1) High-school kids are not prepared for the mathematics involved.
2) It is never a good a idea to teach someone somethying that is false, deliberately.
3) An exercise like that would teach them that teachers are deliberately misleading them.
mathematics is an abtract formalism that TRIES to comprehend real stuff. . . . . like gravity. . . . but often fails, until we contruct an equation that has all the right mathematical features that are needed. Probably you didn't think of this necessary exercise of learning to contruct a formula, and computing theoretical results, and then comparing the results to some objective sort of experiment. Probably you consider "education" to consist of passing out "truth" like candy to kids, that's why it just looks cruel to make them learn to think. I'd say the objective of education should be the development of students' inate abilities to creatively conceive concepts, and to check them out constructively for their usefulness. If you set kids out on a quest that requires some mathematical skills, you will possibly motivate them and teach them how math can be useful.
second. . . . while we have no real need to deliberately teach anything we know is just rubbish, trying to make the students dissatisfied with us and angry enough to try to prove how wrong we are. . . . . it is the fact that everything we teach needs to be questioned, and will one day yield to some future concept that explains things more satisfactorily. . . . so in effect there is the likelihood that what we do teach could be called "false" and produce the same result, no matter how diligent and concerned we are to teach what's right. I'd even say that it is the important truth we should thoroughly teach, that the quest for understanding is a systematic progression through ideas towards a goal we might not have satisfactoriy comprehended yet. And yes, there are ideas we can teach that are for practical purposes useful enough. . . . but there is no "State Interest" in closing the discussion.
There is no "State Interest" in limiting the human mind, or establishing norms or acceptable beliefs in "Science" or "Religion", or even in "Game Theory". I disagree with John Dewey in the claim that there is any "State Interest" in training workers to meet the requirements of corporate "clients" with hiring needs. . . . training plumbers, carpenters, electricians, architects, engineers, doctors, nurses, schoolteachers, computer programmers, chemists or physicists, or in licensing professionals in any way.
Teaching kids that these are legitimate concerns of the State is exactly what you wish to avoid, teaching them that teachers are deliberately misleading them.
The "State" is us. Every time we set some 'standard' for a profession, we do so at a cost, to "us", of limiting the range of acceptable creativity. While we might gain something in establishing standards for, say building codes or zoning ordinances, there is a creativity cost as well as an administrative cost. The belief fostered by public education that "The State" has any authority/interest in managing "us" is THE LIE. The reason we are not a pure democracy is that we once had people in the formation of our government who feared the dictatorship of a simple majority as much as they feared the tyrrany of financial/commercial interests. They tried to construct a system of balanced, limited powers, but realized it could only work so long as the people were willing to claim their inate rights. Among those inate rights is the right to question authority. . . . and in the environment of cartel/corporate/commercial interests with motive to cultivate connections to government, to lawmakers, administrators, it becomes a civic duty for people to closely regulate their "State" and it's claimed "interests'.
The failure of a state-operated "Public Education System" to resist the claim of "State interest" is diagnostic of education gone amok. The failure of any professional line of service to resist the claim of "needed regulations" backed by the police power of the State, is diagnostic of a profession that has itself yielded to a fascist mechanism of enforcing restrictions against competition. It always has a practical cost in terms of products made available to the people, as well as a cost in terms of human liberty.
The result will surely be people becoming convinced "that teachers are deliberately misleading them."
The alternative is simply allowing private education to compete. . . . . if the "State" got entirely out of the way, you might think some people will not be trained to useful tasks, and indeed that might happen. . . . but the reality of liberty and the consequences of liberty is actually compelling. While the state-run education system we have has produced millions of citizens incarcerated for say personal abuse of psycoactive substances, and a very large rate of illiterate survivors of the public school regime, you fear the possibility of some people refusing to learn marketable skills that corporates need. In my view, people would do better on their own self-interest, and the so-called "State Interest" is not nearly as efficient at addressing the "needs" of people. It's been about a hundred years in our country now, and we can see the results. What's the unemployment rate now. . . . . higher than ever. . . . . poverty, unenployment, millions of displaced workers abandoned by corporates who just relocated their plants in labor markets abroad. The whole "train to the task" concept has been breached by the corporates who demanded it in the first place.