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    • I'm inclined to agree, actually. There is a collection of facts that are very important to further work and understanding. It's just a smaller collection than you might think.

      We delude ourselves if we think all math is just memorizing a larger and larger body of isolated facts. In reality, we explore and make connections, and our understanding grows. We need to know certain facts and algorithms by heart (i.e., sums & products of one-digit numbers), but it's in connecting those facts and algorithms through observations, ideas, arguments etc. to the wider body of mathematics that they stay meaningful and at our fingertips.

    • This is the tough question right now, and frankly, there's no easy answer. Remote learning is hard. We're not prepared for it. It's just deeply challenging.

      Ideally, if you can get a child curious about something, they might be motivated to go off and try to mess with it on their own. So there's an art to helping kids see that there's something they don't get yet, but that they can play around with it and learn more.

      I think choosing tasks that require less explanation, and have a flavor of the internet meme of "here's a weird math trick. Does it really always work?" might be helpful right now. And the fewer words involved, the more accessible. But frankly, I'm trying to figure out the answer to this question too.

    • Thanks for this question. I think of struggle as pertaining to any situation that challenges you. And challenge is good! But our goal is to help the struggle be productive, because that's fundamentally where learning happens. It's the balance between challenge and success.

      So what makes struggle productive? Most important is a sense of movement, of not being totally stymied. The key is to have experiences where kids can have initial success, have a sense of possibility about what to try, but not necessarily know all the answers.

      Think about playing a game. If the rules aren't clear or if you lose every time, it's dispiriting. If you win every time, it's boring. But if the rules are clear and you win sometimes, but also lose sometimes, that's when things get interesting. That's when the struggle gets productive.

      Some kids thrive on challenge. But for a lot of kids, I'd help with that sense of early success, and making sure the "rules" of the game, or whatever challenge you're working on, is clear. If you check out my subtraction challenge problems, in the links above, I've got one on Diffy Squares. https://mathforlove.com/2020/03/diffy-squares/

      Kids should be able to do a Diffy Square on their own. That's understanding the rules of the game, and that's the entrance for playing. But how in the world can you make a Diffy Square go on for more levels? Super challenging question. It's between those two places that productive struggle can happen.