I like this post a lot. It might explain why I feel like an expert at addition, but not on addition. I notice when I am struggling with things like this in math, I often start blaming my own intellect instead of trying to understand what is making this hard and if this is perhaps just bad design that is to blame. The second approach seems much more likely to solve the problem. Noticing that word problems are harder seems like a good thing to notice, especially if you want to become an expert at using a particular math tool. For example I don’t think I currently really get exterior products and searching for relevant word problems might be a good way to practice. LLMs might be useful in creating problems I can’t solve (although I found it astonishing a while ago when Sonnet 3.5 was not able to consistently create word problems for applying bayes rule (~50% were just wrong)).
I like this post a lot. It might explain why I feel like an expert at addition, but not on addition. I notice when I am struggling with things like this in math, I often start blaming my own intellect instead of trying to understand what is making this hard and if this is perhaps just bad design that is to blame. The second approach seems much more likely to solve the problem. Noticing that word problems are harder seems like a good thing to notice, especially if you want to become an expert at using a particular math tool. For example I don’t think I currently really get exterior products and searching for relevant word problems might be a good way to practice. LLMs might be useful in creating problems I can’t solve (although I found it astonishing a while ago when Sonnet 3.5 was not able to consistently create word problems for applying bayes rule (~50% were just wrong)).