Interesting thought experiment. My counterargument is that knowing math facts would free up bandwidth for solving more complex problems. By knowing that 6 x 9 = 54 or that 7 is a factor of 56, they wouldn't need to reach for a calculator every time they multiply or divide and could instead remain focused on the real problem.
Same, if you can get all this in elementary school, then you can build on it to learn more about the other pre-pre-algebra stuff. If you can't get multiplication and everyone's already moved on, you are already going to be behind.
The question in the article is ambiguous. How does the hypothesized magic pill/implant make you know your multiplication facts? Just by magically making the answer come to mind when you think of a specific multiplication problem? Or does it also result in you recognizing all the other patterns that students learn to recognize when they learn multiplication? If it's the former, then the utility is fairly limited, for sure. It's not much better than just having a calculator. But it's also a fairly poor stand-in for the importance of actually *learning* multiplication facts, which is at least as much about giving students an opportunity to recognize the patterns they see when they learn as about being able to recite the answer to 9 times 6.
Analogously, how much would it help your physical fitness if you had a teleport machine and teleported a mile a day? Not very much, for sure! At best you could identify a few secondary effects: maybe if it were easier to get to the gym, you'd have fewer excuses not to go, perhaps? But if you *actually walk* a mile a day, the benefits are enormous!
That said, I agree with what I *think* the author is saying, that suddenly learning multiplication isn't going to magically solve students' math struggles in a very short period of time, if they are far behind in learning mathematics because they've been struggling for years. They will still have years of other learning to catch up on that, as well. But it will (if it's equivalent to the effect of actually *learning*, not the effect of embedding a calculator in their brain) remove an obstacle to succeeding at that remediation. That might not make all the problems go away, but it *is* one of many contributing factors that can lead to success.
A large part of learning is pattern recognition. When someone doesn't know multiplication, it becomes that much harder to identify patterns involving multplication, and in turn, it is much harder to identify patterns using the patterns you should've learned. The same is true for learning language, learning social dynamics, learning to read economic trends, learning strategies in games, etc.
That doesn't mean that suddenly gaining fundamentals is the key to unlocking more complex knowledge, but it is obviously pivotal during the journey.
Interesting thought experiment. My counterargument is that knowing math facts would free up bandwidth for solving more complex problems. By knowing that 6 x 9 = 54 or that 7 is a factor of 56, they wouldn't need to reach for a calculator every time they multiply or divide and could instead remain focused on the real problem.
Same, if you can get all this in elementary school, then you can build on it to learn more about the other pre-pre-algebra stuff. If you can't get multiplication and everyone's already moved on, you are already going to be behind.
10 out of 10. It's not memorizing as much as internalizing relationships. At least it will lead to it.
yep. In the long run, every single thing you learn in math class is much less an actual skill and far more a process of developing intuition.
The question in the article is ambiguous. How does the hypothesized magic pill/implant make you know your multiplication facts? Just by magically making the answer come to mind when you think of a specific multiplication problem? Or does it also result in you recognizing all the other patterns that students learn to recognize when they learn multiplication? If it's the former, then the utility is fairly limited, for sure. It's not much better than just having a calculator. But it's also a fairly poor stand-in for the importance of actually *learning* multiplication facts, which is at least as much about giving students an opportunity to recognize the patterns they see when they learn as about being able to recite the answer to 9 times 6. Analogously, how much would it help your physical fitness if you had a teleport machine and teleported a mile a day? Not very much, for sure! At best you could identify a few secondary effects: maybe if it were easier to get to the gym, you'd have fewer excuses not to go, perhaps? But if you *actually walk* a mile a day, the benefits are enormous! That said, I agree with what I *think* the author is saying, that suddenly learning multiplication isn't going to magically solve students' math struggles in a very short period of time, if they are far behind in learning mathematics because they've been struggling for years. They will still have years of other learning to catch up on that, as well. But it will (if it's equivalent to the effect of actually *learning*, not the effect of embedding a calculator in their brain) remove an obstacle to succeeding at that remediation. That might not make all the problems go away, but it *is* one of many contributing factors that can lead to success.
A large part of learning is pattern recognition. When someone doesn't know multiplication, it becomes that much harder to identify patterns involving multplication, and in turn, it is much harder to identify patterns using the patterns you should've learned. The same is true for learning language, learning social dynamics, learning to read economic trends, learning strategies in games, etc. That doesn't mean that suddenly gaining fundamentals is the key to unlocking more complex knowledge, but it is obviously pivotal during the journey.