I feel this article's argument is weak, largely for one key reason: They don't clearly define anything. Their references might clarify some things, but not all. They argue against "general problem-solving strategies" with a reference to Polya, but they don't provide a clear definition of what these strategies entail. How broad is the set of strategies they're arguing against? What are some examples of such strategies? I'd like something beyond two sentences on Polya.

Furthermore, what audience and level of mathematics education are we discussing? The goals (and hence appropriate metrics of success) are certainly different for high schoolers targeting non-STEM careers vs. engineering undergrads vs. math grad students. The authors reference "aspiring mathematicians" and "domain specific mathematical problem-solving skills", indicating they're arguing about education for math majors, or at least students in STEM fields. In that case, the argument is somewhat meaningless - who's arguing math majors shouldn't learn math-specific skills? But, as I understand it, the argument for general problem-solving skills is that students outside of math don't actually need many specific math skills. Instead, math is a vessel for teaching logic, reasoning, and problem-solving skills. Then again, this might not be the type of problem-solving the authors are referencing - as I said above, it's not very clear.

On a similar note, they cite evidence that studying worked examples is more effective than "general problem-solving strategies", citing an "improvement in subsequent problem-solving performance" without explaining how this performance is measured. If students are tested on specific problem types, of course they'll perform better when taught strategies for those specific problem types. But it's not clear that this is meaningful. For STEM majors, sure, solving specific problems is a skill worth cultivating. But for most students, solving specific problems isn't as important as learning logic, reasoning, and general problem-solving skills. In my anecdotal experience tutoring math, students tend to just memorize strategies for specific problem types instead of learning transferable logic and reasoning skills because that's what's tested. I'd be curious to see which method of learning facilitates better performance on a more general problem-solving test of some sort.

Now, I'm not an education researcher or an educator of any sort. But I am passionate about good STEM education, especially in math. I genuinely feel that math education fails most students, at least here in America. If I'm being generous, this article is a well-intentioned but poorly-executed argument for effective math education strategies. If I'm not being so generous, this article advocates for the status quo in math education that forces students to slog through years of math classes for little discernible benefit. Either way, it's a disappointing article with a poorly-explained thesis.