I have thought for a long time that it would make a lot of sense to teach elementary statistics, probability theory, and logic at the high school level instead of much of algebra and trig (not everyone takes trig, I know, but most college-bound kids I knew took it). I do agree that some of algebra is useful, mind – e.g., everyone should know about exponential functions!
Everyone needs a certain amount of statistics, probability, and logic – we need them to navigate the daily news, not to mention various choices we might be making and various things that might happen to us over the years – and I feel like it’s a skill that very few people tend to have. I see people making poor arguments and/or choices that stem from incomplete knowledge that would be more informed if they only knew these things.
The big problem with my great plan is that I don’t actually know who would teach the courses. See also the part where very few people have been taught these skills.
ETA: TheSeaOtter, I somehow missed your post before posting. Yes.
One of the great things about higher math is that you are given a list of building blocks (axioms, theorems, etc.) and you learn to put those together in logical ways to build more blocks. This kind of thinking is a skill applicable in many areas of life.
One other point is that school isn’t supposed to be all easy. It is a valuable experience to struggle through something hard and succeed, even if it is a subject not easily applicable to daily life.
Theoretical math? As in “abstract math” or “pure mathematics”? That’s more of the math-major course. I’d probably torture very few college students with that, much less high schoolers.
I think logic and basic statistics should be taught before middle school ends, long before high school. A lot of that could be useful in High School itself (even if no changes are made to the structure of education except teaching this stuff earlier.)
I have never in my life needed to fix a flat tire. I have, however, needed high school level Stats and Algebra in my job.
And deconstructing literature came in very handy when I needed to apply deconstructive analysis to work issues. My ability to pull apart a situation into pieces, to analyze those pieces, to see multiple interpretations. I was prized in my job for my ability to do that, and I learned it deconstructing literature.
I’ll take a stab at this. What people need to learn is a combination of everyday level skills, history and critical thinking. Everything else sort of falls into place naturally after that. For the sake of simplicity we shall assume that we are discussing the high school level, and nothing more.
Math: Everyone should demonstrate proficiency in arithmetic, basic algebra and basic geometry; the sort that you use everyday to figure out everyday types of problems. Advanced learners should have classes available or alternative syllabi available. This should be taught as an “as needed” skill. That is to say, that students should be tested twice a year for proficiency. Those who score adequately need not take more unless they are interested.
English/Literature and philosophy: Everyone should demonstrate proficiency in reading and writing coherently. This should be taught integrated with other classes rather than as a separate class. Students should be writing essays, reports, descriptions, requests, lab reports, etc. Students should learn about basic philosophical schools of thought and how they have shaped modern society.
History and Civics: Everyone should demonstrate a coherent understanding of Western civilization and a brief, but accurate understanding of the major points of Eastern civilizations. (United States) Students should demonstrate a proper understanding of the separation of powers, their general applications by those in office, and how laws are enacted and enforced.
Sciences: Everyone should demonstrate basic proficiency in understanding Biology, Earth Sciences, Newtonian-level physics, and basic astronomy/cosmology.
NEW MATERIAL
Critical Thinking: Everyone should demonstrate a basic proficiency in logical thought, understanding of the research/fact finding process, the difference between assertion/opinion/ and facts, a basic recognition and understanding of the most common logical fallacies.
Technology: Students should demonstrate a basic understanding of how the major technological systems we utilize work: Mechanical systems, Electric, Electronic, and Computerized systems. This needs only be very basic; but students should have a better understanding of how the daily used items function. For many of us, the answer might as well be “magic”.
Life Skills: Students should learn the basics of adult, independent living. Budgeting, credit, diet and exercise, automotive skills, and employment related basics such as interviewing, dress and demeanor, tax forms, and accountability.
I am as much in favor of teaching people what they want to know, when they want to know it, as possible. The flip side of which is that I am also very much in favor of not forcing people to have to study things they have no desire to study. Let them come back to it later if their interests shift (of course, this requires a model of education which is not “Cram everything in you could ever possibly have a use for during adolescence, because you won’t get a chance later”). Ineffectively attempting to ram material down uninterested students’ throats is surely not the best use of resources; not for the reluctant students (who are prevented from devoting their energy to those passions they do have), not for the teacher (who is forced to water down their curriculum for sake of appearing to be transmitting something), and not for those students who are actually interested in the subject (who are now forced to deal with the watered down curriculum). Everyone has better ways to spend their time.
I think there’s a very high bar to be cleared for a subject to be considered compulsory, and while a few qualify (basic literacy and arithmetic [which includes things like “5(x + 7) + 3 = 9; what is x?”, don’t worry; one doesn’t understand subtraction and division if they can’t do that]), most do not.
Yeah, plenty of adults could find use for, say, solving polynomial inequalities if they sought it… but all the compulsory algebra education in the world hasn’t actually left the layperson a master of this skill, and it’s perfectly fine for them to get by without it. It’s no more useful than legislating a massive effort to instruct all teenagers to play the piano. (And note that those who do want to play the piano, or become engineers, or what have you, don’t shy away from opting in to the classes necessary for their goals, no compulsion necessary.)
> What my argument was:my guess is that Bill Gates, should he have been forced
> to learn a huge amount more history or chemistry, wouldn’t necessarily have
> been relevant to his success or his life. As far as his financial success in the
> computer industry, he has done a really good job.
And my argument was that Gates and Zuckerberg could drop out of Harvard and start a business that made them rich because they grew up in families that were somewhere between the top of the upper-middle class and the bottom of the outright rich (and who were thus able to send them to high-level computer classes and computer clubs that poorer students could never possibly go to) and because they each spent two years at Harvard. Those high-level classes and clubs allowed them to learn computer skills that were far beyond what an average high school student had any chance to learn at that age. They improved those skills at Harvard because they had the best teachers. Furthermore, they acquired the connections they needed to start their businesses from their rich families and from the people they met at Harvard.
The problem I have with people pointing out Gates and Zuckerberg as examples of why college isn’t important is that such advice will screw over extremely bright kids from poor families much more than extremely bright kids from rich (or even upper-middle-class) families. Only a minority of the people who quit college to start a computer business can build it into a successful firm. Most of them eventually have to fold the company and start over, probably having to then first finish their college degrees. And only an extremely tiny percentage of them will create a business anywhere close to being as successful as Microsoft or Facebook.
That’s why I think that the advice that someone who’s extremely bright should forget about college and start their own business is about the worst thing you can tell a poor kid, while it won’t hurt a rich kid nearly as much. Even if the poor kid and the rich kid are equally bright, the rich kid will almost certainly have taken better courses, done more useful extracurricular learning activities, and acquired more connections than the poor kid. There is some small chance that a rich kid will actually start a successful business, and even if he doesn’t, his family will then pay for him to finish college. There is very little chance that a poor kid will succeed, and if he doesn’t, he’s simply screwed.
An extremely bright kid from a poor (or even an average family) has to be told, "Look, kid, there are a lot of rich kids that are just as bright as you. You have to do better in college than they will do if you want to compete with them. If you do just as well as them in college and apply for the best jobs, the people who do the hiring will choose the rich kids and not you. They have taken better courses and done better extracurricular activities in high school than you have. They have learned the appropriate social skills for success better than you have. They have acquired more connections than you have. Your only chance at beating them out is to show that you can do better than them in all the courses you take, not just the ones in your major, so the people doing the hiring will be impressed by your ability to learn anything you set your mind to. You have to show the people doing the hiring that although you don’t have as many social skills, don’t have as many connections, and didn’t have as good high school classes and activities, you are better at learning new things than those rich kids and will be more successful at your job.
I suspect “higher stuff” is anything that isn’t fun, or at least isn’t fun to someone who’d rather socialize. I say that because everything that’s being proposed for the block is all of the stuff that I was and am interested in.
I’ve never seen anything really advanced taught in high school and for sure nothing advanced was required. (Yes, I took HS Calculus and physics. Neither was torture and neither was required to graduate. We had to sign up for them.) You can dink along with business math and the easy electives and graduate. If you’re on the college prep path, you’ll take more, but that’s because you’ve chosen it, or your parents have.
Also that mathematicians have no use for science. Does anyone know if the story that mathematicians developed matrix theory in order to have a field that “would be of no use to those damned physicists” is an Academic Legend?
I’m going to have to ask if you’ve had any experience in math beyond being a student. Because “methodical review” isn’t a math thing and math sculpts the neurons in identifiable ways that nothing else matches, except perhaps music. What non-math critical thinking are you wanting?
Some people need the particulars to help them understand math. Some people have no trouble dealing with raw, naked math concepts, but have trouble when trying to apply them. That’s a learning style difference, not an excuse to say “I don’t like it, make it go away.”
And I know that you’ve backed away from your first list, but I have to go back to part of it and make a comment. This is cherry picking from part of your list" “emotions, health, well being, mental health, getting along with others, economic and political UNDERSTANDING, futurism, critical thinking.” My comment (besides critical thinking not matching the rest) is good luck getting a community to approve a high school textbook on any of those things, except in the abstract ways in which they’re already available in classes with other names. You’ll get a real education in political understanding.
Other folks have made lists including budgeting, applying for jobs, changing tires, etc. First, high school students will mostly find these things boring and they’ll say they don’t apply to them. And they won’t. As soon as you generalize enough to create a textbook, you’ve stepped back from what’s happening to them, individually, in their town, this year. And if you don’t generalize, you won’t have a big enough market for the textbook.
Do you know what would have been the most valuable for me to have known right out of high school? How to work a bureaucratic system. And I bet that it’s never going to be taught in high school, either. Because every system is different and every system changes, sometimes as a result of you working it.
Any student who thinks that they can just attend high school and get everything they need to know is going to be badly disappointed. You can never just sit and passively allow others to decide what you will know and what you will know how to do. The minute you expect someone else to be responsible for your education, especially if you include life skills as well as academic preparation, you’ve lost.
Talk to the people around you. Ask questions. Try things. Talk to people older than you. Ask what they needed to know that no one ever taught them. Join 4-H. Join the SCA. Get a summer job. Browse the library.
You know what I think would improve school results? Smaller class sizes. We already have electives. We can never have every elective. But with smaller class sizes there’s less need for crowd control and more opportunity to tailor explanations and assignments to individuals, and more opportunity to get to know students and to encourage assets and interests.
Smaller classes. I won’t say that anything else is just rearranging deck chairs on the Titanic, but that’s just because I don’t think anything’s sinking. So let’s say that anything else is just rearranging desks.
They do teach these things in high school. Along with other things you didn’t mention, like how to figure out the per ounce price on different sized packages to figure out if the large economy size is a better buy. At our school it’s a semester long class called Take Charge of Your Finances. Heck, our 6th grade teacher had us fill out a 1040 long form to show us that it’s not as complicated as people make it out to be. Clear back in 1971.
An analogy I’d make is that school is like dating. You could make the theoretical argument that dating is a bad idea. You should just marry the person who’s going to end up being your spouse and start your life together right away rather than wasting your time with a bunch of other people who you’re not going to marry.
Obviously, this theory has flaws in translating it into reality. And I think the OP’s education argument has the same flaws. You can’t expect students just starting out high school to know what classes will be useful in their lives. The purpose of high school is to learn a lot of different things in order to find out what you want to do with your life. You’re going on dates with a bunch of different classes in order to find the career you want to marry.
Yeah, but no one forces you to date people you aren’t interested in. You get to choose who you’d like to spend time getting to know; there’s no compulsion!
What do you mean “Beyond being a student”? I use math constantly. The math level I use tops out at about basic calculus level in my daily life. If you mean “do you study mathematics,” that would be a no.
Methodical review was my attempt to put into words the concept of solving a problem methodically.
For instance, you go “I have boxes that can fit 5 widgets and 24 widgets, how many boxes do I need to pack them them?” and then trying to figure out the solution. You can do it the brute force way: stuff things into a box until it’s full, rinse, lather, repeat. You can do it the “solve way” and go (albeit in this case mentally and very quickly) 5*x = 24; x = 24/5; x = 4.8; x = 5 boxes. You methodically solve the problem instead of just hammering at it.
This is a core concept of critical thinking. You review the evidence in front of you, eliminate anything that doesn’t really help (in my simplistic example: distilling the word problem into an equation) and then use that evidence to reach an ending point, in my example a solution but outside of a discrete math problem it’s usually a decision of some kind.
As for your note about sculpting neurons, can you link to a cite on that? Granted, I don’t keep abreast of neural science, but I haven’t seen anything in my passive review of medical material that suggests our brains maintain that bond without maintaining that stimulus. In simple terms: If you constantly use something, the brain habituates to the path for processing for that use. This is “learning.” But learning something doesn’t keep it permanent unless you constantly use it. Those neurons will get repurposed if you never use what you learned again. Thus, any effect you’d have on a brain in teenagers would fade away unless they continue to use it past the expiration of that particular course.
Not just ‘higher’ math - mathematics (and logic) is really just a process of taking a few very basic axioms and building ever-more-complex theorems on top of them. Over the last few thousand years, we’ve built some very impressive structures on top of those axioms.
My assertion, though, is that the average person doesn’t actually need the entire structure - their real-world needs are met by giving them the basic tools and the first few layers. I think there’s no harm in leaving anything more complicated for people who either want to learn it for its own sake or want to go into a field that requires it.
I’m not by any means arguing that ‘school should be easy’, only that it’s inefficient to teach everyone specialized tools for tasks they’re unlikely to perform, especially at the expense of teaching them the basic tools that everyone is going to need.
Yeah, fair enough. Although I can see some of the topics being complex enough that you might want to delay them until high school. For example, I’d probably wait a bit on probability theory. There are also statistics topics that I think would be more relevant to a high school math curriculum, like talking about confidence intervals and what they mean (at least on a conceptual level).
I don’t know enough “higher math” to know if this is what you mean by "probability theory, " but at least some curricula do things like dice rolls, creating tables of m and m colors, letter distribution in the students’ names, and so on, and teach them how to recognize patterns and probabilities, beginning in second grade (7 and 8 year olds). I know things get far more complicated later, but the conceptual seeds are being planted much younger these days. If I could remember what confidence intervals are, I could maybe identify them in the young un’s homework, but that’s one of those things that flew out of my head years ago, and unless I go into research, I don’t think I will use them, at least not under that term.
I was curious if you used math outside of a classroom, yes. I expected that, like most people, me included, you use math to solve problems rather than solving math problems. The question was just to confirm my assumptions and make sure I wasn’t getting off track.
Ah. That works. Not the math, itself, but the way to go about using math.
Critical thinking, at least when most people think of teaching it, also includes other things, like not letting your emotions or other people’s emotions mislead you, assessing the reliability of statements made by other people, basic logic and semantics, etc.
I haven’t looked for new research in awhile (a long while), and most of it will be centered on young children, because they show the effects the most. Here’s one.
This one’s from the other end of the age and experience scale.
Apparently the key generalized concept is
It’s easier to find studies showing that teaching music to children increases their writing and math skills, or how children with math disabilities have different brain scans.
Exactly. The increased abilities will be used for other purposes. If those enlarged brain areas or cross-connections between brain areas aren’t there to be used, then solving other problems, even recognizing other problems as being solvable, becomes harder.
That’s why I called it “a piece of” of critical thinking. One piece of an orange is the peel. That doesn’t mean I think all oranges are nothing but peels.
Ehhhh. That first study seems to me to have a problem with methodology. They took one group of second graders “with little instruction in arithmetic” and compared them to a group of third graders “after a year of arithmetic instruction” and then compared the results. They don’t seem to give any indication of controlling for age (the brain aggressively prunes itself all through your childhood/adolescence) or other potential factors. I think that would have been better done of a series of MRIs on the same pool of students, one before and one after the introduction of arithmetic, followed by studies that performed the same scan on older and younger students of school systems that introduce arithmetic at older and younger time frames to make sure it’s ability and not just a normal linking that happens when you learn anything.
Granted, it’s a linking of the “math” center of the brain and working memory, but you’d need that for understanding math, just like you’d need it between different segments of the brain for understanding history. It also didn’t show a control for relative abilities (was an “A” student showing more connections?) so it shows a correlation to learning, but not necessarily a connection to ability. Would the slowest students show few connections? The fastest show the most connections?
The second one is intriguing, but it leaves me questioning how much of an influence mathematicians have from their genes versus their environment(learning) regarding their brain formation. I would want to see followup studies on that over a longer term (30 years?).
As much fun as I’m sure it is to repeatedly cram a six year old into an MRI, it should be done. For science!
