Theatrics. Yes, that's exactly what a lot of people think teaching is. Thank you for clarifying what to me is an obvious point, but missed by so many on social media who get a kick out of their popularity as entertainers and not educators. Harsh? Maybe, but I've been in this profession for too long to entertain - pun intended - this kind of misguided promotion of what teaching and learning is all about.
Hi Dan… I used to use your videos as inspiration for my own math lessons. Another influence that helped me design more engaging lessons was Daniel Pink’s book “Drive”… have you ever read it? Autonomy, purpose, and pursuit of mastery are his 3 pillars of motivation and I would often have my students pick problems from 3 tiers of rigor, integrating Pink’s principles. Each problem would test the same standard but in a different way. It was awesome how engaged students were when I presented it. I don’t think me acting like Robin Williams would have had the same sustainable effect.
I think this scans well against the overall research on "flipped" instruction versus lectures. There's two findings that are pretty robust across a number of studies--first, that "flipped" styles of instruction (which are fundamentally about 'co-construction' in your sense here) result in more retention of skills and information by the largest proportion of students across a range of prior competencies but that students strongly prefer lectures, to the point that a 'flipped' instructor can be in professional peril if they're not already fully established as a teacher due to negative feedback.
The reason why that preference shows up is pretty apparent: that it is easier to listen to a lecture than to engage in 'active learning', especially in a subject that a student may view as difficult or challenging. That is especially true if a lecturer is a talented performer. And as you note, performance isn't the opposite of learning--all of us have had experiences where we've learned a great deal from watching a superior performance of a theatrical work, a speech, etc., and thus also from classroom lecturers that are rewarding to watch. But the idea that the missing ingredient in math or science pedagogy is engaging or entertaining performativity just misses the mark. It's a sign once again of the way that certain people keep searching for a single magic trick that will make education work, in part because they have a fixed ideological belief that all existing teachers are underpeforming or incompetent.
I'm curious how you're understanding my use of "co-construction" and how the flipped classroom relates. The two are not related, indeed opposed, in my use. No reservations about the rest of your comment FWIW.
I see what you're concerned about. I suppose I'm thinking a bit about what "flipping" and "active learning" have involved in humanities and social science classrooms that I've worked with or discussed with other teachers, where I think what you call co-construction is going on all the time--say, for example, building a possible approach to a paper prompt where the paper prompt itself is invented right there on the spot in the classroom, or where there's a page of text up on a screen and the teacher and students are reading it live together and creating an interpretation that isn't already fixed in some kind of lesson plan. But I know that in many STEM classrooms, flipping involves problem sets that are already made being worked live in the classroom, which would be the opposite of what you mean by co-construction. I think? that you could still go with the idea of "doing the homework in the classroom together", which is one way STEM teachers describe flipping but iterate it towards co-construction in your sense--e.g., taking a problem and working it 'standard' first, then asking students to help iterate the problem in new ways that aren't preset or pre-planned, then move to headless and tailless problems inspired by the first more 'normal' presentation of a problem. Essentially to work up towards open-ended mathematical reasoning where all students at all levels of skill might feel engaged rather than rapidly supplying a series of 'right' answers.
One way to avoid the students' yearning for what they already know is of course is to record your whiteboard presentations and have them on tap (every year refining them until you have your own - but better because based on feedback from your classroom learners- Khan Academy). That was our flipped math classroom. But it works best with "Bruce Lee math" sets (I fear the student who practices one problem 10,000 times, not etc ...) – in other words continuous review/incremental progression problem sets which the kids could start on right away while the teacher worked with individuals on "problem problems" identified by a quiz at the end of each pre-recorded presentation. Then of course we added TAPS for real time coaching – where two or three students watched each others presentations and practice solving problems (to which they already had the answer) until they felt they were fluent and they checked themselves off with a "Pass." https://youtu.be/z9N8b58m_iU?si=IEh5xf4a3nil6Ci1
Three keys to Math success… if I had to choose just three (but we actually had 9 keys... because we're not running an experiment and the kids aren't guinea pigs! But the real way to flip a school, I found, is to share all the learning goals with the kids so you get buy-in --then they push the learning process demanding somebody help them progress along your prepared path
For how to help avoid students yearning for what they already know: is your answer your whole paragraph or specifically recording your whiteboard presentations? How did you get student feedback?
Hi, well keeping in mind that I had many different teachers at my schools--all using slightly different versions of 1. Flipped classroom designed to maximize coaching (crucial here to have continuous review incremental progression practice sets + cumulative tests every 4 or 5 lessons + pass/try again grading on those cumulative tests so that students know they are not earning a Pass (say >80 or 85% on the test) unless they ID their "problem problems" and get help); 2. a computer lab session 1-2X a week for individualized practice with a separate lab coach in K-3, and with an assistant coach in grades 4-8 ; 3. TAPS sessions on 4-5 word problems each quarter, coached by a STEM Teacher and volunteers, not the classroom Math Teacher (TAPS provides great FEEDBACK as you listen to the student think out loud as they solve select word problems)— the answer to the feedback question is the students would take a quiz in Quizlet or something similar on each new lesson the teacher would have the results (FEEDBACK) at the beginning of each class. Students would begin on their cumulative daily smart practice problems sets (what I jokingly call Bruce Lee Math because of the continuous), while the teacher went around and worked individually or in small groups with students on the problems they had trouble with. After that session was over the teacher focused on helping students as they asked for help (FEEDBACK: we used red/green two-sided bookmarks: if a student needed help --which they were determined by going to check their answers every 10 problems – answers simply taped to the whiteboard and three different places with multiple copies , available on a computer, or projected in the corner of the room- they would turn turn the bookmark to red and move onto another problem while they waited for the teacher) etc. etc. too much detail maybe and apologies if you already have all the stuff worked out!
We just did the lesson. Students generated a lot of good questions and we narrowed it down to a) what’s the area of the inside square b) what are the coordinates of the vertices (they immediately wanted to put the square onto a coordinate grid with the bottom left hand corner at the origin), c) find the measures of the acute angles of the surrounding triangles, d) find the equations of the sides of the inside square.
There's an element of this that reflects the industrial model of education. Role of educator is to be expert that fills the heads of the students with knowledge. We now need to move to a competency based system where the role of teacher is to facilitate skill building - thus a transition from lecture to engagement... I will also add that in our current context, student mental health and connectivity is a forefront set of needs, too.
I used to beg my teachers not to be try to put on a show. I said "If you're that good you belong up on stage in Las Vegas" The goals instead should be to find ways to maximize your students' hands-on learning/problem-solving time and maximize your own one-on-one or small group coaching time. With the best tools you can find to help you do that- Desmos, white boards, "Bruce Lee math" problem sets, TAPS, etc.
Thanks Dan. I really love this perspective. Just to add on: I have long thought that there's a difference between educators who are fundamentally fascinated by the SUBJECT versus the STUDENTS. Those most excited by the subject are great researchers (who happen to wind up teaching); those who are interested in the students are wonderful teachers, and can potentially teach anything.
At a session last night with teachers and students at a local high school, we talked about the promise & peril of AI. The promise: the much lauded "always on" tutor can potentially help you learn anything easily. The peril: If you don't have to work or engage with an idea, you may not learn much at all. I love your "topless" and "bottomless" problems -- they're intriguing ways to get people to think about the problem. (And bring their "assets" and curiousity into play). I wonder whether AI has the potential to make "learning" easier much like, say, cars made traveling longer distances easier. One unintended consequence of cars, of course, is that you don't have to "work" (ie: walk/run) to get somewhere. Ergo many of us get to be couch potatoes.
I wonder whether AI has the potential to make us "intellectual couch potatoes"?
"I have long thought that there's a difference between educators who are fundamentally fascinated by the SUBJECT versus the STUDENTS. Those most excited by the subject are great researchers (who happen to wind up teaching); those who are interested in the students are wonderful teachers, and can potentially teach anything."
Love this. For some teachers, it's the love of students that drives a love of subject. "Okay these kids are bringing goods that I don't have the content knowledge to understand or appreciate. I need to learn this math a little more deeply."
Theatrics. Yes, that's exactly what a lot of people think teaching is. Thank you for clarifying what to me is an obvious point, but missed by so many on social media who get a kick out of their popularity as entertainers and not educators. Harsh? Maybe, but I've been in this profession for too long to entertain - pun intended - this kind of misguided promotion of what teaching and learning is all about.
Hi Dan… I used to use your videos as inspiration for my own math lessons. Another influence that helped me design more engaging lessons was Daniel Pink’s book “Drive”… have you ever read it? Autonomy, purpose, and pursuit of mastery are his 3 pillars of motivation and I would often have my students pick problems from 3 tiers of rigor, integrating Pink’s principles. Each problem would test the same standard but in a different way. It was awesome how engaged students were when I presented it. I don’t think me acting like Robin Williams would have had the same sustainable effect.
I think this scans well against the overall research on "flipped" instruction versus lectures. There's two findings that are pretty robust across a number of studies--first, that "flipped" styles of instruction (which are fundamentally about 'co-construction' in your sense here) result in more retention of skills and information by the largest proportion of students across a range of prior competencies but that students strongly prefer lectures, to the point that a 'flipped' instructor can be in professional peril if they're not already fully established as a teacher due to negative feedback.
The reason why that preference shows up is pretty apparent: that it is easier to listen to a lecture than to engage in 'active learning', especially in a subject that a student may view as difficult or challenging. That is especially true if a lecturer is a talented performer. And as you note, performance isn't the opposite of learning--all of us have had experiences where we've learned a great deal from watching a superior performance of a theatrical work, a speech, etc., and thus also from classroom lecturers that are rewarding to watch. But the idea that the missing ingredient in math or science pedagogy is engaging or entertaining performativity just misses the mark. It's a sign once again of the way that certain people keep searching for a single magic trick that will make education work, in part because they have a fixed ideological belief that all existing teachers are underpeforming or incompetent.
I'm curious how you're understanding my use of "co-construction" and how the flipped classroom relates. The two are not related, indeed opposed, in my use. No reservations about the rest of your comment FWIW.
I see what you're concerned about. I suppose I'm thinking a bit about what "flipping" and "active learning" have involved in humanities and social science classrooms that I've worked with or discussed with other teachers, where I think what you call co-construction is going on all the time--say, for example, building a possible approach to a paper prompt where the paper prompt itself is invented right there on the spot in the classroom, or where there's a page of text up on a screen and the teacher and students are reading it live together and creating an interpretation that isn't already fixed in some kind of lesson plan. But I know that in many STEM classrooms, flipping involves problem sets that are already made being worked live in the classroom, which would be the opposite of what you mean by co-construction. I think? that you could still go with the idea of "doing the homework in the classroom together", which is one way STEM teachers describe flipping but iterate it towards co-construction in your sense--e.g., taking a problem and working it 'standard' first, then asking students to help iterate the problem in new ways that aren't preset or pre-planned, then move to headless and tailless problems inspired by the first more 'normal' presentation of a problem. Essentially to work up towards open-ended mathematical reasoning where all students at all levels of skill might feel engaged rather than rapidly supplying a series of 'right' answers.
One way to avoid the students' yearning for what they already know is of course is to record your whiteboard presentations and have them on tap (every year refining them until you have your own - but better because based on feedback from your classroom learners- Khan Academy). That was our flipped math classroom. But it works best with "Bruce Lee math" sets (I fear the student who practices one problem 10,000 times, not etc ...) – in other words continuous review/incremental progression problem sets which the kids could start on right away while the teacher worked with individuals on "problem problems" identified by a quiz at the end of each pre-recorded presentation. Then of course we added TAPS for real time coaching – where two or three students watched each others presentations and practice solving problems (to which they already had the answer) until they felt they were fluent and they checked themselves off with a "Pass." https://youtu.be/z9N8b58m_iU?si=IEh5xf4a3nil6Ci1
Three keys to Math success… if I had to choose just three (but we actually had 9 keys... because we're not running an experiment and the kids aren't guinea pigs! But the real way to flip a school, I found, is to share all the learning goals with the kids so you get buy-in --then they push the learning process demanding somebody help them progress along your prepared path
For how to help avoid students yearning for what they already know: is your answer your whole paragraph or specifically recording your whiteboard presentations? How did you get student feedback?
Hi, well keeping in mind that I had many different teachers at my schools--all using slightly different versions of 1. Flipped classroom designed to maximize coaching (crucial here to have continuous review incremental progression practice sets + cumulative tests every 4 or 5 lessons + pass/try again grading on those cumulative tests so that students know they are not earning a Pass (say >80 or 85% on the test) unless they ID their "problem problems" and get help); 2. a computer lab session 1-2X a week for individualized practice with a separate lab coach in K-3, and with an assistant coach in grades 4-8 ; 3. TAPS sessions on 4-5 word problems each quarter, coached by a STEM Teacher and volunteers, not the classroom Math Teacher (TAPS provides great FEEDBACK as you listen to the student think out loud as they solve select word problems)— the answer to the feedback question is the students would take a quiz in Quizlet or something similar on each new lesson the teacher would have the results (FEEDBACK) at the beginning of each class. Students would begin on their cumulative daily smart practice problems sets (what I jokingly call Bruce Lee Math because of the continuous), while the teacher went around and worked individually or in small groups with students on the problems they had trouble with. After that session was over the teacher focused on helping students as they asked for help (FEEDBACK: we used red/green two-sided bookmarks: if a student needed help --which they were determined by going to check their answers every 10 problems – answers simply taped to the whiteboard and three different places with multiple copies , available on a computer, or projected in the corner of the room- they would turn turn the bookmark to red and move onto another problem while they waited for the teacher) etc. etc. too much detail maybe and apologies if you already have all the stuff worked out!
I definitely do not have all the stuff worked out, thanks for this! I really like the red/green bookmark idea, thanks for sharing.
Here is a quick adaptation of the square animation into Desmos. I was just thinking about how to get me students to re-engage with equations of perpendicular lines and this might provide an opening. https://teacher.desmos.com/activitybuilder/custom/6609bf23c272f0f27922305e
We just did the lesson. Students generated a lot of good questions and we narrowed it down to a) what’s the area of the inside square b) what are the coordinates of the vertices (they immediately wanted to put the square onto a coordinate grid with the bottom left hand corner at the origin), c) find the measures of the acute angles of the surrounding triangles, d) find the equations of the sides of the inside square.
There's an element of this that reflects the industrial model of education. Role of educator is to be expert that fills the heads of the students with knowledge. We now need to move to a competency based system where the role of teacher is to facilitate skill building - thus a transition from lecture to engagement... I will also add that in our current context, student mental health and connectivity is a forefront set of needs, too.
Umm, we do remember what happened to Robin Williams' character: a student committed suicide and he was drummed out of school...
I used to beg my teachers not to be try to put on a show. I said "If you're that good you belong up on stage in Las Vegas" The goals instead should be to find ways to maximize your students' hands-on learning/problem-solving time and maximize your own one-on-one or small group coaching time. With the best tools you can find to help you do that- Desmos, white boards, "Bruce Lee math" problem sets, TAPS, etc.
Thanks Dan. I really love this perspective. Just to add on: I have long thought that there's a difference between educators who are fundamentally fascinated by the SUBJECT versus the STUDENTS. Those most excited by the subject are great researchers (who happen to wind up teaching); those who are interested in the students are wonderful teachers, and can potentially teach anything.
At a session last night with teachers and students at a local high school, we talked about the promise & peril of AI. The promise: the much lauded "always on" tutor can potentially help you learn anything easily. The peril: If you don't have to work or engage with an idea, you may not learn much at all. I love your "topless" and "bottomless" problems -- they're intriguing ways to get people to think about the problem. (And bring their "assets" and curiousity into play). I wonder whether AI has the potential to make "learning" easier much like, say, cars made traveling longer distances easier. One unintended consequence of cars, of course, is that you don't have to "work" (ie: walk/run) to get somewhere. Ergo many of us get to be couch potatoes.
I wonder whether AI has the potential to make us "intellectual couch potatoes"?
"I have long thought that there's a difference between educators who are fundamentally fascinated by the SUBJECT versus the STUDENTS. Those most excited by the subject are great researchers (who happen to wind up teaching); those who are interested in the students are wonderful teachers, and can potentially teach anything."
Love this. For some teachers, it's the love of students that drives a love of subject. "Okay these kids are bringing goods that I don't have the content knowledge to understand or appreciate. I need to learn this math a little more deeply."
What do you think about Art of Problem Solving?
Love 'em for enrichment. I bought a set for my own kids.