>There’s also a tendency in contemporary textbooks to try to relate topics to concrete things in the real world.
This seems to be a personality thing. I was doing a Linear Algebra course last year and complained at the lack of applications in our textbook.
It seemed so strange to me. Here's this wonderful subject with literally dozens of wonderful, practical, illuminating real-world applications, which make the subject more concrete and easier to understand (and help you understand what's the point of all these obscure manipulations). And the book just... doesn't mention a single one of them? It felt both dishonest and pedagogically unskillful.
I expressed these feelings to my classmates and was met with disgust: "We are pure mathematicians. We do not concern ourselves with applications!"
Lucky for me, their disgust led them to discard several wonderful "Linear Algebra With Applications" books to the "free book pile", which I made excellent use of and greatly enjoyed.
That being said, in most of these books the "applications" are confined to a bonus section at the end of each chapter, and do not interfere with the main text.
I might have explained that poorly. What I’m talking about is not so much demonstrating applications by including practical problems in the problem sets (show, don’t tell), but instead opening every chapter with a paragraph or two about those applications. It often starts with an anecdote and then goes on to make a convoluted case for why the topic matters in the real world. These anecdotes are supposed to intrigue the student into wanting to learn more, but more often than not they just end up being skipped over. If the student had to be motivated to learn about the topic, he wouldn’t be reading the textbook in the first place.
I can usually distill everything I truly need to know in a (densely-printed) 30 page chapter down to less than 3 pages of notes, but that information tends to be spread out across those 30 pages, making reading the book much less efficient than it ought to be. These texts will often have a three-page-long introduction explaining how to read the textbook, and in my opinion most of them are trying to fill a role that can only be meaningfully satisfied by an experienced instructor.
An instructor can assess his students and relate lessons to what they already know. A textbook cannot do this, so it ends up offering several explanations, metaphors, and anecdotes that many students might not even understand. This leads a lot of students to skip over the readings in favor of reading their lecture notes.
This seems to be a personality thing. I was doing a Linear Algebra course last year and complained at the lack of applications in our textbook.
It seemed so strange to me. Here's this wonderful subject with literally dozens of wonderful, practical, illuminating real-world applications, which make the subject more concrete and easier to understand (and help you understand what's the point of all these obscure manipulations). And the book just... doesn't mention a single one of them? It felt both dishonest and pedagogically unskillful.
I expressed these feelings to my classmates and was met with disgust: "We are pure mathematicians. We do not concern ourselves with applications!"
Lucky for me, their disgust led them to discard several wonderful "Linear Algebra With Applications" books to the "free book pile", which I made excellent use of and greatly enjoyed.
That being said, in most of these books the "applications" are confined to a bonus section at the end of each chapter, and do not interfere with the main text.