Hard disagree with the sentiment of this author. Maths is cool on an aesthetic level AND maths is a tool that people should learn regardless of their interest in it.
If you want to give people a liberal education in maths, fantastic, do it, but not at the expense of Joe Plumber's ability to quickly estimate a job's costs. It's simply not as important, and this idea that we should preserve the spirit of maths aggravates me because of its entitlement.
You're making assumptions about my motive and experience, and have sadly misinterpreted the point I was attempting to make. I am a little disheartened by your interpretation.
My aggravation is not because I have had a bad experience with maths. I had quite a pleasant one actually - despite elementary and secondary school being rather easy. Even in elementary school, though, there was an obvious tension for teachers. There are students who are excelling and need to be extended, and those who were struggling. The issue is, teacher time is limited, and they need to ensure the entire class is on track. This means there has to be a compromise between the two paces.
If you have taught maths, you will be acutely aware that a students performance depends on a number of things, with one of the most important variables being 'do they do enough questions'. This is the source of the 'volume' of tasks that can seem repetitious.
There is another important variable, which is the appropriateness of the questions that the student is studying. This is discussed in the original essay but in a perspective that I think is unproductive, because it emphasises the issue as student autonomy and not as student comprehension. It can be seen on page 23 within the dialogue, where the student could enjoy the subject even more had they led the investigation.
Importantly, you can reason for yourself that a student who is doing well that is doing lots of problems that are too easy will not improve at the same rate as if they solved suitably difficult problems (though admittedly this can depend on whether boredom inspires creative solutions in that particular student). Similarly, a struggling student will not be able to internalise the meaning of solutions to problems that assume too many structures they have not yet seen (though admittedly this can depend on the tenacity of the student and their motivation to understand structures they haven't learnt).
The idea of managing question appropriateness is then a source of attention tension for the teacher. Do you track the expected progress of the class against the strongest students, and give extra attention to the weaker ones? What if the stronger students notice this and act out due to the lack of contact time?
Or conversely, do you only track against the weakest students, and then provide extension activities for the stronger performers? What if the stronger students notice that they get "more work" for doing well?
These are not the only approaches btw, but it is sufficient to service the point that there is an optimisation problem in student engagement.
So maybe yes, it is possibly true that self led learning would service a students interest in the topic, but it presupposes that the gifted student doing well is of greater value than the struggling student reaching a minimum level to enter a majority of study programs they might be interested in. This assumption is wrong, and I won't debate it - if you disagree there is simply too much different between us to hope to reconcile our views.
Importantly, though, I do think gifted students should be able to ALSO pursue their interests, in a tertiary environment which they can elect to participate in. This is the nature of my "liberal" education comment - I don't refer to the political liberal, but the philosophical one.
What math will Joe Plumber use? What he does might just as well be called "Spreadsheet Skills" instead of math.
The closest thing I can think of to doing math is he might divide hours by number of fittings to see how long it took him to do one joint, then multiply that to find how long he thinks it will take now to do N.
I'd still call that spreadsheet and calculator skills rather than anything that actually requires being able to do math, because someone with zero algebra training can figure out those steps and do them.
Whatever the reason is to learn math, it's gotta be something more than just doing what we can already do with free software and $100 used laptops, unless we expect to have to do without tech.
But in that case, there are probably way more important skills one would need if they expect to survive in a tech free world, and I don't know enough to even start commenting on that.
Arithmetic is separate from mathematics and should be taught as such. The spirit of mathematics should be kept because it is part of the human spirit, not because of any entitlement.
If you want to give people a liberal education in maths, fantastic, do it, but not at the expense of Joe Plumber's ability to quickly estimate a job's costs. It's simply not as important, and this idea that we should preserve the spirit of maths aggravates me because of its entitlement.