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biggest mistake in the early 2000s was using those yellow and orange books for remedial course, since it already requires the student already knowing how to do it in the first place, and word problems tend to be more advanced because they havnt learned how to do the simple problems yet. this led to people not even doing hw in our school.
Ideally they could just stop using AI to generate both the text and practice problems.
Math should be fun no matter it has practical applications or not. Math is an art, not a trade to make money. For those narrow minded ‘practical’ people, even pure math has sooner or later some applications.
This is the most important part, especially when teaching math to children. The practical aspects of math (beyond arithmetic counting with basic addition and subtraction) are not going to be fully realized until one is an adult, so they aren’t going to be a motivator for learning math.
It needs to be fun and engaging for them to want to keep learning and engaging with it.
Forgive me, I’m not super versed on Dewey’s mathematics ideas. Quick skimming of some articles and papers seems to suggest he was very practical and wanted kids to tie into the real world. How does that differ from the pink side? Both, to me, seem the opposite of classical logic training.
From reading some of the comments here, it seems that some people think learning is a net negative or neutral for whoever is doing the learning and that one should learn as little as possible.
They seem to think that because they don’t literally write down the equation of “x²+6” that they never use it in their lives and so it is pointless to learn.
There are also people who seem to think that basing your education off of what could help you not being taken advantage of, or misunderstanding the world around you, is silly and you should only follow what is in your heart. Learning what interests you and nothing else.
I don’t understand either of you, idiots.
Debate me, I guess.
Debate me, I guess.
As per your instruction, I shall.
I am a certified flight instructor, I have studied the fundamentals of instruction and can speak with authority on the subject.
it seems that some people think learning is a net negative or neutral for whoever is doing the learning and that one should learn as little as possible.
Learning is an active process. There’s a reason for turn of phrases like “spend time” and “pay attention,” these actions aren’t free. Any act of learning comes with a real cost in time, energy and likely money. It also comes with an opportunity cost. The time and effort a student spends learning could always be spent doing something else; resting, playing, working, caring for family, or learning something else. It is possible for those costs to be so great as to be a genuine net negative for the student. Especially when the reality of formalized school comes into play.
One of Edward Thorndike’s six fundamental principles of learning is the Principle of Readiness. This ties into Maslowe’s hierarchy of needs. As a teacher, you have to always ask yourself “Where on their pyramid does my lesson fit? Is everything below that on their pyramid of needs well taken care of?” Your students will not be willing to pay attention in algebra class if they’re hungry, thirsty, sleepy, freezing or scared, because their needs for homeostasis and security aren’t being met well enough for an intellectual lesson such as higher math.
Okay, we got the kids fed, rested and secured. Now they should pay attention right? Nope. That isn’t good enough. Where on their pyramid does this lesson fit? What need of theirs will learning this satisfy? Genuine curiosity about the universe and its workings are always always always at the stabby point of the very tippy top of the pyramid, you want to satisfy that need you’ve got to categorically solve every other need these kids can have from romance to personal prestige. Schools and universities love the image of the career scholar, the men with SI units named after them who conducted experiments for the good of humanity…the reality is the very few extremely privileged people who got to play that game were old money wealthy, they owned land and had servants if not slaves to take care of all their material needs.
When a child asks why they have to go to school, they’re told that school is where they learn the skills they need to survive as adults. though Elementary school, you can take this argument seriously. Learning how to add and subtract is necessary for the basic act of paying for things, reading is the most OP skill you can have, reading clocks and calendars is demonstrably important, etc. That argument starts falling apart when you’re preventing people from going out and earning money to live so they can generate standardized test scores in pre-calculus algebra, or being told not asked what the symbology of the blue curtains in some novel is.
Because here’s another thing about the principle of readiness: It is the teacher’s responsibility to inform the students of the value of the lesson to them in their lives. “Someday algebra will save your life” is meaningless; we live in a world with quiz game shows, literally any trivia knowledge can be life changing. You have to be specific and realistic. Otherwise your students aren’t going to spend the effort, they’ll merely go through the motions, like pretending to be sad at a great aunt’s husband’s funeral.
Especially on Lemmy I’ve seen the argument that education shouldn’t be mere job training, it should be about ultimate enlightenment. Except we need to achieve a world where everyone can afford rent before we can play that game, Tiffany. And we haven’t. Survival skills come before abstract beautiful truths and if we’re honest we’re doing a piss poor job of both.
I agree with just about everything you said. Well put and reasoned. But it doesn’t really wrap back around to what should be taught to the children. Do we let them decide everything for themselves or regiment what is necessary to live in our
hellscapesociety?Then you can ask what is necessary to live in this society? Is it comp sci degrees? Everyone thought so. Now they’re basically useless. That has happened to every generation for the last 30 years or so.
Additionally, as a child I was driven to learn because I was genuinely curious despite crushing depression. It has left me grasping to understand how others approach the world, because let me tell you, it is not how I do so. I would need to look at some good data about how students/adults learn generally, which I have not done much of admittedly.
Specifically what should be in the curriculum? Well, the way I see it, school gets more and more useless the older students get. Elementary school is mostly on the money because reading, writing and arithmetic. We probably need to shake out some of the whitewashing that’s done in social studies class; all the “And then the Indians showed the pilgrims how to plant a fish with the corn seeds to act as fertilizer” shit but I think you get it.
Throughout middle school, they started letting kids choose the electives they wanted to take. For me this started out as “do you want to take Spanish, Band, Orchestra, Chorus or ‘Career Studies’?” There was one period a day that we didn’t ALL share in common. We need to do more of that, cater to students’ interests better. I think high school should have majors like college does.
The best education I find is when the environment simulates or actually is real work. Auto shop class in which real maintenance and repair is done to real roadworthy vehicles, conducted in an environment that simulates a service station is vastly superior to “Here are five random cars the owners abandoned with the school as a tax write off. They were broken when they got here and nine classes before you broke them worse. Take the wheels off and put them back on I guess.” My high school carpentry shop teacher treated us like employees of a general contractor, and we built a house. We would go to the job site, divide into work teams and work on a section of the building, from girder beam to shingles. I came out of high school not only with a head full of theory, but I was ready to walk onto a job site and work because I knew the job.
Shop classes have been disappearing. Students who didn’t take those, who took AP classes and such…what did they emerge from high school ready to go do as an adult?
I’m also of a mind to reject the notion that, you spend the entirety of your childhood and adolescence on school, and maybe even early adulthood if you go to college, and then once you’re done that’s it, no more learning now you work. That’s insane. “I’m in school.” “I’m out of school.” “I’m going back to school.” This notion of everything having to be multi-year curricula that must be entirely completed to earn a certificate and those four semesters of chemistry and physics don’t count because you failed persuasive writing so no future for you…it’s psychotic.
You know shit’s fucked when The King In Yellow, the very manifestation of the idea that knowledge can kill, is having to defend the value of education.
Every day we stray
further from godtoward lost CarcosaSong of my soul, my voice is dead; Die thou, unsung, as tears unshed Shall dry and die in Lost Carcosa.
I agree with you on both points, and the third (these people are idiots), but I’m happy to debate you anyways.
I think that we must actively dismantle traditional forms of knowledge (copyrights, private libraries, most of education) in favor of developing new completely open archives and internet based methods of organizing, developing, and interacting with knowledge.
Does that do it for you?
I mean I like your ideas but that doesn’t really address the “how” of educating. As in how are those materials presented to people?
How do we ensure that children are actually being educated and not just glazing their eyes over as the info flows past? How do we ensure that that education is not just “God did it, now shit up.” How do we get people to be interested in learning and not just stop the second someone isn’t pointing a gun at their head?
I guess we’ll have to learn how to do that.
For a lot of people, education is “we will hold a gun to your head until you pass the exam”. For a lot of people, education is seminary school, and in many circles the priests are the best educated folks around.
If I don’t send my kids to school, a nice lady with a uniform and a gun comes around, and this is ‘civilization’?
It sounds like you’re worried education will, ‘become Bible school at the point of a gun’, but where I am it already is, and these aren’t the new models I’m talking about.
I’m talking about free access and communication as the pillars of education.
I’m not worried about that specifically, although it is headed there in some states. It is just the general degradation in the quality of education and the veracity of the information presented at just about every level that really bums me out.
I agree that it shouldn’t result in anyone coming to your house to force the subject. How to present it and provide a service that people can recognize as a net benefit? Decentralized would probably be good but it cannot be denied, as you said, that apprenticeships and hands on learning are very effective. Yet, they are very difficult to decentralize as they require a lot of equipment at each location.
Virtual reality with haptic feedback would be pretty close, if we can get it to work in an open source meshnet sort of way.
People who want school to be practical scare me.
yes, practical skills change year to year.
what’s important is to learn to learn.
I’m genuinely curious why, if this is serious. I feel like adulting badly needs to be taught better. I’m nearing mid twenties and still get so confused at a lot of adult things, especially government shit, because it’s just so much to figure out for the first time.
It’s definitely important to teach math and science and language, and to teach people how to do their own research, and think, and learn, etc. But are you saying practical skills shouldn’t also be taught?
I interpreted it as a criticism of those who think there’s no point to learning something if there isn’t an immediately-obvious application for that knowledge. Like those who say, “What’s the point of learning history? I’m not going to become a historian,” as if learning needs to have a clear end-goal or else it’s useless. Or those who think it’s pointless to learn to play an instrument because you’re not going to become a famous musician. It’s a mentality that ties in with capitalism, where if you’re not being productive, you have no use.
A well-rounded education should equip students with skills they can apply independently no matter what they do. Learning history provides context for the world we live in, why it is the way it is, and can inform us on how to move forward. Learning to play an instrument builds new connections in the brain, strengthens fine motor skills, and (in the case of reading music) how to move information between abstract concepts and a tangible form.
These skills provide benefits to people that can be built upon in the future. They may not have immediate usage to a student, but they create a foundation upon which a student can reach higher as they progress in life. Not every lesson is practical in the moment, but that doesn’t mean it can’t have value to a growing mind.
If anyone taught you how to do your taxes at school age I bet you’d forgotten all about it by the time you needed it
As OP said, what’s important is to learn to learn
I was actually working and worrying about my taxes when i was in 10th grade. I think that’s pretty common. It could be taught in 10th to 12th depending on when kids decide to learn it, maybe.
One of my math professors sugggested adding a formal logic class to early childhood education.
One of my math professors told us that when he started elementary school they tried starting maths classes with logic and combinatorics, because they were most essential maths and in principle could be experienced by children by seeing, feeling etc. He said it was a stupid approach. I say he turned out a math professor, so maybe it worked.
The human brain is not capable of formal logic at this stage.
It is sad that the general population is unable to see learning math as good in of itself. Not everything must be solely “practical.”
Math education is basically a Time waster designed to justify hierarchies, it’s tangentially related to math but not really in purpose, there’s just numbers involved
Wow, that’s one of the worst takes on math education I’ve ever heard.
It’s based on my personal experience being burned by the system. Endless math drills that could have just been a calculator in order tobget grade points to get into a “good college” and a job, if you’re lucky. There’s a reason people come away from contemporary math education completely burned out
Not really. Not everyone enjoys advanced mathematics the same way not everyone enjoys english literature or engineering, or arts and crafts. People have different interests, aptitudes, and skills. That’s how the world works.
they still should learn them.
you need to know how the world works a bit to be a good citizen capable of critical thinking.
Did you actually read what I wrote or the context behind it? I don’t think you did. I am saying not everyone wants to learn these things just for the sake of it. Some people want to learn the parts of maths that are more practical and want to be given practical examples. I don’t see a problem with accommodating those students or looking down on people who think that way like the original commenter was doing.
Yeah, not understanding math and statistics makes propaganda so easy! I’ve seen so many people invest their savings into things that were mathematically or physically impossible from the get go. Gambling too!
Did you actually read what I wrote or the context behind it? I don’t think you did.
I am saying not everyone wants to learn these things just for the sake of it. Some people want to learn the parts of maths that are more practical and want to be given practical examples. I don’t see a problem with accommodating those students or looking down on people who think that way like the original commenter was doing.
What I am not saying is that no one should learn any maths at all. I don’t know how you got that from my comment. It’s like you are deliberately trying to misinterpret what I am saying.
I’m the guy in the background saying “go back to teaching Euclid and proof in schools”, as the real point was to teach logical deduction from established facts.
Logic puzzles should be applied in more classrooms. Start with simple problems in elementary school, and progress to more challenging ones as students grow. Critical thinking needs to start early.
A lot of the issue with logic problems is the “common sense” element required. With purely geometric problems, there are less of these to worry about.
Chess problems also work well to teach logical step application.
If you are talking about school curriculum, nearly the entire population will keep not learning it as long as it doesn’t have some practical application so people can understand WTF the teacher is talking about.
Citation needed.
Seriously, though, that’s not what the research is showing. Peter Liljedahl’s research, for example, supports that a very effective way to teach mathematics is by having students actually think about math, instead of just passively receiving info dumps (as is common in most traditional math classes). See Building Thinking Classrooms for details but, in short, it’s a method of getting students playing with math concepts for almost the entire class time every day.
No “practical applications” needed. Counterintuitive, but it’s a highly effective practice.
What’s core to practical applications working is student motivation, and practical applications are one way to induce motivation. But it’s often not the best option, especially for inherently abstract skills.
Peter Liljedahl
So… From the publications, looks like he uses problem solving, not “having students actually think about math”.
You want students think about what exactly if you don’t give them an application?
Anyway, thanks, I’m listing his work as evidence supporting my claim.
If by “practical application” you mean “motivation for learning the skill”, which is I think the way you’re using it, then yes. But that’s not the usual definition in math education, and not what most people mean by it.
Like, for example, to introduce quadratics, a good progression might be to challenge students to build a table of values and graphs for x², then x² + 3, then graph x² – 5 without a table of values, then 2x² vs. 5x² vs. ½x², –x², etc.
And if you have a Thinking Classroom, every student in the class is working on figuring out that progression collaboratively in small groups. The teacher guides students to discover the math themselves through a series of examples, and mostly interacts with the students by asking questions, never giving them the answers.
That’s not “a practical application of quadratics”—at least not in the usual definition—that’s a learning activity sequence (paired with a set of interrelated pedagogical practices).
A good, practical application of quadratics is more like a Dan Meyer “3 Act Math” lesson on predicting the trajectory of a basketball shot. Also cool, good teaching. But not a great way to introduce quadratics.
(P.S. Yes, I use and like em dashes. I’m not a robot.)
To be honest, i’m not sure what you want.
Like, if i was the student, i think i would be extremely confused from this lesson. I would not know what you want from me. I have had my fair share of teachers trying to get me to “just think about something and figure stuff out myself” which mostly amounted to me sitting there in classroom, staring into the air, confused about what the task is, and mostly waiting till the hour is over.
My brain works differently. When i learn something, before i even start caring about what the topic is, i ask why I’m learning this; and i need to have a proper reason to learn something. The reason needs to be strong enough, and is only strong enough if it is derived from some other, stronger reason. For example, i learned maths because i understood how important it is to grasp the universal, those things that cannot be taken away from us. I grew up in a kinda abusive household, and my mother had a habit of taking away the things that were most precious to me, so i clinged on to maths because i knew that maths was eternal and not dependent on the whims of my mother. That is a clear, practical reason. Maths gives me mental stability, like a skeleton gives stability to the body. It does not shake nor break; for it’s eternal.
Now, if you want me to play around with polynomials, idk what i would do.
Typically, when i learn something, i want to know why but also how to learn something. Especially, to express it in an analogy, my brain is like the C programming language. I need to reserve memory manually, it does not happen automatically, and i need to know how much space will be needed beforehand, in other words i need to have a clear understanding of how big a topic will be before i actually start learning it. When i have no idea what i’m getting myself into, then i don’t get into it, because my brain is very very very (i hope i have made this clear enough) bad at learning many small incremental pieces of knowledge. In fact, it’s similar to if you had to put on your jacket, leave the building, go through the cold icy air into the neighboring building each time you want to get yourself a glass of water. Needless to say, you will not drink a lot of water. You will dehydrate. Obviously you would put yourself a large bottle of water into your room, for which you only have to leave the building once. The same applies to me and learning. I have to take very few, appropriately sized portions of knowledge into me at once. Not many many small ones.
I don’t have time to get into the full 13 (? iirc) steps of Liljedahl’s Thinking Classrooms approach, but it’s exactly designed to meet the needs of students like you. Since highlights:
- Students are randomly assigned to a new group of 3 daily
- All students work on vertical whiteboards, or equivalents
- The teacher presents a math task that starts easy-ish, but requires some work/thought to figure out
- If 30% of students in the room understand the task, then it will quickly trickle between groups
- The teacher circles exemplars of great thinking; students are not allowed to erase these until the next debrief
- The teacher regularly cycles back to get students to explain their work to the class, showcasing and explaining the bits the teacher circled
- Start over with a more advanced task/“next step”
It’s an incredibly effective teaching method for secondary math. And there’s clear motivation every step of the way for what you’re doing and why it matters.
And the teacher only explains about 5-10% of the material; everything else is explained by the students as the carefully curated progression of activities guides them through discovering the math themselves.
motivation for learning the skill
I mean motivation for why somebody cares about the idea at all, but I think that is less strict so yes. A hole in theory or something emerging from an activity are perfectly fine. But there has to be something there.
Anyway, thanks, I’m listing his work as evidence supporting my claim.
Remembering this for next time I clearly don’t understand something. lol
Not sure why you’re getting downvoted. Having practical applications for higher math makes that shit stick like glue when otherwise it would get forgotten immediately after the test.
Apparently knowing people learn differently and that mathematicians are a tiny minority is neoliberal…
Welcome to the Fediverse, I guess.
I use Arch btw.
As the experts say: “Use it or lose it.”
They’re getting downvoted because there’s a lot of esoterical people demanding that we learn stuff either for the joy of it (which many are not at all having btw) or because it “purifies character” or sth.
Practical applications are felt like an impurity to that.
Neither. Math builds a lot on other math. And the curriculum is very standardized. That’s why, when people just happen to miss something at any point, because maybe they have more important stuff going on in their live right now, they never catch up. We should drop the requirement that everyone has to learn the same math at the same time, hire more teachers and allow students to flow freely between courses to focus on the stuff they can learn with the math they already know. This will allow students to catch up and, paradoxically, produce a higher over all level of math knowledge, if less standardized and predictable for employers.
Now, to ensure students also want to learn math, both abstract math courses and mixed seminars should be offered. Students could choose to attend either or both. In the seminars, math, physics and engineering would be mixed in challenges where students with different skills and preferences have to work together to produce a cool result (like a robot, a game, an experiment, etc.). The abstract courses shouldn’t be forgotten, because many students actually enjoy learning math. Instead of just teaching rules and how to follow them, they should involve a creative aspect, where students are encouraged to break rules by making their own definitions, formulate their own theorems and try to prove them (like actual mathematicians do).
National level fixes almost never work. Give schools and teachers and districts money and power for the win.
Isn’t this just resigning ourselves to shitty religious “charter schools” in like half the states? Feels like it’d be a massive assault on public education, in practice.
Excellent meme, more like this please!
I’m with the pink guy, fight me
I’m always wary of the idea learning should be “practical”. You never know when something will matter and there is an intrinsic value in learning for learnings sake.
Learning needs to be tangible, but I’m not sure it necessitates practicality.
The hidden Factor here is coercion, if you don’t go to school the cops will literally show up at your door eventually. In light of that it’s completely reasonable for the people who have no choice but to be there to ask what purpose it serves
Sure, but learning tends to be easier when there’s a practical application to the things you’re learning
That kinda breaks down in practice, though. Math is hard for a lot of students. Adding an extra layer of domain-specific application on top of an already confusing topic just makes it worse.
Like, we need polynomials for huge swathes of higher-level math. My favourite application of polynomials is that most continuous functions can be approximated by a Taylor series, which makes some functions that are otherwise impossible to calculate a derivative or integral trivially easy. It’s elegant, beautiful, and deeply practical.
And completely useless for a grade 8 student learning about polynomials for the first time.
Sure, there’s lower-hanging fruit for practical uses for polynomials, but they’re either similarly abstract (albeit simpler) or contrived. Ain’t nobody making a sandbox with length (3x + 5) and width (2x – 7), eh?
I could go on. At length.
Point being, yes, practical applications are better. BUT (and this is a big but) only when there are simple practical applications.
Instead, recent math education research supports teaching fluency through playing with math concepts and exploring things in many ways: symbolically, graphically, forwards and backwards, extending iteratively with increasing complexity, etc. This helps students develop intuition for math concepts and deeper understanding. Then, and only then, teach the standard algorithms and methods, as students will appreciate the efficiency of the tool and understand what they’re doing and why they’re doing it.
Thank you for listening to my TED Talk.
Polynomials:
They exist because they are efficient to compute. Computers do well with basic arithmetic operations like addition (+) and multiplication (*). The polynomial functions are simply those that you can construct from those two operations, and constant numbers.
Like consider a polynomial like f(x) = 5x^3 + 3x^2 + 2x + 7
What it really says is
f(x) = 5*x*x*x + 3*x*x + 2*x + 7and here you can see how it’s all built from + and *.This is why polynomials are useful. Because computers have an easy time calculating them. And all modern mathematics is done on computers. All the engineering uses computer simulations, and we want these simulations to run fast on computer hardware, so we make it easy for computer hardware to do. That is why we’re using polynomials wherever we can.
That is how you explain polynomials to 8th graders. No taylor series / calculus needed.
If you want to be really fancy you can show the taylor series of the sine and cosine function as a polynomial and how to compute it on a computer. Gives some pretty graphs, is simple and fun.
Just tell them that polynomials can be used to computer
sinandcosfunctions without going into the details of why that works first.
Edit: Just to clarify this: Yes i think that explaining why students should learn stuff is extremely important. In fact i tend to say that the only thing that you really have to do is to motivate the students to learn; then the learning happens by itself.
However note that giving esoteric abstract playful descriptions of things in my opinion does not motivate people to learn stuff. That just makes them go “huh, neat but useless”. Giving real world practical examples fulfills exactly the purpose of giving students a reason to learn stuff. Because seeing how one can solve real problems with the tools, one learns to value the tools.
Yes, examples like that are good, of course. But, frankly, abstract examples like that won’t do much to motivate the students who need the most help to get motivated learning math.
I like to interject little anecdotes like that, too. One of my “go tos” to “why are quadratics useful” goes something like “Well, they come up a fair bit, so I could give you some examples—and I will, as we with through the unit, but the real reason we teach quadratics is because they’re the simplest non-linear function. This is the first steps into looking at functions that aren’t a straight line. And the tools you use to work with quadratics are super important for understanding all the really cool functions you get to learn on the next couple of years…”
That’s basically your example, but one step lower and more directly applicable to students, imho. The Taylor Series thing I usually only drop in grade 11/12 (pre)calculus classes, mostly as a hook for the math nerds that they have really cool things to look forward to learning in post secondary. It’s a terrible application to use to try to motivate learning about polynomials for a student who couldn’t care less, lol.
Really, we need to intermix all approaches, depending on the students in the class. At private prep schools, leaning into academic needs works well. In a non-academic math stream, both your example and my examples will go over like a lead balloon.
But, regardless, motivating students to be excited for math, and the excitement of finally figuring out a tricky concept/problem? That’s what we need more of.
Just look at Boolean mathematics. It was developed 100 years before it had a use (digital logic)
I’m always for the feckless hippie over the neoliberal sellout tbh.
Except a lot of those switched to antiscience antivaxers, and some bridged from there to facists. While I do also prefer hippies, antiknowledge and antiscience types scare me.
What about feckless hippies that sold out to the neoliberals?
or the commie that runs out of martyric protest
new words: martyric
heard it here first folks
I mean, that’s the sellout part
It’s because they ran out of fecks
