Today an interesting read by a Columbia professor: The examples you see in the textbooks are not representative of the sorts of problems you see in the real world
I see it too. But what is even more important to me regarding Maths or Physics is that very often the real problems you encounter can only be solved/described/modelled using a mix of various approaches. It is sometimes obviously easy when you’re learning a particular topic that the posed problems can be automatically solved by applying this thing you just learned about. You simply need to use the method or apply the same formula, maybe this time with a slight twist. For me personally it’s hard to apply the knowledge in the real world, if I’ve been using it only in an artificial and very precise problem space.
How to make it better then? One way could be to mix the problems in such a way that you need to apply different methods, not only the latest thing you’ve just learned. Science handbooks do that usually at the ends of chapters as a form of summary. Most of them fail anyway, because those problems are usually listed in the very same order as the topics in the chapter — you don’t need an Einstein to figure out that when you use the tools in roughly the same order you learned them several pages ago, you’ll be fine. Why not randomise the order of the problems in the summary sections? Is this idea really that bold?
Another way would be not to structure the course around the methods, but around the problems. Let’s step back and ask ourselves — why do we want to teach others anything? I guess the most useful reason would be to help them understand the world around them. So why not guide people through their questions and problems they have, or might have in the future, and not stuffing them with some knowledge that you (or the curriculum) find important. Let people try working with the problems themselves and only then teach them various methods and equations that fill in the missing gaps.
Teach problems, not solutions. Solutions are only interesting when you had the opportunity to familiarise with the problems first. People might be not only more interested in the course, but the skills they learn are actually more useful from the day one. This approach is definitely harder for the tutor, because it requires more creative work and it requires them to understand the topics very well — I would argue it’s possible to teach people from a book and not understanding truly what you’re teaching — but I truly believe that if you care about the students, this is the way to go.
I wonder if there’s ever going to be such a shift in education.