Seems to me that constructivist education is already "in the water supply" of Less Wrong. My tweet-length definition of constructivism would be "teaching students so that they *construct* mental gears-level models of the subject, as opposed to just memorizing the teachers' passwords"; and I assume most people here would agree that this is the right thing to do.

My question is how much this is a *fair* characterization - or perhaps it is abstracting away some very important stuff - and what are the best arguments *against* constructivism. Because, per Litany of Tarski, if constructivism is wrong, I want to believe it is wrong; although frankly I do not expect it to be *fundamentally* wrong, more like constructivists having some typical *blind spots*, in which case I want to know where they are.

The motivation for the question is to help a (constructivist) teacher do their job well, or to help a teacher unfamiliar with constructivism learn to do their job better. Therefore if the objection is e.g. that Piaget was historically wrong about some technical detail, the importance of this objection depends on how likely today someone is to make a mistake in designing their lessons because of that fact.

Here are my attempts to steelman the opposition to constructivism:

- Excesses done in the name of constructivism, such as spending four years letting kids discover how addition of natural numbers works. (Either because according to the extreme interpretation,
*any*guidance from the teacher would be a sin against the child's independent construction of mental models; or because there is always one more "weird trick" that according to internet some natives used to add two numbers, and because having more models is always better, it is absolutely necessary to also teach kids this trick. As a result, 10 years old kids know dozen different ways how to add 15+8, each of those takes them five minutes, they will make a mistake in half of them, and they haven't heard about multiplication yet.) These are rare extremes, and are*not*what a typical constructivist believes, but in a debate with an opponent of constructivism expect to get an example or two. - Trying to find a perfect model to teach may lead to unnecessary
*abstraction*introduced too soon, and then having kids (and their parents) stumble over the things that were supposed to help them. For example, we all know that base-10 is arbitrary, but is it a good idea to introduce little kids to binary numbers before they have sufficiently mastered the decimal integers? Will it help them understand more deeply the logic behind the decimals, or will it just confuse them? Similarly, perhaps set theory is important at universities and some consider it a fundament of all math, but is it helpful to introduce the concept of a "set" at elementary school? (How specifically is "a set of two apples" better than "two apples"? Isn't this also a teacher's password on a meta level?) - Students are different. When you tell them facts, some of them will make the correct mental models immediately (or later, when they are reflecting on the lesson at home), others need more help. It is a tradeoff, where the time you spend helping the slower students form better mental models, is the time where the faster students could have been learning new things. The role of the school is not just to teach, but also to
*separate*the better students from the worse, and providing credentials to the former. By teaching the facts and leaving the students to make the mental models on their own, you simultaneously teach more facts and separate the talented from the non-talented. - Constructivism is more
*fragile*, because it requires that those who teach your students in*previous grades*become constructivists, too. If a class spent five years memorizing the teachers' passwords, and you try to give them a constructivist approach in the sixth grade, it's going to be difficult. However, if a class spent five years constructing mental models, giving them a list of passwords in sixth grade is not more difficult than giving a list of passwords to anyone else. Therefore, even if constructivism is superior in theory (which has to be proved yet), in practice it loses in an educational system with mixed teachers. You get a bunch of complaining constructivists, and a bunch of traditional teachers saying "guys, if you can't teach in a real class, why don't you go find a different job?" (Constructivism is also fragile in a system where all teachers try to be constructivists, but some of them do it wrong. Again, imagine teaching the sixth grade after five years of someone else doing constructivism seriously wrong.) - Constructivism goes against our evolved nature. Apes learn by copying, not by understanding. Often the things you copy work, even if you don't understand why. (Washing your hands helps even if you don't understand germ theory.) We may not even have a gears-level model of many things yet. Traditional education is compatible with our instincts, both for teachers and students. Perhaps we should be less confident about our ability to go against our insticts and achieve superior results.
- Helping the students develop mental models might be actively harmful. Maybe they lose the ability to develop mental models without external help. Maybe the lose the ability to
*revise*their mental models (if they believe they were taught the right ones). Or they may develop a habit of premature optimization, like whenever they hear a new fact, they immediately have to fit it into some model, because they were (implicitly) taught that facts not belonging to models are wrong. Teaching everyone the same mental model creates a mental monoculture, and the actual progress depends on some people randomly developing a*superior*model, therefore making all education constructivist may eliminate progress. (Also, if there is a disagreement about which mental model is better, which one should be taught?)

Maybe the constructivist approach works better for subjects with long inferential distances, such as

math. Any individual fact is easier to memorize than to understand, in short term. The problem is, with memorization you are building a tower that will collapse under its own weight. Also, a misremembered fact feels exactly the same as a correctly remembered one, so there is no self-check.I think you can't use constructivism to learn what is the capital of France.

My first approximation for "when to use constructivist approach" would be like:

- if there actuall

... (read more)