"You'll Use This Everyday for the Rest of Your Life..."

[Wahoo Redux]

[. . . ]

because of some recent posting activity on another thread.

[. . .]

I know the thread of which you speak. It's been difficult trying to keep it from turning into a total train wreck.

Agreed.  The condescending, unreasonably dictatorial, sometimes ridiculous and largely myopic comments by some posters simply generated heat.

Basically knowing how and when to use tools for modelling/forecasting.

Beyond that, I use basic geometry all the time for home repairs, etc.

Again, lots of us do these things without geometry involved.  Sure, it might be helpful but certainly not necessary to actually do the math in a great many if not most situations in life.

Which makes me think there are other reasons for math in an educational setting.

I think it's important for people to understand why it's so dumb to buy a house on a flood plain or in a wildfire zone.

Should not need math to figure these out.  You should only need Google and common sense.

Or how to judge the effectiveness of different medical treatments.

NO, NO, NO.  DO NOT SECOND GUESS YOUR DOCTOR.  If you want a second opinion, find another doctor, preferably a specialist.  Math in this context could kill you.  Cosmetic surgery for sheer vanity is always a bad idea.

I never received formal instruction in some of the skills that I use daily in that capacity -- such as how to decipher the structure of an academic journal article.

I think this is the whole point of education and why we take a wide sampling of classes----we gain elastic, multi-functional minds capable of formulating solutions without formal training.

That's actually a brilliant example.  Nice.

[Parasaurolophus]

Every day of my life, I use that kind of knowledge to damp the echo in the halls of my brain.

[Aster]

I use algebra regularly in database macros.

Geometry is super useful in landscaping and general construction. It might not be complex geometry, but its geometry.
I actually have students that don't know what a 45 degree angle is. God only knows how they were allowed out of K-12. Maybe those are the folks that buy homes in floodplains. Having a basic knowledge of angles is what I would argue is most definitely a learned "common sense".

I love it when students google stuff but have no base knowledge of the topic. Copy/pasting useless garbage makes it real easy for me to detect plagiarism and assign automatic F's.

[spork]

[. . .]

Or how to judge the effectiveness of different medical treatments.

NO, NO, NO.  DO NOT SECOND GUESS YOUR DOCTOR.  If you want a second opinion, find another doctor, preferably a specialist.  Math in this context could kill you.  Cosmetic surgery for sheer vanity is always a bad idea.

[. . .]

Assuming you're being serious here: Based on ongoing personal experience -- e.g., being told that I had liver cirrhosis due to a condition that would eventually kill me if I didn't get a transplant, and then being told that guess what? the original pathology report was wrong -- I could not disagree more. Most physicians are terrible at evaluating basic probabilities. Gerd Gigerenzer's book Risk Savvy has a whole chapter on this.

[Wahoo Redux]

You know, folks, I think we can all agree that math is very useful and lots of people use it.  That's never been in contention.

And we can agree that doctors make mistakes; the cost of malpractice insurance is part of the reason our health care is so outrageous-----which is why we seek second opinions...from doctors preferably, not mathematicians.

What is under consideration is the way in which we approach academic subjects secondary to our ultimate goals.

[kaysixteen]

Polly, how exactly do you keep that hr/sr hs math 'in your back pocket', when you never use math at that level?  I aced 11th grade trig, even did maybe A- work in geometry and AP calc, but I've never had to use any of this since I gave my hs valedictorian address.  Many moons ago.  I'm not ashamed to note that I for years now have had no bounden clue as to how to do a proof, figure out the cosine of anything, or differentiate a whatever... Indeed I've only the vaguest notion of what the trig and calc terms even mean.  Classicists just don't use these things, neither do historians, nor all but a handful of specialized librarians.  Obviously almost no one uses and most also don't recall their hs Latin either, but the real value, for the vast majority of hs students of advanced hs maths or Latin, lies not in the substance of the skills learned therein, but rather the logical, rigorous thinking and study skills learning these fosters.

[polly_mer]

Polly, how exactly do you keep that hr/sr hs math 'in your back pocket', when you never use math at that level?

I did use math at that level for decades.  Because of all that practice, I can do algebra more easily than I can write a compound English sentence and the most common trig identities are as readily available in memory as the state capitals or standard unit conversion.  Years of practice mean I can do a quick refresh on something like integrating by parts (something I have looked up in the past year).  It's much like knowing the plot and main points of literature that I haven't reread this decade, but are still there.  I know words that I have to look up because I don't use them all the time and I've even been known to consult a map when I return to an area where I used to be quite familiar, but I need to know something specific today.

Logical, rigorous thinking is not transferable and relies heavily on background knowledge in an area along with substantial practice in that particular area.  That's why calls to Google for math questions are misguided--you're assuming that whatever comes up is credible and won't have the background necessary to check that credibility.  Sure, the calculator for one equation with given values is probably correct for the one right answer.  I would bet folding money that the statistical analyses that are nicely prepped with clear, standard English explanations are generally done that way because someone has an agenda that will not be apparent until one starts poking at the assumptions underlying the models.

What I think I resent is the insistence that to learn something one MUST justify learning it, particularly when that justification is bogus.

We learn stuff.  We are better.  Why pretend otherwise?

Opportunity cost and limited resources immediately come to mind about why we (as a community/state/nation/world and individually as specific people) should allocate time and energy according to priorities.

Neglecting high priority areas for the general public in favor of things that are much lower priority for the general public is a short-sighted thing to do.  Yes, schools-in-the-sense-of-teaching-individuals-more-about-existing-human-knowledge are important.  So are roads, medical care, bridges, food, clean water, clean air, care for bitsy children, care for the elderly, and care for others who cannot currently care for themselves.  We need a certain amount of people keeping the systems of modern life running and ensuring domestic tranquility.  We need some people creating new human knowledge as research areas, but that's the smallest fraction of anything else mentioned and not the typical undergrad experience.

People's good will is another important consideration.  If we have demonstrable evidence that an eighth grade education is sufficient (and that's exactly what the case is when people assert they don't use specific subjects past that level), then that's all the standard education has to be before people specialize in other things the world needs.  Many people are not book-minded and it's just cruel to insist that people waste their time in areas that don't matter when those people could be polishing their skills in other areas, especially with the knowledge that rapid changes in what's important to know is better accommodated outside formal, extended education.

One absolutely does have to justify spending resources in such a way that few benefit when so many more would benefit from spending those resources in a different way.  We could provide a fabulous education for essential no money out of pocket to students if we limited higher education to those who can benefit and focus on true education instead of check boxing. 

Lack of prioritization and following through on the actual priorities tend to be parts of critical thinking that bites people in the ass repeatedly, regardless of amount of time in school or knowledge in other areas.  Knowing flat out that the justification is bogus for assigning a higher priority and yet insisting on assigning that priority anyway to preserve one's own job is unethical.

[Caracal]

Polly, how exactly do you keep that hr/sr hs math 'in your back pocket', when you never use math at that level?  I aced 11th grade trig, even did maybe A- work in geometry and AP calc, but I've never had to use any of this since I gave my hs valedictorian address.  Many moons ago.  I'm not ashamed to note that I for years now have had no bounden clue as to how to do a proof, figure out the cosine of anything, or differentiate a whatever... Indeed I've only the vaguest notion of what the trig and calc terms even mean.  Classicists just don't use these things, neither do historians, nor all but a handful of specialized librarians.  Obviously almost no one uses and most also don't recall their hs Latin either, but the real value, for the vast majority of hs students of advanced hs maths or Latin, lies not in the substance of the skills learned therein, but rather the logical, rigorous thinking and study skills learning these fosters.

My memory works really differently for things I liked and things I didn't. Four years of Spanish is all but gone, but I still remember Great Gatsby and On the Road pretty well even though I haven't picked up either book since I was sixteen. I'm not good with languages, but I did fine in my sciences classes and still can't remember much. I think it just didn't pique my interest much and got stored in my brain as just a collection of discrete pieces that got dumped out at some point.

[Caracal]

Knowing flat out that the justification is bogus for assigning a higher priority and yet insisting on assigning that priority anyway to preserve one's own job is unethical.

Assigning nefarious motives to people who disagree with you isn't particularly conducive to a civil and productive conversation.

[polly_mer]

Knowing flat out that the justification is bogus for assigning a higher priority and yet insisting on assigning that priority anyway to preserve one's own job is unethical.

Assigning nefarious motives to people who disagree with you isn't particularly conducive to a civil and productive conversation.

Oh, are we going to start having civil and productive conversations now?  When did that start and did someone hide the frying pan?

[polly_mer]

My memory works really differently for things I liked and things I didn't. Four years of Spanish is all but gone, but I still remember Great Gatsby and On the Road pretty well even though I haven't picked up either book since I was sixteen. I'm not good with languages, but I did fine in my sciences classes and still can't remember much. I think it just didn't pique my interest much and got stored in my brain as just a collection of discrete pieces that got dumped out at some point.

OK, with that realization (and you are far from the only one), what should we do about mandatory education?

Where's the line on how to allocate our limited resources so that we get the best return on investment, even if that return is social good, not more money?

[ciao_yall]

Polly, how exactly do you keep that hr/sr hs math 'in your back pocket', when you never use math at that level?  (A) I aced 11th grade trig, even did maybe A- work in geometry and AP calc, but I've never had to use any of this since I gave my hs valedictorian address.  Many moons ago.  I'm not ashamed to note that I for years now have had no bounden clue as to(B) how to do a proof, figure out the cosine of anything, or differentiate a whatever... Indeed I've only the vaguest notion of what the trig and calc terms even mean.  Classicists just don't use these things, neither do historians, nor all but a handful of specialized librarians.  Obviously almost no one uses and most also don't recall their hs Latin either, but the real value, for the vast majority of hs students of advanced hs maths or Latin, lies not in the substance of the skills learned therein, (C) but rather the logical, rigorous thinking and study skills learning these fosters.

(A) Geometry and calculus develop spacial and conceptual understanding.
(B) Proofs develop logical thinking. Cosines and differentials develop pattern recognition.
(C) Which is why we study these things. To develop our thinking, to build knowledge in fields that may be useful in later careers, and to expose one to skills that we may not realize we had, and thus to careers we may not realize existed.

[Caracal]

My memory works really differently for things I liked and things I didn't. Four years of Spanish is all but gone, but I still remember Great Gatsby and On the Road pretty well even though I haven't picked up either book since I was sixteen. I'm not good with languages, but I did fine in my sciences classes and still can't remember much. I think it just didn't pique my interest much and got stored in my brain as just a collection of discrete pieces that got dumped out at some point.

OK, with that realization (and you are far from the only one), what should we do about mandatory education?

Where's the line on how to allocate our limited resources so that we get the best return on investment, even if that return is social good, not more money?

I'm not sure that it is really a problem. Or, to put it an other way, it is part of the nature of education. Some people, like me, suck at languages and also will be bad at applying themselves to things they aren't good at. But does that mean that language education isn't important? Or that we should ditch it as a requirement? Focusing on the utility of education is always going to be a trap, because it is impossible to know what skills, knowledge or ways of thinking about the world might be helpful to someone in the future. The more you focus on utility, the more you crush all the life out of the whole thing. For an example of this, just see the suggestion above about universal testing for each major, which I'm quite sure would make for deadly boring classes which taught to the test and were not about the things instructors and students were interested in.

[marshwiggle]

I'm not sure that it is really a problem. Or, to put it an other way, it is part of the nature of education. Some people, like me, suck at languages and also will be bad at applying themselves to things they aren't good at. But does that mean that language education isn't important? Or that we should ditch it as a requirement? Focusing on the utility of education is always going to be a trap, because it is impossible to know what skills, knowledge or ways of thinking about the world might be helpful to someone in the future. The more you focus on utility, the more you crush all the life out of the whole thing. For an example of this, just see the suggestion above about universal testing for each major, which I'm quite sure would make for deadly boring classes which taught to the test and were not about the things instructors and students were interested in.

Fields like medicine, law, and accounting rely on universal testing because it means that people who pass have a definable level of knowledge of the material. By not having an external test to "teach to", instructors can just do their own thing, and may not even really cover their own syllabus, but rather focus on their own pet topics. It's a double-edged sword.

[Wahoo Redux]

Knowing flat out that the justification is bogus for assigning a higher priority and yet insisting on assigning that priority anyway to preserve one's own job is unethical.

Assigning nefarious motives to people who disagree with you isn't particularly conducive to a civil and productive conversation.

Oh, are we going to start having civil and productive conversations now?  When did that start and did someone hide the frying pan?

Frying pan goes away when we are, in fact, civil and productive.  As now.