I personally think that " education (just the act) is the purpose" cannot be separated from the learner. " education (just the act) is the purpose" presupposes that a learner is involved. So please clarify your point.
When I hear the word "education" I think "successful education". I don't think the word keeps the meaning you are ascribing to it, no matter how hard the teachers or students are trying, if the education is ultimately not successful. In other words, a teacher is teaching when they are successfully teaching, not if they are just trying to teach and a student is learning when they are successfully learning, not if they are just trying to learn. That is why when I said "a student of X" I meant a successful student of X, not a student just trying. But the industry of education appears to have gone from an industry of teaching to an industry of trying.
Consider the doctor that treats those things that can be successfully treated, like broken bones, infections, etc. The general practitioner. For every 100 patients they treat, 95 are cured and fully recover. Now consider the doctor that treats those things that cannot be successfully treated, like many cancers. For every 100 patients they treat, 95 die. You can't call both of these scenarios "doctoring" and leave it at that. At best, you can say that they doctors in the second case are trying to treat.
Likewise, when a teacher who is teaching students that are interested, prepared and able to take algebra, the process of teaching algebra is as well defined as is the process of mending a broken bone. Remove the preparedness, interest and ability and now teaching algebra becomes just "trying to teach algebra".
The problem with an industry of trying is that there is no clear standard of success or sense of purpose. For example, in the case of cancer the standard of success would be total remission, but when 95% of your patients are dying, that standard doesn't really work for you. So you change the standards to fit what you can do, not what you set out to do. Instead of full remission, success is measured in months and years. You even change the fundamental purpose. Instead of life it is now quality of life. Very often you can't even tell the difference between your treatment and chance or fate. And this transformation from an industry of doing to an industry of trying doesn't happen overnight, it takes time (decades) to recondition a public used to an industry of doing to an industry of trying.
And this is what has occurred with algebra and education in general. We went from an industry of teaching to an industry of trying. In the beginning the effort to teach algebra to more students was genuine. They started with the traditional principles that worked with traditional students, but success was elusive and over time the standards of success that define algebra were lost. Even the purpose of teaching algebra was lost. Algebra's simple mathematical certainty of reasoning was replaced with notions like creativity, diversity or equality. In the worse cases, such as with Richard, Dan and his little cult, they have not only abandoned the principles of algebra, they have abandoned their own students. What I mean by that is that you realize quickly that their blogs are not about the success of math, they are about its failure. They have abandoned the teaching of mathematics and have become more interested in studying its failure. Even if their original urge was to devise a cure, that is long past. They have invented another purpose for their time and their students be damned.
My chief problem with this is that algebra as a skill ranks pretty damn low in importance unless you are a quant. And I don't mean just the quants in finance, I mean the quants in all professions where mathematical reasoning and analysis is fundamental to the profession. These students could have been studying something else. Something more akin to their likes and aspirations. There was no real reason to create an industry of trying and fill it with non-teachers who for lack of anything better to do, spend their time discussing the failure of mathematics. These students will eventually become adults and have to provide a life for themselves. In place of every site like dan's there should be a site geared to students of construction, nursing, home finance, fashion, beauty, etc. etc. etc.
If education's purpose was the student then that is how it would be. Education's purpose should have never been algebra. It damn sure should have never been to give a bunch of failed algebra teachers something to talk about.
RE:Turning STEM to STEAM into STREAM
When I read the article referenced below, I immediately thought, well now, isn't this just how it was before we broke STEM out from the rest of the subjects? Even with an overarching goal of working to get my students to do more critical thinking as I came up with lesson plans this year, I found that many students had not grown much in their ability to think deeply using multiple perspectives.