Like you need to learn phonics first to be able to read, there are basics skills at first to gain. Without factual knowledge there will not be any critical thinking. Therefore the conceptual understanding happens after some initial experience.
This is like learning to ride a bike. To be able to ride it with some certain technique, you need to be able to ride it first.
I agree. I do think there's a risk in spending too much time on shallow knowledge because "they aren't ready" but seeing it as a spectrum to steadily move along is a key perspective. And that's the case in pretty much anything humans want to learn.
In my mind, I'm also thinking that noticing ANYTHING is actually rather brilliant. They've noticed that in this situation you have to subtract. Well that's AWESOME. At the very least they've internalised some pattern they have noticed. This is a good thing!
I agree! One contradiction in how I used to approach this is that I tried to hold an asset orientation and look for strengths in student thinking, but I also had rigid ideas about not using tricks or truly understanding that got in the way of my asset orientation. I'm not saying tricks are always a good thing, just that I would end up shutting down certain avenues of thinking because they didn't fit what I was looking for, when that avenue might have been really central to how a student was thinking about a concept! That is often really great thinking given where a student is starting, and I needed to build off of it.
Like you need to learn phonics first to be able to read, there are basics skills at first to gain. Without factual knowledge there will not be any critical thinking. Therefore the conceptual understanding happens after some initial experience.
This is like learning to ride a bike. To be able to ride it with some certain technique, you need to be able to ride it first.
What you are pointing is something crucial.
Thanks for sharing.
I agree. I do think there's a risk in spending too much time on shallow knowledge because "they aren't ready" but seeing it as a spectrum to steadily move along is a key perspective. And that's the case in pretty much anything humans want to learn.
Thank you for writing this. This is so true for people with deep understanding of maths, teaching/writing books for beginners.
Thanks for reading! I'm curious if this idea shows up in other disciplines/places as well.
Thank you. I think this is really important.
In my mind, I'm also thinking that noticing ANYTHING is actually rather brilliant. They've noticed that in this situation you have to subtract. Well that's AWESOME. At the very least they've internalised some pattern they have noticed. This is a good thing!
I agree! One contradiction in how I used to approach this is that I tried to hold an asset orientation and look for strengths in student thinking, but I also had rigid ideas about not using tricks or truly understanding that got in the way of my asset orientation. I'm not saying tricks are always a good thing, just that I would end up shutting down certain avenues of thinking because they didn't fit what I was looking for, when that avenue might have been really central to how a student was thinking about a concept! That is often really great thinking given where a student is starting, and I needed to build off of it.