[mmmmpancakes]

The ability to communicate math this way is honestly rare. It comes from a combination of deep understanding, long experience in communicating math, and a certain level of "culturing" that is specific to the academic experience.

Among the best, Feynman was singular in his ability to communicate math and physics.

In other words, don't be so hard on the teachers who were disappointing in comparison to the stellar examples you see from top mathematical communicators. What you're reading is quite rare and, while education quality could certainly improve, its not fair to expect this of a 5th grade teacher who covers 5 topics in a day. Even for the best, developing this type of material takes time and thought that a school teacher probably does not have.

[melagonster]

but government hired professors to design content of mathematics textbooks for students. there are some problem...

[mmmmpancakes]

Disagree. The purpose of a textbook and a lecture is very different. A good textbook can be a helpful resource for teaching and lecturing, but it is not sufficient to guarantee high quality math education. Conversely, a good educator who deeply understands the material can deliver fantastic education without a good textbook. Claiming that profs writing bad textbooks is the cause of poor quality in class math instruction is absurd.

[mlyle]

> Claiming that profs writing bad textbooks is the cause of poor quality in class math instruction is absurd.

It certainly doesn't help. The tendency to pile more and more into standards, and then to have haphazard treatment in the textbooks, with problems that don't make sense... isn't great.

Stick a new teacher in the classroom, and they're going to run their book's recommended pacing and content. And even a veteran is probably going to lean on the book a lot in a pinch.

And, your course needs to fit together with 2 other teachers who are too likely to be running the absurd pacing and content in the courses before and after yours. The rushed pace leaves no choice but to devote a huge fraction of the time to procedural knowledge.

The net result doesn't serve anyone: the top students are left unchallenged and without the context and enrichment that could let them really grow. The bottom students are in painful struggle. And the middle are perpetually slightly confused, learning specific tools that they'll immediately forget when the unit completes.