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 actually is a gears-level model;
if it is important to remember for more than one week (and writing it down is not an option);
especially if learning new skills depends on getting this one thing right.
If one student is taught addition via constructivism, and the other by imitation, is there really a fundamental difference in their understanding of addition?
It is hard for me to imagine someone not having a gears-level model of addition. But I guess someone who doesn’t, is at risk of making some stupid mistake in future (like, after returning from summer vacation, not having practiced addition for two months; or maybe a few years after finishing school), such as not aligning two numbers correctly, so that 111 + 22 = 331, or maybe with decimals 11.1 + 22 = 133 or 13.3, or something like that. Or would get confused when seeing an unusually written problem, such as 13½ + 24½.
My impression was that with constructivism, the question is not whether the student ultimately achieves a gears-level model, but whether they discover (“construct”) it for themselves.
I agree it’s hard to imagine addition without a gears level model.
Yes, but there can be a lot of nudging towards the discovery.
Like, if you want kids to find out that “a + b = b + a”, you give them hundred pairs of problems like “2 + 7 = ?; 7 + 2 = ?”. That achieves the goal more reliably and more quickly than merely giving them hundred random addition problems.
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 actually is a gears-level model;
if it is important to remember for more than one week (and writing it down is not an option);
especially if learning new skills depends on getting this one thing right.
It is hard for me to imagine someone not having a gears-level model of addition. But I guess someone who doesn’t, is at risk of making some stupid mistake in future (like, after returning from summer vacation, not having practiced addition for two months; or maybe a few years after finishing school), such as not aligning two numbers correctly, so that 111 + 22 = 331, or maybe with decimals 11.1 + 22 = 133 or 13.3, or something like that. Or would get confused when seeing an unusually written problem, such as 13½ + 24½.
My impression was that with constructivism, the question is not whether the student ultimately achieves a gears-level model, but whether they discover (“construct”) it for themselves.
I agree it’s hard to imagine addition without a gears level model.
Yes, but there can be a lot of nudging towards the discovery.
Like, if you want kids to find out that “a + b = b + a”, you give them hundred pairs of problems like “2 + 7 = ?; 7 + 2 = ?”. That achieves the goal more reliably and more quickly than merely giving them hundred random addition problems.