Earlier quoted context omitted.
Many students, especially those who are poor, intuitively know what the schools do for them You wish they knew but they don't. The kids, especially the poor ones, want worksheets, not problems. They want to pass but not learn. They want a degree without the competence. They want a job without possibility of advancement and if you don't provide that they resent you because you are in the way.
You're describing the Nth generation in a hopeless environment, not children in general. This is an encultured attitude, not an innate one. Illich's point, and one born out by learning research is that the desire to learn, to gain knowledge and mastery for its own sake - is innate to such an extent that it can actually be diminished by extrinsic rewards. All children share this.
The only encultured attitude I see here is the modern western delusion that the average child (or person) intrinsically wants to make the substantial, multi year effort required to learn complex subjects.
The vast majority of people do not enjoy learning. No one wants to spend their time on math problems (outside of a tiny minority).
This is also tied to the nonsensical idea that we are all equally capable of everything; the ability to learn (both in general and by specific subject) is randomly distributed and probably normally so like many biological processes. That itself ensures that given equal curiosity, not all children will make the varied effort required to learn.