Interesting comment by a "leading astrophysicist." What does this person know about what students can and cannot do at early ages? Has he read any of the research? We actually know that students can do much more than what most adults think. However, if we bypass their thinking and try to push them to follows rules without understanding, this will negatively impact their thinking. If they don't learn why, they will invent a reason why. Should we help them understand why or leave it to chance?
It's a lot easier to learn why a certain method works than to come up with that method de novo, as Investigations requires. I believe that elementary teachers should explain why the standard methods work, by covering the concepts of place value and the distributive property earlier than they currently do (not necessarily by using those names, or calling the commutative and associative properties by name), but what is most important is giving students those moorings in the standard algorithms.
This is a statement that seems reasoned, though it ignores the considerable research in this area. It is dangerous to underestimate what students can and cannot do. Research has shown that students can and do invent algorithms. Those that do are much more successful figuring out why. What is most important is developing a deep understanding of what mathematics is and the reasoning that supports it. Algorithms invented over 100s of years are not easily obtained by learners.
Exactly. "Creative comprehension" is only useful if you know what it is that you're even trying to comprehend, and if you have a way to gauge whether or not you're even doing things right. Teach the "what" first, then the "how" and "why".
Interesting comment by a "leading astrophysicist." What does this person know about what students can and cannot do at early ages? Has he read any of the research? We actually know that students can do much more than what most adults think. However, if we bypass their thinking and try to push them to follows rules without understanding, this will negatively impact their thinking. If they don't learn why, they will invent a reason why. Should we help them understand why or leave it to chance?
sleeper2345 3 years ago
It's a lot easier to learn why a certain method works than to come up with that method de novo, as Investigations requires. I believe that elementary teachers should explain why the standard methods work, by covering the concepts of place value and the distributive property earlier than they currently do (not necessarily by using those names, or calling the commutative and associative properties by name), but what is most important is giving students those moorings in the standard algorithms.
jelewis2 2 years ago
This is a statement that seems reasoned, though it ignores the considerable research in this area. It is dangerous to underestimate what students can and cannot do. Research has shown that students can and do invent algorithms. Those that do are much more successful figuring out why. What is most important is developing a deep understanding of what mathematics is and the reasoning that supports it. Algorithms invented over 100s of years are not easily obtained by learners.
sleeper2345 2 years ago
Exactly. "Creative comprehension" is only useful if you know what it is that you're even trying to comprehend, and if you have a way to gauge whether or not you're even doing things right. Teach the "what" first, then the "how" and "why".
Silverfilm 4 years ago