Comment by this-pony

I suppose that this differs at how mathematically mature the student is. For undergrads and high school students it is, as you say, probably a good idea to give a lot of motivation and applied examples for the theory being taught. I suppose this article is more geared towards teaching university students, and then it can well be that examples and applications become more abstract. Of course, introductory topics such as Linear algebra and Calculus would lend themselves very well for a wide range of application examples. On the other hand, in more advanced and abstract university courses the 'realistic problems' should already be reasonably clear for the student when starting the course.