly teach the metacognitive skills that Schoenfeld talks about. I work to have students reflect on their process, articulate why they expect any particular strategy to be effective, what they are trying to accomplish, etc. When we go over problems at the board, I am always zooming out to that level rather than talking about any specific moves. To me, that is the actual act of teaching problem solving, and I do believe that I make meaningful progress helping my students to become better problem solvers!
PS I'm also not certain how widely accepted Willingham's view on transfer is in the cognitive science community. I have always wrestled with his description of it, because I always saw transfer as the whole point of education: yes, there are few specific facts that students will learn that they need later, but there are many skills that can be foundational throughout their lives. (I also found the fortress/tumor supposed study of transfer to be silly, which he uses as a cornerstone of his argument.) Thus, I was pleased to discover a robust literature that takes a much more nuanced view on transfer. I've been reading this article and it speaks to me much more:
Thanks for reading! I definitely had a specific conversation we had about BEAM in mind while working on this (about open math time).
Re teaching metacognition: There are some things here that I think are real. If you're asking kids to articulate their strategies...there is no doubt that drawing attention to structure and making implicit things explicit is going to help build knowledge. I've had way more success with this sort of teaching move when it's focused on (even high-level) mathematical structure. When it's about the structure of problem solving itself, that's where I see people get lost in teaching.
I also think there's a certain teaching of expectations that is real. I think of it as enculturation. Yeah -- you should try *something.* Then you should expect to get stuck, and you'll have to try something else. At a much smaller level: your algebraic work *should* be neat and tidy so that you can avoid errors.
I'm not totally on board with metacognition as a body of knowledge ABOUT thinking that itself operates and manages thinking. I don't know if there's really such a distinction between metacognition and actual problem solving. And most importantly, I just haven't felt successful doing that sort of thing in the classroom.
Re transfer: Back in the 90s (I think) there was a whole big back and forth with learning scientists about how to conceptualize it. Maybe transfer doesn't even make sense as a concept. Whatever! What I describe in this post is how I see things -- that there is a way to build more abstract knowledge, skills, and habits, but it requires weaving together a lot of specific experiences that can't be skipped.
Interesting! I don't see metacognition as being fundamentally about knowledge, but rather skills and habits. Similarly, in problem solving, you need knowledge about the field in which you're solving the problem, but I don't think knowledge about problem solving itself is all that helpful. That's why I also don't like that poster!
When it comes to teaching metacognition, I'm a fan of how Schoenfeld does it, which also is not about delivering knowledge to students. Here's a description from a 1992 article:
Roughly one third of the time in Schoenfeld’s problem-solving classes is spent with the students working problems in small groups. The class divides into groups of three or four students and works on problems that have been distributed, while the instructor circulates through the room as “roving consultant.” As he moves through the room, he reserves the right to ask the following three questions at any time:
What (exactly) are you doing? (Can you describe it precisely?)
Why are you doing it? (How does it fit into the solution?)
How does it help you? (What will you do with the outcome when
you obtain it?)
He begins asking these questions early in the term. When he does so, the students are generally at a loss regarding how to answer them. With the recognition that, despite their uncomfortableness, he is going to continue asking those questions, the students begin to defend themselves against them by discussing the answers to them in advance. By the end of the term, this behavior has become habitual. (Note, however, that the better part of a semester is necessary to obtain such changes.)
Finally, on the transfer piece, I totally agree that you need to have specifics to build up to more general ideas, and a major failure of teaching is going to the general idea before enough specifics have been developed. What I've seen in the literature about transfer (and my own experiences) is that to best achieve transfer, deep learnings works better than surface-level, and teaching with some abstraction works better than teaching only specific knowledge or methods.
I'm loving this discussion; we have different but complementary points of view!
Audrey Watters sent me here through her recent post. Oh, how this all resonates! As a PE specialist who teaches students across the elementary years and has the opportunity to witness many of those kids graduate from the same institution, your point about the long-term learning that goes on speaks to my decades of experience. None of the emotional regulation, problem-solving capabilities or approaches to learning that students develop are built in a year or through a series of specialized lessons. No, the processes are fuzzy and varied and cumulative, and neoliberal sensibilities have a hard time accepting that. Thanks for this deep breath of an essay on what we know as teachers, what much of the evidence suggests, and what those tasked with creating education policy and purchasing "tools" least wish to hear.
This reminds me of the "Collaborative & Proactive Solutions" approach. You start by identifying lagging skills like "difficulty making transitions." But instead of trying to directly teach kids to get better at making transitions, the method involves getting very specific and working a problem-solving process on one specific issue at a time (e.g. difficulty coming in from recess to go to art class on Wednesday).
Skill-building is not a direct goal of the method, but the founder, Dr. Ross Greene, does claim that kids often do develop general skills as they go through the process of coming up with solutions to specific instances of difficulty.
I will always remember the day a student said to me "you're a really strong person" because, it turns out, I respond calmly no matter what is being thrown at me. The student (who has not always managed situations well) went on to say it takes a lot more strength to be calm than "lose it". Now I'm never going to be so blind as to think this realisation has developed just through knowing me but through a number of different efforts and insights over years. However, those are the moments that can make being a teacher so amazing. That is something they don't teach you and you don't find in text books.
Audrey Watters sent me here through her recent post. Oh, how this all resonates! As a PE specialist who teaches students across the elementary years and has the opportunity to witness many of those kids graduate from the same institution, your point about the long-term learning that goes on speaks to my decades of experience. None of the emotional regulation, problem-solving capabilities or approaches to learning that students develop are built in a year or through a series of specialized lessons. No, the processes are fuzzy and varied and cumulative, and neoliberal sensibilities have a hard time accepting that. Thanks for this deep breath of an essay on what we know as teachers, what much of the evidence suggests, and what those tasked with creating education policy and purchasing "tools" least wish to hear.
I'm also making connections to the Monad Burrito Fallacy:
"Joe Haskeller is trying to learn about monads. After struggling to understand them for a week, looking at examples, writing code, reading things other people have written, he finally has an “aha!” moment: everything is suddenly clear, and Joe Understands Monads!
"What has really happened, of course, is that Joe’s brain has fit all the details together into a higher-level abstraction, a metaphor which Joe can use to get an intuitive grasp of monads; let us suppose that Joe’s metaphor is that Monads are Like Burritos. Here is where Joe badly misinterprets his own thought process: “Of course!” Joe thinks. “It’s all so simple now. The key to understanding monads is that they are Like Burritos. If only I had thought of this before!”
"The problem, of course, is that if Joe HAD thought of this before, it wouldn’t have helped: the week of struggling through details was a necessary and integral part of forming Joe’s Burrito intuition, not a sad consequence of his failure to hit upon the idea sooner."
https://byorgey.wordpress.com/2009/01/12/abstraction-intuition-and-the-monad-tutorial-fallacy/
It was at Twitter Math Camp that a speaker noted that rather than Polya's stuff, "you try something. When it doesn't work, you try something else."
Thank you! Firstly I 100% agree with everything you just said. Secondly, you gave shape to something amorphous that I have believed for a long time about the value of education that I couldn’t put into words.
I would also add that ‘socialising’ individuals is a key value of schools, both inside and outside the classroom, as interpersonal skills are crucial for success in life and are built intensively by being with 30 of your peers in a class or 100+ in the courtyard.
Super interesting, and almost exactly what I've spent the past few months thinking about with BEAM. Thank you. :)
Let me share one place where I think I disagree, though. I was intrigued by your saying that you agree with Willingham on there being no way to teach problem solving skills (and other general skills) directly, especially when you cite Schoenfeld later, because I disagree. I also find those problem solving strategies to be silly and impossible to meaningfully teach at that level of generality. At best, you can point some of them out after students have used them in the course of their work.
However, I *do* work to directly teach the metacognitive skills that Schoenfeld talks about. I work to have students reflect on their process, articulate why they expect any particular strategy to be effective, what they are trying to accomplish, etc. When we go over problems at the board, I am always zooming out to that level rather than talking about any specific moves. To me, that is the actual act of teaching problem solving, and I do believe that I make meaningful progress helping my students to become better problem solvers!
PS I'm also not certain how widely accepted Willingham's view on transfer is in the cognitive science community. I have always wrestled with his description of it, because I always saw transfer as the whole point of education: yes, there are few specific facts that students will learn that they need later, but there are many skills that can be foundational throughout their lives. (I also found the fortress/tumor supposed study of transfer to be silly, which he uses as a cornerstone of his argument.) Thus, I was pleased to discover a robust literature that takes a much more nuanced view on transfer. I've been reading this article and it speaks to me much more:
https://rapunselshair.pbworks.com/f/barnett_2002.pdf
Thanks for reading! I definitely had a specific conversation we had about BEAM in mind while working on this (about open math time).
Re teaching metacognition: There are some things here that I think are real. If you're asking kids to articulate their strategies...there is no doubt that drawing attention to structure and making implicit things explicit is going to help build knowledge. I've had way more success with this sort of teaching move when it's focused on (even high-level) mathematical structure. When it's about the structure of problem solving itself, that's where I see people get lost in teaching.
I also think there's a certain teaching of expectations that is real. I think of it as enculturation. Yeah -- you should try *something.* Then you should expect to get stuck, and you'll have to try something else. At a much smaller level: your algebraic work *should* be neat and tidy so that you can avoid errors.
I'm not totally on board with metacognition as a body of knowledge ABOUT thinking that itself operates and manages thinking. I don't know if there's really such a distinction between metacognition and actual problem solving. And most importantly, I just haven't felt successful doing that sort of thing in the classroom.
Re transfer: Back in the 90s (I think) there was a whole big back and forth with learning scientists about how to conceptualize it. Maybe transfer doesn't even make sense as a concept. Whatever! What I describe in this post is how I see things -- that there is a way to build more abstract knowledge, skills, and habits, but it requires weaving together a lot of specific experiences that can't be skipped.
Interesting! I don't see metacognition as being fundamentally about knowledge, but rather skills and habits. Similarly, in problem solving, you need knowledge about the field in which you're solving the problem, but I don't think knowledge about problem solving itself is all that helpful. That's why I also don't like that poster!
When it comes to teaching metacognition, I'm a fan of how Schoenfeld does it, which also is not about delivering knowledge to students. Here's a description from a 1992 article:
Roughly one third of the time in Schoenfeld’s problem-solving classes is spent with the students working problems in small groups. The class divides into groups of three or four students and works on problems that have been distributed, while the instructor circulates through the room as “roving consultant.” As he moves through the room, he reserves the right to ask the following three questions at any time:
What (exactly) are you doing? (Can you describe it precisely?)
Why are you doing it? (How does it fit into the solution?)
How does it help you? (What will you do with the outcome when
you obtain it?)
He begins asking these questions early in the term. When he does so, the students are generally at a loss regarding how to answer them. With the recognition that, despite their uncomfortableness, he is going to continue asking those questions, the students begin to defend themselves against them by discussing the answers to them in advance. By the end of the term, this behavior has become habitual. (Note, however, that the better part of a semester is necessary to obtain such changes.)
Finally, on the transfer piece, I totally agree that you need to have specifics to build up to more general ideas, and a major failure of teaching is going to the general idea before enough specifics have been developed. What I've seen in the literature about transfer (and my own experiences) is that to best achieve transfer, deep learnings works better than surface-level, and teaching with some abstraction works better than teaching only specific knowledge or methods.
I'm loving this discussion; we have different but complementary points of view!
Audrey Watters sent me here through her recent post. Oh, how this all resonates! As a PE specialist who teaches students across the elementary years and has the opportunity to witness many of those kids graduate from the same institution, your point about the long-term learning that goes on speaks to my decades of experience. None of the emotional regulation, problem-solving capabilities or approaches to learning that students develop are built in a year or through a series of specialized lessons. No, the processes are fuzzy and varied and cumulative, and neoliberal sensibilities have a hard time accepting that. Thanks for this deep breath of an essay on what we know as teachers, what much of the evidence suggests, and what those tasked with creating education policy and purchasing "tools" least wish to hear.
This reminds me of the "Collaborative & Proactive Solutions" approach. You start by identifying lagging skills like "difficulty making transitions." But instead of trying to directly teach kids to get better at making transitions, the method involves getting very specific and working a problem-solving process on one specific issue at a time (e.g. difficulty coming in from recess to go to art class on Wednesday).
Skill-building is not a direct goal of the method, but the founder, Dr. Ross Greene, does claim that kids often do develop general skills as they go through the process of coming up with solutions to specific instances of difficulty.
https://livesinthebalance.org/educators-tour/#step-3
I will always remember the day a student said to me "you're a really strong person" because, it turns out, I respond calmly no matter what is being thrown at me. The student (who has not always managed situations well) went on to say it takes a lot more strength to be calm than "lose it". Now I'm never going to be so blind as to think this realisation has developed just through knowing me but through a number of different efforts and insights over years. However, those are the moments that can make being a teacher so amazing. That is something they don't teach you and you don't find in text books.
Audrey Watters sent me here through her recent post. Oh, how this all resonates! As a PE specialist who teaches students across the elementary years and has the opportunity to witness many of those kids graduate from the same institution, your point about the long-term learning that goes on speaks to my decades of experience. None of the emotional regulation, problem-solving capabilities or approaches to learning that students develop are built in a year or through a series of specialized lessons. No, the processes are fuzzy and varied and cumulative, and neoliberal sensibilities have a hard time accepting that. Thanks for this deep breath of an essay on what we know as teachers, what much of the evidence suggests, and what those tasked with creating education policy and purchasing "tools" least wish to hear.