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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.
It is sad that the general population is unable to see learning math as good in of itself. Not everything must be solely “practical.”
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.
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!
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
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.
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.
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.
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.
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.
As the experts say: “Use it or lose it.”
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. Some 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.
Anyway, thanks, I’m listing his work as evidence supporting my claim.
Remembering this for next time I clearly don’t understand something. lol
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’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.
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.
Maths education is pointlessly overcomplicated. We need to simplify and streamline it. And also add in more practical real-world examples.
Especially when you’re forced to use a complicated method to do basic calculations with. People should be allowed to learn different ways to get to the same answer.
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.
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.
