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> this is a clear demonstration that a fundamental understanding of fractions was skipped in order to grind out solutions Leaving aside that you concluded this

by dkarl 4y ago

> this is a clear demonstration that a fundamental understanding of fractions was skipped in order to grind out solutions Leaving aside that you concluded this from a one-sentence story about solving a single problem, it's funny that the idea that a "clear understanding of fractions" can make the skills easy to learn is something that virtually every trained teacher has believed for the last (I'm not sure how many) decades and yet nobody alive today is reporting that it happened that way for them. It's possible that every future teacher getting certified to teach politely pretends to believe these things, but secretly wishes to spend their career torturing children, so they abandon the teaching of concepts as soon as they step into a classroom. Or maybe they go through the motions of teaching kids to understand the meaning behind fractions, but they intentionally do it wrong and laugh with each other about it in the teacher's lounge. That's one explanation. Another explanation is that this opposition of "understanding" to "execution" and "concepts" to "skills" is an incomplete way of looking at things that has limited application to how people learn but isn't a panacea, and people still struggle with skills no matter how much you try to prepare them with concepts. I think it does a vast disservice to anyone when we assume that their job performance would be radically improved by the first cliché we ever learned about their field. If the idea is so magical, and we know that it has permeated the field of education for generations, where are the generations of students who remember math as being "trivial, intuitive, beautiful, clever?" Different educational philosophies have come and gone, emphasis has shifted, so where's the generation of parents saying math was much easier for them than for their kids? Where's the PTA meeting where all the parents say, "We think there's something wrong with the way math is taught here, because we all remember fractions being trivial and intuitive, but our kids are finding them hard?" Maybe teachers aren't such idiots that they consistently overlook the value of the most cherished and shopworn truism their field has produced in its history?

thesuitonym 4y ago
I'll start my reply with this: I'm not a teacher, nor am I an understander of maths, but whenever I talk to teachers at any level, and especially mathematics teachers, they lament that they want to teach differently, but due to time constraints, or predetermined lesson plans, or any number of reasons, they simply can't. They have to teach in a way that gets students enough knowledge to pass the test, but only those that seem to have a natural aptitude end up really learning anything. The rest discard the information as soon as it's no longer necessary. I don't think it's a disservice to teachers to say it's a better way of teaching, because they say it themselves. It's just a model that only really works one on one. It can't be done in a room full of 30 bored children, and especially in a room of 400 university sophomores who are ready to get out of class to go to a party.
- dkarl 4y ago
  You are saying some things that are guaranteed to generate skepticism. First, that the great power of this teaching method only manifests under circumstances that very few people get to experience. Second, that concepts make skills "trivial" and "intuitive" but testing skills prevents teachers from teaching concepts. Both of those statements call into question the effectiveness of what you're promoting.
  - Viliam1234 4y ago
    It is okay to be suspicious when it sounds like someone just made this up, but actually in educational research it is one of the few well known things. See Wikipedia: https://en.wikipedia.org/wiki/Bloom%27s_2_sigma_problem https://en.wikipedia.org/wiki/Bloom%27s_2_sigma_problem Anyone who tried both teaching and tutoring knows that the difference is just incredibly large. A part of it is that 1:1 you can pay more attention individually; a similar argument can be used in favor of smaller classes. But the other part is that as a tutor, you are free to actually use your best judgment, while in school it is more of "yeah, I know that I should do X, but the rules say that I have to do Y instead". The school is just insanely ineffective, for various reasons. You need to follow a predetermined schedule, whether it makes sense for the given classroom or not. Your students are expected to already have some knowledge from their previous grade, and if they don't (which happens quite often) you don't get any extra time to catch up. There are all kinds of disruptions, like students who never pay attention and interrupt you and their classmates during lessons, but you must proceed at the speed that was designed for a hypothetical classroom without disruptions. The school inspection randomly checks whether you follow the latest fad, usually based on some pseudoscience, like whether your lessons are okay for both visual and kinesthetic learners, or whether your math lessons are sufficiently decolonialized. So the same teacher who fails to teach her class fractions at school, may be a successful tutor during the afternoon and explain the fractions properly.
mattwilsonn888 4y ago
While I don't share your skepticism that school teaching could be improved, I will note that you have done what you accused me of: not reading. When did I say anything about schools? My sadness at the opportunity lost came from 'avoiding conventional education.'

by dkarl 4y ago

thesuitonym 4y ago

I'll start my reply with this: I'm not a teacher, nor am I an understander of maths, but whenever I talk to teachers at any level, and especially mathematics teachers, they lament that they want to teach differently, but due to time constraints, or predetermined lesson plans, or any number of reasons, they simply can't. They have to teach in a way that gets students enough knowledge to pass the test, but only those that seem to have a natural aptitude end up really learning anything. The rest discard the information as soon as it's no longer necessary. I don't think it's a disservice to teachers to say it's a better way of teaching, because they say it themselves. It's just a model that only really works one on one. It can't be done in a room full of 30 bored children, and especially in a room of 400 university sophomores who are ready to get out of class to go to a party.

dkarl 4y ago
You are saying some things that are guaranteed to generate skepticism. First, that the great power of this teaching method only manifests under circumstances that very few people get to experience. Second, that concepts make skills "trivial" and "intuitive" but testing skills prevents teachers from teaching concepts. Both of those statements call into question the effectiveness of what you're promoting.
- Viliam1234 4y ago
  It is okay to be suspicious when it sounds like someone just made this up, but actually in educational research it is one of the few well known things. See Wikipedia: https://en.wikipedia.org/wiki/Bloom%27s_2_sigma_problem https://en.wikipedia.org/wiki/Bloom%27s_2_sigma_problem Anyone who tried both teaching and tutoring knows that the difference is just incredibly large. A part of it is that 1:1 you can pay more attention individually; a similar argument can be used in favor of smaller classes. But the other part is that as a tutor, you are free to actually use your best judgment, while in school it is more of "yeah, I know that I should do X, but the rules say that I have to do Y instead". The school is just insanely ineffective, for various reasons. You need to follow a predetermined schedule, whether it makes sense for the given classroom or not. Your students are expected to already have some knowledge from their previous grade, and if they don't (which happens quite often) you don't get any extra time to catch up. There are all kinds of disruptions, like students who never pay attention and interrupt you and their classmates during lessons, but you must proceed at the speed that was designed for a hypothetical classroom without disruptions. The school inspection randomly checks whether you follow the latest fad, usually based on some pseudoscience, like whether your lessons are okay for both visual and kinesthetic learners, or whether your math lessons are sufficiently decolonialized. So the same teacher who fails to teach her class fractions at school, may be a successful tutor during the afternoon and explain the fractions properly.

mattwilsonn888 4y ago

While I don't share your skepticism that school teaching could be improved, I will note that you have done what you accused me of: not reading. When did I say anything about schools? My sadness at the opportunity lost came from 'avoiding conventional education.'