but at some moment after the understanding is solid (maybe a year later, not sure) the kids should practice until they memorize it.
I totally disagree. This alienates kids from their developing inner agency. “You’ll now learn this because we said so.” As opposed to learning what they need because they can see & feel their own need for it.
Also, let’s empathise with the parents a little.
Obviously.
I’m not going to filter my speech to be appropriate across all dimensions. I don’t regret what I said or how I said it.
But obviously I agree with you.
(I mean, it’s kind of the main point of the PCK stuff!)
Realistically, teachers need a textbook with a linear progression of topics, with the right problems already provided for them.
Only if you’re teaching computation classes instead of mathematics.
Notice this isn’t an issue in English literature, or music.
But I agree that given the current bonkers goals — both overt and implicit — for math classes, this kind of linearity is key.
I just also think those goals are bollocks and in some cases downright nasty.
Now, one thing that is missing from your story, and which seems very relevant to me. The Wikipedia page on constructivism mentions something called “radical constructivism”…
Oh jeez. I honestly just forgot about those guys.
The heyday of radical constructivism was before my time. But my impression was that it was mostly philosophy that math ed researchers used to confused each other. Kind of like how modern art is some bizarre combo of oneupmanship amongst artists plus a front for tax evasion. Radical constructivism was part of the wave of postmodern philosophy justifying grants for all kinds of weird research projects. It offered context for endless intelligent-sounding debate.
It had incoherent suggestions about what to do for education. It was kind of the behaviorism of education theory. It sounded technically right and quite compelling if you didn’t look too closely. Once you started trying to figure out what to actually do with it though… :-P
But I don’t recall it claiming there’s no objective reality. I remember it rejecting the ability to know about any objective reality, so talking about it directly is a kind of absurdity in their view. But like all postmodern philosophies, it runs into a basic paradox: Is that claim absolutely true, meaning you can access some parts of objective reality, thereby invalidating the point? Or is it only sometimes true, which also implies there are some objective truths you can access somewhere sometimes?
(I could totally believe some radical constructivists thought about this and tried to get around it by claiming there’s no objective reality. This is exactly the same postmodern move as when radical social relativism insists that the laws of physics are just a bunch of ideas imposed by the racist patriarchy to support the established social structures of power. It tries to sidestep the logical challenge by shattering the mind’s ability to follow reason at all.)
I don’t recall the radical constructivists having an oversized effect on the math wars. They affected how math ed researchers thought and talked, but roughly the kind of way behaviorism affected how psychologists thought. I think it’d be pretty weird to list behaviorism as an influence on the math wars (even though it actually did play a pretty big role for context-setting in decades prior).
But hey, I could be mistaken. Maybe the postmodern philosophers of math ed research shoved themselves to the front and started babbling gibberish at teachers until everything fell apart. And maybe if we could own that and stop it from happening again, we could get sane policies into schools.
I’m not holding my breath for that one though.
So to me it seems like the teachers / politicians / school administrators were told to do “constructivism”, but then there came two groups of people claiming to be experts…
I honestly wasn’t aware that the word “constructivism” was a hot topic. I wouldn’t have thought there’d be much point in talking about “constructivism” explicitly when proposing education policy. That’d be like a plumber trying to explain viscosity and Bernoulli’s principle to house owners.
But given that math ed researchers did, I think the cause is messier than what you’re describing.
Basically anyone who was inspired by Piaget called their thing “constructivism”. There are lots of variations. The “radical” vs. “trivial” split isn’t the only one. Like I hinted at before, mathematicians created a “constructivist” approach based on constructing (!) mathematical objects and operations in the minds of children following the same rigorous pathway the mathematicians used to derive their tools from ZMF.
I faintly remember encountering at least one paper that claimed that it was constructivist because it was looking at levels of development. Because Piaget inspired the idea of levels of development, you see, and that’s based on constructing understanding, and so with “Piaget” and “construction” in the same idea cluster surely that makes you a constructivist, right?
I remember one of my teachers was basically a Piaget scholar and encouraged us to refer to Piagetian Constructivism, and to dissect various papers for where their implicit philosophy or explicit methodology differed from key points of Piaget’s approach (as she interpreted it). Frankly there weren’t many papers that survived that kind of analysis.
It’s possible the word “constructivism” also underwent something kind of like “nanotechnology” did: If funding appeared for “constructivist” approaches, then anyone who wanted funding could get it by finding a way to describe their pet project as “constructivist”, thus diluting the term.
For the most part I never want to use that word in educational contexts. It’s a messy ball of confusion just begging for pointless arguments. Some of the reason I honed in on Gears is precisely because it promises to cut through… gosh, I don’t know, but my gut claims it’s something like 2⁄3 of the babbling nonsense that shows up in education spheres once someone brings up “constructivism” (or “understanding”).
(BTW I didn’t “×-vote” your comment. Saying it explicitly, because now it’s just the two of us debating.)
Okay. I wasn’t worried about it. But thanks for mentioning.
And… honestly I really dislike framing this as a debate. I guess it is now? I wasn’t debating you before this. Just letting you know my impressions. I thought we were just comparing notes.
This alienates kids from their developing inner agency.
If you have 20-30 kids in the classroom, and an externally given list of goals to achieve, this puts a constraint on agency.
Also, some kids have an aversion against practicing stuff. Often the smart ones—they sometimes identify as “intelligent”, and it is a part of their self-image that they are supposed to learn things by mere understanding; anything that resembles work means for them that they have failed, because they were supposed to learn it without working hard. I knew very smart kids who just couldn’t learn a foreign language, because the idea of “memorizing by repetition” horrified them, and… nothing else worked. Their less smart classmates already learned the languages by practicing.
There are schools that try to maximize agency. And there is also unschooling, with the same goal. I suspect that kids who learn this way, will usually miss all the stuff that has very long inferential distances—because to get there, you need to walk a long way, and not each step is intrinsically exciting. (Reminds me of people in Mensa who can spend endless hours debating relativity or quantum physics, but never find time to read a textbook and fix their elementary misconceptions.)
So… yeah, I would seek some compromise between agency and knowledge. I might be convinced otherwise by some research that would show that average unschooled kids are more successful along some dimension than average school kids. It seems to me that unschooling is more enjoyable, but does not typically translate into following one’s own educational goals or projects.
Basically anyone who was inspired by Piaget called their thing “constructivism”.
If the label is diluted to uselessness, we need some new way to talk about the useful parts. One possibility is to just list the useful parts individually, without having an umbrella term. Not sure how well this would work… I guess I would need to compile the list first.
So… yeah, I would seek some compromise between agency and knowledge.
To each their own. I don’t value any knowledge so dearly that it’s worth sacrificing chunks of children’s agency to make sure they have said knowledge. The willingness to make that trade is key to the lifecycle of that which would create unFriendly AI.
If the label is diluted to uselessness, we need some new way to talk about the useful parts. One possibility is to just list the useful parts individually, without having an umbrella term.
Well… if you look above, you’ll see that you were the one who introduced the label!
As I said, I gave up using “constructivism” to describe things in this space years ago.
Cool. Have fun.
I totally disagree. This alienates kids from their developing inner agency. “You’ll now learn this because we said so.” As opposed to learning what they need because they can see & feel their own need for it.
Obviously.
I’m not going to filter my speech to be appropriate across all dimensions. I don’t regret what I said or how I said it.
But obviously I agree with you.
(I mean, it’s kind of the main point of the PCK stuff!)
Only if you’re teaching computation classes instead of mathematics.
Notice this isn’t an issue in English literature, or music.
But I agree that given the current bonkers goals — both overt and implicit — for math classes, this kind of linearity is key.
I just also think those goals are bollocks and in some cases downright nasty.
Oh jeez. I honestly just forgot about those guys.
The heyday of radical constructivism was before my time. But my impression was that it was mostly philosophy that math ed researchers used to confused each other. Kind of like how modern art is some bizarre combo of oneupmanship amongst artists plus a front for tax evasion. Radical constructivism was part of the wave of postmodern philosophy justifying grants for all kinds of weird research projects. It offered context for endless intelligent-sounding debate.
It had incoherent suggestions about what to do for education. It was kind of the behaviorism of education theory. It sounded technically right and quite compelling if you didn’t look too closely. Once you started trying to figure out what to actually do with it though… :-P
But I don’t recall it claiming there’s no objective reality. I remember it rejecting the ability to know about any objective reality, so talking about it directly is a kind of absurdity in their view. But like all postmodern philosophies, it runs into a basic paradox: Is that claim absolutely true, meaning you can access some parts of objective reality, thereby invalidating the point? Or is it only sometimes true, which also implies there are some objective truths you can access somewhere sometimes?
(I could totally believe some radical constructivists thought about this and tried to get around it by claiming there’s no objective reality. This is exactly the same postmodern move as when radical social relativism insists that the laws of physics are just a bunch of ideas imposed by the racist patriarchy to support the established social structures of power. It tries to sidestep the logical challenge by shattering the mind’s ability to follow reason at all.)
I don’t recall the radical constructivists having an oversized effect on the math wars. They affected how math ed researchers thought and talked, but roughly the kind of way behaviorism affected how psychologists thought. I think it’d be pretty weird to list behaviorism as an influence on the math wars (even though it actually did play a pretty big role for context-setting in decades prior).
But hey, I could be mistaken. Maybe the postmodern philosophers of math ed research shoved themselves to the front and started babbling gibberish at teachers until everything fell apart. And maybe if we could own that and stop it from happening again, we could get sane policies into schools.
I’m not holding my breath for that one though.
I honestly wasn’t aware that the word “constructivism” was a hot topic. I wouldn’t have thought there’d be much point in talking about “constructivism” explicitly when proposing education policy. That’d be like a plumber trying to explain viscosity and Bernoulli’s principle to house owners.
But given that math ed researchers did, I think the cause is messier than what you’re describing.
Basically anyone who was inspired by Piaget called their thing “constructivism”. There are lots of variations. The “radical” vs. “trivial” split isn’t the only one. Like I hinted at before, mathematicians created a “constructivist” approach based on constructing (!) mathematical objects and operations in the minds of children following the same rigorous pathway the mathematicians used to derive their tools from ZMF.
I faintly remember encountering at least one paper that claimed that it was constructivist because it was looking at levels of development. Because Piaget inspired the idea of levels of development, you see, and that’s based on constructing understanding, and so with “Piaget” and “construction” in the same idea cluster surely that makes you a constructivist, right?
I remember one of my teachers was basically a Piaget scholar and encouraged us to refer to Piagetian Constructivism, and to dissect various papers for where their implicit philosophy or explicit methodology differed from key points of Piaget’s approach (as she interpreted it). Frankly there weren’t many papers that survived that kind of analysis.
It’s possible the word “constructivism” also underwent something kind of like “nanotechnology” did: If funding appeared for “constructivist” approaches, then anyone who wanted funding could get it by finding a way to describe their pet project as “constructivist”, thus diluting the term.
For the most part I never want to use that word in educational contexts. It’s a messy ball of confusion just begging for pointless arguments. Some of the reason I honed in on Gears is precisely because it promises to cut through… gosh, I don’t know, but my gut claims it’s something like 2⁄3 of the babbling nonsense that shows up in education spheres once someone brings up “constructivism” (or “understanding”).
Okay. I wasn’t worried about it. But thanks for mentioning.
And… honestly I really dislike framing this as a debate. I guess it is now? I wasn’t debating you before this. Just letting you know my impressions. I thought we were just comparing notes.
If you have 20-30 kids in the classroom, and an externally given list of goals to achieve, this puts a constraint on agency.
Also, some kids have an aversion against practicing stuff. Often the smart ones—they sometimes identify as “intelligent”, and it is a part of their self-image that they are supposed to learn things by mere understanding; anything that resembles work means for them that they have failed, because they were supposed to learn it without working hard. I knew very smart kids who just couldn’t learn a foreign language, because the idea of “memorizing by repetition” horrified them, and… nothing else worked. Their less smart classmates already learned the languages by practicing.
There are schools that try to maximize agency. And there is also unschooling, with the same goal. I suspect that kids who learn this way, will usually miss all the stuff that has very long inferential distances—because to get there, you need to walk a long way, and not each step is intrinsically exciting. (Reminds me of people in Mensa who can spend endless hours debating relativity or quantum physics, but never find time to read a textbook and fix their elementary misconceptions.)
So… yeah, I would seek some compromise between agency and knowledge. I might be convinced otherwise by some research that would show that average unschooled kids are more successful along some dimension than average school kids. It seems to me that unschooling is more enjoyable, but does not typically translate into following one’s own educational goals or projects.
If the label is diluted to uselessness, we need some new way to talk about the useful parts. One possibility is to just list the useful parts individually, without having an umbrella term. Not sure how well this would work… I guess I would need to compile the list first.
To each their own. I don’t value any knowledge so dearly that it’s worth sacrificing chunks of children’s agency to make sure they have said knowledge. The willingness to make that trade is key to the lifecycle of that which would create unFriendly AI.
Well… if you look above, you’ll see that you were the one who introduced the label!
As I said, I gave up using “constructivism” to describe things in this space years ago.