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That's all fine and dandy when you're teaching maths to someone interested in pursuing or studying maths, if your point is to teach someone who hasn't yet made

That's all fine and dandy when you're teaching maths to someone interested in pursuing or studying maths, if your point is to teach someone who hasn't yet made the connection between the abstractions and their meaning then you should use relatable things - and as their knowledge increases move to remove the familiar labels and show what is the underlying abstraction. I would think that by now that shouldn't even be up for discussion - much less for programming where your objectives, besides achieving a calculation or a side-effect, are also that your code be intelligible to other human beings. Even in assembly you have symbols for move, jump, etc. And no, different people have different ways of thinking, not everyone has the same combination of nature and nurture to be completely comfortable with pure abstract mathematical notation - and for most part they don't need to. When you assign fancy greek letters as symbols you're also labelling them, so why not label them with something that a person learning might recognise. Outside of teaching people that aren't familiar with it, yeah, sure, use all the numerical elegance you can muster (and I would still argue that even there it's still detrimental if the objective is sharing knowledge as widely as possible).

username90 5y ago
That sounds good in theory, but in practice it is the other way around, the worst students needs purity the most. It is well known that word problems are much harder for students to read, learn and solve than pure problems. Only really good students do well on word problems, the students who are less good at abstractions do the worst at them. Or do people here really think that nobody has ever tried to make a math textbook with lengthier names and descriptions? It isn't used since it doesn't make things better, it makes them worse.
- Flex247A 5y ago
  As someone who wasn't that good at math, I think the convention of x and y feels pretty abstract and arbitrary. Bad students have trouble connecting real world quantities to single letter variables. Lengthier and meaningful variable names will make the task slightly easier, as carSpeed is easier to reason about than x or y. Once students grasp the concept of a variable, the names can be switched. Just my 2 cents.
  - username90 5y ago
    Why do you assume that students know what speed is? Have you seen this video? https://www.youtube.com/watch?v=Qhm7-LEBznk https://www.youtube.com/watch?v=Qhm7-LEBznk The problem here is that she don't know what speed is. She knows a lot of formulas, but not what speed actually is. That is a typical student, if you add speed in a formula you will make them confused and the problem will get harder.
    - hdctambien 5y ago
      My first year teaching math (12th grade, "standard" level (below "intensive" and "honors")), I had a student that could solve "equations with fractions for x" but she was struggling with a word problem. I knew she could do the math, but I was struggling to understand where she was losing it. The word problem was basically the same as in the video. If you're moving 20 miles/hour how long will it take to go 40 miles. (honestly, this was 20 years ago ... the problem probably said "20 MPH" ... it wasn't a very good textbook) I read the problem to her, similarly to how the guy in the video was trying to explain. "If you are going 20 miles... per hour..." She was in drivers ed at the time, so I tried talking about her speedometer and "MPH and how that stands for Miles Per Hour"... Eventually I wrote it down for her as a fraction "20 miles / 1 hour" and not only did she figure it out but she also said "Oh my god, that's what MPH means? I thought that was just a number I had to match with the speed limit signs!" One of the toughest parts of teaching is figuring out where you need to start (for each student). The thing that gets a student stuck might not even be related to the material... they may have an incorrect preconceived notion that you're not aware of so they think they know what MPH is, but it's actually something completely different, so you are not effectively communicating with each other because all the words you are using have different meanings.
      - thelittleprince 5y ago
        Well, I think the author got a point here. There is no perfect solution for this problem, yes. Maybe for this student, this way works, but not for others. What I am saying is First, if student don't even understand what is carAccerleration or carSpeed is, then how do you expect them to understand the X and Y term? Second, to explain an example, you may not use carSpeed or anything related to it at all, but why use X and Y while there are so many better names out there. It really depends on the context of the example trying to show. So my point is using carSpeed or carAccerlation as programming naming technique bad? Yes, it's bad. But using greek terms to show a student who are really bad at understanding things comes even worse. How we can explain them what is alpha, what is beta, etc I am not an official teacher at any school, but I volunteered to an educational organization to teach students about science experiments. The odd is there is a huge gap in knowledge in ONE class, students range from 6th grade to 9th grade. Student of 6th grade in class don't even know what is physics and chemistry (all stuffs they know is adding and substracting). My job is explaining to them what electromagnetic field is and how the tesla coil works. That's come to my point, you can't just throw to them a bunch of equations and tell them it is it. I had to solve this by breaking the term down into smaller pieces and didn't talk about any equations at all. After that, could I expect them know how to solve physics problems? Of course, it's not. But at least they had a push, and if you want someone to move forward, a small push is what they need (Newton's first law related). That is the 'A-hah' moment. One more point, if you have read 'A Brief History of Time' of Stephen Hawking, you'll see he barely used any complicated terms or equations in his book (he did use, but not much), he just explain things and break it down into small pieces so even non-physiscal peoples will understand. And in conclude, if it's for generalize things, then an equation with greek terms is needed. However, to explain things to student who are bad at math and really need help, there is so many better ways to name terms in math examples instead of using greek letters.
- hnedeotes 5y ago
  I'm not sure that actually pans out in the real world. It seems that there's a gap between people understanding the very basics and anything slightly more complex. We can either believe that there's just a big percentage of people that will never be able to grasp beyond arithmetic (mathematically dumb) or that perhaps we aren't teaching things in the best way possible? When I say using descriptive/relatable labels, is in the context of a relatable problem. I also think this is common, in the very first levels of introducing maths for small children it's a normal procedure. At some point between that and more advanced topics it seems to jump off and the conclusion seems to be "Many students fail to master requisite concepts before advancing to more complex ideas, leaving them ill-prepared to succeed in higher level Science, Technology, Engineering, and Mathematics (STEM) coursework.". Of course it's the students (usually kids) that fail, not the very smart lecturers and teachers. At every point in time probably people think of the way they're doing something as the most sensible or best way of doing it. I think there was quite a leap when programming let go of pure mathematical notation to more regular language likeness - it seems many at the time voiced their opposition to that too. Not long ago I spent some hours chasing around a problem where had the authors I encountered tried to explain it using more descriptive problems I would have grasped it in minutes, because it was really basic. But yeah, maybe it sounds really smart when it's shrouded in jargon, symbols and meanings that only someone immersed in that field of study would understand.
- nmfisher 5y ago
  Didn’t I read recently that Polya attributed Russia’s better performance in high school maths (vs the USA) to its preference for word problems?

username90 5y ago

That sounds good in theory, but in practice it is the other way around, the worst students needs purity the most. It is well known that word problems are much harder for students to read, learn and solve than pure problems. Only really good students do well on word problems, the students who are less good at abstractions do the worst at them. Or do people here really think that nobody has ever tried to make a math textbook with lengthier names and descriptions? It isn't used since it doesn't make things better, it makes them worse.

Flex247A 5y ago
As someone who wasn't that good at math, I think the convention of x and y feels pretty abstract and arbitrary. Bad students have trouble connecting real world quantities to single letter variables. Lengthier and meaningful variable names will make the task slightly easier, as carSpeed is easier to reason about than x or y. Once students grasp the concept of a variable, the names can be switched. Just my 2 cents.
- username90 5y ago
  Why do you assume that students know what speed is? Have you seen this video? https://www.youtube.com/watch?v=Qhm7-LEBznk https://www.youtube.com/watch?v=Qhm7-LEBznk The problem here is that she don't know what speed is. She knows a lot of formulas, but not what speed actually is. That is a typical student, if you add speed in a formula you will make them confused and the problem will get harder.
  - hdctambien 5y ago
    My first year teaching math (12th grade, "standard" level (below "intensive" and "honors")), I had a student that could solve "equations with fractions for x" but she was struggling with a word problem. I knew she could do the math, but I was struggling to understand where she was losing it. The word problem was basically the same as in the video. If you're moving 20 miles/hour how long will it take to go 40 miles. (honestly, this was 20 years ago ... the problem probably said "20 MPH" ... it wasn't a very good textbook) I read the problem to her, similarly to how the guy in the video was trying to explain. "If you are going 20 miles... per hour..." She was in drivers ed at the time, so I tried talking about her speedometer and "MPH and how that stands for Miles Per Hour"... Eventually I wrote it down for her as a fraction "20 miles / 1 hour" and not only did she figure it out but she also said "Oh my god, that's what MPH means? I thought that was just a number I had to match with the speed limit signs!" One of the toughest parts of teaching is figuring out where you need to start (for each student). The thing that gets a student stuck might not even be related to the material... they may have an incorrect preconceived notion that you're not aware of so they think they know what MPH is, but it's actually something completely different, so you are not effectively communicating with each other because all the words you are using have different meanings.
    - thelittleprince 5y ago
      Well, I think the author got a point here. There is no perfect solution for this problem, yes. Maybe for this student, this way works, but not for others. What I am saying is First, if student don't even understand what is carAccerleration or carSpeed is, then how do you expect them to understand the X and Y term? Second, to explain an example, you may not use carSpeed or anything related to it at all, but why use X and Y while there are so many better names out there. It really depends on the context of the example trying to show. So my point is using carSpeed or carAccerlation as programming naming technique bad? Yes, it's bad. But using greek terms to show a student who are really bad at understanding things comes even worse. How we can explain them what is alpha, what is beta, etc I am not an official teacher at any school, but I volunteered to an educational organization to teach students about science experiments. The odd is there is a huge gap in knowledge in ONE class, students range from 6th grade to 9th grade. Student of 6th grade in class don't even know what is physics and chemistry (all stuffs they know is adding and substracting). My job is explaining to them what electromagnetic field is and how the tesla coil works. That's come to my point, you can't just throw to them a bunch of equations and tell them it is it. I had to solve this by breaking the term down into smaller pieces and didn't talk about any equations at all. After that, could I expect them know how to solve physics problems? Of course, it's not. But at least they had a push, and if you want someone to move forward, a small push is what they need (Newton's first law related). That is the 'A-hah' moment. One more point, if you have read 'A Brief History of Time' of Stephen Hawking, you'll see he barely used any complicated terms or equations in his book (he did use, but not much), he just explain things and break it down into small pieces so even non-physiscal peoples will understand. And in conclude, if it's for generalize things, then an equation with greek terms is needed. However, to explain things to student who are bad at math and really need help, there is so many better ways to name terms in math examples instead of using greek letters.
hnedeotes 5y ago
I'm not sure that actually pans out in the real world. It seems that there's a gap between people understanding the very basics and anything slightly more complex. We can either believe that there's just a big percentage of people that will never be able to grasp beyond arithmetic (mathematically dumb) or that perhaps we aren't teaching things in the best way possible? When I say using descriptive/relatable labels, is in the context of a relatable problem. I also think this is common, in the very first levels of introducing maths for small children it's a normal procedure. At some point between that and more advanced topics it seems to jump off and the conclusion seems to be "Many students fail to master requisite concepts before advancing to more complex ideas, leaving them ill-prepared to succeed in higher level Science, Technology, Engineering, and Mathematics (STEM) coursework.". Of course it's the students (usually kids) that fail, not the very smart lecturers and teachers. At every point in time probably people think of the way they're doing something as the most sensible or best way of doing it. I think there was quite a leap when programming let go of pure mathematical notation to more regular language likeness - it seems many at the time voiced their opposition to that too. Not long ago I spent some hours chasing around a problem where had the authors I encountered tried to explain it using more descriptive problems I would have grasped it in minutes, because it was really basic. But yeah, maybe it sounds really smart when it's shrouded in jargon, symbols and meanings that only someone immersed in that field of study would understand.
nmfisher 5y ago
Didn’t I read recently that Polya attributed Russia’s better performance in high school maths (vs the USA) to its preference for word problems?